Portfolio optimization via strategy-specific eigenvector shrinkage

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