Computing portfolio risk using Gaussian mixtures and Independent Component Analysis

Addressing the problem of non-normal portfolio returns, we introduce a new approach for estimating the distribution of portfolio returns considering higher order mutual information. It allows us to extend the standard variance-covariance framework and efficiently re-compute measures of market risk such as the standard Value-at-Risk or any other probability density based measure. The approach combines two clean and transparent methodologies-Independent Component Analysis and finite Gaussian mixture distributions-and is formulated algorithmically in three steps. Keywords. independent Component Analysis, Gaussian mixture model, convolution, non-normal returns, probability density prediction, EM algorithm, risk estimation.