# 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?