Size Matters: Optimal Calibration of Shrinkage Estimators for Portfolio Selection
London Business School
Universidad Carlos III de Madrid - Department of Statistics and Econometrics
Francisco J. Nogales
Universidad Carlos III de Madrid - Department of Statistics
July 21, 2011
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.
Number of Pages in PDF File: 39
Keywords: Portfolio choice, estimation error, shrinkage intensity, bootstrap
JEL Classification: G11, C14working papers series
Date posted: July 21, 2011 ; Last revised: April 22, 2013
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