Consider historical data showing that the average annual rate of return on the S

Question

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 35% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 3%.

Calculate the utility levels of each portfolio for an investor with A = 3. Assume the utility function is U =E(r) 0.5 × A2

Calculate the utility levels of each portfolio for an investor with A = 3. Assume the utility function is U = E(r) 0.5 × A2

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 35% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 3%.

Explanation / Answer

Average annual return above Treasury bill return = 8%

Treasury bill return = 3%

Value of A = 3

Standard deviation () = 35%

Expected return = 8% + 3%

                              = 11%

Expected return is 11%.

Utility levels of each portfolio for an investor is calculated below using following formula:

Utility levels (U) = E(r) 0.5 × A2

                          = 11% 0.5 × (3 × 35% ^2)

                          = 11% 18.375%

                          = 7.375%

Utility levels of each portfolio for an investor is 7.375%

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