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Risk reduction and efficiency increase in large portfolios: leverage and shrinkage


Zhao, Zhao; Ledoit, Olivier; Jiang, Hui (2020). Risk reduction and efficiency increase in large portfolios: leverage and shrinkage. Working paper series / Department of Economics 328, University of Zurich.

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 efficiency 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.

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 efficiency 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.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Economics
Working Paper Series > Department of Economics
Dewey Decimal Classification:330 Economics
JEL Classification:C13, C58, G11
Uncontrolled Keywords:DCC, nonlinear shrinkage, leverage constraint, large portfolios, risk reduction, Markowitz mean-variance efficiency, multivariate GARCH
Language:English
Date:January 2020
Deposited On:17 Jul 2019 15:09
Last Modified:25 Mar 2020 15:19
Series Name:Working paper series / Department of Economics
Number of Pages:33
ISSN:1664-705X
Additional Information:Revised version
OA Status:Green
Official URL:https://www.econ.uzh.ch/static/release/workingpapers.php?id=1007

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