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	Std. Deviation
X	15%	50%
M	10%	20%
T-bills	5%	0%

The correlation coefficient between X and M is 2 .2

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.