Risk Reduction and Efficiency Increase in Large Portfolios: Leverage and Shrinkage

University of Zurich, Department of Economics, Working Paper No. 328, Revised version

34 Pages Posted: 18 Jul 2019 Last revised: 25 Jan 2020

See all articles by Zhao Zhao

Zhao Zhao

Huazhong University of Science and Technology - Department of Economics

Olivier Ledoit

University of Zurich - Department of Economics

Hui Jiang

Huazhong University of Science and Technology (Formerly Tongi Medical University)

Date Written: January 2020

Abstract

We investigate the effects of constraining leverage and shrinking covariance matrix in constructing large portfolios, both theoretically and empirically. Considering a wide variety of setups that involve conditioning or not conditioning the covariance matrix estimator on the recent past (multivariate GARCH), smaller vs. larger universe of stocks, alternative portfolio formation objectives (Global Minimum Variance vs. exposure to profitable factors), and various transaction cost assumptions, we find that a judiciously-chosen shrinkage method always outperforms an arbitrarily-determined leverage constraint. By extending the mathematical connection between leverage and shrinkage from static to dynamic, we provide a new theoretical explanation for our finding from the perspective of degrees of freedom. In addition, both simulation and empirical analysis show that the DCC-NL estimator results in risk reduction and effciency increase in large portfolios as long as a small amount of leverage is allowed, whereas tightening the leverage constraint often hurts a DCC-NL portfolio.

Keywords: DCC, nonlinear shrinkage, leverage constraints, large portfolios, risk reduction, Markowitz mean-variance efficiency, multivariate GARCH

JEL Classification: C13, C58, G11

Suggested Citation

Zhao, Zhao and Ledoit, Olivier and Jiang, Hui, Risk Reduction and Efficiency Increase in Large Portfolios: Leverage and Shrinkage (January 2020). University of Zurich, Department of Economics, Working Paper No. 328, Revised version, Available at SSRN: https://ssrn.com/abstract=3421538 or http://dx.doi.org/10.2139/ssrn.3421538

Zhao Zhao (Contact Author)

Huazhong University of Science and Technology - Department of Economics ( email )

Wuhan, Hubei 430074
China

Olivier Ledoit

University of Zurich - Department of Economics ( email )

Wilfriedstrasse 6
Zürich, 8032
Switzerland

Hui Jiang

Huazhong University of Science and Technology (Formerly Tongi Medical University) ( email )

1037 Luoyu Rd
Wuhan, Hubei 430074
China

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