Ranking of VaR and ES Models: Performance in Developed and Emerging Markets

There is an inherent problem with comparing and ranking competing Value at Risk (VaR) and Expected shortfall (ES) models since we are measuring only a single realization of the underlying data generation process. The question is whether there is any significant statistical difference in the performance of different models. It all comes down to whether something that we subjectively perceive as different is actually statistically different. We introduce a new methodology for ranking the performance of VaR and ES models based on a nonparametric test. The relative performance of models is analysed using returns for sixteen stock market indices (eight each from developed and emerging markets) prior to and during the global financial crisis. Results show that for a large number of models there is no statistically significant difference. The top performers are conditional extreme value GARCH model and models based on volatility updating. ES results are similar to VaR results with the models being even more closely matched. The same models that were the top performers in VaR comparison also perform significantly better in ES estimation.