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Unequal returns: Using the Atkinson index to measure financial risk

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  • Fischer, Thomas
  • Lundtofte, Frederik

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.

Suggested Citation

  • Fischer, Thomas & Lundtofte, Frederik, 2020. "Unequal returns: Using the Atkinson index to measure financial risk," Journal of Banking & Finance, Elsevier, vol. 116(C).
    • Handle: RePEc:eee:jbfina:v:116:y:2020:i:c:s0378426620300868
    DOI: 10.1016/j.jbankfin.2020.105819
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    More about this item

    Keywords

    Risk; Performance; Non-Gaussian distributions; Cumulants; Hedge funds;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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