Portfolio optimisation via strategy-specific eigenvector shrinkage

Abstract

We estimate covariance matrices that are tailored to portfolio optimisation constraints. We rely on a generalised version of James–Stein for eigenvectors (JSE), a data-driven operator that reduces estimation error in the leading sample eigenvector by shrinking towards a target subspace determined by constraint gradients. Unchecked, this error gives rise to excess volatility for optimised portfolios. Our results include a formula for the asymptotic improvement of JSE over the leading sample eigenvector as an estimate of ground truth, and provide improved optimal portfolio estimates when variance is to be minimised subject to finitely many linear constraints.