Shrinkage Estimation of Covariance Matrix for Portfolio Choice with High Frequency Data

This paper examines the usefulness of high frequency data in estimating the covariance matrix for portfolio choice when the portfolio size is large. A computationally convenient nonlinear shrinkage estimator for the integrated covariance (ICV) matrix of financial assets is developed in two steps. The eigenvectors of the ICV are first constructed from a designed time variation adjusted realized covariance matrix of noise-free log-returns of rel- atively low frequency data. Then the regularized eigenvalues of the ICV are estimated by quasi-maximum likelihood based on high frequency data. The estimator is always positive definite and its inverse is the estimator of the inverse of ICV. It minimizes the limit of the out-of-sample variance of portfolio returns within the class of rotation-equivalent estimators. It works when the number of underlying assets is larger than the number of time series ob- servations in each asset and when the asset price follows a general stochastic process. Our theoretical results are derived under the assumption that the number of assets (p) and the sample size (n) satisfy p/n -> y > 0 as n -> 8. The advantages of our proposed estimator are demonstrated using real data.