Expected Shortfall Backtesting

This paper is on the change in risk measure from Value at Risk (VaR) to Expected Shortfall (ES) as stipulated by the Basel Committee of Banking Supervision, and in particular, the backtesting methods that have been developed for this new risk measure ES. The contribution of this research to the literature is an analysis of the performance of the most relevant contemporary backtests in several different modelling scenarios and a more simple scenario where their performances are compared to the currently used VaR setting. We analyse the (size-adjusted) power of six different methods in a variety of statistical modelling scenarios, and comment on computational time and implementational complexity of these methods. This is done for the consideration of widespread use throughout the financial system, and in particular for regulatory purposes. We observe that both the methods by Graham and Pál (2014) (GP) and by Moldenhauer and Pitera (2018) (MP) outperform the other methods in terms of size-adjusted power throughout the analyses. In terms of computational time, the GP method beats out the calibration time necessary for the MP method, though the MP method performs (daily) evaluations much faster, once the initial calibration is done. Furthermore, the MP method is slightly more consistent than the GP method, and it is much more easily implemented due to its relatively low mathematical complexity. Therefore, we recommend its use as the primary methodology for backtesting ES in matters related to risk management in the financial sector. Lastly, the MP method seems to be slightly more sensitive to misspecifications than the currently used VaR backtest is in the VaR framework. This suggests that, if the MP method is to be applied, the quantity and size of fees for inadequate risk management will increase for financial services organisations, if their current models remain in use.