a.) Assume that you manage a risky portfolio with an expected rate of return of 22% and a standard deviation of 35%. The T-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 reward-to-volatility ratio (S) of your risky portfolio and your clients portfolio?

Your reward to volatility ratio______

Your clients reward to volatility ratio______

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 roughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 21% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 4%.

Calculate the expected return and variance of portfolios invested in T-bills and the S&P 500 index with weights as follows: (Leave no cells blank - be certain to enter "0" wherever required. Do not enter your answer as a percentage but in a decimal format. Round "Expected Return" to 4 decimal places and the "Variance" to 4 decimal places.)

WBills	WIndex	Expected Return	Variance
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.)Assume that you manage a risky portfolio with an expected rate of return of 21% and a standard deviation of 33%. The T-bill rate is 7%. Your clients degree of risk aversion is A = 2.7, assuming a utility function U = E(r) - A.

-What proportion, y, of the total investment should be invested in your fund? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "%" sign in your response.)

-What is the expected value and standard deviation of the rate of return on your clients optimized portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "%" sign in your response.)