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Covariance matrix estimation methods for constrained portfolio optimization in a South African setting
One of the major topics of concern in Modern Portfolio Theory is portfolio optimization which is centred on the mean-variance framework. In order for this framework to be implemented, esti- mated parameters (covariance matrix for the constrained portfo- lio) are required. The problem with these esti...
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| Format: | Thesis |
| Language: | English |
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School of Economics
2014
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| _version_ | 1867613150515298304 |
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| access_status_str | Open Access |
| author | Madume, Jaison Pezisai |
| author2 | Bradfield, David |
| author_browse | Bradfield, David Madume, Jaison Pezisai |
| author_facet | Bradfield, David Madume, Jaison Pezisai |
| author_sort | Madume, Jaison Pezisai |
| collection | Thesis |
| description | One of the major topics of concern in Modern Portfolio Theory is portfolio optimization which is centred on the mean-variance framework. In order for this framework to be implemented, esti- mated parameters (covariance matrix for the constrained portfo- lio) are required. The problem with these estimated parameters is that they have to be extracted from historical data based on certain assumptions. Because of the di erent estimation methods that can be used the parameters thus obtained will su er either from estimation error or speci cation error. In order to obtain results that are realistic in the optimization, one needs then to establish covariance matrix estimators that are as good as possi- ble. This paper explores the various covariance matrix estimation methods in a South African setting focusing on the constrained portfolio. The empirical results show that the Ledoit shrinkage to a constant correlation method, the Principal Component Analy- sis method and the Portfolio of estimators method all perform as good as the Sample covariance matrix in the Ex-ante period but improve on it slightly in the Ex-post period. However, the im- provement is of a small magnitude, as a result the sample covari- ance matrix can be used in the constrained portfolio optimization in a South African setting. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/5745 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:31:34.243Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2014 |
| publishDateRange | 2014 |
| publishDateSort | 2014 |
| publisher | School of Economics |
| publisherStr | School of Economics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/5745 Covariance matrix estimation methods for constrained portfolio optimization in a South African setting Madume, Jaison Pezisai Bradfield, David Munro, Brian Mathematical Finance One of the major topics of concern in Modern Portfolio Theory is portfolio optimization which is centred on the mean-variance framework. In order for this framework to be implemented, esti- mated parameters (covariance matrix for the constrained portfo- lio) are required. The problem with these estimated parameters is that they have to be extracted from historical data based on certain assumptions. Because of the di erent estimation methods that can be used the parameters thus obtained will su er either from estimation error or speci cation error. In order to obtain results that are realistic in the optimization, one needs then to establish covariance matrix estimators that are as good as possi- ble. This paper explores the various covariance matrix estimation methods in a South African setting focusing on the constrained portfolio. The empirical results show that the Ledoit shrinkage to a constant correlation method, the Principal Component Analy- sis method and the Portfolio of estimators method all perform as good as the Sample covariance matrix in the Ex-ante period but improve on it slightly in the Ex-post period. However, the im- provement is of a small magnitude, as a result the sample covari- ance matrix can be used in the constrained portfolio optimization in a South African setting. 2014-07-31T12:25:08Z 2014-07-31T12:25:08Z 2010 Master Thesis Masters MCom http://hdl.handle.net/11427/5745 eng application/pdf School of Economics Faculty of Commerce University of Cape Town |
| spellingShingle | Mathematical Finance Madume, Jaison Pezisai Covariance matrix estimation methods for constrained portfolio optimization in a South African setting |
| thesis_degree_str | Master's |
| title | Covariance matrix estimation methods for constrained portfolio optimization in a South African setting |
| title_full | Covariance matrix estimation methods for constrained portfolio optimization in a South African setting |
| title_fullStr | Covariance matrix estimation methods for constrained portfolio optimization in a South African setting |
| title_full_unstemmed | Covariance matrix estimation methods for constrained portfolio optimization in a South African setting |
| title_short | Covariance matrix estimation methods for constrained portfolio optimization in a South African setting |
| title_sort | covariance matrix estimation methods for constrained portfolio optimization in a south african setting |
| topic | Mathematical Finance |
| url | http://hdl.handle.net/11427/5745 |
| work_keys_str_mv | AT madumejaisonpezisai covariancematrixestimationmethodsforconstrainedportfoliooptimizationinasouthafricansetting |