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Robust portfolio optimization with Value-at-Risk-adjusted Sharpe ratios

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  • Geng Deng

    (Geng Deng, Securities Litigation and Consulting Group, 3998 Fair Ridge Dr.)

  • Tim Dulaney
  • Craig McCann
  • Olivia Wang

Abstract

We propose a robust portfolio optimization approach based on Value-at-Risk (VaR)-adjusted Sharpe ratios. Traditional Sharpe ratio estimates using a limited series of historical returns are subject to estimation errors. Portfolio optimization based on traditional Sharpe ratios ignores this uncertainty and, as a result, is not robust. In this article, we propose a robust portfolio optimization model that selects the portfolio with the largest worse-case-scenario Sharpe ratio within a given confidence interval. We show that this framework is equivalent to maximizing the Sharpe ratio reduced by a quantity proportional to the standard deviation in the Sharpe ratio estimator. We highlight the relationship between the VaR-adjusted Sharpe ratios and other modified Sharpe ratios proposed in the literature. In addition, we present both numerical and empirical results comparing optimal portfolios generated by the approach advocated here with those generated by both traditional and alternative optimization approaches.

Suggested Citation

  • Geng Deng & Tim Dulaney & Craig McCann & Olivia Wang, 2013. "Robust portfolio optimization with Value-at-Risk-adjusted Sharpe ratios," Journal of Asset Management, Palgrave Macmillan, vol. 14(5), pages 293-305, October.
    • Handle: RePEc:pal:assmgt:v:14:y:2013:i:5:d:10.1057_jam.2013.21
    DOI: 10.1057/jam.2013.21
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    References listed on IDEAS

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    1. Zakamouline, Valeri & Koekebakker, Steen, 2009. "Portfolio performance evaluation with generalized Sharpe ratios: Beyond the mean and variance," Journal of Banking & Finance, Elsevier, vol. 33(7), pages 1242-1254, July.
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    5. Frank Fabozzi & Dashan Huang & Guofu Zhou, 2010. "Robust portfolios: contributions from operations research and finance," Annals of Operations Research, Springer, vol. 176(1), pages 191-220, April.
    6. Zymler, Steve & Rustem, Berç & Kuhn, Daniel, 2011. "Robust portfolio optimization with derivative insurance guarantees," European Journal of Operational Research, Elsevier, vol. 210(2), pages 410-424, April.
    7. Victor DeMiguel & Francisco J. Nogales, 2009. "Portfolio Selection with Robust Estimation," Operations Research, INFORMS, vol. 57(3), pages 560-577, June.
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    Cited by:

    1. 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.
    2. Parul BHATIA & Priya GUPTA, 2020. "Portfolio optimization with VaR approach: A comparative analysis for Japan, London, New York and India," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania / Editura Economica, vol. 0(4(625), W), pages 245-262, Winter.
    3. Ran Ji & Miguel A. Lejeune, 2021. "Data-Driven Optimization of Reward-Risk Ratio Measures," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1120-1137, July.
    4. Seixas, Mário & Barbosa, António, 2019. "Optimal Value-at-Risk Disclosure," MPRA Paper 97526, University Library of Munich, Germany.
    5. Jang Ho Kim & Woo Chang Kim & Frank J. Fabozzi, 2018. "Recent advancements in robust optimization for investment management," Annals of Operations Research, Springer, vol. 266(1), pages 183-198, July.
    6. Syed Kumail Abbas Rizvi & Nawazish Mirza & Bushra Naqvi & Birjees Rahat, 2020. "Covid-19 and asset management in EU: a preliminary assessment of performance and investment styles," Journal of Asset Management, Palgrave Macmillan, vol. 21(4), pages 281-291, July.
    7. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2022. "Robust portfolio selection problems: a comprehensive review," Operational Research, Springer, vol. 22(4), pages 3203-3264, September.
    8. Sally G. Arcidiacono & Damiano Rossello, 2022. "A hybrid approach to the discrepancy in financial performance’s robustness," Operational Research, Springer, vol. 22(5), pages 5441-5476, November.
    9. Sandra Cruz Caçador & Pedro Manuel Cortesão Godinho & Joana Maria Pina Cabral Matos Dias, 2022. "A minimax regret portfolio model based on the investor’s utility loss," Operational Research, Springer, vol. 22(1), pages 449-484, March.
    10. Chakrabarti, Deepayan, 2021. "Parameter-free robust optimization for the maximum-Sharpe portfolio problem," European Journal of Operational Research, Elsevier, vol. 293(1), pages 388-399.
    11. Xidonas, Panos & Mavrotas, George & Hassapis, Christis & Zopounidis, Constantin, 2017. "Robust multiobjective portfolio optimization: A minimax regret approach," European Journal of Operational Research, Elsevier, vol. 262(1), pages 299-305.
    12. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2021. "Robust Portfolio Selection Problems: A Comprehensive Review," Papers 2103.13806, arXiv.org, revised Jan 2022.
    13. Syed Kumail Abbas Rizvi & Nawazish Mirza & Bushra Naqvi & Birjees Rahat, 0. "Covid-19 and asset management in EU: a preliminary assessment of performance and investment styles," Journal of Asset Management, Palgrave Macmillan, vol. 0, pages 1-11.
    14. Esparcia, Carlos & López, Raquel, 2024. "Performance of crypto-Forex portfolios based on intraday data," Research in International Business and Finance, Elsevier, vol. 69(C).
    15. Xidonas, Panos & Hassapis, Christis & Soulis, John & Samitas, Aristeidis, 2017. "Robust minimum variance portfolio optimization modelling under scenario uncertainty," Economic Modelling, Elsevier, vol. 64(C), pages 60-71.

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