IDEAS home Printed from https://ideas.repec.org/a/spr/sankhb/v83y2021i2d10.1007_s13571-020-00240-z.html
   My bibliography  Save this article

Sparse Portfolio Selection via Bayesian Multiple Testing

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13571-020-00240-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13571-020-00240-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Harvey, Campbell R. & Zhou, Guofu, 1990. "Bayesian inference in asset pricing tests," Journal of Financial Economics, Elsevier, vol. 26(2), pages 221-254, August.
    3. 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.
    4. 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.
    5. 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.
    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. 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.
    8. Shanken, Jay, 1987. "A Bayesian approach to testing portfolio efficiency," Journal of Financial Economics, Elsevier, vol. 19(2), pages 195-215, December.
    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. 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.
    11. 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.
    12. 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.
    13. Black, Fischer, 1972. "Capital Market Equilibrium with Restricted Borrowing," The Journal of Business, University of Chicago Press, vol. 45(3), pages 444-455, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bodnar, Taras & Reiß, Markus, 2016. "Exact and asymptotic tests on a factor model in low and large dimensions with applications," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 125-151.
    2. Gilles Boevi Koumou, 2020. "Diversification and portfolio theory: a review," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(3), pages 267-312, September.
    3. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, November.
    4. Seyoung Park & Eun Ryung Lee & Sungchul Lee & Geonwoo Kim, 2019. "Dantzig Type Optimization Method with Applications to Portfolio Selection," Sustainability, MDPI, vol. 11(11), pages 1-32, June.
    5. Michele Costola & Bertrand Maillet & Zhining Yuan & Xiang Zhang, 2024. "Mean–variance efficient large portfolios: a simple machine learning heuristic technique based on the two-fund separation theorem," Annals of Operations Research, Springer, vol. 334(1), pages 133-155, March.
    6. Zura Kakushadze & Willie Yu, 2016. "Multifactor Risk Models and Heterotic CAPM," Papers 1602.04902, arXiv.org, revised Mar 2016.
    7. Geweke, John & Zhou, Guofu, 1996. "Measuring the Pricing Error of the Arbitrage Pricing Theory," The Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 557-587.
    8. Constantinos Kardaras & Hyeng Keun Koo & Johannes Ruf, 2022. "Estimation of growth in fund models," Papers 2208.02573, arXiv.org.
    9. Rocciolo, Francesco & Gheno, Andrea & Brooks, Chris, 2022. "Explaining abnormal returns in stock markets: An alpha-neutral version of the CAPM," International Review of Financial Analysis, Elsevier, vol. 82(C).
    10. Svetlana Bryzgalova & Jiantao Huang & Christian Julliard, 2023. "Bayesian Solutions for the Factor Zoo: We Just Ran Two Quadrillion Models," Journal of Finance, American Finance Association, vol. 78(1), pages 487-557, February.
    11. Cederburg, Scott & O’Doherty, Michael S., 2015. "Asset-pricing anomalies at the firm level," Journal of Econometrics, Elsevier, vol. 186(1), pages 113-128.
    12. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    13. Enrique Sentana, 2009. "The econometrics of mean-variance efficiency tests: a survey," Econometrics Journal, Royal Economic Society, vol. 12(3), pages 65-101, November.
    14. Cosemans, M. & Frehen, R.G.P. & Schotman, P.C. & Bauer, R.M.M.J., 2009. "Efficient Estimation of Firm-Specific Betas and its Benefits for Asset Pricing Tests and Portfolio Choice," MPRA Paper 23557, University Library of Munich, Germany.
    15. Francisco Barillas & Jay Shanken, 2018. "Comparing Asset Pricing Models," Journal of Finance, American Finance Association, vol. 73(2), pages 715-754, April.
    16. Zura Kakushadze & Willie Yu, 2016. "Statistical Risk Models," Papers 1602.08070, arXiv.org, revised Jan 2017.
    17. Fang, Ming & Taylor, Stephen, 2021. "A machine learning based asset pricing factor model comparison on anomaly portfolios," Economics Letters, Elsevier, vol. 204(C).
    18. Constantinos Antoniou & John A. Doukas & Avanidhar Subrahmanyam, 2016. "Investor Sentiment, Beta, and the Cost of Equity Capital," Management Science, INFORMS, vol. 62(2), pages 347-367, February.
    19. Abugri, Benjamin A. & Dutta, Sandip, 2014. "Are we overestimating REIT idiosyncratic risk? Analysis of pricing effects and persistence," International Review of Economics & Finance, Elsevier, vol. 29(C), pages 249-259.
    20. repec:dau:papers:123456789/2256 is not listed on IDEAS
    21. Ali K. Ozdagli, 2012. "Financial Leverage, Corporate Investment, and Stock Returns," The Review of Financial Studies, Society for Financial Studies, vol. 25(4), pages 1033-1069.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sankhb:v:83:y:2021:i:2:d:10.1007_s13571-020-00240-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.