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 weights as follows:

Wbill	Windex
0	1
0.2	0.8
0.4	0.6
0.6	0.4
0.8	0.2
1	0

B. Calculate the utility levels (i.e., use the utility function, U = E(r) - 1/2*A*^2) of each portfolio of Problem A for an investor with A = 2. What do you conclude?

C. Repeat Problem B for an investor with A = 3. What do you conclude?