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6. The Famous Markowitz Portfolio Problem (15 points) An investor wants to determine the safest way to structure a portfolio from several investments. Investment A produces an average annual return of 14% with a variance of 025. Investment B produces an average rate of return of 9% with a variance of .015 Investment C produces an average rate of return of 8% with a variance of .010. Investments A and B have a covariance of 0.00028 and investments A and C have a covariance of-0.006. Investments B and c have a covariance of 0.00125. Suppose that we need to decide the fraction of our money to put in investment A, B and C. Thus, we can simply use the decision variables A, B and C to denote the fraction (or percentage) of our money to put in investments A, B, and C respectively. Answer the following questions. (a) Suppose that the investor wants to achieve at least a 12% return. Develop an algebraic model to find the least risky way of doing this, using portfolio standard deviation as a measure of risk. (Recall that standard deviation = square root of variance.) (Handwrite answer, 5 points) (b) Construct an EXCEL model corresponding to your algebraic model from part (a). Give the formula sheet. (Hand in via Blackboard, 5 points) (c) Optimize your EXCEL model using Solver and give the Answer Report. From the Answer Report, what is the optimal solution and the optimal objective value? (Hand in via Blackboard, 5 points) 6. The Famous Markowitz Portfolio Problem (15 points) An investor wants to determine the safest way to structure a portfolio from several investments. Investment A produces an average annual return of 14% with a variance of 025. Investment B produces an average rate of return of 9% with a variance of .015 Investment C produces an average rate of return of 8% with a variance of .010. Investments A and B have a covariance of 0.00028 and investments A and C have a covariance of-0.006. Investments B and c have a covariance of 0.00125. Suppose that we need to decide the fraction of our money to put in investment A, B and C. Thus, we can simply use the decision variables A, B and C to denote the fraction (or percentage) of our money to put in investments A, B, and C respectively. Answer the following questions. (a) Suppose that the investor wants to achieve at least a 12% return. Develop an algebraic model to find the least risky way of doing this, using portfolio standard deviation as a measure of risk. (Recall that standard deviation = square root of variance.) (Handwrite answer, 5 points) (b) Construct an EXCEL model corresponding to your algebraic model from part (a). Give the formula sheet. (Hand in via Blackboard, 5 points) (c) Optimize your EXCEL model using Solver and give the Answer Report. From the Answer Report, what is the optimal solution and the optimal objective value? (Hand in via Blackboard, 5 points)