Risk – Return Analysis of Optimal Portfolio using the Sharpe Ratio

Thumbnail Image
Journal Title
Journal ISSN
Volume Title
The Modern portfolio Theory is based on Harry Markowitz’s 1952 work on mean – variance portfolios. He stated that a rational investor should either maximize his expected return for a given level of risk, or minimize his risk for a given expected return. These two principles lead to an efficient frontier of portfolios, among which the investor is free to choose. Fifty years on, there are no widely accepted practical implementations of mean – variance portfolio theory. The mean – variance approach puts excessive weights on assets with large excess returns, regardless of possible estimation errors. It yields unstable portfolios and extra gains do not make up for the excess transaction costs. The goal of this project is to develop robust portfolio optimization methods. We develop a multi - factor objective function reflecting our investment preferences and solve the subsequent optimization problem using the Sharpe’s ratio. Many investors and portfolio managers always seek maximum returns with relative low risk or conversely, minimum risk with maximum expected returns. Which model or approach best meets investor’s investment decisions and portfolio selection. The Markowitz model in 1952 and subsequently 1959, amongst other things seeks to address such dilemma faced by investors. In this thesis, we shall explore the Markowitz model in constructing optimal stock portfolio, analyze its modern relevance, and also predict its future durability in finance theory. We explore the mean – variance approach by Harry M. Markowitz in portfolio selection in single – period index model, and provides the basis for many important financial economic advances, including the Sharpe single – index model (Sharpe, 1964). This thesis highlights the concept of utility function in determining the risk preference of investors. Again, we analyze diversification under Markowitz portfolio construction and its impact on risk minimization, given unsystematic risk of a corporate organization. We shall be dealing with optimization problem like maximize expected return of a portfolio subject to a given level of risk, or conversely minimize risk subject to a given expected return (Markowitz, 1952, 1959, 1991), Merton (1972), Kroll, Levy and Markowitz (1984). In addition, we shall use some statistical parameters such as mean, variance (standard deviation), co – variance and correlation for our model formulation of the Markowitz framework.
A Thesis submitted to the School of Graduate Studies, Kwame Nkrumah University of Science and Technology, Kumasi, in partial fulfilment of the requirements for the Degree of Master of Science in Industrial Mathematics,