Abstract
In this paper, we study the high dimensional minimum variance portfolio (MVP) problem under approximate factor models. We extend the theoretical results of POET covariance estimator by [1] and propose a MVP estimator that bears risk close to the theoretical minimum risk with the ratio converging to one. The convergence properties of the MVP estimator are established under two asymptotic risk scenarios: (i) when the minimum risk converges to zero with increasing number of assets; and (ii) when the minimum risk is bounded away from zero. Simulation and extensive empirical studies on S&P 100 stock returns demonstrate that our MVP estimator controls risk effectively.