Large Dynamic Covariance Matrices

Abstract

Second moments of asset returns are important for risk management and portfolio selection. The problem of estimating second moments can be approached from two angles: time series and the cross-section. In time series, the key is to account for conditional heteroscedasticity; a favored model is Dynamic Conditional Correlation (DCC), derived from the ARCH/GARCH family started by Engle (1982). In the cross-section, the key is to correct in-sample biases of sample covariance matrix eigenvalues; a favored model is nonlinear shrinkage, derived from Random Matrix Theory (RMT). The present article marries these two strands of literature to deliver improved estimation of large dynamic covariance matrices. Supplementary material for this article is available online.

KEY WORDS:

• Composite likelihood
• Dynamic conditional correlation
• GARCH
• Markowitz portfolio selection
• Nonlinear shrinkage.

ACKNOWLEDGMENTS

The authors thank Zhao Zhao (Department of Economics, Huazhong University of Science and Technology, China) for providing research assistance. The authors also thank Kevin Sheppard for having made publicly available the UCSD GARCH Toolbox as well as its successor, the Oxford MFE Toolbox. Last but not least, the authors thank the associate editor and two anonymous referees for helpful comments that have improved the exposition of the article. Any errors are of authors.