Question 3 : A universe of securities includes a risky stock (X), a stock-index fund (M), and T-bills. The data for the universe are:

Expected Return Standard Deviation

X 20% 60%

M 15% 25%

T-bill 5% 0%

The correlation coefficient between X and M is -0.8.

a. Draw the opportunity set of securities X and M.

b. Find the optimal risky portfolio (O), its expected return, standard deviation, and Sharpe ratio. Compare with the Sharpe ratio of X and M.

c. Find the slope of the CAL generated by T-bills and portfolio O.

d. Suppose an investor places 2/9 (i.e., 22.22%) of the complete portfolio in the risky portfolio O and the remainder in T-bills. Calculate the composition of the complete portfolio, its expected return, SD, and Sharpe ratio