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Risk management under Omega measure

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  • Michael R. Metel
  • Traian A. Pirvu
  • Julian Wong

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.

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  • Michael R. Metel & Traian A. Pirvu & Julian Wong, 2015. "Risk management under Omega measure," Papers 1510.05790, arXiv.org, revised Apr 2017.
    • Handle: RePEc:arx:papers:1510.05790
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    Cited by:

    1. Eric Benhamou & Beatrice Guez & Nicolas Paris1, 2019. "Omega and Sharpe ratio," Papers 1911.10254, arXiv.org.
    2. 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.
    3. 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.
    4. 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.

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