Monte Carlo Value-At-Risk and Expected Shortfall of Efficient-Frontier Investment Portfolios: Testing Gaussian Versus Vine Copulas and Normal Versus Empirical Marginals

We examined historical return distributions of 60 global investment funds, generated mean–variance efficient frontier “funds of funds”, and compared the industry-standard risk metrics, notably Value-at-Risk (VaR) and Expected Shortfall (ES), obtained from parametric Monte Carlo simulations under 3 sets of assumptions, namely multivariate normality, Gaussian copula with empirical marginals, and vine copula with empirical marginals, to see which came closest to results from historical Monte Carlo simulations, herewith taken as ground truth. We found that multivariate normality runs got closest to historical simulation in terms of mean and standard deviation (quite a surprise) but fared worst in terms of VaR and ES (to be expected). In addition, vine copula runs outperformed Gaussian copula runs, albeit the performance differentials were less dramatic when compared with the gain from ditching Gaussian marginals in favour of empirical marginals.