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.
Portfolio Choice, High Frequency Data; Integrated Covariance Matrix; Shrinkage Function.
LIU, Cheng; XIA, Ningning; and Jun YU.
Shrinkage Estimation of Covariance Matrix for Portfolio Choice with High Frequency Data. (2016). 1-33. Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/1892
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.