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’ expectations for future performance and that the current T-bill rate is 5%. Required:
Calculate the utility levels of each portfolio for an investor with A = 3.

Assume the utility function is U =E(r) - 0.5 x A σ^2

Wbills Windex U (A=2)
0.0 1.0
0.2 0.8
0.4 0.6
0.6 0.4
0.8 0.2
1.0 0.0