Comparing Univariate and Multivariate Models to Forecast Portfolio Value-at-Risk

This paper compares multivariate and univariate GARCH models to forecast portfolio value-at-risk (VaR). We provide a comprehensive look at the problem by considering realistic models and diversified portfolios containing a large number of assets, using both simulated and real data. Moreover, we rank the models by implementing statistical tests of comparative predictive ability. We conclude that multivariate models outperform their univariate counterparts on an out-of-sample basis. In particular, among the models considered in this paper, the dynamic conditional correlation model with Student-t errors seems to be the most appropriate specification when implemented to estimate the VaR of the real portfolios analyzed