Title: Loss function derived expected shortfall backtests under estimation error
Authors: Sander Barendse - Erasmus University Rotterdam (Netherlands) [presenting]
Abstract: The purpose is to investigate estimation error effects on expected shortfall (ES) backtests that are based on first order conditions of a recently introduced joint consistent loss function for Value-at-Risk (VaR) and ES. We show that the asymptotic covariance of the test statistics contain additional terms when estimation error is present, and provide explicit expressions for these terms, which are functions of the model specification. We develop a bootstrap procedure to correct for estimation error. In Monte-Carlo experiments we observe that the robust backtests based on bootstrap critical values have correct size properties, whereas the uncorrected backtests overreject considerably. Finally, we compare the ES backtests studied with competing backtests for several data generating processes. We find that no backtest consistently outranks other backtests in terms of power.