Powerful Backtests for Historical Simulation Expected Shortfall Models

Abstract

Since 2016, the Basel Committee on Banking Supervision has regulated banks to switch from a Value-at-Risk (VaR) to an Expected Shortfall (ES) approach to measuring the market risk and calculating the capital requirement. In the transition from VaR to ES, the major challenge faced by financial institutions is the lack of simple but powerful tools for evaluating ES forecasts (i.e., backtesting ES). This article first shows that the unconditional backtest is inconsistent in evaluating the most popular Historical Simulation (HS) and Filtered Historical Simulation (FHS) E S models, with power even less than the nominal level in large samples. To overcome this problem, we propose a new class of conditional backtests for E S that are powerful against a large class of alternatives. We establish the asymptotic properties of the tests, and investigate their finite sample performance through some Monte Carlo simulations. An empirical application to stock indices data highlights the merits of our method.