Sample Problems
—
Risk and rates of return
1.
An investor is forming a portfolio by investing $50,000 in stock A which has a beta of 1.50, and
$25,000 in stock B which has a beta of 0.90.
The return on the market is equal to 6 percent and
Treasury bonds have
a yield of 4 percent.
What is the required rate of return on the investor’s
portfolio?
2.
Given the following probability distribution, what is the expected return and the standard deviation of
returns for Security J?
State
P
i
r
j
1
0.2
10%
2
0.6
15%
3
0.2
20%
3.
You hold four stocks in your portfolio
—
Stock A, Stock B, Stock C, and Stock D.
Your portfolio beta
is 1.2.
Stock C constitutes 40 percent of the dollar value of your holdings and has a beta of 0.60.
If
you sell all of your holdings in Stock C, and replace them with an equal investment in Stock E (which
has a beta of 0.95), your new portfolio beta will be
.
4.
If R
f
= 7%, R
M
= 12%, and r
j
= 15%, what is the stock's beta?
5.
You are given the following distribution of dollar returns:
Probability
Return
40%
50%
10%
$30
$25
$25
What is the standard deviation of the expected dollar returns?
6.
If the riskfree rate is 7 percent, the expected return on the market is 10 percent, and the expected
return on Security J is 13 percent, what is the beta of Security J?
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 Fall '10
 hamdibilici
 Stock J, J K L Portfolio

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