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

30 Pages Posted: 25 Jun 2016

See all articles by Susanne Emmer

Susanne Emmer

ESSEC Business School

Marie Kratz

ESSEC Business School, CREAR

Dirk Tasche

Swiss Financial Market Supervisory Authority (FINMA)

Multiple version iconThere are 2 versions of this paper

Date Written: November 17, 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 criticized 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, for example, backtesting for VaR. Expectiles have been suggested as potentially better alternatives to both ES and VaR. In this paper, we revisit the commonly accepted desirable properties of risk measures such as 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 of replacing ES by a set of four quantiles, which should allow us to make use of backtesting methods for VaR.

Keywords: backtesting, capital allocation, coherence, diversification, conditional elicitability, risk measures

Suggested Citation

Emmer, Susanne and Kratz, Marie and Tasche, Dirk, What Is the Best Risk Measure in Practice? A Comparison of Standard Measures (November 17, 2015). Journal of Risk, Vol. 18, No. 2, 2015, Available at SSRN: https://ssrn.com/abstract=2799732

Susanne Emmer

ESSEC Business School ( email )

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

Marie Kratz

ESSEC Business School, CREAR ( email )

Avenue Bernard Hirsch
BP 50105 CERGY
CERGY, CERGY PONTOISE CEDEX 95021
France

Dirk Tasche (Contact Author)

Swiss Financial Market Supervisory Authority (FINMA) ( email )

Einsteinstrasse 2
Bern, 3003
Switzerland

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