Forecasting and Evaluating Portfolio Value-at-Risk

This paper compares RiskMetrics and several multivariate GARCH models that are used to forecast Value-at-Risk. We consider a data set that includes the benchmarks that SAMCo uses, the data consists of both fixed income and equity indices. We evaluate the forecasting power of the Value-at-Risk of these models by using the backtesting test and the Comparative Predictive Ability test (CPA). Also the economic significance of time-varying, predictable volatility is examined by using both the minimum-variance and the mean-variance asset allocation rules. We find that incorporating the asymmetry in the correlation between assets in the models to forecast Value-at-Risk bears fruit, as they have a better performance for the statistical tests. In general, assigning a Student-t distribution to the error terms leads to an improvement of the model according to the CPA-test. Finally, we find that it is unlikely that the gains to volatility-timing are due to chance.