A Nodewise Regression Approach to Estimating Large Portfolios

TL;DR

This paper introduces a nodewise regression method using Lasso to estimate inverse covariance matrices, enabling consistent estimation of large portfolio risk and weights even with more assets than observations, outperforming traditional methods.

Contribution

The paper develops a novel approach using nodewise regression with Lasso for high-dimensional portfolio estimation, demonstrating its consistency and empirical advantages.

Findings

Consistent estimation of portfolio variance, weights, and risk in high dimensions.

Nodewise regression outperforms factor models and shrinkage methods empirically.

Effective for portfolios with more assets than observations.

Abstract

This paper 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 (Lasso) of Tibshirani (1994) 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.