Unequal Returns: Using the Atkinson Index to Measure Financial Risk
61 Pages Posted: 1 Dec 2017 Last revised: 30 Jan 2019
Date Written: January 14, 2019
We apply the Atkinson (1970) inequality index to time series of asset returns to offer a novel measure of financial risk consistent with expected-utility theory. This measure is converted to a certainty-equivalent return serving as a performance measure. We extend the Atkinson index to HARA utility and derive closed-form solutions to our measures for a number of preference-return combinations. Further, we establish relationships between risk aversion and the weights assigned to the cumulants of the return distribution for our performance measure. Using data from hedge funds and asset-pricing anomalies, we find that our performance measure contains additional, economically meaningful information.
Keywords: risk, performance, non-Gaussian distributions, cumulants, hedge funds
JEL Classification: G11
Suggested Citation: Suggested Citation