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The effect of regularization in portfolio selection problems

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  • Bernardo K. Pagnoncelli

    (Adolfo Ibáñez University)

  • Felipe del Canto

    (Pontificia Universidad Católica de Chile)

  • Arturo Cifuentes

    (Clapes-UC)

Abstract

Portfolio selection problems have been thoroughly studied under the risk-and-return paradigm introduced by Markowitz. However, the usefulness of this approach has been hindered by some practical considerations that have resulted in poorly diversified portfolios, or, solutions that are extremely sensitive to parameter estimation errors. In this work, we use sampling methods to cope with this issue and compare the merits of two approaches: a sample average approximation approach and a performance-based regularization (PBR) method that appeared recently in the literature. We extend PBR by incorporating three different risk metrics—integrated chance-constraints, quantile deviation, and absolute semi-deviation—and deriving the corresponding regularization formulas. Additionally, a numerical comparison using index-based portfolios is presented using historic data that includes the subprime crisis.

Suggested Citation

  • Bernardo K. Pagnoncelli & Felipe del Canto & Arturo Cifuentes, 2021. "The effect of regularization in portfolio selection problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 156-176, April.
    • Handle: RePEc:spr:topjnl:v:29:y:2021:i:1:d:10.1007_s11750-020-00578-7
    DOI: 10.1007/s11750-020-00578-7
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    1. Homem-de-Mello, Tito & Pagnoncelli, Bernardo K., 2016. "Risk aversion in multistage stochastic programming: A modeling and algorithmic perspective," European Journal of Operational Research, Elsevier, vol. 249(1), pages 188-199.
    2. Green, Richard C & Hollifield, Burton, 1992. "When Will Mean-Variance Efficient Portfolios Be Well Diversified?," Journal of Finance, American Finance Association, vol. 47(5), pages 1785-1809, December.
    3. Best, Michael J & Grauer, Robert R, 1991. "On the Sensitivity of Mean-Variance-Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results," The Review of Financial Studies, Society for Financial Studies, vol. 4(2), pages 315-342.
    4. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    5. Frankfurter, George M. & Phillips, Herbert E. & Seagle, John P., 1971. "Portfolio Selection: The Effects of Uncertain Means, Variances, and Covariances," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 6(5), pages 1251-1262, December.
    6. Dai, Zhifeng & Wen, Fenghua, 2018. "Some improved sparse and stable portfolio optimization problems," Finance Research Letters, Elsevier, vol. 27(C), pages 46-52.
    7. Jeff Linderoth & Alexander Shapiro & Stephen Wright, 2006. "The empirical behavior of sampling methods for stochastic programming," Annals of Operations Research, Springer, vol. 142(1), pages 215-241, February.
    8. Kolm, Petter N. & Tütüncü, Reha & Fabozzi, Frank J., 2014. "60 Years of portfolio optimization: Practical challenges and current trends," European Journal of Operational Research, Elsevier, vol. 234(2), pages 356-371.
    9. Fernandes, Betina & Street, Alexandre & Valladão, Davi & Fernandes, Cristiano, 2016. "An adaptive robust portfolio optimization model with loss constraints based on data-driven polyhedral uncertainty sets," European Journal of Operational Research, Elsevier, vol. 255(3), pages 961-970.
    10. Frost, Peter A. & Savarino, James E., 1986. "An Empirical Bayes Approach to Efficient Portfolio Selection," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(3), pages 293-305, September.
    11. Andrzej Ruszczyński & Alexander Shapiro, 2006. "Optimization of Convex Risk Functions," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 433-452, August.
    12. B. Fastrich & S. Paterlini & P. Winker, 2015. "Constructing optimal sparse portfolios using regularization methods," Computational Management Science, Springer, vol. 12(3), pages 417-434, July.
    13. Malkiel, Burton G, 1995. "Returns from Investing in Equity Mutual Funds 1971 to 1991," Journal of Finance, American Finance Association, vol. 50(2), pages 549-572, June.
    14. Victor DeMiguel & Francisco J. Nogales, 2009. "Portfolio Selection with Robust Estimation," Operations Research, INFORMS, vol. 57(3), pages 560-577, June.
    15. Elton, Edwin J & Gruber, Martin J & Blake, Christopher R, 1996. "The Persistence of Risk-Adjusted Mutual Fund Performance," The Journal of Business, University of Chicago Press, vol. 69(2), pages 133-157, April.
    16. Quaranta, Anna Grazia & Zaffaroni, Alberto, 2008. "Robust optimization of conditional value at risk and portfolio selection," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2046-2056, October.
    17. Mansini, Renata & Ogryczak, Wlodzimierz & Speranza, M. Grazia, 2014. "Twenty years of linear programming based portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 518-535.
    18. D. Goldfarb & G. Iyengar, 2003. "Robust Portfolio Selection Problems," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 1-38, February.
    19. Stefania Corsaro & Valentina Simone, 2019. "Adaptive $$l_1$$ l 1 -regularization for short-selling control in portfolio selection," Computational Optimization and Applications, Springer, vol. 72(2), pages 457-478, March.
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