Question: I. Multiple Objective Optimization Consider a situ...

I. Multiple Objective Optimization Consider a situation where you have 3 stocks (X, Y and Z) in which to invest. Stock X has an expected return of 10%, whereas Stock Y and Z have respective returns of 12% and 7% respectively. The variance of Stocks X, Y and Z are respectively .025, .03 and .004. The covariances between the stocks are as follows: .015 between Stocks X and Y; .005 between Stocks X and Z; and -.002 between Stocks Y and Z.

1. Letting x, y and z denote the fraction of your investment money to invest in the stocks X, Y and Z respectively, formulate your problem of minimizing risk (as given by your portfolio standard deviation) while exactly getting an expected return of 0.07.

2. What is the optimal value of the objective and the optimal values of x, y and z in the above problem? Indicate your answer in the corresponding row of the Table below, including the corresponding fractions of your money to invest in each Stock? Include your Answer Sheet as a worksheet in your Excel file.

3. Repeat question 2 for Expected portfolio returns of .08, .09, .10, .11 and .12.

4. Using your answers to questions 1 and 2, approximate the Trade-off Curve of Portfolio Standard Deviation (on the vertical axis) with respect to Portfolio Expected Return (on the horizontal axis) using a Scatter Chart.

5. Now approximate the Trade-off Curve of Portfolio Standard Deviation (on the horizontal axis) with respect to Portfolio Expected Return (on the vertical axis) using a Scatter Chart.

Table :

Expected Portfolio Return 0.07 0.08 0.09 0.1 0.11 0.12

Port Std Dev

Fraction in X

Fraction in Y

Fraction in Z