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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| Published in | Finance and stochastics Vol. 29; no. 3; pp. 665 - 706 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.07.2025
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0949-2984 1432-1122 |
| DOI | 10.1007/s00780-025-00566-4 |
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| 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. |
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| AbstractList | 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. |
| Author | Gurdogan, Hubeyb Kercheval, Alec Goldberg, Lisa R. |
| Author_xml | – sequence: 1 givenname: Lisa R. surname: Goldberg fullname: Goldberg, Lisa R. email: lrg@berkeley.edu organization: Department of Economics and Consortium for Data Analytics in Risk, UC Berkeley, Aperio Group LLC, a wholly-owned indirect subsidiary of BlackRock, Inc – sequence: 2 givenname: Hubeyb surname: Gurdogan fullname: Gurdogan, Hubeyb organization: Department of Mathematics, UCLA – sequence: 3 givenname: Alec surname: Kercheval fullname: Kercheval, Alec organization: Department of Mathematics, Florida State University |
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| Keywords | Eigenvector estimation High dimension 91G10 James–Stein 62P05 C38 62H12 Portfolio optimisation |
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| SubjectTerms | 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 |
| Title | Portfolio optimisation via strategy-specific eigenvector shrinkage |
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