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

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

doi:10.1016/j.jbankfin.2018.12.013

Cited by 7 publications

(11 citation statements)

References 25 publications

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“…However, most of the extant literature is restricted to lower-order Stochastic Dominance, i.e., FSD or SSD. Bi et al (2019) extended Klar and Müller's (2018) work to a higher-order framework and proved the one-to-one consistency between higher-order Omega and its corresponding higher-order Stochastic Dominance. However, there are very limited discussions on the consistency of higher-order Omega with Stochastic Dominance criteria since the development of higher-order Omega.…”

Section: Introductionmentioning

confidence: 90%

“…This index is rooted in the framework of acceptance dominance. Bi et al (2019) provide a theoretical foundation by showing the consistency between Stochastic Dominance and higher-order Omega. In this section, we examine the consistency between higher-order Omega and Almost Stochastic Dominance.…”

Section: Definitions and Theoriesmentioning

confidence: 99%

“…Some equivalent representations are derived in the literature (as seen in Bi et al 2019). The Nth-order Omega is equal to the following form:…”

Section: Higher-order Omegamentioning

confidence: 99%

“…Moreover, it is proved that the Omega function provides a consistent ranking as the First-order Stochastic Dominance (hereafter, FSD) (Benhamou et al 2019). Bi et al (2019) extend the Omega function to the Nth-order Omega based on the concept of Almost Acceptance Dominance (hereafter, AAD). The Nth-order Omega includes the Omega function as a special case when N equals 1.…”

Section: Introductionmentioning

confidence: 99%

“…Stochastic Dominance suffers the well-known partial order problem, only employing partial information on the investor's preferences such as risk aversion. With Omega types of measures, including higher-order Omega (Bi et al 2019), Omega (Keating and Shadwick 2002) can generate a complete order through analytical calculations. If the consistency between the two is proved, it does not only imply the use of Stochastic Dominance among portfolios but also confirms the decision making based on higher-order Omega.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Zhang

Xiao

et al. 2022

JRFM

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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 Nth-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 Nth-order Omega in the concept of Almost Stochastic Dominance rules. Furthermore, the empirical results also show the superiority of the Nth-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.

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Section: Introductionmentioning

confidence: 90%

Section: Definitions and Theoriesmentioning

confidence: 99%

“…Some equivalent representations are derived in the literature (as seen in Bi et al 2019). The Nth-order Omega is equal to the following form:…”

Section: Higher-order Omegamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%