A pension fund manager is considering three mutual funds. The first is a stock fund (S) (with expected return 15% and standard deviation 30%), the second is a long-term government and corporate bond fund (B) (with expected return 7% and standard deviation 10%), and the third is a T-bill money market fund (with expected return 3%). The correlation between the stock fund (S) and the bond fund (B) is 0.5. Note that in this scenario, the stock fund and bond fund are risky assets, while the T-bill money market fund is risk-free.

(a) With careful estimation and calculation, the manager found the optimal proportions of each asset in the optimal risky portfolio (the point where the Capital Allocation Line is tangent to the efficient frontier) as follows: WS=0.25 and WB=0.75. That is, they put a 25% weight on (S) and a 75% weight on (B). Solve for the expected return of the optimal risky portfolio.

(b) Solve for the standard deviation of the optimal risky portfolio.

(b.1) Suppose now the best feasible CAL available to investor has the slope coefficient of 0.40. If you require that your portfolio on this best feasible CAL yield an expected return of 8%, what is the standard deviation of your portfolio?

(b.2) What is the proportion invested in the T-bill fund to achieve an expected return of 8%?