Consider the following statistics of the returns of Stock A, Stock B and the market (m):

s_A = 0.20 corr_A,m = 0.4

s_B = 0.30 corr_B,m = 0.7

s_m = 0.15

E(r_m) = 0.10

Suppose further that the risk-free rate is 5%.

(a) According to the Capital Asset Pricing Model, what should be the expected return of Stock A and of Stock B? [Hint: This is an open-book exam.] (8 marks)

(b) Suppose that the correlation between the return of Stock A and the return of Stock B is 0.5. What are the expected return and the standard deviation of the return of a portfolio that has a 40% investment in Stock A and a 60% investment in Stock B? (6 marks)

(c) Assume that the Capital Asset Pricing Model is valid. How could you construct a new portfolio (P) using the market portfolio (m) and the risk-free asset that has the same expected return as the portfolio you considered in part (b)? What is the standard deviation of the return of this portfolio (P)? (9 marks)

(d) i) Suppose that the correlation between the return of Stock A and the return of Stock B is -0.7. What are the expected return and the standard deviation of the return of a portfolio that has a 40% investment in Stock A and a 60% investment in Stock B? Explain the difference in value between the standard deviations of the return of the portfolios in parts (c) and (d). (6 marks)

ii) Consider an investment that is made up of a combination of the risky portfolio in (i) and the risk-free asset. In this case, would it be advisable to switch to a portfolio made up of the market portfolio and the risk-free asset? In other words, is the market portfolio mean-variance efficient in this case? [Hint: Consider the measure that captures the risk- return trade-off.]