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
Date Written: January 2020
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: Suggested Citation