Large Portfolio Risk Management with Dynamic Copulas

Abstract

Modeling the dynamic high-dimensional multivariate distribution is very useful for active risk management and optimal portfolio allocation; however, available dynamic models are not easily applied for high-dimensional problems due to the curse of dimensionality. In the light of the recent development of multivariate GARCH techniques for a large number of underlying securities, I extend the framework of the Dynamic Conditional Correlation/Equicorrelation (DCC/DECO) (Engle, 2002 and Engle and Kelly, 2008) and an extreme value approach (McNeil and Frey, 2000) into a series of Dynamic Conditional Elliptical Copulas. By constructing portfolios of 89 stocks from CDX-listed …rms between 1995 and 2005, I examine Value at Risk (VaR) and Expected Shortfall (ES) by Monte Carlo simulation for passive portfolios and dynamic optimal portfolios through Mean-Variance and ES criteria. I …nd: (1) Modeling the marginal distribution is important for the dynamic high-dimensional multivariate models. (2) Neglecting the dynamic dependence in the copula causes over-aggressive risk management. (3) The DCC/DECO Gaussian copula and t-copula work very well for both VaR and ES. The DCC copula is necessary for value-weighted portfolios. For equally-weighted portfolios, the DECO copula performs about as well as the DCC copula. (4) Grouped t-copula and t-copula with dynamic degrees of freedom further match the fat tail. (5) Correctly modeling dependence structure makes an improvement in portfolio optimization. The optimal portfolio by ES does a good job against the tail risk in both DECO and DCC copulas. (6) Since portfolio optimization induces statistical error maximization, the assumption of multivariate t innovations with exogenously given degrees of freedom provides a ‡exible and applicable method for optimal portfolio risk management.