Ranking the predictive performances of value-at-risk estimation methods

We introduce a ranking model and a complementary predictive ability test statistic to investigate the forecasting performances of different Value at Risk (VaR) methods, without specifying a fixed benchmark method. The period including the recent credit crisis offers a unique laboratory for the analysis of the relative successes of different VaR methods when used in both emerging and developed markets. The proposed ranking model aims to form a unified framework which penalizes not only the magnitudes of errors between realized and predicted losses, but also the autocorrelation between the errors. The model also penalizes excessive capital allocations. In this respect, the ranking model seeks for VaR methods which can capture the delicate balance between the minimum governmental regulations for financial sustainability, and cost-efficient risk management for economic vitality. As a complimentary statistical tool for the ranking model, we introduce a predictive ability test which does not require the selection of a benchmark method. This statistic, which compares all methods simultaneously, is an alternative to existing predictive ability tests, which compare forecasting methods two at a time. We test and rank twelve different popular VaR methods on the equity indices of eleven emerging and seven developed markets. According to the ranking model and the predictive ability test, our empirical findings suggest that asymmetric methods, such as CAViaR Asymmetric and EGARCH, generate the best performing VaR forecasts. This indicates that the performance of VaR methods does not depend entirely on whether they are parametric, non-parametric, semi-parametric or hybrid; but rather on whether they can model the asymmetry of the underlying data effectively or not.