Backtesting Expected Shortfall: Accounting for Tail Risk

Abstract

The Basel Committee on Banking Supervision (BIS) has recently sanctioned Expected Shortfall (ES) as the market risk measure to be used for banking regulatory purposes, replacing the well-known Value-at-Risk (V aR). This change is motivated by the appealing theoretical properties of ES as a measure of risk and the poor ones of V aR. In particular, V aR fails to control for "tail risk". In this transition, the major challenge faced by …nancial institutions is the unavailability of simple tools for evaluation of ES forecasts (i.e. backtesting ES). The main purpose of this article is to propose such tools. Speci…cally, we propose a conditional backtest for ES based on cumulative violations, which is the natural analogue of the commonly used conditional backtest for V aR. We establish the asymptotic properties of the test, and investigate its …nite sample performance through some Monte Carlo simulations. An empirical application to three major stock indexes shows that V aR is generally unresponsive to extreme events such as those experienced during the recent …nancial crisis, while ES provides a more accurate description of the risk involved.

Time‐varying dynamics of expected shortfall in commodity futures markets

“…Nevertheless, various rudimentary backtests have been proposed over the years and applied in the commodity sector (see, e.g., Del Brio et al, 2020; Youssef et al, 2015). In a recent article, Du and Escanciano (2017) make an important contribution to ending the backtesting debate for ES by developing unconditional and conditional coverage tests (with suitable size and power properties), which are easy to implement and to comprehend because they use ideas similar to the established VaR backtests. In many fields, these new tests are receiving significant attention because, after years of theoretical research, they finally allow a judgment of available ES estimators (see Hoga, 2019; Le, 2020; Novales & Garcia‐Jorcano, 2019).…”

“…To investigate whether our ES estimators can provide accurate forecasts of future ES, we rely on the unconditional and conditional backtests of Du and Escanciano (2017). We do this in a rolling‐window setting because the quality of ES predictions may vary over time.…”

Automatic Portmanteau Tests with Applications to Market Risk Management

“…We also provide the rtau command to estimate τ j for more general cases, including MDS as in Escanciano and Lobato (2009), as well as backtests for VAR and ES with estimation effects as in Escanciano and Olmo (2010) and Du and Escanciano (2017), respectively.…”

“…U [0, 1] variables (see Rosenblatt [1952]). Cumulative violations have been recently introduced in Du and Escanciano (2017). The variables {u t } ∞ t=1 necessary to construct {H t (α)} ∞ t=1 are generally unknown because the distribution of the data G is unknown.…”

“…To illustrate the use of the two commands, we consider the DAX Index return data from January 1, 1997, to June 30, 2009 as in Du and Escanciano (2017). The in-sample period is from January 1, 1997, to June 30, 2007.…”