Scandinavian Working Papers in Economics

Working Papers,
Lund University, Department of Economics

No 2018:25: Unequal Returns: Using the Atkinson Index to Measure Financial Risk

Thomas Fischer () and Frederik Lundtofte ()
Additional contact information
Thomas Fischer: Department of Economics, Lund University, Postal: Department of Economics, School of Economics and Management, Lund University, Box 7082, S-220 07 Lund, Sweden
Frederik Lundtofte: Department of Economics, Lund University, Postal: Department of Economics, School of Economics and Management, Lund University, Box 7082, S-220 07 Lund, Sweden

Abstract: 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-codes: G11

68 pages, October 3, 2018

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