A Nodewise Regression Approach to Estimating Large Portfolios

This article investigates the large sample properties of the variance, weights, and risk of high-dimensional portfolios where the inverse of the covariance matrix of excess asset returns is estimated using a technique called nodewise regression. Nodewise regression provides a direct estimator for the inverse covariance matrix using the least absolute shrinkage and selection operator to estimate the entries of a sparse precision matrix. We show that the variance, weights, and risk of the global minimum variance portfolios and the Markowitz mean-variance portfolios are consistently estimated with more assets than observations. We show, empirically, that the nodewise regression-based approach performs well in comparison to factor models and shrinkage methods. Supplementary materials for this article are available online.

本文针对高维投资组合的方差、权重与风险的大样本性质展开研究。该类投资组合的超额资产收益率协方差矩阵的逆矩阵，采用一种名为节点回归（nodewise regression）的技术进行估计。节点回归借助最小绝对收缩与选择算子（Least Absolute Shrinkage and Selection Operator，LASSO）估计稀疏精度矩阵的元素，从而为协方差逆矩阵提供直接估计量。本文证明，当资产数量多于观测样本量时，全局最小方差投资组合与马科维茨均值-方差投资组合的方差、权重及风险均可获得一致估计。本文通过实证分析表明，相较于因子模型与收缩估计方法，基于节点回归的方法表现优异。本文的补充材料可在线获取。