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

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dc.contributor.advisorVan Vuuren, Gary
dc.contributor.advisorHuang, Chun-Sung
dc.contributor.authorClayton, Joseph Gregory
dc.date.accessioned2026-07-02T08:07:00Z
dc.date.available2026-07-02T08:07:00Z
dc.date.issued2026
dc.date.updated2026-07-02T08:02:52Z
dc.description.abstractIn 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.
dc.identifier.apacitationClayton, J. G. (2026). <i>The impact of linear covariance matrix shrinkage on mean-variance efficient frontier portfolio characteristics</i>. (). University of Cape Town ,Faculty of Commerce ,Department of Finance and Tax. Retrieved from http://hdl.handle.net/11427/43448en_ZA
dc.identifier.chicagocitationClayton, Joseph Gregory. <i>"The impact of linear covariance matrix shrinkage on mean-variance efficient frontier portfolio characteristics."</i> ., University of Cape Town ,Faculty of Commerce ,Department of Finance and Tax, 2026. http://hdl.handle.net/11427/43448en_ZA
dc.identifier.citationClayton, J.G. 2026. The impact of linear covariance matrix shrinkage on mean-variance efficient frontier portfolio characteristics. . University of Cape Town ,Faculty of Commerce ,Department of Finance and Tax. http://hdl.handle.net/11427/43448en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Clayton, Joseph Gregory AB - 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. DA - 2026 DB - OpenUCT DP - University of Cape Town KW - variance-covariance KW - matrix KW - market turbulence LK - https://open.uct.ac.za PB - University of Cape Town PY - 2026 T1 - The impact of linear covariance matrix shrinkage on mean-variance efficient frontier portfolio characteristics TI - The impact of linear covariance matrix shrinkage on mean-variance efficient frontier portfolio characteristics UR - http://hdl.handle.net/11427/43448 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/43448
dc.identifier.vancouvercitationClayton JG. The impact of linear covariance matrix shrinkage on mean-variance efficient frontier portfolio characteristics. []. University of Cape Town ,Faculty of Commerce ,Department of Finance and Tax, 2026 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/43448en_ZA
dc.language.isoen
dc.language.rfc3066eng
dc.publisher.departmentDepartment of Finance and Tax
dc.publisher.facultyFaculty of Commerce
dc.publisher.institutionUniversity of Cape Town
dc.subjectvariance-covariance
dc.subjectmatrix
dc.subjectmarket turbulence
dc.titleThe impact of linear covariance matrix shrinkage on mean-variance efficient frontier portfolio characteristics
dc.typeThesis / Dissertation
dc.type.qualificationlevelMasters
dc.type.qualificationlevelMCom
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