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

• Main Authors: LIU, Cheng, XIA, Ningning, Jun YU
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2016
• Subjects: Portfolio Choice; High Frequency Data; Integrated Covariance Matrix; Shrinkage Function.; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/1892; https://ink.library.smu.edu.sg/context/soe_research/article/2892/viewcontent/9983285.pdf
• Institution: Singapore Management University

This paper examines the usefulness of high frequency data in estimating the covariancematrix for portfolio choice when the portfolio size is large. A computationally convenientnonlinear shrinkage estimator for the integrated covariance (ICV) matrix of financial as-sets is developed in two steps. The eigenvectors of the ICV are first constructed from adesigned 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 byquasi-maximum likelihood based on high frequency data. The estimator is always positivedefinite and its inverse is the estimator of the inverse of ICV. It minimizes the limit of theout-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. Ourtheoretical results are derived under the assumption that the number of assets (p) and thesample size (n) satisfy p/n → y > 0 as n → ∞. The advantages of our proposed estimatorare demonstrated using real data.