Portfolio analytics via dynamic graph learning: Modelling and testing

The literature on dynamic graphical models has mainly focused on Gaussian dependence structures. This paper extends those models to non-Gaussian settings by introducing a framework based on the skew group-t family of distributions. This family includes the Student-t, skew-t, and grouped skew-t copula models as special cases.

We develop an efficient estimation approach that combines the Alternating Direction Method of Multipliers (ADMM) with the Expectation–Maximization (EM) algorithm. Two variants are proposed: an outer-EM scheme, which embeds ADMM within the M-step, and an inner-EM scheme, which places the EM updates inside the ADMM optimization iteration.

The proposed methodology is showcased for two problems in financial engineering: portfolio optimization and change-point detection. The first case study focuses on dynamic portfolio construction, where sparse graphical models are learned over time from multivariate asset returns. These graphs are then used to find portfolio weights. The example illustrates how the approach can incorporate Environmental, Social, and Governance (ESG) considerations into portfolio decisions. We show that the heavy-tailed extensions improve portfolio metrics relative to covariance-based methods, according to standard measures such as the Sharpe ratio, Omega ratio, and maximum drawdown.

The second case study extends the approach to the allocation problem in mixed funded–unfunded pension systems. Here, the dynamic graphs capture time-varying correlations between assets and inform how the relative weight between funded and unfunded components evolves across market regimes.