(10 Marks) Consider two utility maximizing investors (A and B) with negative exponential utility functions. Suppose that there is a risk-free asset and that 2 returns on risky assets are normally distributed. Hence, the preferences of these Investors can be described by EU = ep (1/t) S²_p1

where ep denotes the expected return on the Investors portfolio, sp denotes the standard deviation of returns, and t is the Investors risk tolerance. The optimal portfolio for Investor A has the expected return 8% and standard deviation of returns 12%. It is optimal for Investor B to invest all her holdings in Stock 1, which has an expected return 10% and a standard deviation of returns 20%.

(a) Find the equation for the efficient frontier. Graph the efficient frontier in (ep, sp) space where ep is the expected return on the portfolio and sp the standard deviation of the return on the portfolio. Mark in the graph the optimal portfolio choices for the two investors and the risk-free asset. Find risk tolerance of the two investors. (3.5 marks)

(b) Suppose an Investor C appears on the market. Her preferences are described by EU = ep 0.01s_p² . Is a portfolio with the expected return of 8.75% percent and a standard deviation of 16% optimal for Investor C? Justify your answer. (1.5 marks)

Now suppose that the riskless asset disappears from the market. Instead, Stock 2 with an expected return e2 = 6% and standard deviation s2 = 10% is being traded. Assume that the correlation between the returns on Stock 1 and Stock 2 is 0.5 (i.e. the correlation coefficient r12 = 0.5)

(c) Find the minimum variance portfolio. What is the expected return and variance of this portfolio? (2.5 marks)

(d) Suppose the investors expected utility function is given by: EU = ep 0.02v_p. What is the investors optimal portfolio, assuming she is an expected utility maximizer? (2.5 marks)