High dimensional minimum variance portfolio estimation under statistical factor models

We propose a high dimensional minimum variance portfolio estimator under statistical factor models, and show that our estimated portfolio enjoys sharp risk consistency. Our approach relies on properly integrating ℓ₁ constraint on portfolio weights with an appropriate covariance matrix estimator. In terms of covariance matrix estimation, we extend the theoretical results of POET (Fan et al., 2013) to a setting that is coherent with principal component analysis. Simulation and extensive empirical studies on S&P 100 Index constituent stocks demonstrate favorable performance of our MVP estimator compared with benchmark portfolios.