Portfolio Management by Normal Mean-Variance Mixture Distributions

Abstract

According to the empirical evidence, financial returns show leptokurtosis, skewness and heavy-tailness. Regarding this behavior, we apply normal mixture mean variance distributions for portfolio management and allocating best weights for portfolio optimization and efficient frontiers. These distributions are appropriate for portfolio optimization and have a natural multivariate that consists of NIG, VG, NTS, GH and skewed t. Conditional Value-at-Risk (CVaR) is utilized as a measure of risk to evaluate the level of risk and simulated by Monte Carlo method. If we do not have closed density function of distribution, for example NTS distribution, we can use characteristic function with Fourier transformation to compute CVaR and portfolio modeling. Finally, real data in Iran stock market are given to illustrate the effectiveness our model by skewed t distribution.