Solving the Markowitz Optimization Problem for Large Portfolios
75 Pages Posted: 6 Dec 2015 Last revised: 22 Dec 2017
Date Written: December 22, 2017
This paper studies the large dimensional Markowitz optimization problem. Given any risk constraint level, we introduce a new approach for estimating the optimal portfolio. 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, asymptotically achieves mean-variance efficiency and meanwhile effectively controls the risk. To the best of our knowledge, this is the first approach that can achieve these two goals simultaneously for large portfolios. The superior properties of our approach are demonstrated via comprehensive simulation and empirical studies.
Keywords: Markowitz optimization; Large portfolio selection; Unconstrained regression; LASSO; Sharpe ratio
JEL Classification: G11; C10
Suggested Citation: Suggested Citation