Abstract - A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms

We provide a general framework for finding portfolios that perform well out-of-sample in the presence of estimation error. This framework relies on solving the traditional minimum-variance problem but subject to the additional constraint that the norm of the portfolio-weight vector be smaller than a given threshold. We show that our framework nests as special cases the shrinkage approaches of Jagannathan and Ma (2003) and Ledoit and Wolf (2003, 2004), and the 1/N portfolio studied in DeMiguel, Garlappi, and Uppal (2007). We also use our framework to propose several new portfolio strategies. For the proposed portfolios, we provide a momentshrinkage interpretation and a Bayesian interpretation where the investor has a prior belief on portfolio weights rather than on moments of asset returns. Finally, we compare empirically the out-of-sample performance of the new portfolios we propose to ten strategies in the literature across five datasets. We find that the norm-constrained portfolios often have a higher Sharpe ratio than the portfolio strategies in Jagannathan and Ma (2003), Ledoit and Wolf (2003, 2004), the 1/N portfolio, and other strategies in the literature, such as factor portfolios.

Raman Uppal
London Business School
14.Oct 2008

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