This thesis proposes a new estimation method for the high-dimensional mean-variance portfolio of risky assets, allowing factor investing. Our estimator mainly consists of two parts: (1) a consistent estimator of the weight vector on factors, and (2) an estimator of the high-dimensional weight vector on idiosyncratic components based on linear constrained LASSO. The foundation of applying the linear constrained LASSO is an equlivalent constrained regression representation of the weight vector on the idiosyncratic component. Under a mild sparsity assumption, the new estimator enjoys the mean-variance efficiency asymptotically. In simulation and empirical study on the S&P 500 index components and Fama-French three factor investment universe, the new estimator can control the risks and gain...[ Read more ]

This thesis proposes a new estimation method for the high-dimensional mean-variance portfolio of risky assets, allowing factor investing. Our estimator mainly consists of two parts: (1) a consistent estimator of the weight vector on factors, and (2) an estimator of the high-dimensional weight vector on idiosyncratic components based on linear constrained LASSO. The foundation of applying the linear constrained LASSO is an equlivalent constrained regression representation of the weight vector on the idiosyncratic component. Under a mild sparsity assumption, the new estimator enjoys the mean-variance efficiency asymptotically. In simulation and empirical study on the S&P 500 index components and Fama-French three factor investment universe, the new estimator can control the risks and gains high portfolio returns simultaneously at different risk levels.