How Help 89% Fri 14:13 EF306 Exam Semester 1_2021.pdf (page 2 of 4) Q 1(a) [25 Marks] Consider that historical data shows that the average annual rate of return on the S&P 500 index portfolio over the past 90 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 index portfolio 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 described in the table below for an investor with risk aversion coefficient A = 2. Assume the utility function is U = E(1) - 0.5 x Ao2 (with notation as defined in class). Comment on the investor's portfolio preference from amongst these portfolios. Wpius (portfolio weighting in T-bills) 0.0 0.2 0.4 0.6 0.8 1.0 Windex (portfolio weighting S&P 500 index portfolio) 1.0 1 0.8 0.6 0.4 0.2 0.0 Support your answer with a discussion of utility theory and the functional form of the utility function U. How Help 89% Fri 14:13 EF306 Exam Semester 1_2021.pdf (page 2 of 4) Q 1(a) [25 Marks] Consider that historical data shows that the average annual rate of return on the S&P 500 index portfolio over the past 90 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 index portfolio 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 described in the table below for an investor with risk aversion coefficient A = 2. Assume the utility function is U = E(1) - 0.5 x Ao2 (with notation as defined in class). Comment on the investor's portfolio preference from amongst these portfolios. Wpius (portfolio weighting in T-bills) 0.0 0.2 0.4 0.6 0.8 1.0 Windex (portfolio weighting S&P 500 index portfolio) 1.0 1 0.8 0.6 0.4 0.2 0.0 Support your answer with a discussion of utility theory and the functional form of the utility function U