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

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 37% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 5%.

Calculate the utility levels of each portfolio for an investor with A = 2. Assume the utility function is U = E(r) − 0.5 × Aσ2.

WBills WIndex U(A = 2)
0.0 1.0 (0.0069)
0.2 0.8
0.4 0.6
0.6 0.4
0.8 0.2
1.0 0.0
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