7. Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 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' expectations for future performance and that the current T-bill rate is 5%. Calculate the expected return, variance and standard deviation of portfolios invested in T-bills and the S&P 500 index with weights as follows:

8. Assume that you manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 28%. The T-bill rate is 8%. Your clients degree of risk aversion is A = 3.5 , assuming a utility function U = E(r) A . a) What proportion of the total investment should be invested in your fund? b) What is the expected value and standard deviation of the rate of return on your clients optimized portfolio?

7. Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 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' expectations for future performance and that the current T-bill rate is 5%. Calculate the expected return, variance and standard deviation of portfolios invested in T-bills and the S&P 500 index with weights as follows: Standard Deviation W Bills Expected Return Variance w Index 1.0 0.0 0.2 0.8 0.4 0.6 0.6 0.4 0.8 0.2 1.0 0.0 8. Assume that you manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 28%. The T-bill rate is 8%. Your client's degree of risk aversion is A = 3.5, assuming a utility function U = E(r) 12A02. a) What proportion of the total investment should be invested in your fund? b) What is the expected value and standard deviation of the rate of return on your client's optimized portfolio