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.

中文翻译：

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大型投资组合的风险降低和效率提高：总敞口约束和协方差矩阵收缩

我们从理论上和经验上研究了约束总暴露和缩小协方差矩阵在构建大型投资组合中的影响。考虑各种设置，包括调节或不调节最近过去的协方差矩阵估计量（多元 GARCH）、较小与较大的股票范围、替代投资组合形成目标（全局最小方差与盈利因素的敞口）以及各种交易成本假设，我们发现明智选择的收缩方法总是优于任意确定的总暴露约束。我们将协方差矩阵的总曝光和收缩约束之间的数学联系从静态扩展到动态，并从自由度的角度为我们的发现提供了新的解释。此外，模拟和实证分析都表明，只要允许少量空头头寸，动态条件相关-非线性收缩 (DCC-NL) 估计量就可以降低大型投资组合的风险并提高效率，而对总体风险敞口通常会损害 DCC-NL 投资组合。