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Consider historical data showing that the average annual rate of return on the S&P 500
portfolio over the past 80 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 Tbills and the S&P 500
index with weights given below
(Do not round intermediate calculations and round your
final answers to 4 decimal places. Enter your answers as numbers not in percentage.
Leave no cells blank  be certain to enter "0" wherever required)
:
W
Bills
W
Index
Expected return
Variance
0.0
1.0
0.2
0.8
0.4
0.6
0.6
0.4
0.8
0.2
1.0
0.0
Which of the following statements is true?
With a fixed riskfree rate, doubling the expected return and standard deviation of the risky
portfolio will double the Sharpe ratio.
Holding constant the risk premium of the risky portfolio, a higher riskfree rate will increase
the Sharpe ratio of investments with a positive allocation to the risky asset.
A lower allocation to the risky portfolio reduces the Sharpe (rewardtovolatility) ratio.
The higher the borrowing rate, the lower the Sharpe ratios of levered portfolios.
Assume that you manage a risky portfolio with an expected rate of return of 18% and a
standard deviation of 28%. The Tbill rate is 8%. Your client chooses to invest 70% of his
portfolio in your fund and 30% in a Tbill money market fund.
What is the rewardtovolatility ratio (
S
) of your risky portfolio and your client's portfolio?
(Round your answers to 4 decimal places.)
Your rewardtovolatility
ratio
Client's rewardtovolatility
ratio
Assume that you manage a risky portfolio with an expected rate of return of 18% and a
standard deviation of 28%. The Tbill rate is 8%.
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 Spring '11
 john

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