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

Suzanne Emmer (1) , Marie Kratz (2, 3) , Dirk Tasche (4)

1 CREAR - Center of Research in Econo-finance and Actuarial sciences on Risk / Centre de Recherche Econo-financière et Actuarielle sur le Risque
2 ESSEC Business School
3 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
4 Prudential Regulation Authority

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 straight-forward 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. In particular, there is no sufficient evidence to justify an all-inclusive replacement of ES by Expectiles in applications, especially as we provide an alternative way for backtesting of ES.

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

Domaines: Gestion des risques [q-fin.RM]

Suzanne Emmer, Marie Kratz, Dirk Tasche. What Is the Best Risk Measure in Practice? A Comparison of Standard Measures. 2013. ⟨hal-00921283⟩