Dynamic Factor Copulas for Minimum-CVaR Portfolio Optimization

Copula models have become popular for minimum conditional value-at-risk (CVaR) portfolio optimization, especially due to their ability to deal with nonlinear dependencies. Nevertheless, as the number of assets in a portfolio increases, the estimation of copulas, particularly dynamic ones, becomes computationally burdensome. In this work, our novel contribution is to adapt and implement a dynamic factor copula model for the asset returns dependencies and find an optimal, potentially high dimensional, portfolio via minimizing its CVaR. The resulting model is capable of addressing the “curse of dimensionality” for the dependencies, while maintaining enough complexity and flexibility. The factor copula dynamics are described by a generalized autoregressive scores (GAS) model for the factor loadings. Using data consisting of B3 Brazilian stocks from January 2013 to December 2020, we find the optimal portfolio and evaluate its out of sample economic performance. Empirical results suggest that our min-CVaR-factor-copula strategy has either equal or better risk/return metrics when compared to a traditional Gaussian copula, while being considerably superior than both Markowitz mean-variance and equal weights portfolios as well as the IBRX50 index.