High dimensional mean-variance optimization through factor analysis

A factor analysis-based approach for estimating high dimensional covariance matrix is proposed and is applied to solve the mean-variance portfolio optimization problem in finance. The consistency of the proposed estimator is established by imposing a factor model structure with a relative weak assumption on the relationship between the dimension and the sample size. Numerical results indicate that the proposed estimator outperforms the plug-in, linear shrinkage and bootstrap-corrected approaches.