Risk Reduction and Efficiency Increase in Large Portfolios: Gross-Exposure Constraints and Shrinkage of the Covariance Matrix
研究了在构建大型投资组合时，约束总风险暴露与收缩协方差矩阵的效果，发现精心选择的收缩方法总是优于任意设定的总风险暴露约束，并提出了动态条件相关-非线性收缩估计器。
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.