IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v275y2019i2p755-767.html
   My bibliography  Save this article

Optimal strategies under Omega ratio

Author

Listed:
  • Bernard, Carole
  • Vanduffel, Steven
  • Ye, Jiang

Abstract

We study portfolio selection under the objective of maximizing the Omega ratio, proposed by Keating and Shadwick (2002) as an alternative to the Sharpe ratio for performance assessment of investment strategies. We show that in a continuous-time setting of the financial market the problem is ill-posed, i.e., maximizing the Omega ratio leads to excessive risk taking. By imposing additional restrictions we show that the Omega ratio maximizing strategy is still very risky and may coincide with the choice made by risk neutral investors. We conclude that caution is needed when using the Omega ratio for making asset allocation decisions.

Suggested Citation

  • Bernard, Carole & Vanduffel, Steven & Ye, Jiang, 2019. "Optimal strategies under Omega ratio," European Journal of Operational Research, Elsevier, vol. 275(2), pages 755-767.
    • Handle: RePEc:eee:ejores:v:275:y:2019:i:2:p:755-767
    DOI: 10.1016/j.ejor.2018.11.046
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221718309871
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2018.11.046?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. 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. 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.
    3. Dybvig, Philip H, 1988. "Distributional Analysis of Portfolio Choice," The Journal of Business, University of Chicago Press, vol. 61(3), pages 369-393, July.
    4. Johanna F. Ziegel, 2016. "Coherence And Elicitability," Mathematical Finance, Wiley Blackwell, vol. 26(4), pages 901-918, October.
    5. Valeri Zakamouline, 2014. "Portfolio performance evaluation with loss aversion," Quantitative Finance, Taylor & Francis Journals, vol. 14(4), pages 699-710, April.
    6. Bertrand, Philippe & Prigent, Jean-luc, 2011. "Omega performance measure and portfolio insurance," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1811-1823, July.
    7. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    8. Massimiliano Caporin & Grégory M. Jannin & Francesco Lisi & Bertrand B. Maillet, 2014. "A Survey On The Four Families Of Performance Measures," Journal of Economic Surveys, Wiley Blackwell, vol. 28(5), pages 917-942, December.
    9. Fabio Bellini & Valeria Bignozzi, 2015. "On elicitable risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 15(5), pages 725-733, May.
    10. Fabio Bellini & Bernhard Klar & Alfred Müller, 2018. "Expectiles, Omega Ratios and Stochastic Ordering," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 855-873, September.
    11. Guastaroba, G. & Mansini, R. & Ogryczak, W. & Speranza, M.G., 2016. "Linear programming models based on Omega ratio for the Enhanced Index Tracking Problem," European Journal of Operational Research, Elsevier, vol. 251(3), pages 938-956.
    12. Carole Bernard & Franck Moraux & Ludger R�schendorf & Steven Vanduffel, 2015. "Optimal payoffs under state-dependent preferences," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1157-1173, July.
    13. Jonathan Ingersoll & Ivo Welch, 2007. "Portfolio Performance Manipulation and Manipulation-proof Performance Measures," The Review of Financial Studies, Society for Financial Studies, vol. 20(5), pages 1503-1546, 2007 17.
    14. Marco Scarsini & Alfred Muller, 2001. "Stochastic comparison of random vectors with a common copula," Post-Print hal-00540198, HAL.
    15. Lau, Hon-Shiang & Wingender, John R, 1989. "The Analytics of the Intervaling Effect on Skewness and Kurtosis of Stock Returns," The Financial Review, Eastern Finance Association, vol. 24(2), pages 215-233, May.
    16. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    17. Fogler, H. Russell & Radcliffe, Robert C., 1974. "A Note on Measurement of Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 9(3), pages 485-489, June.
    18. Farinelli, Simone & Tibiletti, Luisa, 2008. "Sharpe thinking in asset ranking with one-sided measures," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1542-1547, March.
    19. J. Dhaene & R. J. A. Laeven & S. Vanduffel & G. Darkiewicz & M. J. Goovaerts, 2008. "Can a Coherent Risk Measure Be Too Subadditive?," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(2), pages 365-386, June.
    20. Christian Pedersen & Stephen Satchell, 2002. "On the foundation of performance measures under asymmetric returns," Quantitative Finance, Taylor & Francis Journals, vol. 2(3), pages 217-223.
    21. Bernard, C. & Vanduffel, S., 2014. "Mean–variance optimal portfolios in the presence of a benchmark with applications to fraud detection," European Journal of Operational Research, Elsevier, vol. 234(2), pages 469-480.
    22. Jean-Luc Prigent & Philippe Bertrand, 2011. "Omega performance measure and portfolio insurance," Post-Print hal-01833064, HAL.
    23. Alfred Müller & Marco Scarsini, 2001. "Stochastic Comparison of Random Vectors with a Common Copula," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 723-740, November.
    24. Fabio Bellini & Elena Di Bernardino, 2017. "Risk management with expectiles," The European Journal of Finance, Taylor & Francis Journals, vol. 23(6), pages 487-506, May.
    25. Christopher Adcock & Martin Eling & Nicola Loperfido, 2015. "Skewed distributions in finance and actuarial science: a review," The European Journal of Finance, Taylor & Francis Journals, vol. 21(13-14), pages 1253-1281, November.
    26. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    27. C. Bernard & D. Cornilly & S. Vanduffel, 2018. "Optimal portfolios under a correlation constraint," Quantitative Finance, Taylor & Francis Journals, vol. 18(3), pages 333-345, March.
    28. Carole Bernard & Phelim P. Boyle & Steven Vanduffel, 2014. "Explicit Representation of Cost-Efficient Strategies," Finance, Presses universitaires de Grenoble, vol. 35(2), pages 5-55.
    29. Edgars Jakobsons & Steven Vanduffel, 2015. "Dependence Uncertainty Bounds for the Expectile of a Portfolio," Risks, MDPI, vol. 3(4), pages 1-25, December.
    30. Antonio E. Bernardo & Olivier Ledoit, 2000. "Gain, Loss, and Asset Pricing," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 144-172, February.
    31. Arditti, Fred D & Levy, Haim, 1975. "Portfolio Efficiency Analysis in Three Moments: The Multiperiod Case," Journal of Finance, American Finance Association, vol. 30(3), pages 797-809, June.
    32. Bernard, Carole & Chen, Jit Seng & Vanduffel, Steven, 2015. "Rationalizing investors’ choices," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 10-23.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Bernard, C. & De Gennaro Aquino, L. & Vanduffel, S., 2023. "Optimal multivariate financial decision making," European Journal of Operational Research, Elsevier, vol. 307(1), pages 468-483.
    3. Guohui Guan & Zongxia Liang & Yi xia, 2021. "Optimal management of DC pension fund under relative performance ratio and VaR constraint," Papers 2103.04352, arXiv.org.
    4. Hongcan Lin & David Saunders & Chengguo Weng, 2019. "Portfolio Optimization With Performance Ratios," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(05), pages 1-38, August.
    5. Eric Benhamou & Beatrice Guez & Nicolas Paris1, 2019. "Omega and Sharpe ratio," Papers 1911.10254, arXiv.org.
    6. Sehgal, Ruchika & Sharma, Amita & Mansini, Renata, 2023. "Worst-case analysis of Omega-VaR ratio optimization model," Omega, Elsevier, vol. 114(C).
    7. 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.
    8. Johannes Hendrik Venter & Pieter Juriaan De Jongh, 2022. "Trading Binary Options Using Expected Profit and Loss Metrics," Risks, MDPI, vol. 10(11), pages 1-21, November.
    9. Carole Bernard & Gero Junike & Thibaut Lux & Steven Vanduffel, 2022. "Cost-efficient Payoffs under Model Ambiguity," Papers 2207.02948, arXiv.org, revised Aug 2023.

    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. 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.
    2. 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.
    3. 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.
    4. Sehgal, Ruchika & Sharma, Amita & Mansini, Renata, 2023. "Worst-case analysis of Omega-VaR ratio optimization model," Omega, Elsevier, vol. 114(C).
    5. León, Angel & Moreno, Manuel, 2017. "One-sided performance measures under Gram-Charlier distributions," Journal of Banking & Finance, Elsevier, vol. 74(C), pages 38-50.
    6. Bernard, C. & De Gennaro Aquino, L. & Vanduffel, S., 2023. "Optimal multivariate financial decision making," European Journal of Operational Research, Elsevier, vol. 307(1), pages 468-483.
    7. 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.
    8. Carole Bernard & Franck Moraux & Ludger R�schendorf & Steven Vanduffel, 2015. "Optimal payoffs under state-dependent preferences," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1157-1173, July.
    9. Bernard, Carole & Chen, Jit Seng & Vanduffel, Steven, 2015. "Rationalizing investors’ choices," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 10-23.
    10. Bertrand, Philippe & Prigent, Jean-luc, 2019. "On the optimality of path-dependent structured funds: The cost of standardization," European Journal of Operational Research, Elsevier, vol. 277(1), pages 333-350.
    11. Zieling, Daniel & Mahayni, Antje & Balder, Sven, 2014. "Performance evaluation of optimized portfolio insurance strategies," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 212-225.
    12. Bi, Hongwei & Huang, Rachel J. & Tzeng, Larry Y. & Zhu, Wei, 2019. "Higher-order Omega: A performance index with a decision-theoretic foundation," Journal of Banking & Finance, Elsevier, vol. 100(C), pages 43-57.
    13. Penaranda, Francisco, 2007. "Portfolio choice beyond the traditional approach," LSE Research Online Documents on Economics 24481, London School of Economics and Political Science, LSE Library.
    14. L. Rüschendorf & Steven Vanduffel, 2020. "On the construction of optimal payoffs," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 129-153, June.
    15. Eric Benhamou & Beatrice Guez & Nicolas Paris1, 2019. "Omega and Sharpe ratio," Papers 1911.10254, arXiv.org.
    16. Massimiliano Caporin & Grégory M. Jannin & Francesco Lisi & Bertrand B. Maillet, 2014. "A Survey On The Four Families Of Performance Measures," Journal of Economic Surveys, Wiley Blackwell, vol. 28(5), pages 917-942, December.
    17. Tawil, Dima, 2018. "Risk-adjusted performance of portfolio insurance and investors’ preferences," Finance Research Letters, Elsevier, vol. 24(C), pages 10-18.
    18. Hamidi, Benjamin & Maillet, Bertrand & Prigent, Jean-Luc, 2014. "A dynamic autoregressive expectile for time-invariant portfolio protection strategies," Journal of Economic Dynamics and Control, Elsevier, vol. 46(C), pages 1-29.
    19. repec:ipg:wpaper:2014-510 is not listed on IDEAS
    20. Vanduffel, Steven & Yao, Jing, 2017. "A stein type lemma for the multivariate generalized hyperbolic distribution," European Journal of Operational Research, Elsevier, vol. 261(2), pages 606-612.
    21. Darolles, Serge & Gourieroux, Christian, 2010. "Conditionally fitted Sharpe performance with an application to hedge fund rating," Journal of Banking & Finance, Elsevier, vol. 34(3), pages 578-593, March.

    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:eee:ejores:v:275:y:2019:i:2:p:755-767. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.