Choosing Expected Shortfall Over VaR in Basel III Using Stochastic Dominance

USC-INET Research Paper No. 16-05

42 Pages Posted: 13 Mar 2016

See all articles by Chia-Lin Chang

Chia-Lin Chang

National Chung Hsing University - Department of Applied Economics, Department of Finance

Juan-Angel Jiménez-Martin

Complutense University of Madrid

Esfandiar Maasoumi

Emory University

Michael McAleer

Erasmus University Rotterdam - Erasmus School of Economics, Econometric Institute; Tinbergen Institute; University of Tokyo - Centre for International Research on the Japanese Economy (CIRJE), Faculty of Economics

Teodosio Perez Amaral

Complutense University of Madrid - Facultad de Económicas y Empresariales

Date Written: February 2016

Abstract

We compare Value at Risk (VaR) and Expected Shortfall (ES) following a Stochastic Dominance (SD) approach frequently used to order distributions in terms of welfare and in portfolio selection. Basel Committee on Banking Supervision (BCBS) recommends bank risk managers to shift the current quantitative risk metrics system, based on Value-at-Risk (VaR), to Expected Shortfall (ES). “Welfare costs” of such a reform in terms of capital requirements and penalties are a central concern for risk managers and regulators. Policy makers’ concerns can be addressed with many different value functions. A uniform ranking analysis based on stochastic dominance is provided here as an effective tool for comparing distributions of daily capital requirement charges produced under different regulations. On the basis of empirical results, it is concluded that ES should be preferred by risk averse policy makers who favour larger but less volatile capital requirements, and reduces the sensitivity of capital charges to changes in the probability of default.

Keywords: Stochastic dominance, Welfare, Value-at-Risk, Expected Shortfall, Optimizing strategy, Basel III Accord

JEL Classification: G32, G11, G17, C53, C22

Suggested Citation

Chang, Chia-Lin and Jiménez-Martin, Juan-Angel and Maasoumi, Esfandiar Essie and McAleer, Michael and Perez Amaral, Teodosio, Choosing Expected Shortfall Over VaR in Basel III Using Stochastic Dominance (February 2016). USC-INET Research Paper No. 16-05, Available at SSRN: https://ssrn.com/abstract=2746710 or http://dx.doi.org/10.2139/ssrn.2746710

Chia-Lin Chang (Contact Author)

National Chung Hsing University - Department of Applied Economics, Department of Finance ( email )

Taichung, Taiwan
China

Juan-Angel Jiménez-Martin

Complutense University of Madrid ( email )

Complutense University of Madrid
Campus de somosaguas
Pozuelo de Alarcon, Madrid 28223
Spain
+34 91 3942355 (Phone)

HOME PAGE: http://www.ucm.es/fundamentos-analisis-economico2/jajm

Esfandiar Essie Maasoumi

Emory University ( email )

1602 Fishburne Drive
Atlanta, GA 30322
United States

HOME PAGE: http://economics.emory.edu/home/people/faculty/Maasoumiesfandiar_Home.html

Michael McAleer

Erasmus University Rotterdam - Erasmus School of Economics, Econometric Institute ( email )

Rotterdam
Netherlands

Tinbergen Institute

Rotterdam
Netherlands

University of Tokyo - Centre for International Research on the Japanese Economy (CIRJE), Faculty of Economics

Tokyo
Japan

Teodosio Perez Amaral

Complutense University of Madrid - Facultad de Económicas y Empresariales ( email )

Madrid, 28223
Spain

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