Size Matters: Optimal Calibration of Shrinkage Estimators for Portfolio Selection

39 Pages Posted: 21 Jul 2011 Last revised: 22 Apr 2013

See all articles by Victor DeMiguel

Victor DeMiguel

London Business School

Alberto Martin-Utrera

Iowa State University

Francisco J. Nogales

Universidad Carlos III de Madrid - Department of Statistics; Institute of Financial Big Data UC3M-BS

Date Written: July 21, 2011

Abstract

We carry out a comprehensive investigation of shrinkage estimators for asset allocation, and we find that size matters -- the shrinkage intensity plays a significant role in the performance of the resulting estimated optimal portfolios. We study both portfolios computed from shrinkage estimators of the moments of asset returns (shrinkage moments), as well as shrinkage portfolios obtained by shrinking the portfolio weights directly. We make several contributions in this field. First, we propose two novel calibration criteria for the vector of means and the inverse covariance matrix. Second, for the covariance matrix we propose a novel calibration criterion that takes the condition number optimally into account. Third, for shrinkage portfolios we study two novel calibration criteria. Fourth, we propose a simple multivariate smoothed bootstrap approach to construct the optimal shrinkage intensity. Finally, we carry out an extensive out-of-sample analysis with simulated and empirical datasets, and we characterize the performance of the different shrinkage estimators for portfolio selection.

Keywords: Portfolio choice, estimation error, shrinkage intensity, bootstrap

JEL Classification: G11, C14

Suggested Citation

DeMiguel, Victor and Martin-Utrera, Alberto and Nogales, Francisco J., Size Matters: Optimal Calibration of Shrinkage Estimators for Portfolio Selection (July 21, 2011). Available at SSRN: https://ssrn.com/abstract=1891847 or http://dx.doi.org/10.2139/ssrn.1891847

Victor DeMiguel

London Business School ( email )

Sussex Place
Regent's Park
London, London NW1 4SA
United Kingdom

Alberto Martin-Utrera (Contact Author)

Iowa State University ( email )

613 Wallace Road
Ames, IA 50011-2063
United States

Francisco J. Nogales

Universidad Carlos III de Madrid - Department of Statistics ( email )

Avda. de la Universidad, 30
Leganes, Madrid 28911
Spain
+34 916248773 (Phone)

HOME PAGE: http://www.est.uc3m.es/Nogales

Institute of Financial Big Data UC3M-BS ( email )

CL. de Madrid 126
Madrid, Madrid 28903
Spain

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