Modelling of volatility of stock prices using GARCH models & its importance in portfolio construction

Master Thesis

2009

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http://hdl.handle.net/11427/8958
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thesis_sci_2009_mtemeri_t.pdf (4.87 MB)
Authors
Mtemeri, Tinotenda
Supervisors
Guo, Renkuan
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University of Cape Town

Department
Department of Mathematics and Applied Mathematics
Faculty
Faculty of Science
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Abstract
This thesis is aimed at investigating the possibility to model the risk of stocks in financial markets and evaluating the adequacy and effectiveness of univariate GARCH models such as the symmetric GARCH and a few other variations such as the EGARCH, TARCH and PARCH in modelling volatility in monthly returns of stocks traded on the Johannesburg Stock Exchange. This is further used to investigate the importance of GARCH modelling in portfolio construction using Improved Sharpe Single Index Models. The data used for model estimation has been randomly selected from different sectors of the South African economy. GARCH models are estimated and validated for the data series of the randomly selected 15 JSE stocks. Conclusions are drawn regarding the different GARCH models, best lag structure and best error distributions for modelling. The GARCH (1,1) model demonstrates a relatively good forecasting performance as far as the short term forecasting horizon is concerned. However, the use of alternatives to the more common GARCH (1,1) and use of non-normal distributions is not clearly supported. Also, the use of higher order GARCH models such as the GARCH (1,2), GARCH (2,1) and GARCH (2,2) is not clearly supported and the GARCH (1, 1) remains superior overall to these models. The results obtained from this thesis are of paramount importance in portfolio construction, option pricing and formulating hedging strategies. An illustration of the importance of the G ARCH (1,1) model in portfolio construction is given and conclusions are drawn regarding its usefulness in improving our volatility estimations for purposes of portfolio construction.
Description

Includes bibliographical references (leaves 93-96).

Keywords
Financial Mathematics

Reference:

Mtemeri, T. 2009. Modelling of volatility of stock prices using GARCH models & its importance in portfolio construction. University of Cape Town.

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