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Robust portfolio selection under downside risk measures

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  • Shushang Zhu
  • Duan Li
  • Shouyang Wang

Abstract

We investigate a robust version of the portfolio selection problem under a risk measure based on the lower-partial moment (LPM), where uncertainty exists in the underlying distribution. We demonstrate that the problem formulations for robust portfolio selection based on the worst-case LPMs of degree 0, 1 and 2 under various structures of uncertainty can be cast as mathematically tractable optimization problems, such as linear programs, second-order cone programs or semidefinite programs. We perform extensive numerical studies using real market data to reveal important properties of several aspects of robust portfolio selection. We can conclude from our results that robustness does not necessarily imply a conservative policy and is indeed indispensable and valuable in portfolio selection.

Suggested Citation

  • Shushang Zhu & Duan Li & Shouyang Wang, 2009. "Robust portfolio selection under downside risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 9(7), pages 869-885.
    • Handle: RePEc:taf:quantf:v:9:y:2009:i:7:p:869-885
    DOI: 10.1080/14697680902852746
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    1. Unser, Matthias, 2000. "Lower partial moments as measures of perceived risk: An experimental study," Journal of Economic Psychology, Elsevier, vol. 21(3), pages 253-280, June.
    2. Arjen Siegmann & André Lucas, 2005. "Discrete-Time Financial Planning Models Under Loss-Averse Preferences," Operations Research, INFORMS, vol. 53(3), pages 403-414, June.
    3. Costa, O. L. V. & Paiva, A. C., 2002. "Robust portfolio selection using linear-matrix inequalities," Journal of Economic Dynamics and Control, Elsevier, vol. 26(6), pages 889-909, June.
    4. Bertsimas, Dimitris & Lauprete, Geoffrey J. & Samarov, Alexander, 2004. "Shortfall as a risk measure: properties, optimization and applications," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1353-1381, April.
    5. Karthik Natarajan & Dessislava Pachamanova & Melvyn Sim, 2008. "Incorporating Asymmetric Distributional Information in Robust Value-at-Risk Optimization," Management Science, INFORMS, vol. 54(3), pages 573-585, March.
    6. Mulvey, John M. & Erkan, Hafize G., 2006. "Applying CVaR for decentralized risk management of financial companies," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 627-644, February.
    7. Bawa, Vijay S., 1975. "Optimal rules for ordering uncertain prospects," Journal of Financial Economics, Elsevier, vol. 2(1), pages 95-121, March.
    8. Mao, James C. T., 1970. "Models of Capital Budgeting, E-V VS E-S," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 4(5), pages 657-675, January.
    9. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    10. Bawa, Vijay S. & Lindenberg, Eric B., 1977. "Abstract: Capital Market Equilibrium in a Mean-Lower Partial Moment Framework," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 635-635, November.
    11. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    12. Laurent El Ghaoui & Maksim Oks & Francois Oustry, 2003. "Worst-Case Value-At-Risk and Robust Portfolio Optimization: A Conic Programming Approach," Operations Research, INFORMS, vol. 51(4), pages 543-556, August.
    13. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
    14. David R. Cariño & William T. Ziemba, 1998. "Formulation of the Russell-Yasuda Kasai Financial Planning Model," Operations Research, INFORMS, vol. 46(4), pages 433-449, August.
    15. Bawa, Vijay S., 1978. "Safety-First, Stochastic Dominance, and Optimal Portfolio Choice," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(2), pages 255-271, June.
    16. Lionel Martellini & Branko Uroševi'{c}, 2006. "Static Mean-Variance Analysis with Uncertain Time Horizon," Management Science, INFORMS, vol. 52(6), pages 955-964, June.
    17. Bawa, Vijay S. & Lindenberg, Eric B., 1977. "Capital market equilibrium in a mean-lower partial moment framework," Journal of Financial Economics, Elsevier, vol. 5(2), pages 189-200, November.
    18. Grootveld, Henk & Hallerbach, Winfried, 1999. "Variance vs downside risk: Is there really that much difference?," European Journal of Operational Research, Elsevier, vol. 114(2), pages 304-319, April.
    19. Huang, Dashan & Zhu, Shu-Shang & Fabozzi, Frank J. & Fukushima, Masao, 2008. "Portfolio selection with uncertain exit time: A robust CVaR approach," Journal of Economic Dynamics and Control, Elsevier, vol. 32(2), pages 594-623, February.
    20. Peter C. Fishburn, 1984. "Foundations of Risk Measurement. I. Risk As Probable Loss," Management Science, INFORMS, vol. 30(4), pages 396-406, April.
    21. D. Goldfarb & G. Iyengar, 2003. "Robust Portfolio Selection Problems," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 1-38, February.
    22. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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    3. Atwood, Joseph & Shaik, Saleem, 2020. "Theory and statistical properties of Quantile Data Envelopment Analysis," European Journal of Operational Research, Elsevier, vol. 286(2), pages 649-661.
    4. Panos Xidonas & Ralph Steuer & Christis Hassapis, 2020. "Robust portfolio optimization: a categorized bibliographic review," Annals of Operations Research, Springer, vol. 292(1), pages 533-552, September.
    5. Huang, Jinbo & Li, Yong & Yao, Haixiang, 2022. "Partial moments and indexation investment strategies," Journal of Empirical Finance, Elsevier, vol. 67(C), pages 39-59.
    6. Ling, Aifan & Sun, Jie & Wang, Meihua, 2020. "Robust multi-period portfolio selection based on downside risk with asymmetrically distributed uncertainty set," European Journal of Operational Research, Elsevier, vol. 285(1), pages 81-95.
    7. Ling, Aifan & Sun, Jie & Yang, Xiaoguang, 2014. "Robust tracking error portfolio selection with worst-case downside risk measures," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 178-207.
    8. Xu Leiyan & Zhiqing Meng, 2019. "Multi-Loss WCVaR Risk Decision Optimization Based On Weight for Centralized Supply Problem of Direct Chain Enterprises," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(02), pages 1-16, April.
    9. Baule, Rainer & Korn, Olaf & Kuntz, Laura-Chloé, 2019. "Markowitz with regret," Journal of Economic Dynamics and Control, Elsevier, vol. 103(C), pages 1-24.
    10. Fima Klebaner & Zinoviy Landsman & Udi Makov & Jing Yao, 2017. "Optimal portfolios with downside risk," Quantitative Finance, Taylor & Francis Journals, vol. 17(3), pages 315-325, March.
    11. Zhenlong Jiang & Ran Ji & Kuo-Chu Chang, 2020. "A Machine Learning Integrated Portfolio Rebalance Framework with Risk-Aversion Adjustment," JRFM, MDPI, vol. 13(7), pages 1-20, July.
    12. Jang Ho Kim & Woo Chang Kim & Frank J. Fabozzi, 2017. "Penalizing variances for higher dependency on factors," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 479-489, April.
    13. Zhiping Chen & Shen Peng & Abdel Lisser, 2020. "A sparse chance constrained portfolio selection model with multiple constraints," Journal of Global Optimization, Springer, vol. 77(4), pages 825-852, August.
    14. Maria Scutellà & Raffaella Recchia, 2013. "Robust portfolio asset allocation and risk measures," Annals of Operations Research, Springer, vol. 204(1), pages 145-169, April.
    15. Xinwei Zhao & Xinsong Yang & Geng Peng & Shengjie Yue, 2023. "International Trade and Carbon Emissions: Evaluating the Role of Trade Rule Uncertainty," Sustainability, MDPI, vol. 15(15), pages 1-19, July.
    16. Zhu, Shushang & Fan, Minjie & Li, Duan, 2014. "Portfolio management with robustness in both prediction and decision: A mixture model based learning approach," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 1-25.
    17. Shushang Zhu & Masao Fukushima, 2009. "Worst-Case Conditional Value-at-Risk with Application to Robust Portfolio Management," Operations Research, INFORMS, vol. 57(5), pages 1155-1168, October.

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