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Title: Regression based expected shortfall backtesting Authors:  Timo Dimitriadis - University of Konstanz (Germany) [presenting]
Sebastian Bayer - University of Konstanz (Germany)
Abstract: A new backtest for the risk measure Expected Shortfall is introduced. This backtest is based on a Mincer-Zarnowitz regression using a joint linear regression technique for the quantile and the Expected Shortfall. Developing accurate backtests for the Expected Shortfall is particularly relevant in light of the recent swap from Value at Risk to Expected Shortfall in the Basel regulatory framework for banks. We compare the empirical performance of our new backtest to existing approaches in terms of its size and power by simulating returns stemming from standard financial time series models such as the GARCH and the autoregressive stochastic volatility model. Our new backtest exhibits better size and (size-adjusted) power properties compared to existing backtesting procedures in the literature. This shows that our backtest is superior in determining whether banks issue correct risk forecasts for their financial products. We apply this backtesting procedure to Expected Shortfall forecasts for the historical S\&P500 index return series. Furthermore, we provide an R package for this backtest which is easily applicable for practitioners.