Alicia wants to divide her budget between two investments, A and B, with respective expected returns and and risks and . Assume < and < . 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 (, ), where is expected portfolio return and is portfolio risk.

b) Now suppose (, ) = 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 realised in period 1. How should she invest in period 2?