Large Dynamic Covariance Matrices

University of Zurich, Department of Economics, Working Paper No. 231, Revised version

43 Pages Posted: 28 Jul 2016 Last revised: 20 Apr 2017

See all articles by Robert F. Engle

Robert F. Engle

New York University - Leonard N. Stern School of Business - Department of Economics; New York University (NYU) - Department of Finance; National Bureau of Economic Research (NBER)

Olivier Ledoit

University of Zurich - Department of Economics

Michael Wolf

University of Zurich - Department of Economics

Date Written: April 1, 2017

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 heteroskedasticity; 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 paper marries these two strands of literature in order to deliver improved estimation of large dynamic covariance matrices.

Keywords: Composite likelihood, dynamic conditional correlations, GARCH, Markowitz portfolio selection, nonlinear shrinkage

JEL Classification: C13, C58, G11

Suggested Citation

Engle, Robert F. and Ledoit, Olivier and Wolf, Michael, Large Dynamic Covariance Matrices (April 1, 2017). University of Zurich, Department of Economics, Working Paper No. 231, Revised version. Available at SSRN: https://ssrn.com/abstract=2814555 or http://dx.doi.org/10.2139/ssrn.2814555

Robert F. Engle (Contact Author)

New York University - Leonard N. Stern School of Business - Department of Economics ( email )

269 Mercer Street
New York, NY 10003
United States

New York University (NYU) - Department of Finance

Stern School of Business
44 West 4th Street
New York, NY 10012-1126
United States

National Bureau of Economic Research (NBER)

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Cambridge, MA 02138
United States

Olivier Ledoit

University of Zurich - Department of Economics ( email )

Wilfriedstrasse 6
Zürich, 8032
Switzerland

Michael Wolf

University of Zurich - Department of Economics ( email )

Wilfriedstrasse 6
Zurich, 8032
Switzerland

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