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Portfolio selection using Random Matrix theory and L-Moments
Includes bibliographical references
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
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Division of Actuarial Science
2016
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| _version_ | 1867613281020018688 |
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| access_status_str | Open Access |
| author | Ushan, Wardah |
| author2 | Bosman, Petrus |
| author_browse | Bosman, Petrus Ushan, Wardah |
| author_facet | Bosman, Petrus Ushan, Wardah |
| author_sort | Ushan, Wardah |
| collection | Thesis |
| description | Includes bibliographical references |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/16921 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:33:37.862Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | Division of Actuarial Science |
| publisherStr | Division of Actuarial Science |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/16921 Portfolio selection using Random Matrix theory and L-Moments Ushan, Wardah Bosman, Petrus Taylor, David Mathematical Finance Includes bibliographical references Markowitz's (1952) seminal work on Modern Portfolio Theory (MPT) describes a methodology to construct an optimal portfolio of risky stocks. The constructed portfolio is based on a trade-off between risk and reward, and will depend on the risk- return preferences of the investor. Implementation of MPT requires estimation of the expected returns and variances of each of the stocks, and the associated covariances between them. Historically, the sample mean vector and variance-covariance matrix have been used for this purpose. However, estimation errors result in the optimised portfolios performing poorly out-of-sample. This dissertation considers two approaches to obtaining a more robust estimate of the variance-covariance matrix. The first is Random Matrix Theory (RMT), which compares the eigenvalues of an empirical correlation matrix to those generated from a correlation matrix of purely random returns. Eigenvalues of the random correlation matrix follow the Marcenko-Pastur density, and lie within an upper and lower bound. This range is referred to as the "noise band". Eigenvalues of the empirical correlation matrix falling within the "noise band" are considered to provide no useful information. Thus, RMT proposes that they be filtered out to obtain a cleaned, robust estimate of the correlation and covariance matrices. The second approach uses L-moments, rather than conventional sample moments, to estimate the covariance and correlation matrices. L-moment estimates are more robust to outliers than conventional sample moments, in particular, when sample sizes are small. We use L-moments in conjunction with Random Matrix Theory to construct the minimum variance portfolio. In particular, we consider four strategies corresponding to the four different estimates of the covariance matrix: the L-moments estimate and sample moments estimate, each with and without the incorporation of RMT. We then analyse the performance of each of these strategies in terms of their risk-return characteristics, their performance and their diversification. 2016-02-08T14:27:09Z 2016-02-08T14:27:09Z 2015 Master Thesis Masters MPhil http://hdl.handle.net/11427/16921 eng application/pdf Division of Actuarial Science Faculty of Commerce University of Cape Town |
| spellingShingle | Mathematical Finance Ushan, Wardah Portfolio selection using Random Matrix theory and L-Moments |
| thesis_degree_str | Master's |
| title | Portfolio selection using Random Matrix theory and L-Moments |
| title_full | Portfolio selection using Random Matrix theory and L-Moments |
| title_fullStr | Portfolio selection using Random Matrix theory and L-Moments |
| title_full_unstemmed | Portfolio selection using Random Matrix theory and L-Moments |
| title_short | Portfolio selection using Random Matrix theory and L-Moments |
| title_sort | portfolio selection using random matrix theory and l moments |
| topic | Mathematical Finance |
| url | http://hdl.handle.net/11427/16921 |
| work_keys_str_mv | AT ushanwardah portfolioselectionusingrandommatrixtheoryandlmoments |