The paper by Ravi Jagannathan and Tongshu Ma explores the impact of imposing incorrect constraints on portfolio weights in mean-variance efficient portfolio construction. The authors argue that while Green and Hollifield (1992) suggest that extreme weights in sample-efficient portfolios are due to a single dominant factor, empirical evidence often contradicts this view. They show that constraining portfolio weights to be nonnegative is equivalent to reducing the sample covariance matrix's large elements, which helps reduce risk even when the true covariance matrix involves large negative weights. This shrinkage effect can improve the performance of optimal portfolios, particularly when using the sample covariance matrix. The study also examines the impact of upper bounds on portfolio weights and finds that these constraints do not significantly improve out-of-sample performance when no-shortsales restrictions are already in place. The authors conclude that imposing nonnegativity constraints can help, even when the constraints are incorrect, by reducing sampling error. Additionally, they find that using daily data instead of monthly data can improve tracking error minimization, but the sample covariance matrix without corrections for microstructure effects performs best. The paper provides theoretical and empirical evidence to support these findings, offering insights into the practical implications of portfolio weight constraints in portfolio optimization.The paper by Ravi Jagannathan and Tongshu Ma explores the impact of imposing incorrect constraints on portfolio weights in mean-variance efficient portfolio construction. The authors argue that while Green and Hollifield (1992) suggest that extreme weights in sample-efficient portfolios are due to a single dominant factor, empirical evidence often contradicts this view. They show that constraining portfolio weights to be nonnegative is equivalent to reducing the sample covariance matrix's large elements, which helps reduce risk even when the true covariance matrix involves large negative weights. This shrinkage effect can improve the performance of optimal portfolios, particularly when using the sample covariance matrix. The study also examines the impact of upper bounds on portfolio weights and finds that these constraints do not significantly improve out-of-sample performance when no-shortsales restrictions are already in place. The authors conclude that imposing nonnegativity constraints can help, even when the constraints are incorrect, by reducing sampling error. Additionally, they find that using daily data instead of monthly data can improve tracking error minimization, but the sample covariance matrix without corrections for microstructure effects performs best. The paper provides theoretical and empirical evidence to support these findings, offering insights into the practical implications of portfolio weight constraints in portfolio optimization.