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Risk aversion vs. the Omega ratio: Consistency results

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  • Balder, Sven
  • Schweizer, Nikolaus

Abstract

This paper clarifies when the Omega ratio and related performance measures are consistent with second order stochastic dominance and when they are not. To avoid consistency problems, the threshold parameter in the ratio should be chosen as the expected return of some benchmark – as is commonly done in the Sharpe ratio. When the ratio is below one, its value should be discarded – just like a negative Sharpe ratio. Finally, we show that a class of closely related performance measures has both better consistency properties and greater flexibility.

Suggested Citation

  • Balder, Sven & Schweizer, Nikolaus, 2017. "Risk aversion vs. the Omega ratio: Consistency results," Finance Research Letters, Elsevier, vol. 21(C), pages 78-84.
    • Handle: RePEc:eee:finlet:v:21:y:2017:i:c:p:78-84
    DOI: 10.1016/j.frl.2016.12.012
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    References listed on IDEAS

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    1. Caporin, Massimiliano & Costola, Michele & Jannin, Gregory & Maillet, Bertrand, 2018. "“On the (Ab)use of Omega?”," Journal of Empirical Finance, Elsevier, vol. 46(C), pages 11-33.
    2. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    3. Martin Branda & Miloš Kopa, 2014. "On relations between DEA-risk models and stochastic dominance efficiency tests," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(1), pages 13-35, March.
    4. Eling, Martin & Schuhmacher, Frank, 2007. "Does the choice of performance measure influence the evaluation of hedge funds?," Journal of Banking & Finance, Elsevier, vol. 31(9), pages 2632-2647, September.
    5. Alexander Cherny & Dilip Madan, 2009. "New Measures for Performance Evaluation," Review of Financial Studies, Society for Financial Studies, vol. 22(7), pages 2371-2406, July.
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    Citations

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    Cited by:

    1. Monica Billio & Bertrand Maillet & Loriana Pelizzon, 2022. "A meta-measure of performance related to both investors and investments characteristics," Annals of Operations Research, Springer, vol. 313(2), pages 1405-1447, June.
    2. Xu Guo & Cuizhen Niu & Wing-Keung Wong, 2019. "Farinelli and Tibiletti ratio and stochastic dominance," Risk Management, Palgrave Macmillan, vol. 21(3), pages 201-213, September.
    3. Carole Bernard & Massimiliano Caporin & Bertrand Maillet & Xiang Zhang, 2023. "Omega Compatibility: A Meta-analysis," Computational Economics, Springer;Society for Computational Economics, vol. 62(2), pages 493-526, August.
    4. Gianfranco Guastaroba & Renata Mansini & Wlodzimierz Ogryczak & M. Grazia Speranza, 2020. "Enhanced index tracking with CVaR-based ratio measures," Annals of Operations Research, Springer, vol. 292(2), pages 883-931, September.
    5. Kroll, Yoram & Marchioni, Andrea & Ben-Horin, Moshe, 2024. "Sortino(γ): a modified Sortino ratio with adjusted threshold," MPRA Paper 120203, University Library of Munich, Germany.
    6. Xu Guo & Xuejun Jiang & Wing-Keung Wong, 2017. "Stochastic Dominance and Omega Ratio: Measures to Examine Market Efficiency, Arbitrage Opportunity, and Anomaly," Economies, MDPI, vol. 5(4), pages 1-16, October.
    7. Cuizhen Niu & Wing-Keung Wong & Qunfang Xu, 2017. "Kappa ratios and (higher-order) stochastic dominance," Risk Management, Palgrave Macmillan, vol. 19(3), pages 245-253, August.
    8. Guan, Guohui & Liang, Zongxia & Xia, Yi, 2023. "Optimal management of DC pension fund under the relative performance ratio and VaR constraint," European Journal of Operational Research, Elsevier, vol. 305(2), pages 868-886.
    9. Díaz, Antonio & Esparcia, Carlos & Huélamo, Diego, 2023. "Stablecoins as a tool to mitigate the downside risk of cryptocurrency portfolios," The North American Journal of Economics and Finance, Elsevier, vol. 64(C).
    10. Philippe Goulet Coulombe & Maximilian Goebel, 2023. "Maximally Machine-Learnable Portfolios," Papers 2306.05568, arXiv.org, revised Apr 2024.
    11. Philippe Goulet Coulombe & Maximilian Gobel, 2023. "Maximally Machine-Learnable Portfolios," Working Papers 23-01, Chair in macroeconomics and forecasting, University of Quebec in Montreal's School of Management, revised Apr 2023.

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    More about this item

    Keywords

    Performance measurement; Stochastic dominance; Omega ratio; Sharpe ratio;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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