A Combination of High and Relatively Low Frequency Data in Portfolio Studies


Ningning Xia, Shanghai University of Finance and Economics


2017.11.09 15:00-16:00


Middle Lecture Room, Math Building


This paper examines the usefulness of high and low frequency data in estimating the covariance matrix for portfolio choice when the portfolio size is large. A com- putationally 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 relatively low frequency data. Then the regularized eigenvalues of the ICV are estimated by quasi-maximum likelihood based on high fre- quency 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 observations 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 → ∞. The advantages of our proposed estimator are demonstrated using real data. This is a joint work with Dr. Cheng Liu and Prof. Jun Yu.