Backtesting Expected Shortfall via Multi-Quantile Regression

Ophélie Couperier (1) , Jérémy Leymarie (2)

1 CREST - Centre de Recherche en Economie et Statistique [Bruz]
2 LEO - Laboratoire d'Économie d'Orleans [UMR7322]

In this article, we propose a new approach to backtest Expected Shortfall (ES) exploiting the definition of ES as a function of Value-at-Risk (VaR). Our methodology jointly examines the validity of the VaR forecasts along the tail distribution of the risk model, and hence encompasses the Basel Committee recommendation of verifying quantiles at risk levels 97.5%, and 99%. We introduce four easy-to-use backtests in which we regress the ex-post losses on the VaR forecasts in a multi-quantile regression model, and test the resulting parameter estimates. Monte-Carlo simulations show that our tests are powerful to detect various model misspecifications. We apply our backtests on S&P500 returns over the period 2007-2012. Our tests clearly identify misleading ES forecasts in this period of financial turmoil. Empirical results also show that the detection abilities are higher when the evaluation procedure involves more than two quantiles, which should accordingly be taken into account in the current regulatory guidelines.

Mots clés: Banking regulation; Financial risk management; Forecast evaluation; Hypothesis testing; Tail risk

Domaines: Economies et finances

Ophélie Couperier, Jérémy Leymarie. Backtesting Expected Shortfall via Multi-Quantile Regression. 2019. ⟨halshs-01909375v3⟩