Optimal Investment Portfolio Based On Models of Risk and Expected Returns

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The most prominent problem facing every investor is to maximize returns and at the same time minimize the risk associated with the investment. Unfortunately, all the efforts by the investors to develop a reliable mathematical model to solve this problem optimally for both long term and short term in order to maximize profit, have proved futile. The aim of this thesis is to develop optimization models based on Dynamic Programming (DP) algorithm and Modern Portfolio Theory (MPT), and use them to determine the optimal returns and the risk involved. To achieve these aims, secondary data were collected from six financial institutions in Sunyani municipality from 2006 – 2011. The price series were normalized such that each commodity’s price changes have annualized volatility of ten percent (10%). Financial ratio such as coefficient of variation (CV) which measures the relative probability of investing in each of the investments was calculated and used to analyze the data. Based on this empirical data MPT and DP models were formulated and used to find the risk and the corresponding returns involved in various investments. From the analysis, it was found out that, the optimal investment return was GH¢1.51x104. Ghana Guinness Limited, StateInsurance Company,Zenith BankBarclays Bankwere the prime investments which contributed most to the optimal expected return. Government of Ghana’s Treasury bill and Ghana Commercial Bank were not profitable since their total contribution to the portfolio return were zero. No investor will be interested in investing in these financial institutions. There was a strong positive correlation coefficient between the optimal investments portfolio and the risk associated with investments. This suggests that short term investments in these portfolios are not profitable.
A thesis submitted to the College of Science, Kwame Nkrumah University of Science and Technology in partial fulfilment of the requirement for the award of Master of Science in Industrial Mathematics