The Power of (Non-)Linear Shrinking: A Review and Guide to Covariance Matrix Estimation

Design-Free Estimation of Variance Matrices

Olivier Ledoit and Michael Wolf

Journal of Financial Econometrics, 2022, vol. 20, issue 1, 187-218

Abstract: Many econometric and data-science applications require a reliable estimate of the covariance matrix, such as Markowitz’s 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 article, 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’s portfolio selection; rotation equivariance (search for similar items in EconPapers)
JEL-codes: C13 C58 G11 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (13)

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