An investment portfolio is a collection of financial assets consisting of investment tools such as stocks, bonds, and bank deposits, among others, which are held by a person or a group of persons. Constructing a portfolio with standardized optimization remains a myth in Ghana and hence this study displayed how the Markowitz model can be applied on the Ghana Stock Exchange and also unraveled the most efficient portfolio among selected stocks to the relief of the investor. Historical monthly data of the stock returns from 2011 to 2016 was used for the study. The study revealed that, GCB Bank limited had the best average returns (returns of 4.2%) with a risk of 13.1% followed by CAL (returns of 3.5%) and 11.7% risk. UGL had the lowest risk (risk of 6.8%) and lowest average returns of 2.1%. A risk lover may go in for GCB and CAL while an investor who is completely risk averse can opt for UGL since it comes with the lowest risk. A two-way combination of the portfolios also concluded that, the most efficient portfolio is the combination of GCB and CAL and recommended that a risk tolerant investor can invest all his assets in GCB while a risk averse investor can invest 39.21% of his assets in GCB and 60.79% in CAL. In terms of expected returns, a combination of CAL and GCB bank limited gives the highest returns of about 3.9% with a risk of 10.6%, followed by the combination of TOTAL and GCB with expected returns of about 3.40% and a high risk of 12.3%. The relatively high expected return of the combination of TOTAL and GCB could not reflect in the Sharpe ratio because of the high level of risk which implies that the portfolio cannot compensate much for this high level of risk. Also, CAL and GCB achieving the highest Sharpe ratio shows that, this portfolio is expected to offer the best compensation for the risk taken by an investor and therefore the most efficient portfolio for investor. The lowest risk (which is what the risk averse investor is interested in) was achieved from the combination of HFC and UGL which is 5.2% with a Sharpe ratio of 6.7% and a covariance of -0.00051.