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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:

1. Calculate the utility levels of each portfolio of Question 1 for an investor with A = 2. What do you conclude?
2. Repeat Question 2 for an investor with A = 3. What do you conclude?