Size matters: optimal calibration of shrinkage estimators for portfolio selection Articles uri icon

publication date

  • August 2013

start page

  • 3018

end page

  • 3034


  • 8


  • 37

International Standard Serial Number (ISSN)

  • 0378-4266

Electronic International Standard Serial Number (EISSN)

  • 1872-6372


  • 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. (c) 2013 Elsevier B.V. All rights reserved.


  • portfolio choice; estimation error; shrinkage intensity; out-of-sample evaluation; bootstrap