Portfolio selection using Random Matrix theory and L-Moments

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dc.contributor.advisorBosman, Petrusen_ZA
dc.contributor.advisorTaylor, Daviden_ZA
dc.contributor.authorUshan, Wardahen_ZA
dc.date.accessioned2016-02-08T14:27:09Z
dc.date.available2016-02-08T14:27:09Z
dc.date.issued2015en_ZA
dc.descriptionIncludes bibliographical referencesen_ZA
dc.description.abstractMarkowitz'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.en_ZA
dc.identifier.apacitationUshan, W. (2015). <i>Portfolio selection using Random Matrix theory and L-Moments</i>. (Thesis). University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science. Retrieved from http://hdl.handle.net/11427/16921en_ZA
dc.identifier.chicagocitationUshan, Wardah. <i>"Portfolio selection using Random Matrix theory and L-Moments."</i> Thesis., University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science, 2015. http://hdl.handle.net/11427/16921en_ZA
dc.identifier.citationUshan, W. 2015. Portfolio selection using Random Matrix theory and L-Moments. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Ushan, Wardah AB - 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. DA - 2015 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2015 T1 - Portfolio selection using Random Matrix theory and L-Moments TI - Portfolio selection using Random Matrix theory and L-Moments UR - http://hdl.handle.net/11427/16921 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/16921
dc.identifier.vancouvercitationUshan W. Portfolio selection using Random Matrix theory and L-Moments. [Thesis]. University of Cape Town ,Faculty of Commerce ,Division of Actuarial Science, 2015 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/16921en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDivision of Actuarial Scienceen_ZA
dc.publisher.facultyFaculty of Commerceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematical Financeen_ZA
dc.titlePortfolio selection using Random Matrix theory and L-Momentsen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMPhilen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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