Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 80 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%.

1. Calculate the expected return and variance of portfolios invested in T-bills and the S&P 500 index with weights as follows:

i. Calculate the utility levels of each portfolio of Question 1 for an investor with A = 2. What do you conclude?

ii. Repeat Question for an investor with A = 3. What do you conclude?

Use these inputs for Questions 2: You manage a risky portfolio with expected rate of return of 18% and standard deviation of 28%. The T-bill rate is 8%.

2. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund. What is the expected value and standard deviation of the rate of return on his portfolio?