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Nonlinear shrinkage of the covariance matrix for portfolio Selection: Markowitz Meets Goldilocks


Ledoit, Olivier; Wolf, Michael (2017). Nonlinear shrinkage of the covariance matrix for portfolio Selection: Markowitz Meets Goldilocks. Review of Financial Studies, 30(12):4349-4388.

Abstract

Markowitz (1952) portfolio selection requires an estimator of the covariance matrix of returns. To address this problem, we promote a nonlinear shrinkage estimator that is more flexible than previous linear shrinkage estimators and has just the right number of free parameters (i.e., the Goldilocks principle). This number is the same as the number of assets. Our nonlinear shrinkage estimator is asymptotically optimal for portfolio selection when the number of assets is of the same magnitude as the sample size. In backtests with historical stock return data, it performs better than previous proposals and, in particular, it dominates linear shrinkage.

Abstract

Markowitz (1952) portfolio selection requires an estimator of the covariance matrix of returns. To address this problem, we promote a nonlinear shrinkage estimator that is more flexible than previous linear shrinkage estimators and has just the right number of free parameters (i.e., the Goldilocks principle). This number is the same as the number of assets. Our nonlinear shrinkage estimator is asymptotically optimal for portfolio selection when the number of assets is of the same magnitude as the sample size. In backtests with historical stock return data, it performs better than previous proposals and, in particular, it dominates linear shrinkage.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Economics
Dewey Decimal Classification:330 Economics
Uncontrolled Keywords:Large-dimensional asymptotics, Markowitz portfolio selection, nonlinear shrinkage.
Language:English
Date:2017
Deposited On:09 Feb 2018 09:27
Last Modified:20 Sep 2018 04:28
Publisher:Oxford University Press
ISSN:0893-9454
OA Status:Closed
Publisher DOI:https://doi.org/10.1093/rfs/hhx052
Related URLs:https://academic.oup.com/rfs/article-abstract/30/12/4349/3863121?redirectedFrom=fulltext
https://www.zora.uzh.ch/id/eprint/90273/

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Embargo till: 2019-12-01