Question

1. 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%.

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
0.0	1.0	0.1300	0.0400	Example
0.2	0.8	?	?
0.4	0.6	?	?
0.6	0.4	?	?
0.8	0.2	?	?
1.0	0.0	?	?

2.

Assume that you manage a risky portfolio with an expected rate of return of 19% and a standard deviation of 34%. The T-bill rate is 8%.

Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund. What is the expected value and standard deviation of the rate of return on his portfolio?

Expected return	%?
Standard deviation	%?

3. Assume that you manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 30%. The T-bill rate is 6%. Your client chooses to invest 65% of a portfolio in your fund and 35% in a T-bill money market fund.

What is the reward-to-volatility ratio (S) of your risky portfolio and your client’s portfolio?

Your reward-to-volatility ratio	?
Client's reward-to-volatility ratio	?

Answer 1

Expected return=wbills*Tbill rate+windex*S&P500 return=wbills*5%+windex*13%

Variance=(windex*standard deviation of S&P500)^2

Wbills	Windex	Expected return	Variance
0	1	0.1300	0.04000
0.2	0.8	0.1140	0.02560
0.4	0.6	0.0980	0.01440
0.6	0.4	0.0820	0.00640
0.8	0.2	0.0660	0.00160
1	0	0.0500	0.00000

Expected return=70%*19%+30%*8%=15.7000%

Standard deviation=70%*34%=23.8000%

Your reward to volatility ratio=(18%-6%)/30%=0.40000

Client's reward to volatility ratio=(65%*18%+35%*6%-6%)/(65%*30%)=0.40000

Answer 2

Calculate the expected return and variance of portfolios invested in T-bills and the S&P500 index with weights as follows. Work to FOUR decimal places. (12) Portfolio WBills WIndex P1 0.0 1.0 P2 0.2 0.8 P3 0.4 0.6 P4 0.6 0.4 P5 0.8 0.2 P6 1.0 0.0 5.2 Calculate the utility levels of each portfolio of Problem 5.1 for an investor with A = 2. Which