Title: Solving the Markowitz optimization problem for large portfolios
Authors: Mengmeng Ao - Xiamen University (China) [presenting]
Yingying Li - Hong Kong University of Science and Technology (Hong Kong)
Xinghua Zheng - HKUST (China)
Abstract: The large dimensional Markowitz optimization problem is studied. 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.