Testing the Gaussian and Student's t copulas in a risk management framework

This paper introduces a semiparametric framework for selecting either a Gaussian or a Student's t copula in a d-dimensional setting. We compare the two models using four different approaches: (i) four goodness-of-fit graphical plots, (ii) a bootstrapped correlation matrix generated in each scenario with the empirical correlation matrix used as a benchmark, (iii) Value-at-Risk (VaR) and Expected Shortfall (ES) as risk measures, and (iv) co-Value-at-Risk (CoVaR) and Marginal Expected Shortfall (MES) as co-risk measures. We illustrate this four-step procedure using a portfolio of daily returns of six international stock indices. The VaR results confirm that the t-based copula model is an attractive alternative to the Gaussian. The ES analysis is less conclusive, and indicates that risk managers should jointly use the risk measure as well as the copula model. The results highlight the importance of promoting stress testing rather than ES in the risk management industry, particularly in the aftermath of a financial crisis.