1.[12 points] Consider a bond return R0 and two risky returns R1 and R2 with 1 = 0.2, 2 = 0.25, 12 = 0.01, and r = 3% 1 = 7%, 2 = 10%. One way to find an investment strategy with low risk and high return is to minimize ^2 over all self-financed .

(a) (2pts) Write down the Lagrangian for this problem.

(b) (4pts) Compute the optimal portfolio for this problem.

(c) (3pts) What should an investor do with $500 and what would be the expected amount after one year using this specific choice of balancing against ? (d) (3pts) What is the mutual fund portfolio in this market? Justify your answer.