Assume the CAPM holds. Consider three feasible portfolios of stocks X, Y and Z with the following return characteristics:

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Portfolio Y Z Expected return 7.5% 5% 10% Standard deviation 5% 10% 15% a) Explain why beta is the appropriate measure of risk in this world. (5 marks) b) Portfolio Y is known to be uncorrelated with the market. Explain why this property implies that the risk-free rate in the economy is 5%. (5 marks) c) It is known that one of the portfolios X, Y, Z lies on the efficient frontier (which includes the risk-free asset). Which portfolio is efficient? Explain/justify your answer. (5 marks) d) An investment manager approaches you and offers you an investment product with a claimed expected return of 12% and standard deviation of 20%. Should you accept this investment? Why/why not? If not, show how the manager can optimally create a portfolio with an identical return volatility to his proposed portfolio but with a superior expected return. Illustrate your answer graphically, making sure to label all relevant elements of your picture. (6 marks) e) Consider an investor who invests $50,000 in a portfolio consisting of X and Z. $10,000 of that investment was funded with risk-free borrowing. The expected return of the investor's portfolio is 9.375%. i. Calculate the dollar amounts invested in each of X and Z. (4 marks) ii. If the correlation between X and Z is 2/3, what is the standard deviation of the investor's portfolio? (2 marks) f) Show that any portfolio on the Capital Market Line (CML) with a positive weight in the market portfolio is perfectly correlated with the market portfolio. Interpret this result. (6 marks) Portfolio Y Z Expected return 7.5% 5% 10% Standard deviation 5% 10% 15% a) Explain why beta is the appropriate measure of risk in this world. (5 marks) b) Portfolio Y is known to be uncorrelated with the market. Explain why this property implies that the risk-free rate in the economy is 5%. (5 marks) c) It is known that one of the portfolios X, Y, Z lies on the efficient frontier (which includes the risk-free asset). Which portfolio is efficient? Explain/justify your answer. (5 marks) d) An investment manager approaches you and offers you an investment product with a claimed expected return of 12% and standard deviation of 20%. Should you accept this investment? Why/why not? If not, show how the manager can optimally create a portfolio with an identical return volatility to his proposed portfolio but with a superior expected return. Illustrate your answer graphically, making sure to label all relevant elements of your picture. (6 marks) e) Consider an investor who invests $50,000 in a portfolio consisting of X and Z. $10,000 of that investment was funded with risk-free borrowing. The expected return of the investor's portfolio is 9.375%. i. Calculate the dollar amounts invested in each of X and Z. (4 marks) ii. If the correlation between X and Z is 2/3, what is the standard deviation of the investor's portfolio? (2 marks) f) Show that any portfolio on the Capital Market Line (CML) with a positive weight in the market portfolio is perfectly correlated with the market portfolio. Interpret this result. (6 marks)