Improving the Accuracy of Tail Risk Forecasts

Value at Risk (VaR) is the most widely used measure for quantifying portfolio tail risk. Backtesting of VaR forecasts is therefore an essential part of evaluating the accuracy of a tail risk model. The authors propose a backtesting methodology and then focus on improving the accuracy of tail risk forecasts within the framework of Monte Carlo simulation using a multifactor risk model. This is accomplished via modeling improvements in three areas. The first crucial improvement is to begin with more accurate estimates of factor volatilities and correlations, which serve as the essential starting point for tail risk forecasts. The second improvement is to use more realistic marginal distributions when performing Monte Carlo simulations, which includes using symmetric fat-tailed t-distributions and asymmetric (skewed) t-distributions as appropriate for the individual factors. The third technique the authors employ is to slightly inflate tail risk forecasts, which serves to reduce the frequency of VaR violations. The authors show that such VaR scaling is necessary to remove the excess violation frequency that occurs whenever one uses unbiased but noisy VaR estimates. Finally, the authors attribute the improved accuracy to the three improvements.