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Risk Management under Omega Measure

Author

Listed:
  • Michael R. Metel

    (Laboratoire de Recherche en Informatique, Université Paris-Sud, 91405 Orsay, France)

  • Traian A. Pirvu

    (Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, ON L8S 4K1, Canada)

  • Julian Wong

    (Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, ON L8S 4K1, Canada)

Abstract

We prove that the Omega measure, which considers all moments when assessing portfolio performance, is equivalent to the widely used Sharpe ratio under jointly elliptic distributions of returns. Portfolio optimization of the Sharpe ratio is then explored, with an active-set algorithm presented for markets prohibiting short sales. When asymmetric returns are considered, we show that the Omega measure and Sharpe ratio lead to different optimal portfolios.

Suggested Citation

  • Michael R. Metel & Traian A. Pirvu & Julian Wong, 2017. "Risk Management under Omega Measure," Risks, MDPI, vol. 5(2), pages 1-14, May.
    • Handle: RePEc:gam:jrisks:v:5:y:2017:i:2:p:27-:d:97820
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    References listed on IDEAS

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    5. Adelchi Azzalini, 2005. "The Skew‐normal Distribution and Related Multivariate Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 159-188, June.
    6. Yew Low, Rand Kwong & Faff, Robert & Aas, Kjersti, 2016. "Enhancing mean–variance portfolio selection by modeling distributional asymmetries," Journal of Economics and Business, Elsevier, vol. 85(C), pages 49-72.
    7. Owen, Joel & Rabinovitch, Ramon, 1983. "On the Class of Elliptical Distributions and Their Applications to the Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 38(3), pages 745-752, June.
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    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. Eric Benhamou & Beatrice Guez & Nicolas Paris1, 2019. "Omega and Sharpe ratio," Papers 1911.10254, arXiv.org.
    3. Yu, Jing-Rung & Paul Chiou, Wan-Jiun & Hsin, Yi-Ting & Sheu, Her-Jiun, 2022. "Omega portfolio models with floating return threshold," International Review of Economics & Finance, Elsevier, vol. 82(C), pages 743-758.
    4. Albert Cohen, 2018. "Editorial: A Celebration of the Ties That Bind Us: Connections between Actuarial Science and Mathematical Finance," Risks, MDPI, vol. 6(1), pages 1-3, January.

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