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Improving Minimum-Variance Portfolios by Alleviating Overdispersion of Eigenvalues

Published online by Cambridge University Press:  24 October 2019

Fangquan Shi ,
Lianjie Shu Open the ORCID record for Lianjie Shu [Opens in a new window] ,
Aijun Yang  and
Fangyi He
Fangquan Shi
Affiliation:
Shi, shi.fangquan@connect.um.edu.mo, University of Macau Faculty of Business Administration
Lianjie Shu*
Affiliation:
Shu, ljshu@um.edu.mo, University of Macau Faculty of Business Administration
Aijun Yang
Affiliation:
Yang, ajyang81@163.com, Nanjing Forest University College of Economics and Management
Fangyi He
Affiliation:
He, fangyi_he@swufe.edu.cn, Southwestern University of Finance and Economics School of Finance
*
Shu (corresponding author), ljshu@um.edu.mo
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Abstract

In portfolio risk minimization, the inverse covariance matrix of returns is often unknown and has to be estimated in practice. Yet the eigenvalues of the sample covariance matrix are often overdispersed, leading to severe estimation errors in the inverse covariance matrix. To deal with this problem, we propose a general framework by shrinking the sample eigenvalues based on the Schatten norm. The proposed framework has the advantage of being computationally efficient as well as structure-free. The comparative studies show that our approach behaves reasonably well in terms of reducing out-of-sample portfolio risk and turnover.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 55 , Issue 8 , December 2020 , pp. 2700 - 2731
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2019

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Footnotes

We thank the editor and an anonymous referee for their valuable comments. Shu’s work was supported in part by the Macau Science and Technology Development Fund (FDCT/0064/2018/A2) and the University Research Grant (MYRG2018-00087-FBA). He’s work was supported by the National Natural Science Foundation of China (No. 71772153).

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