The impact of linear covariance matrix shrinkage on mean-variance efficient frontier portfolio characteristics

Clayton, Joseph Gregory

The impact of linear covariance matrix shrinkage on mean-variance efficient frontier portfolio characteristics

Thesis / Dissertation

2026

Publisher

University of Cape Town

Department

Department of Finance and Tax

Faculty

Faculty of Commerce

Abstract

In investment cases with many stocks under consideration compared to the available historical return observations, the sample variance-covariance (VCV) matrix is often estimated with considerable error, particularly during market turbulence. Errors arise due to extreme differences in VCV matrix eigenvalues. Traditional mean-variance portfolio optimisation naively employs these extreme values, leading to investment decisions placed on unreliable and unrealistic values. Shrinkage techniques (in which high eigenvalues are reduced, and low eigenvalues increased thereby “shrinking” the range of VCV eigenvalues) is one of the proposed suggestions to address this issue. This study extends previous work by applying linear shrinkage estimators to S&P 500 index-based stock portfolios over the sample period of 01-Jan-18 – 20-May-24. Findings indicate that no linear shrinkage estimator affects the VCV matrix sufficiently to repair the spurious risk-return characteristics of efficient portfolios under stressed market conditions. While some improvements in portfolio risk-adjusted return are observed, the instability of the efficient frontier under stressed market conditions largely remains. Future work could extend this research by considering more sophisticated (non-linear) VCV shrinkage estimators that may mitigate these observed instabilities and yield more stable and improved portfolio performance statistics.