Copula-GARCH versus dynamic conditional correlation: an empirical study on VaR and ES forecasting accuracy

Abstract

In this paper, we analyze the accuracy of the copula-GARCH and Dynamic Conditional Correlation (DCC) models for forecasting the value-at-risk (VaR) and expected shortfall (ES) of bivariate portfolios. We then try to answer two questions: First, does the correlation-based DCC model outperform the copula models? Second, how can the optimal model for forecasting portfolio risk be identified via in-sample analysis? We address these questions using an extensive empirical study of 1,500 bivariate portfolios containing data on stocks, commodities and foreign exchange futures. Furthermore, we propose to use linear discriminant analysis estimated from descriptive statistics on bivariate data samples as independent variables to identify a parametric model yielding optimal portfolio VaR and ES estimates. In particular, we try to answer the question whether the quality of a parametric model’s VaR and ES estimates is driven by common data characteristics. The results show that the proposed use of linear discriminant analysis is superior to both the Kullback-Leibler Information Criterion and several copula goodness-of-fit tests in terms of overall classification accuracy. Furthermore, the results show that the quality of the DCC model’s VaR and ES estimates is positively correlated with the portfolio marginals’ volatility, while the opposite is true for the elliptical copulas. For the Archimedean copulas in particular, the excess kurtosis of the marginals has a significant positive influence on quality of the VaR and ES estimates.