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 6%.

Calculate the utility levels of each portfolio for an investor with A = 2. Assume the utility function is U = E(r) 0.5 × A2. (Do not round intermediate calculations. Round your answers to 4 decimal places.)

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

Explanation / Answer

1 2 3 4 5 6 (1*2)+(3*4) 3*35% 6^2 Wbills Rbills Windex R index Return of portfolio Standard deviation of portfolio Variance of Portfolio U 0 6% 1 14% 0.14 0.35 0.1225 0.0175 0.2 6% 0.8 14% 0.124 0.28 0.0784 0.0456 0.4 6% 0.6 14% 0.108 0.21 0.0441 0.0639 0.6 6% 0.4 14% 0.092 0.14 0.0196 0.0724 0.8 6% 0.2 14% 0.076 0.07 0.0049 0.0711 1 6% 0 14% 0.06 0 0 0.06 U = E(R ) - 0.50*A*Variance 0.14-(0.5*2*0.1225) 0.0175 0.124-(0.5*2*0.0784) 0.0456 0.108-(0.5*2*0.0441) 0.0639 0.092-(0.5*2*0.0196) 0.0724 0.076-(0.5*2*0.0049) 0.0711 0.06-(0.5*2*0) 0.06

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