Approaching Mean-Variance Efficiency for Large Portfolios

This paper introduces a new approach to constructing optimal mean-variance portfolios. The approach relies on a novel unconstrained regression representation of the mean-variance optimization problem combined with high-dimensional sparse-regression methods. Our estimated portfolio, under a mild sparsity assumption, controls for risk and attains the maximum expected return as both the numbers of assets and observations grow. The superior properties of our approach are demonstrated through comprehensive simulation and empirical analysis. Notably, using our strategy, we find that investing in individual stocks, in addition to the Fama-French three-factor portfolios, leads to substantially improved performance.Received October 6, 2014; editorial decision July 13, 2018 by Editor Andrew Karolyi. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.