Sparse Graphical Modelling for Minimum Variance Portfolios

Graphical models have shown remarkable performance in uncovering the conditional dependence structure across a set of given variables. In this paper, we introduce two new graphical modelling approaches - called Gslope and Tslope - to the portfolio selection literature for directly estimating the inverse of the covariance matrix, using the so called Sorted L1 -Penalized Estimator (SLOPE). Spanning Gaussian and non-Gaussian distributed data, our new methods directly acknowledge the empirically observed distributional characteristics of asset returns. Extensive simulation analysis and real-world applications highlight the superiority of our new methods, especially with regard to clustering and stability characteristics, compared to state-of-the-art covariance matrix estimation techniques