Alicia wants to divide her budget between two investments, A and B, with respective expected returns r_A and r_B and risks _A and _B. Assume r_A < r_B and _A < _B. The correlation between the investment returns is .

a. Explain, using equations and a graph, how she should decide how to allocate her budget between the two investments given her utility function U(r,), where r is expected portfolio return and is portfolio risk.

b. Now suppose U(r,) = r - ² /2. Calculate what fraction of her budget she should invest in A.

c. Alicia invests in period 1 according to your answer in b). By the end of period 1, her budget has changed by the return realized in period 1. How should she invest in period 2?