Shrinkage Estimation of Covariance Matrix for Portfolio Choice with High Frequency Data
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...
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Main Authors: | , , |
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Format: | text |
Language: | English |
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Institutional Knowledge at Singapore Management University
2016
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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 |
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Institution: | Singapore Management University |
Language: | English |
Summary: | 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. |
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