a) Suppose you manage a risky portfolio with an expected rate of return of 22% and a standard deviation of 35%. The Treasury bill rate is 6%. Your client chooses to invest 75% of a portfolio in your fund and 25% in a T-bill money market fund.

What is the relationship between reward and volatility ( S ) of your risky portfolio and your client's portfolio?

Your reward to volatility ratio______

Relationship between the reward and the volatility of your clients______

b.) Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has averaged about 8% more than the yield on Treasury bills and that the standard deviation of the S&P 500 has been approximately 21% per year. Assume that these values are representative of investors' expectations for future performance and that the current rate on Treasury bills is 4%.

Calculate the expected return and variance for portfolios invested in Treasury bills and the S &P 500 Index with weights as follows: 

W -bills	W- index	expected return	Difference
0.2	0.8	0.1040	0.0282	Example
0.4	0.6	?		?
0.0	1.0	?		?
0.8	0.2	?		?
1.0	0.0	?		?
0.6	0.4	?		?

c.) Suppose you manage a risky portfolio with an expected rate of return of 21% and a standard deviation of 33%. The Treasury bill rate is 7%. Your client's degree of risk aversion is A = 2.7, assuming a utility function U = E ( r ) - ½ A σ².

-What proportion, and , of the total investment should be invested in your fund? 

-What is the expected value and standard deviation of the rate of return of your client's optimized portfolio?