Unequal returns: Using the Atkinson index to measure financial risk

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 preferencereturn 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.

Unequal Benefits: The Effects of Health Insurance Integration on Consumption Inequality in Rural China

“…Measurement methods for consumption inequality can be categorized into group-level and individual-level indicators. Common group indicators include the Gini coefficient(Gayán-Navarro and Sanso-Navarro, 2024), the Atkinson index (Fischer and Lundtofte, 2020), the generalized entropy index (Dufour et al, 2024), and the interquartile ratio (Girsberger et al, 2020), which provide insights into societal or group-level consumption disparities. However, recent studies have increasingly focused on individual-level measurements to address consumers' specific concerns about the relative deprivation they face.…”