Variable Clustering via Distributionally Robust Nodewise Regression
This provides an incremental improvement for financial analysts needing robust variable clustering in portfolio optimization.
The authors tackled variable clustering by developing a distributionally robust nodewise regression method with a convex relaxation and ADMM algorithm, achieving interpretable clusters for stock returns that outperformed other methods in out-of-sample portfolio selection.
We study a multi-factor block model for variable clustering and connect it to the regularized subspace clustering by formulating a distributionally robust version of the nodewise regression. To solve the latter problem, we derive a convex relaxation, provide guidance on selecting the size of the robust region, and hence the regularization weighting parameter, based on the data, and propose an ADMM algorithm for implementation. We validate our method in an extensive simulation study. Finally, we propose and apply a variant of our method to stock return data, obtain interpretable clusters that facilitate portfolio selection and compare its out-of-sample performance with other clustering methods in an empirical study.