An Axiomatic Foundation for the Expected Shortfall

• 成果类型: Article
• 署名作者: Wang, Ruodu; Zitikis, Ricardas
• 署名单位: University of Waterloo; Western University (University of Western Ontario)
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2020.3617
• 发表日期: 2021
• 关键词: risk measure; expected shortfall; Risk concentration; diversification; risk aggregation

摘要

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.