A Dynamic Structure for High-Dimensional Covariance Matrices and Its Application in Portfolio Allocation

ABSTRACT

Estimation of high-dimensional covariance matrices is an interesting and important research topic. In this article, we propose a dynamic structure and develop an estimation procedure for high-dimensional covariance matrices. Asymptotic properties are derived to justify the estimation procedure and simulation studies are conducted to demonstrate its performance when the sample size is finite. By exploring a financial application, an empirical study shows that portfolio allocation based on dynamic high-dimensional covariance matrices can significantly outperform the market from 1995 to 2014. Our proposed method also outperforms portfolio allocation based on the sample covariance matrix, the covariance matrix based on factor models, and the shrinkage estimator of covariance matrix. Supplementary materials for this article are available online.

KEYWORDS:

• Dynamic structure
• Factor models
• High-dimensional covariance matrices
• Iterative algorithm
• Kernel smoothing
• Portfolio allocation
• Single-index models

Supplementary Materials

All proofs of Lemma B.2, B.3, C.1, D.1, and D.2 are available online.

Acknowledgement

The authors thank the associate editor and referees for their constructive comments.

Funding

This research is supported by the Singapore National Research Foundation under its Cooperative Basic Research Grant and administered by the Singapore Ministry of Health's National Medical Research Council (Grant No. NMRC/CBRG/0014/2012). John Leigh Box was supported by an EPSRC funded studentship through the University of York. Shaojun Guo was partly supported by Key Laboratory of RCSDS, Chinese Academy of Sciences, and an EPSRC research grant in United Kingdom.