Dynamic and robust estimation of risk and return in modern portfolio theory

Simple item page
dc.contributor.advisorTroskie, Casper Gen_ZA
dc.contributor.authorMupambirei, Rodwelen_ZA
dc.date.accessioned2014-07-31T08:09:01Z
dc.date.available2014-07-31T08:09:01Z
dc.date.issued2008en_ZA
dc.descriptionIncludes abstract.
dc.descriptionIncludes bibliographical references (leaves 134-138).
dc.description.abstractThe portfolio selection method developed by Markowitz gives a rational investor a way of evaluating different investment options in a portfolio using the expected return and variance of the returns. Sharpe uses the same optimization approach but estimates the mean and covariance in a regression framework using the index models. Sharpe makes a crucial assumption that the residuals from different assets are uncorrelated and that the beta estimates are constant. When the Sharpe model parameters are estimated using ordinary least squares, the regression assumptions are violated when there is significant autocorrelation and heteroskedasticity in the residuals. Furthermore, the presence of outlying observations in the data leads to unreliable estimates when the ordinary least squares method is used. We find significant correlation in the residuals from different shares and thus we use the Troskie-Hossain model which relaxes this assumption and ultimately produces an efficient frontier that is almost identical to the Markowitz model. The combination of the GARCH and AR models to remove both autocorrelation and heteroskedasticity is used on the single index model and it causes the efficient frontier to shift significantly to the left. Using dynamic estimation through the Kalman filter, it is noticed that the beta coefficients are not constant and that the resulting efficient frontiers significantly outperform the Sharpe model. In order to deal with the problem of outlying observations in the data, we propose using the Minimum Covariance Determinant, (MCD) estimator as a robust version of the Markowitz formulation. Robust alternatives to the ordinary lea.st squares estimator are also investigated and they all cause the efficient frontier to shift to the left. Finally, to solve the problem of collinearity in the multiple index framework, we construct orthogonal indices using principal components regression to estimate the efficient frontier.en_ZA
dc.identifier.apacitationMupambirei, R. (2008). <i>Dynamic and robust estimation of risk and return in modern portfolio theory</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/4913en_ZA
dc.identifier.chicagocitationMupambirei, Rodwel. <i>"Dynamic and robust estimation of risk and return in modern portfolio theory."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2008. http://hdl.handle.net/11427/4913en_ZA
dc.identifier.citationMupambirei, R. 2008. Dynamic and robust estimation of risk and return in modern portfolio theory. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Mupambirei, Rodwel AB - The portfolio selection method developed by Markowitz gives a rational investor a way of evaluating different investment options in a portfolio using the expected return and variance of the returns. Sharpe uses the same optimization approach but estimates the mean and covariance in a regression framework using the index models. Sharpe makes a crucial assumption that the residuals from different assets are uncorrelated and that the beta estimates are constant. When the Sharpe model parameters are estimated using ordinary least squares, the regression assumptions are violated when there is significant autocorrelation and heteroskedasticity in the residuals. Furthermore, the presence of outlying observations in the data leads to unreliable estimates when the ordinary least squares method is used. We find significant correlation in the residuals from different shares and thus we use the Troskie-Hossain model which relaxes this assumption and ultimately produces an efficient frontier that is almost identical to the Markowitz model. The combination of the GARCH and AR models to remove both autocorrelation and heteroskedasticity is used on the single index model and it causes the efficient frontier to shift significantly to the left. Using dynamic estimation through the Kalman filter, it is noticed that the beta coefficients are not constant and that the resulting efficient frontiers significantly outperform the Sharpe model. In order to deal with the problem of outlying observations in the data, we propose using the Minimum Covariance Determinant, (MCD) estimator as a robust version of the Markowitz formulation. Robust alternatives to the ordinary lea.st squares estimator are also investigated and they all cause the efficient frontier to shift to the left. Finally, to solve the problem of collinearity in the multiple index framework, we construct orthogonal indices using principal components regression to estimate the efficient frontier. DA - 2008 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2008 T1 - Dynamic and robust estimation of risk and return in modern portfolio theory TI - Dynamic and robust estimation of risk and return in modern portfolio theory UR - http://hdl.handle.net/11427/4913 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/4913
dc.identifier.vancouvercitationMupambirei R. Dynamic and robust estimation of risk and return in modern portfolio theory. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2008 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/4913en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematics of Financeen_ZA
dc.titleDynamic and robust estimation of risk and return in modern portfolio theoryen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
thesis_sci_2008_mupambirei_r.pdf
Size:
5.08 MB
Format:
Adobe Portable Document Format
Description:
Download
Collections
Masters