What is the Best Risk Measure in Practice? A Comparison of Standard Measures

Journal of Risk 18(2), 31-60, 2015

27 Pages Posted: 21 Dec 2013 Last revised: 13 Jul 2017

See all articles by Susanne Emmer

Susanne Emmer

ESSEC Business School

Dirk Tasche

Swiss Financial Market Supervisory Authority (FINMA)

Marie Kratz

ESSEC Business School - Information & Decision Sciences Department

Multiple version iconThere are 2 versions of this paper

Date Written: January 30, 2015

Abstract

Expected Shortfall (ES) has been widely accepted as a risk measure that is conceptually superior to Value-at-Risk (VaR). At the same time, however, it has been criticised for issues relating to backtesting. In particular, ES has been found not to be elicitable which means that backtesting for ES is less straightforward than, e.g., backtesting for VaR. Expectiles have been suggested as potentially better alternatives to both ES and VaR. In this paper, we revisit commonly accepted desirable properties of risk measures like coherence, comonotonic additivity, robustness and elicitability. We check VaR, ES and Expectiles with regard to whether or not they enjoy these properties, with particular emphasis on Expectiles. We also consider their impact on capital allocation, an important issue in risk management. We find that, despite the caveats that apply to the estimation and backtesting of ES, it can be considered a good risk measure. As a consequence, there is no sufficient evidence to justify an all-inclusive replacement of ES by Expectiles in applications. For backtesting ES, we propose an empirical approach that consists in replacing ES by a set of four quantiles, which should allow to make use of backtesting methods for VaR.

Keywords: Backtesting; Capital Allocation; Coherence; Diversification; Elicitability; Expected Shortfall; Expectile; Forecasts; Probability Integral Transform (PIT); Risk Measure; Risk Management; Robustnes; Value-at-Risk

Suggested Citation

Emmer, Susanne and Tasche, Dirk and Kratz, Marie, What is the Best Risk Measure in Practice? A Comparison of Standard Measures (January 30, 2015). Journal of Risk 18(2), 31-60, 2015, Available at SSRN: https://ssrn.com/abstract=2370378 or http://dx.doi.org/10.2139/ssrn.2370378

Susanne Emmer (Contact Author)

ESSEC Business School ( email )

3 Avenue Bernard Hirsch
CS 50105 CERGY
CERGY, CERGY PONTOISE CEDEX 95021
France

Dirk Tasche

Swiss Financial Market Supervisory Authority (FINMA) ( email )

Einsteinstrasse 2
Bern, 3003
Switzerland

Marie Kratz

ESSEC Business School - Information & Decision Sciences Department ( email )

Avenue Bernard Hirsch B.P. 50105
Cergy-Pontoise (Paris), 95021
France

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