Multivariate Shrinkage for Optimal Portfolio Weights

Abstract

This paper proposes a multivariate shrinkage estimator for the optimal portfolio weights. The estimated classical Markowitz weights are shrunk to the deterministic target portfolio weights. Assuming log asset returns to be i.i.d. Gaussian, explicit solutions are derived for the optimal shrinkage factors. The properties of the estimated shrinkage weights are investigated both analytically and using Monte Carlo simulations. The empirical study compares the competing portfolio selection approaches. Both simulation and empirical studies show that the proposed shrinkage estimator is robust and provides significant gains to the investor compared to benchmark procedures.

Keywords:

• Portfolio selection
• shrinkage estimation
• multivariate shrinkage
• estimation risk

Acknowledgements

The authors appreciate the helpful comments of the editor, the associate editor, two anonymous referees, which resulted in significant improvements in the paper.