Nonlinear Shrinkage of the Covariance Matrix for Portfolio Selection: Markowitz Meets Goldilocks
提出一种比线性收缩更灵活的非线性收缩估计方法，用于估计资产收益协方差矩阵，在资产数量与样本量相当时渐近最优，回测表现优于线性收缩。
Markowitz (1952) portfolio selection requires an estimator of the covariance matrix of returns. To address this problem, we promote a nonlinear shrinkage estimator that is more flexible than previous linear shrinkage estimators and has just the right number of free parameters (i.e., the Goldilocks principle). This number is the same as the number of assets. Our nonlinear shrinkage estimator is asymptotically optimal for portfolio selection when the number of assets is of the same magnitude as the sample size. In backtests with historical stock return data, it performs better than previous proposals and, in particular, it dominates linear shrinkage. Received January 21, 2014; editorial decision January 25, 2017 by Editor Geert Bekaert.