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Higher-order Omega: A performance index with a decision-theoretic foundation

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  • Bi, Hongwei
  • Huang, Rachel J.
  • Tzeng, Larry Y.
  • Zhu, Wei

Abstract

This paper proposes a new performance index referred to as the Nth-order Omega that includes the well-known Omega as a special case. The index is established by adopting an approach that is free of a utility functional form or/and distributional assumptions. A decision-theoretic foundation for our index is further established through introducing a new distribution ranking criterion. The index is monotonic with respect to Nth-degree stochastic dominance and offers a complete ordering on gambles. An empirical example of deriving the optimal hedge ratio is demonstrated to show the applicability of the index.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jbfina:v:100:y:2019:i:c:p:43-57
    DOI: 10.1016/j.jbankfin.2018.12.013
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    2. Taylor, James W., 2022. "Forecasting Value at Risk and expected shortfall using a model with a dynamic omega ratio," Journal of Banking & Finance, Elsevier, vol. 140(C).
    3. Huang, Jinbo & Li, Yong & Yao, Haixiang, 2022. "Partial moments and indexation investment strategies," Journal of Empirical Finance, Elsevier, vol. 67(C), pages 39-59.
    4. Bignozzi, Valeria & Merlo, Luca & Petrella, Lea, 2024. "Inter-order relations between equivalence for Lp-quantiles of the Student's t distribution," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 44-50.
    5. 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.

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