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

 

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dc.contributor.advisor Troskie, Casper G en_ZA
dc.contributor.author Mupambirei, Rodwel en_ZA
dc.date.accessioned 2014-07-31T08:09:01Z
dc.date.available 2014-07-31T08:09:01Z
dc.date.issued 2008 en_ZA
dc.identifier.citation Mupambirei, R. 2008. Dynamic and robust estimation of risk and return in modern portfolio theory. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/4913
dc.description Includes abstract.
dc.description Includes bibliographical references (leaves 134-138).
dc.description.abstract 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. en_ZA
dc.language.iso eng en_ZA
dc.subject.other Mathematics of Finance en_ZA
dc.title Dynamic and robust estimation of risk and return in modern portfolio theory en_ZA
dc.type Thesis / Dissertation en_ZA
uct.type.publication Research en_ZA
uct.type.resource Thesis en_ZA
dc.publisher.institution University of Cape Town
dc.publisher.faculty Faculty of Science en_ZA
dc.publisher.department Department of Mathematics and Applied Mathematics en_ZA
dc.type.qualificationlevel Masters en_ZA
dc.type.qualificationname MSc en_ZA
uct.type.filetype Text
uct.type.filetype Image


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