Robust Portfolio Optimization with Multivariate Copulas: A Worst-Case CVaR approach

Abstract

Using data from the S&P 500 stocks from 1990 to 2015, we address the uncertainty of distribution of assets’ returns in Conditional Value-at-Risk (CVaR) minimization model by applying multidimensional mixed Archimedean copula function and obtaining its robust counterpart. We implement a dynamic investing viable strategy where the portfolios are optimized using three different length of rolling calibration windows. The out-of-sample performance is evaluated and compared against two benchmarks: a multidimensional Gaussian copula model and a constant mix portfolio. Our empirical analysis shows that the Mixed Copula-CVaR approach generates portfolios with better downside risk statistics for any rebalancing period and it is more profitable than the Gaussian Copula-CVaR and the 1/N portfolios for daily and weekly rebalancing. To cope with the dimensionality problem we select a set of assets that are the most diversified, in some sense, to the S&P 500 index in the constituent set. The accuracy of the VaR forecasts is determined by how well they minimize a capital requirement loss function. In order to mitigate data-snooping problems, we apply a test for superior predictive ability to determine which model significantly minimizes this expected loss function. We find that the minimum average loss of the mixed Copula-CVaR approach is smaller than the average performance of the Gaussian Copula-CVaR.