Question 3 (20 points): A universe of securities includes a risky stock (X), a stock-index fund (M), and T-bills. The data for the universe are:

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.

\begin{tabular}{|l|l|l|} \hline & Expected Return & Standard Deviation \\ \hline X & 20% & 60% \\ \hline M & 15% & 25% \\ \hline T-bill & 5% & 0% \\ \hline \end{tabular}