Nonlinear shrinkage of the covariance matrix for portfolio selection: Markowitz meets Goldilocks

Olivier Ledoit and Michael Wolf

No 137, ECON - Working Papers from Department of Economics - University of Zurich

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 (that is, 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.

Keywords: Large-dimensional asymptotics; Markowitz portfolio selection; nonlinear shrinkage (search for similar items in EconPapers)
JEL-codes: C13 C58 G11 (search for similar items in EconPapers)
Date: 2014-01, Revised 2017-02
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:zur:econwp:137

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