The power of (non-)linear shrinking: a review and guide to covariance matrix estimation

Olivier Ledoit and Michael Wolf

No 323, ECON - Working Papers from Department of Economics - University of Zurich

Abstract: Many econometric and data-science applications require a reliable estimate of the covariance matrix, such as Markowitz portfolio selection. When the number of variables is of the same magnitude as the number of observations, this constitutes a difficult estimation problem; the sample covariance matrix certainly will not do. In this paper, we review our work in this area, going back 15+ years. We have promoted various shrinkage estimators, which can be classified into linear and nonlinear. Linear shrinkage is simpler to understand, to derive, and to implement. But nonlinear shrinkage can deliver another level of performance improvement, especially if overlaid with stylized facts such as time-varying co-volatility or factor models.

Keywords: Dynamic conditional correlations; factor models; large-dimensional asymptotics; Markowitz portfolio selection; rotation equivariance (search for similar items in EconPapers)
JEL-codes: C13 C58 G11 (search for similar items in EconPapers)
Date: 2019-05, Revised 2020-02
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:zur:econwp:323

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