Liquidity-Adjusted Expected Shortfall Tests

Abstract

Market risk regulation by the Basel Committee on Banking Supervision of 2019 requires banks to report Expected Shortfall adjusted for liquidity horizons. This object differs from standard Expected Shortfall, so existing VaR and ES backtests do not directly evaluate the forecasts used in regulations. We develop an econometric framework for defining and backtesting liquidity-adjusted Value-at-Risk and Expected Shortfall. The framework formalises the regulatory risk measures, derives moment restrictions for joint VaR/ES correct specification, and equal predictive ability tests, and estimates the conditioning moments locally using kernel methods. We illustrate forecast construction using multivariate GARCH and filtered historical simulation. Simulations show that the liquidity-adjusted tests have size comparable to standard backtests and are consistent against misspecification. In an application to daily returns on 23 large-cap stocks from 2000 to 2023, liquidity-adjusted forecasts outperform conventional benchmarks. Joint paper with Sander Barendse (University of Amsterdam).