# 1. Consider historical data showing that the average annual rate of return on the S&P 500…

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

?