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A State-of-the-Art Fund Performance Index: Higher-Order Omega and Its Consistency with Almost Stochastic Dominance

Author

Listed:
  • Hengzhen Lu

    (College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China)

  • Yingying Zhang

    (College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China)

  • Ling Xiao

    (School of Business and Management, Royal Holloway, University of London, Egham TW20 0EX, UK)

  • Gurjeet Dhesi

    (Group of Researchers Applying Physics in Economy and Sociology (GRAPES), Beauvallon, Rue de la Belle Jardinière, 483, 0021 Sart Tilman, Angleur, B-4031 Liège, Belgium)

Abstract

This paper provides a mathematical proof and theoretical analysis of the one-to-one consistency between higher-order Omega and Almost Stochastic Dominance rules when evaluating fund performance. The consistency between higher-order Omega and Almost N th-degree Stochastic Dominance reinforces the effectiveness of applying the higher-order Omega function in fund performance measurement, as the Almost Stochastic Dominance rules are more likely to be observed in real life. This study also clarifies that the higher-order Omega decreases when threshold L increases. The ranking of funds based on higher-order Omega changes at different thresholds. Hence, it is critical to specify the L so that the consistency holds. Through evaluating the performance of eleven U.S. funds between 2010 and 2020, we demonstrate the applications of the N th-order Omega in the concept of Almost Stochastic Dominance rules. Furthermore, the empirical results also show the superiority of the N th-order Omega over the traditional fund performance measure, i.e., Sharpe ratio and the lower-order Omega. The ranking of fund performance based on higher-order Omega is consistent with Almost Stochastic Dominance rules.

Suggested Citation

  • Hengzhen Lu & Yingying Zhang & Ling Xiao & Gurjeet Dhesi, 2022. "A State-of-the-Art Fund Performance Index: Higher-Order Omega and Its Consistency with Almost Stochastic Dominance," JRFM, MDPI, vol. 15(10), pages 1-20, September.
    • Handle: RePEc:gam:jjrfmx:v:15:y:2022:i:10:p:438-:d:927900
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    References listed on IDEAS

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    5. Jan Heufer, 2014. "Generating Random Optimising Choices," Computational Economics, Springer;Society for Computational Economics, vol. 44(3), pages 295-305, October.
    6. 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.
    7. 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.
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