Ravi Jagannathan and Tongshu Ma analyze the impact of portfolio weight constraints on the efficiency of mean-variance portfolios. They show that imposing nonnegativity constraints on portfolio weights can reduce sampling error, even when the true covariance matrix suggests negative weights. This shrinkage effect helps improve the out-of-sample performance of optimal portfolios. They also find that minimum variance portfolios constructed using the monthly sample covariance matrix perform as well as those using factor models, shrinkage estimators, or daily data. When minimizing tracking error, daily data improves performance. However, the sample covariance matrix without microstructure corrections performs best. The paper also shows that imposing nonnegativity constraints can help when the true covariance structure has a dominant factor, but hurts when using single-factor models. The results suggest that portfolio weight constraints can reduce sampling error and improve out-of-sample performance, especially when the true covariance matrix is not well estimated. The study provides empirical evidence that nonnegativity constraints can help in constructing efficient portfolios, even when the true covariance matrix suggests negative weights. The paper concludes that portfolio weight constraints can be useful in practice, especially when the true covariance matrix is not well estimated.Ravi Jagannathan and Tongshu Ma analyze the impact of portfolio weight constraints on the efficiency of mean-variance portfolios. They show that imposing nonnegativity constraints on portfolio weights can reduce sampling error, even when the true covariance matrix suggests negative weights. This shrinkage effect helps improve the out-of-sample performance of optimal portfolios. They also find that minimum variance portfolios constructed using the monthly sample covariance matrix perform as well as those using factor models, shrinkage estimators, or daily data. When minimizing tracking error, daily data improves performance. However, the sample covariance matrix without microstructure corrections performs best. The paper also shows that imposing nonnegativity constraints can help when the true covariance structure has a dominant factor, but hurts when using single-factor models. The results suggest that portfolio weight constraints can reduce sampling error and improve out-of-sample performance, especially when the true covariance matrix is not well estimated. The study provides empirical evidence that nonnegativity constraints can help in constructing efficient portfolios, even when the true covariance matrix suggests negative weights. The paper concludes that portfolio weight constraints can be useful in practice, especially when the true covariance matrix is not well estimated.