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The aim of this report is to examine investment risk and returns by looking at the relationship between a stock and an index using the Markowitz Modern Portfolio theory. Monthly Data on IBM and Dow Jones were obtained from yahoo finance for the period 1995 to 2015. A linear regression was utilized to analyze the relationship between the Dow Jones index and the IBM stock returns. The results revealed that there is a positive relationship between IBM stock returns and the Dow Jones index. In their decision making, investors and policy makers are, recommended to additionally consider the micro and macro demand and supply forces that could possibly influence ROI. In other to avoid or reduce risk.