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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. Working paper series / Department of Economics 137, 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.

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.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Economics
Working Paper Series > Department of Economics
Dewey Decimal Classification:330 Economics
JEL Classification:C13, C58, G11
Uncontrolled Keywords:Large-dimensional asymptotics, Markowitz portfolio selection, nonlinear shrinkage
Language:English
Date:February 2017
Deposited On:22 Jan 2014 15:53
Last Modified:08 Dec 2017 02:55
Series Name:Working paper series / Department of Economics
Number of Pages:59
ISSN:1664-7041
Additional Information:Revised version
Official URL:http://www.econ.uzh.ch/static/wp/econwp137.pdf
Related URLs:http://www.econ.uzh.ch/static/workingpapers.php

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