Problem 1 (25 marks). Consider the following properties of the returns of stock 1, the returns of stock 2 and the returns of the market portfolio (m): Standard deviation of stock 1 01 = 0.30 Standard deviation of stock 2 02 = 0.30 Correlation between stock 1 and the market portfolio. P1m = 0.2 Correlation between stock 2 and the market portfolio P2,m=0.5 Standard deviation of the market portfolio Om = 0.2 Expected return of stock 1 E(r) = 0.08 Suppose further that the risk-free rate is 5%. a) According to the Capital Asset Pricing Model, what should be the expected return on the market portfolio and the expected return of stock 2? [10 marks] b) Suppose that the correlation between the return of stock 1 and the return of stock 2 is 0.5. What is the expected return, the beta, and the standard deviation of the return of a portfolio that has a 50% investment in stock 1 and a 50% investment in stock 2? [10 marks) c) Is the portfolio you constructed in part b) an efficient portfolio? Assuming the CAPM is true, could you build a combination of the market portfolio and the portfolio of part b) to increase the expected return of the market portfolio without changing the variance of the combined portfolio. [5 marks