Comparing univariate and multivariate models to forecast portfolio value-at-risk

This article addresses the problem of forecasting portfolio value-at-risk (VaR) with multivariate GARCH models vis-à-vis univariate models. Existing literature has tried to answer this question by analyzing only small portfolios and using a testing framework not appropriate for ranking VaR models. In this work we provide a more comprehensive look at the problem of portfolio VaR forecasting by using more appropriate statistical tests of comparative predictive ability. Moreover, we compare univariate vs. multivariate VaR models in the context of diversified portfolios containing a large number of assets and also provide evidence based on Monte Carlo experiments. We conclude that, if the sample size is moderately large, multivariate models outperform univariate counterparts on an out-of-sample basis.