VaR in High Dimensional Systems – a Conditional Correlation Approach

In empirical finance multivariate volatility models are widely used to capture both volatility clustering and contemporaneous correlation of asset return vectors. In higher dimensional systems, parametric specifications often become intractable for empirical analysis owing to large parameter spaces. On the contrary, feasible specifications impose strong restrictions that may not be met by financial data as, for instance, constant conditional correlation (CCC). Recently, dynamic conditional correlation (DCC) models have been introduced as a means to solve the trade off between model feasibility and flexibility. Here we employ alternatively the CCC and the DCC modeling framework to evaluate the Value-at-Risk associated with portfolios comprising major U.S. stocks. In addition, we compare their performance with corresponding results obtained from modeling portfolio returns directly via univariate volatility models.