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