Improving Performance By Constraining Portfolio Norms: A Generalized Approach to Portfolio Optimization

Abstract:     
In this paper, we provide a general framework for determining the portfolio that has superior out-of-sample performance even in the presence of estimation error. This general framework relies on solving the traditional minimum-variance problem (based on the sample covariance matrix) but subject to the additional constraint that the norm of the portfolio weight vector must be smaller than a given threshold. We show that our general framework nests as special cases the shrinkage approaches of Jagannathan and Ma (2003) and Ledoit and Wolf (2004b), and the 1/N policy studied in DeMiguel, Garlappi, and Uppal (2007), and that all these policies can be interpreted as those of a Bayesian investor who has a certain prior belief on portfolio weights. We also use our general framework to propose several new portfolio strategies. Finally, we compare empirically (in terms of portfolio variance, Sharpe ratio, and turnover), the out-of-sample performance of the new polices we propose to ten strategies in the existing literature across ten datasets. We find that the new policies we propose can outperform the policies proposed in Jagannathan and Ma (2003) and Ledoit and Wolf (2004b), the 1/N policy evaluated in DeMiguel, Garlappi, and Uppal (2007), and also other strategies in the literature such as Brandt, Santa-Clara, and Valkanov (2005).

Keywords: Portfolio choice, asset allocation, estimation error, empirical Bayes, shrinkage, covariance matrix estimation

JEL Classification: G11

working papers series