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Chapter 08 - Portfolio Theory and the Capital Asset Pricing Model
CHAPTER 8
Portfolio Theory and the Capital Asset Pricing Model
Answers to Problem Sets
1.
a.
(.5 x 0%) + (.5 x 14%) = 7%.
b.
With Perfect Positive Correlation:
Portfolio variance =
[(.5)2 x (28) 2] + [(.5) 2 x (26) 2] + 2 (.5 x .5 x 1 x 28 x 26) = 729
Standard deviation = the square root of 729 = 27%.
With Perfect Negative Correlation:
Portfolio variance =
[(.5) 2 x (28) 2] + [(.5) 2 x (26) 2] + 2 (.5 x .5 x -1 x 28 x 26) = 1
Standard deviation = the square root of 1 = 1%.
With no correlation:
Portfolio variance =
[(.5) 2 x (28) 2] + [(.5) 2 x (26) 2] + 2 (.5 x .5 x 0 x 28 x 26) = 365
Standard deviation = the square root of 365 = 19.1%.
c.
See Figure 1 below.
d.
No, measure risk by beta, not by standard deviation.
8-1
© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
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Chapter 08 - Portfolio Theory and the Capital Asset Pricing Model
Est. Time: 06- 10
2.
a.
Portfolio A (higher expected return, same risk)
b.
Cannot say (depends on investor’s attitude -toward risk)
c.
Portfolio F (lower risk, same expected return)
Est. Time: 01 - 05
3.
The long-term risk premium for securities as shown in Chapter 7 is 7.3%, and the
long-term standard deviation for security returns is 20.0%. Therefore the Sharpe
ratio = 7.3/20.0 = .365.
Est. Time: 01 - 05
4.
a.
Figure 8.11b: Diversification reduces risk (e.g., a mixture of portfolios A
and B would have less risk than the average of A and B).
b.
c.
Those along line A in Figure 8.11a
See Figure 2 below.
Est. Time: 01 - 05
5.
a.
See Figure 3 below.
8-2
© 2014 by McGraw-Hill Education. This is proprietary...