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An Axiomatic Foundation for the Expected Shortfall

Ruodu Wang () and Ričardas Zitikis ()
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Ruodu Wang: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 5A7, Canada
Ričardas Zitikis: School of Mathematical and Statistical Sciences, University of Western Ontario, London, Ontario N6A 5B7, Canada

Management Science, 2021, vol. 67, issue 3, 1413-1429

Abstract: In the recent Basel Accords, the expected shortfall (ES) replaces the value-at-risk (VaR) as the standard risk measure for market risk in the banking sector, making it the most popular risk measure in financial regulation. Although ES is—in addition to many other nice properties—a coherent risk measure, it does not yet have an axiomatic foundation. In this paper, we put forward four intuitive economic axioms for portfolio risk assessment—monotonicity, law invariance, prudence, and no reward for concentration—that uniquely characterize the family of ES. Therefore, the results developed herein provide the first economic foundation for using ES as a globally dominating regulatory risk measure, currently employed in Basel III/IV. Key to the main results, several novel notions such as tail events and risk concentration naturally arise, and we explore them in detail. As a most important feature, ES rewards portfolio diversification and penalizes risk concentration in a special and intuitive way, not shared by any other risk measure.

Keywords: risk measure; expected shortfall; risk concentration; diversification; risk aggregation (search for similar items in EconPapers)
Date: 2021
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