Portfolio optimization using the Markowitz model: Case study of selected companies in Ghana

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Over the past few years, there has been increased activity in the Ghanaian capital market. It is important that prospective investors and market watchers are able to determine the risk of listed companies. However, information regarding the beta of companies and what proportions to invest in portfolios to spread the risks for some expected returns are not readily available. Once an investor determines how risky listed companies are, he or she would be able to spread the risk by diversifying the investment, i.e. making the investment commensurate with the risk in order to maximize returns. Three data sets, one containing the Ghana Stock Exchange (GSE) All Share Index, the other containing the monthly beginning and closing stock prices of six of the most liquid stocks listed on the Ghana Stock Exchange and the Bank of Ghana 91-day Treasury bill rates for the period January, 1998 to December, 2002 were obtained from the Bank of Ghana. The sensitivity of the six selected companies was established by calculating their betas using regression analysis. The Markowitz Model was formulated and solved using the quadratic programming add-in and the Microsoft Excel Solver. The results indicated that most of the six selected companies have negative betas, which implies that most of these companies listed on the Ghana Stock Exchange were less risky. The optimal solution to the Markowitz model indicated that in order to ensure diversification and good returns, Ghana Commercial Bank (GCB) stock should make up 19.64% of the portfolio, SG-SSB Bank stock should make up 8.93% of the portfolio, Standard Chartered Bank (SCB) stock should make up 17.86% of the portfolio, Home Finance Company (HFC) 10.71% of the portfolio, Enterprise Insurance (EIC) stock should make up 5.36% of the portfolio and Total Ghana Limited stock should make up 37.5% of the portfolio.
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology, in partial fulfillment of the requirement for the degree of Master of Science in industrial mathematics