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

Hengzhen Lu, Yingying Zhang (), Ling Xiao () and Gurjeet Dhesi
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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

JRFM, 2022, vol. 15, issue 10, 1-20

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.

Keywords: higher-order Omega; Almost Stochastic Dominance rules; fund performance evaluation (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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