2.2 The Shortsale-Constrained Minimum-Variance Portfolio..................... 10

In this paper, we provide a general framework for identifying portfolios that perform well out-of-sample 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 be smaller than a given threshold. We show that our unifying framework nests as special cases the shrinkage approaches of Jagannathan and Ma (2003) and Ledoit and Wolf (2004b), and the 1/N portfolio studied in DeMiguel, Garlappi, and Uppal (2007). We also use our general framework to propose several new portfolio strategies. For these new portfolios, we provide a moment-shrinkage interpreta-tion 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 (in terms of portfo-lio variance, Sharpe ratio, and turnover), the out-of-sample performance of the new portfolios we propose to nine strategies in the existing literature across five datasets. We find that the norm-constrained portfolios we propose have a lower variance and a higher Sharpe ratio than the portfolio strategies in Jagannathan and Ma (2003) and Ledoit and Wolf (2004b), the 1/N portfolio, and also other strategies in the literature such as factor portfolios and the parametric portfolios in Brandt, Santa-Clara, and Valkanov (2005)