Banking Regulation: Backtesting Expected Shortfall

Abstract

Under Basel III, Expected Shortfall (ES) will be the main risk measure since it is a coherent risk measure as opposed to Value-at-Risk (VaR) (BIS 2016). It was believed that ES could not be backtested since it is not elicitable. It is no longer an issue. Validation is vital for adequate risk management. In our thesis we introduce several methods that allow practitioners to backtest ES. Some of these tests prove to be more powerful than the standard VaR backtest. Z2 shows the highest power whereas the Nass test is robust in size and the Pearson test is simpler to implement. We calculate the critical values for all tests and manipulate the assumptions for the null hypothesis and the alternative hypothesis to compare their statistical power. Finally, we run simulations on real data to show that they prove to be as accurate as the VaR backtest with regards to model validation.