Two Sides of Schur Damping: High-Dimensional Pseudo-Likelihoods and Portfolio Allocation

Battle Count: 73

Directly relevant to portfolio allocation: the paper unifies hierarchical risk parity (gamma=0) and minimum-variance (gamma=1) under a single Schur damping parameter, provides a closed-form optimal gamma, and demonstrates that fitted shrinkage (borrowed from spatial statistics) outperforms the closed-form in out-of-sample log-likelihood. The O(pm²) streaming implementation is practical for large portfolios. However, the paper is a short note rather than a comprehensive trading strategy paper, and the experiment is limited.

The core operation—a damped Schur complement of a few neighbour blocks—is computable in a single O(pm²) streaming pass without forming the dense covariance matrix. The closed-form gamma-star is trivial to compute. The Vecchia neighbour ordering requires a correlation-based or maxmin ordering step. The 'precise' library already implements these estimators. Main complexity lies in choosing the neighbour set size m and the ordering strategy for financial data (no natural Euclidean distance).

The paper references the open-source 'precise' library (github.com/microprediction/precise) which implements the damped Schur complement estimators in O(pm²) streaming passes. The experiment specifies p=60 assets, m=15 neighbours, daily returns, and held-out tuning. However, the exact dataset of daily asset returns is not explicitly named, and the paper is primarily a short theoretical note rather than a full empirical study.