Sparse Graphical Modelling for Minimum Variance Portfolios

Graphical models have demonstrated exceptional performance in uncovering the conditional dependence structure among a given set of variables. This paper introduces two novel graphical modeling techniques: Gslope and Tslope, which use the Sorted L1-Penalized Estimator (Slope) to directly estimate the inverse of the covariance matrix. We develop ad hoc algorithms to efficiently solve the underlying optimization problems: the Alternating Direction Method of Multipliers for Gslope, and the Expectation-Maximization (EM) algorithm for Tslope. Our methods are suitable for both Gaussian and non-Gaussian distributed data and take into account the empirically observed distributional characteristics of asset returns. Through extensive simulation analysis and real-world applications, we demonstrate the superiority of our new methods over state-of-the-art covariance matrix estimation techniques, particularly regarding clustering and stability characteristics