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This paper examines the usefulness of high frequency data in estimating thecovariance matrix for portfolio choice when the portfolio size is large. Acomputationally convenient nonlinear shrinkage estimator for the integratedcovariance (ICV) matrix of financial assets is developed in two steps. Theeigenvectors of the ICV are first constructed from a designed time variationadjusted realized covariance matrix of noise-free log-returns of relatively lowfrequency data. Then the regularized eigenvalues of the ICV are estimated byquasi-maximum likelihood based on high frequency data. The estimator is alwayspositive definite and its inverse is the estimator of the inverse of ICV. Itminimizes the limit of the out-of-sample variance of portfolio returns withinthe class of rotation-equivalent estimators. It works when the number ofunderlying assets is larger than the number of time series observations in eachasset and when the asset price follows a general stochastic process. Ourtheoretical results are derived under the assumption that the number of assets(p) and the sample size (n) satisfy p/n \to y >0 as n goes to infty . Theadvantages of our proposed estimator are demonstrated using real data.

Shrinkage estimation of covariance matrix for portfolio choice with high frequency data