Computing portfolio risk using Gaussian mixtures and independent component analysis

Addressing the problem of non-normal portfolio returns, we introduce a novel 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