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 20% per year. Assume these values are representative of investors expectations for future performance and that the current T-bill rate is 5%.

a)Calculate the expected return and variance of portfolios invested in T-bills and the S&P 500 index with the following weights. [5]

Weight in T-Bills	Weight in S& P
0	1.0
0.2	0.8
0.4	0.6
0.6	0.4
0.8	0.2
1	0

b) Calculate the utility levels of each portfolio of Problem in a) for an investor with A =2. What do you conclude? [5]

c) Repeat Problem b) for an investor with A = 3. What do you conclude?