Large Portfolio Risk Management and Optimal Portfolio Allocation with Dynamic Copulas

Previous research focuses on the importance of modeling the multivariate distribution for optimal portfolio allocation and active risk management. However, available dynamic models are not easily applied for high-dimensional problems due to the curse of dimensionality. In this paper, we extend the framework of the Dynamic Conditional Correlation/Equicorrelation and an extreme value approach into a series of Dynamic Conditional Elliptical Copulas. We investigate risk measures like Value at Risk (VaR) and Expected Shortfall (ES) for passive portfolios and dynamic optimal portfolios through Mean-Variance and ES criteria for a sample of US stocks over a period of 10 years. Our results suggest that (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) TheDCC/DECO Gaussian copula and t-copula work very well for both VaR and ES. (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 against the tail risk. (6) Models driven by multivariate t innovations with exogenously given degrees of freedom provide a .exible and applicable alternative for optimal portfolio risk management.