Question

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%. Calculate the utility levels of each portfolio for an investor with A = 2. Assume the utility function is U-E1-0.5 Ao?. (Do not round intermediate calculations. Round your answers to 4 decimal places.) WBills Windex U(A-2) 0.1300 1.0 08 0.6 1.0

Answer 1

A B C B Wbills Windex 0 1 0.2 0. 8 0.4 0.6 0.6 0. 4 0.8 0. 2 1 0 D C Return on T bill 5% 5 % 5% 5 % 5 % 5% E D Return on portfolio (8%+5%) 13% 13% 13% 13% 13% 13% F G (A*C)+(B*D) SD = WINDEX U= E(r) - E (r) * SD(p) 0.5*A*(SD)^2 13.00% 20% 0.0900 11.40% 16% 0.0884 9.80% 12% 0.0836 8.20% 8% 0.0756 6.60% 4% 0.0644 5.00% 0% 0.0500