Adaptive Backtest for Expected Shortfall

Oct 18, 2017

Expected Shortfall (ES) replaced Value at Risk (VaR) under the Basel Committee’s Minimum Capital Requirements for Market Risk in 2016. However, whether ES can be backtested is still an open and critical question. We have recently shown that ES can be only approximately backtested, because any ES backtest is sensitive to VaR predictions. This paper proposes a new ES backtest that has the minimum possible sensitivity to VaR predictions, which makes it an appropriate validation tool for ES-based models, both for financial risk management and regulation. Also, the backtest measures the size of prediction discrepancy as well as model validation probability, allowing the design of self-adaptive risk models. The backtest compares the predicted ES with an emerging notion of “realized ES,” which per se has new potential applications for ex-post risk analysis.