Portfolio optimisation via strategy-specific eigenvector shrinkage

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...

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Bibliographic Details
Published inFinance and stochastics Vol. 29; no. 3; pp. 665 - 706
Main Authors Goldberg, Lisa R., Gurdogan, Hubeyb, Kercheval, Alec
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2025
Springer Nature B.V
Subjects
Arbitrage
Asset allocation
Constraints
Covariance matrix
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Eigenvalues
Eigenvectors
Estimates
Exchange traded funds
Finance
Insurance
Management
Mathematics
Mathematics and Statistics
Matrices
Operators (mathematics)
Optimization
Portfolios
Probability Theory and Stochastic Processes
Quantitative Finance
Sample variance
Statistics for Business
Truth
Eigenvector estimation
High dimension
91G10
James–Stein
62P05
C38
62H12
Portfolio optimisation
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0949-2984
1432-1122
DOI:10.1007/s00780-025-00566-4