Question 2 (20 marks) Consider historical data showing that the average annual rate of return on the S & P 500 portfolio over the past 90 years has averaged roughly 8% more than the Treasury bill return, and that the S & P 500 standard deviation has been about 20% per year. Assume these values are representative of investors' expectation for future performance and that the current T-bill rate is 5%. (a) Calculate the expected return and variance of portfolios invested in T-bills and the S&P 500 index with weights as follows: W bills Windes 0.0 0.2 0.4 0.6 0.8 1.0 1.0 0.8 0.6 0.4 0.2 0 TO (9 marks) (b) Calculate the utility levels of each portfolio of problem (a) for an investor with A = 3. What do you conclude? (7 marks) (C) Repeat problem (b) for an investor with A = 5. What do you conclude? (4 marks) Question 2 (20 marks) Consider historical data showing that the average annual rate of return on the S & P 500 portfolio over the past 90 years has averaged roughly 8% more than the Treasury bill return, and that the S & P 500 standard deviation has been about 20% per year. Assume these values are representative of investors' expectation for future performance and that the current T-bill rate is 5%. (a) Calculate the expected return and variance of portfolios invested in T-bills and the S&P 500 index with weights as follows: W bills Windes 0.0 0.2 0.4 0.6 0.8 1.0 1.0 0.8 0.6 0.4 0.2 0 TO (9 marks) (b) Calculate the utility levels of each portfolio of problem (a) for an investor with A = 3. What do you conclude? (7 marks) (C) Repeat problem (b) for an investor with A = 5. What do you conclude? (4 marks)