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.