Comparative Risk Aversion vs. Threshold Choice in the Omega Ratio

44 Pages Posted: 6 Jan 2023 Last revised: 7 Sep 2023

See all articles by Anne Balter

Anne Balter

Tilburg University; Netspar

Ki Wai Chau

University of Groningen - Faculty of Economics and Business

Nikolaus Schweizer

Tilburg School of Economics and Management

Date Written: January 5, 2023

Abstract

We study conditions under which the threshold parameter in the Omega ratio represents risk aversion in the sense of monotonicity of risk premia. To this end, we derive asymptotic expansions for risk premia associated with taking a small additional risk on top of a background risk. These risk premia have the expected monotonicity behavior if, roughly speaking, the variance of the additional risk decreases with the background risk and if the density of the background risk is log-concave. When these conditions are violated, the threshold in the Omega ratio does not represent risk aversion in general. Finally, we compare our sufficient conditions for the Omega ratio to those that are needed to guarantee monotonicity of risk premia with an expected utility criterion under background risk. We argue that the conditions that are needed for the Omega threshold to represent risk aversion are comparable to those that are needed for expected utility with exponential utility functions.

Keywords: Omega Ratio, Risk Preferences, Decision Criteria

JEL Classification: D81, G11

Suggested Citation

Balter, Anne and Chau, Ki Wai and Schweizer, Nikolaus, Comparative Risk Aversion vs. Threshold Choice in the Omega Ratio (January 5, 2023). Available at SSRN: https://ssrn.com/abstract=4318658 or http://dx.doi.org/10.2139/ssrn.4318658

Anne Balter

Tilburg University ( email )

P.O. Box 90153
Tilburg, DC Noord-Brabant 5000 LE
Netherlands

Netspar ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Ki Wai Chau

University of Groningen - Faculty of Economics and Business ( email )

Postbus 72
9700 AB Groningen
Netherlands

Nikolaus Schweizer (Contact Author)

Tilburg School of Economics and Management ( email )

PO Box 90153
Tilburg, 5000 LE Ti
Netherlands

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