Comparing univariate and multivariate models to forecast portfolio Value-at-Risk

This article compares multivariate and univariate Generalized Autoregressive Conditional Heteroskedasticity (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 ou tperform their univariate counterparts on an out-of-sample basis. In particular, among the models considered in this article, the dynamic conditional correlation model with Student's t errors seems to be the most appropriate specification when implemented to estimate the VaR of the real portfolios analyzedA. A. P. S. acknowledges financial support from research Projects CNPq Universal 481719/2011-3 and UFSC-Funpesquisa 2010/2011 from the Brazilian Government. F. J. N. is supported by the Spanish Government through Project MTM2010-16519. E. R. is supported by the Spanish Government ECO2009-0810