论文标题
两个比一个更好：较大的最小方差投资组合的正则收缩
Two is better than one: Regularized shrinkage of large minimum variance portfolio
论文作者
论文摘要
在本文中，我们通过两种技术的组合构建了全球最小差异（GMV）投资组合的收缩估计器：Tikhonov正则化和投资组合权重的直接收缩。更具体地说，我们采用了双重收缩方法，协方差矩阵和投资组合权重同时缩小。脊参数控制协方差矩阵的稳定性，而投资组合收缩强度将正则投资组合重量收缩为预定义的目标。这两个参数同时将概率最小化，因为资产数量$ p $和样本量$ n $倾向于无穷大，而其比例$ p/n $趋于$ c> 0 $。该方法也可以看作是Ledoit和Wolf（2004年，JMVA）和Bodnar等人的投资组合权重收缩的最佳组合。 （2018，Ejor）。除了假设有限$ 4+\ varepsilon $矩时，没有假定资产回报的特定分布。通过广泛的模拟和经验研究研究了双收缩估计量的性能。建议的方法在大多数情况下，根据样本外差异，SharpE比率和其他经验度量的方面，明显优于其前身（没有正则化）和非线性收缩方法。此外，它遵守最稳定的投资组合权重，并且营业额最小。
In this paper we construct a shrinkage estimator of the global minimum variance (GMV) portfolio by a combination of two techniques: Tikhonov regularization and direct shrinkage of portfolio weights. More specifically, we employ a double shrinkage approach, where the covariance matrix and portfolio weights are shrunk simultaneously. The ridge parameter controls the stability of the covariance matrix, while the portfolio shrinkage intensity shrinks the regularized portfolio weights to a predefined target. Both parameters simultaneously minimize with probability one the out-of-sample variance as the number of assets $p$ and the sample size $n$ tend to infinity, while their ratio $p/n$ tends to a constant $c>0$. This method can also be seen as the optimal combination of the well-established linear shrinkage approach of Ledoit and Wolf (2004, JMVA) and the shrinkage of the portfolio weights by Bodnar et al. (2018, EJOR). No specific distribution is assumed for the asset returns except of the assumption of finite $4+\varepsilon$ moments. The performance of the double shrinkage estimator is investigated via extensive simulation and empirical studies. The suggested method significantly outperforms its predecessor (without regularization) and the nonlinear shrinkage approach in terms of the out-of-sample variance, Sharpe ratio and other empirical measures in the majority of scenarios. Moreover, it obeys the most stable portfolio weights with uniformly smallest turnover.
