and CV
A
> CV
B
.
65
According to the Security Market Line (SML) equation, an increase in beta will increase a
company’s expected return by an amount equal to the market risk premium times the change in
beta.
For example, assume that the riskfree rate is 6 percent, and the market risk premium is 5
percent.
If the company’s beta doubles from 0.8 to 1.6 its expected return increases from 10
percent to 14 percent.
Therefore, in general, a company’s expected return will not double when
its beta doubles.
SOLUTIONS TO ENDOFCHAPTER PROBLEMS
61
Investment
Beta
$20,000
0.7
35,000
1.3
Total
$55,000
($20,000/$55,000)(0.7) + ($35,000/$55,000)(1.3) = 1.08.
62
r
RF
= 4%; r
M
= 12%; b = 0.8; r
s
= ?
r
s
= r
RF
+ (r
M
 r
RF
)b
= 4% + (12%  4%)0.8
= 10.4%.
28
69
Old portfolio beta =
5,000
7
$
00
0
,
70
$
(b) +
5,000
7
$
00
0
,
5
$
(0.8)
1.2 = 0.9333b + 0.0533
1.1467 = 0.9333b
1.229 = b.
New portfolio beta = 0.9333(1.229) + 0.0667(1.6) = 1.25.
Alternative Solutions:
1.
Old portfolio beta = 1.2 = (0.0667)b
1
+ (0.0667)b
2
+...+ (0.0667)b
20
1.2 = (
b
i
)(0.0667)
b
i
= 1.2/0.0667 = 18.0.
New portfolio beta = (18.0  0.8 + 1.6)(0.0667) = 1.253 = 1.25.
2.
b
i
excluding the stock with the beta equal to 0.8 is 18.0  0.8 = 17.2, so the beta of the
portfolio excluding this stock is b = 17.2/14 = 1.2286.
The beta of the new portfolio is:
1.2286(0.9333) + 1.6(0.0667) = 1.1575 = 1.253.
29
610
Portfolio beta =
$4,000,000
$400,000
(1.50) +
$4,000,000
$600,000
(0.50)
+
$4,000,000
$1,000,000
(1.25) +
$4,000,000
$2,000,000
(0.75)
= 0.1)(1.5) + (0.15)(0.50) + (0.25)(1.25) + (0.5)(0.75)
= 0.15  0.075 + 0.3125 + 0.375 = 0.7625.
r
p
= r
RF
+ (r
M
 r
RF
)(b
p
) = 6% + (14%  6%)(0.7625) = 12.1%.
Alternative solution:
First compute the return for each stock using the CAPM equation [r
RF
+ (r
M
 r
RF
)b], and then compute the weighted average of these returns.
r
RF
= 6% and r
M
 r
RF
= 8%.
Stock
Investment
Beta
r
=
r
RF
+
(r
M

r
RF
)b
Weight
A
$
400,000
1.50
18%
0.10
B
600,000
(0.50)
2
0.15
C
1,000,000
1.25
16
0.25
D
2,000,000
0.75
12
0.50
Total
$4,000,000
1.00
r
p
= 18%(0.10) + 2%(0.15) + 16%(0.25) + 12%(0.50) = 12.1%.
613
The answers to a, b, and c are given below:
¯
A
¯
B
Portfolio
2009
(20.00%)
(5.00%)
(12.50%)
30
2010
42.00
15.00
28.50
2011
20.00
(13.00)
3.50
2012
(8.00)
50.00
21.00
2013
25.00
12.00
18.50
Mean
11.80
11.80
11.80
Std Dev
25.28
24.32
16.34
d.
A riskaverse investor would choose the portfolio over either Stock A or Stock B alone, since
the portfolio offers the same expected return but with less risk.
This result occurs because
returns on A and B are not perfectly positively correlated (ρ
AB
= 0.13).
Chapter 25
Portfolio Theory and Asset Pricing Models
ANSWERS TO ENDOFCHAPTER QUESTIONS
251
a.
A portfolio is made up of a group of individual assets held in combination.
An asset
that would be relatively risky if held in isolation may have little, or even no risk if
held in a welldiversified portfolio.
The feasible, or attainable, set represents all portfolios that can be constructed from a given
set of stocks.
This set is only efficient for part of its combinations.
An efficient portfolio is that portfolio which provides the highest expected return for any
degree of risk.
Alternatively, the efficient portfolio is that which provides the lowest degree
of risk for any expected return.
The efficient frontier is the set of efficient portfolios out of the full set of potential portfolios.
On a graph, the efficient frontier constitutes the boundary line of the set of potential
portfolios.
31
b.
An indifference curve is the risk/return tradeoff function for a particular investor and reflects
that investor's attitude toward risk. The indifference curve specifies an investor's required rate
of return for a given level of risk.
The greater the slope of the indifference curve, the greater
is the investor's risk aversion.
The optimal portfolio for an investor is the point at which the efficient set of portfoliosthe