Comparing Univariate and Multivariate Models to Forecast Portfolio Value

Value-at-Risk has become one of the most widely-used financial risk measurement techniques. In this paper, we compare multivariate and univariate Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models in terms of their respective performance in forecasting portfolio Value-at-Risk (VAR). First, we review a few common VaR models both in a univariate and a multivariate setting. Then, we use backtesting methods and CPA test on these models with both simulated and real data of diversified portfolios containing a large number of assets. Last, we rank the models with regards to their comparative forecasting ability. We conclude that on an out-of sample basis, multivariate models have better performance than their univariate counterparts. In particular, we find that, in most cases, the dynamic conditional correlation model with Student’s t errors outperform all the other models considered in this paper. For information about building access for persons with disabilities, please contact Matt Johnston at 773.7020541 or send an email to [email protected]. If you wish to subscribe to our email list, please visit the following web site: https://lists.uchicago.edu/web/arc/statseminars.