Portfolio Optimization with CVaR under VG Process

Formal portfolio optimization methodologies describe the dynamics of financial instruments price with Gaussian Copula (GC). Regardless of the skewness and kurtosis of assets return rate, optimization with GC underestimates the optimal CVaR of portfolio. In the present paper, we develop an approach to portfolio optimization by introducing Lévy processes. It focuses on describing the dynamics of assets’ log price with Variance Gamma copula (VGC) rather than GC. Doing a case study on three Indexes of Iran Stock Market, the best hedge positions of Total Index, Market Index and Industry Index with the performance function CVaR under VG model were calculated. The results indicate that (a) VG copula can efficiently overcome the shortcomings of Gaussian copula which underestimates the CVaR of portfolio; (b) optimal portfolio, VaR and CVaR keep stable each time one parameter of sample’s skewness or kurtosis was changed, but the optimal portfolio change significantly when the sample’s mean increases or decreases; (c) different copula lead to different optimal CVaR; and (d) fat-tailedness and kurtosis are extremely important in portfolio optimization framework.