High-dimensional Portfolio Optimization using Joint Shrinkage

TL;DR

This paper introduces a joint shrinkage method for high-dimensional portfolio optimization that improves estimation accuracy of asset relationships, leading to better portfolio risk and weight estimation in large asset sets.

Contribution

The paper proposes a novel regression-based joint shrinkage approach for estimating asset partial correlations in high-dimensional portfolios, outperforming existing methods.

Findings

Superior variance and risk estimation accuracy.

Enhanced portfolio weight estimation.

Effective on real S&P 500 data.

Abstract

We consider the problem of optimizing a portfolio of financial assets, where the number of assets can be much larger than the number of observations. The optimal portfolio weights require estimating the inverse covariance matrix of excess asset returns, classical solutions of which behave badly in high-dimensional scenarios. We propose to use a regression-based joint shrinkage method for estimating the partial correlation among the assets. Extensive simulation studies illustrate the superior performance of the proposed method with respect to variance, weight, and risk estimation errors compared with competing methods for both the global minimum variance portfolios and Markowitz mean-variance portfolios. We also demonstrate the excellent empirical performances of our method on daily and monthly returns of the components of the S&P 500 index.