An Axiomatic Foundation for the Expected Shortfall

2019 ◽  
Author(s):  
Ruodu Wang ◽  
Ricardas Zitikis
Keyword(s):  
Expected Shortfall ◽  
Axiomatic Foundation

An Axiomatic Foundation for the Expected Shortfall

2020 ◽  
Author(s):  
Ruodu Wang ◽  
Ričardas Zitikis
Keyword(s):  
Value At Risk ◽  
Banking Sector ◽  
Financial Regulation ◽  
Risk Measure ◽  
Expected Shortfall ◽  
Axiomatic Foundation ◽  
Coherent Risk ◽  
The Family ◽  
Economic Foundation ◽  
Tail Events

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. This paper was accepted by Manel Baucells, decision analysis.

Efficient calculation of expected shortfall contributions in large credit portfolios

2007 ◽  
Vol 11 (2) ◽  
pp. 1-43 ◽  
Author(s):  
Michael Kalkbrener ◽  
Anna Kennedy ◽  
Monika Popp
Keyword(s):  
Expected Shortfall ◽  
Efficient Calculation
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