A Mathematical Approach to a Stocks Portfolio Selection: The Case of Uganda Securities Exchange (USE)

Fredrick Mayanja, Sure Mataramvura, Wilson Mahera Charles

Department of Investments and Research, STANLIB, Kampala, Uganda.
Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam, Dar es Salaam, Tanzania.
Division of Actuarial Sciences, University of Cape Town, Rondebosch, South Africa.

DOI: 10.4236/jmf.2013.34051                

Abstract

In this paper, we present the problem of portfolio optimization under investment. This area of investment is traced with works of Professor Markowitz way back in 1952. First, we determine the probability distribution of the Uganda Securities Exchange (USE) stocks returns. Secondly, we develop unrestricted portfolio optimization model based on the classical Modern Portfolio Optimization (MPT) model, and then we incorporate certain restrictions typical of the USE trading or investment environment and hence, develop the modified restricted model. Thirdly, we explore the possibility of diversification under a portfolio of averagely correlated assets. Determination of the model parameters and model development is all done using Excel spreadsheets. We explicitly go through the mathematics of the solution methods for both models. Validation of the models is done using the USE stocks daily trading data, in which case we use a random sample of 6 stocks out of the 13 stocks listed at the USE. To start with, we prove that USE stocks log returns are normally distributed. Data analysis results and the frontier curves show that our modified (restricted) model is valid as the solutions are all consistent with the theoretical foundations of the classical MPT-model but inferior to the unrestricted model. To make the model more useful, accurate and easy to apply and robust, we programme the model using Visual Basic for Applications (VBA). We therefore recommend that before applying investment models such as the MPT, model modifications must be made so as to adapt them to particular investment environments. Moreover, to make them useful so as to serve the intended purpose, the models should be programmed so as to make implementation less cumbersome.

Keywords

Portfolio Optimisation; Uganda Securities Exchange (USE); Stocks; Modern Portfolio Theory (MPT); Markowitz; Portfolio Diversification; Frontier; Efficient Frontier; Constraints

Conflicts of Interest

The authors declare no conflicts of interest.

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