Risk Reduction and Efficiency Increase in Large Portfolios: Gross-Exposure Constraints and Shrinkage of the Covariance Matrix

Abstract

We investigate the effects of constraining gross-exposure 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 versus larger universe of stocks, alternative portfolio formation objectives (global minimum variance versus exposure to profitable factors), and various transaction cost assumptions, we find that a judiciously chosen shrinkage method always outperforms an arbitrarily determined constraint on gross-exposure. We extend the mathematical connection between constraints on the gross-exposure and shrinkage of the covariance matrix from static to dynamic, and provide a new explanation for our finding from the perspective of degrees of freedom. In addition, both simulation and empirical analysis show that the dynamic conditional correlation-nonlinear shrinkage (DCC-NL) estimator results in risk reduction and efficiency increase in large portfolios as long as a small amount of short position is allowed, whereas imposing a constraint on gross-exposure often hurts a DCC-NL portfolio.