Optimal portfolio selection (a case study of Ghana Stock Exchange)

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The knapsack model is employed in many fields of study including Business, Engineering and Economics to solve problems related to resource constraints. The knapsack problem is a form of integer programming problem that has only one constraint and can be used to strengthen cutting planes for general integer programs. These facts make the studies of the knapsack problems and their variants extremely important area of research in the field of operations research. This thesis seeks to apply the branch-and-bound algorithm to construct an optimal portfolio from the listed shares on the Ghana Stock Exchange (GSE) in the model of the 0-1 knapsack problem. This paper will among other things seek to contribute to making the financial market efficient with particular reference to accessing information of listed companies. The paper will also consider the factors to note when forming a portfolio and its capitalization. The model developed could be adopted for decision making in choosing shares for the optimal portfolio. In the end, we form a portfolio from the listed shares on the Ghana Stock Exchange using the concept of the 0-1 knapsack model to see if we will obtain a good return on our investment. All listed shares of the GSE were considered and it proved out that AADS, ACI, AYRTN, CAL, CMLT, CPC, ETI, GCB and GOIL shares should be selected to obtain an optimum output and recommend that Knapsack problem model should be adopted by fund managers and other financial market players.
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fufillment of the requirement for the degree of MSc. Industrial Mathematics, 2014