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Chapter 09  The Capital Asset Pricing Model
91
BA 4814 & BA 5814  INVESTMENTS
CHAPTER 9: THE CAPITAL ASSET PRICING MODEL
PROBLEM SETS
1.
E(r
P
) = r
f
+
β
P
[E(r
M
) – r
f
]
18 = 6 +
β
P
(14 – 6)
⇒
β
P
= 12/8 = 1.5
2.
If the security’s correlation coefficient with the market portfolio doubles (with all other
variables such as variances unchanged), then beta, and therefore the risk premium, will
also double. The current risk premium is: 14 – 6 = 8%
The new risk premium would be 16%, and the new discount rate for the security would
be: 16 + 6 = 22%
If the stock pays a constant perpetual dividend, then we know from the original data that
the dividend (D) must satisfy the equation for the present value of a perpetuity:
Price = Dividend/Discount rate
50 = D/0.14
⇒
D = 50
×
0.14 = $7.00
At the new discount rate of 22%, the stock would be worth: $7/0.22 = $31.82
The increase in stock risk has lowered its value by 36.36%.
3.
a.
False.
β
= 0 implies E(r) = r
f
, not zero.
b.
False. Investors require a risk premium only for bearing systematic
(undiversifiable or market) risk. Total volatility includes diversifiable risk.
c.
False. Your portfolio should be invested 75% in the market portfolio and 25% in
Tbills. Then:
β
P
= (0.75
×
1) + (0.25
×
0) = 0.75
4.
The appropriate discount rate for the project is:
r
f
+
β
[E(r
M
) – r
f
] = 8 + [1.8
×
(16 – 8)] = 22.4%
Using this discount rate:
×
+
−
=
+
−
=
∑
=
15
[$
40
$
224
.
1
15
$
40
$
NPV
10
1
t
t
Annuity factor (22.4%, 10 years)] = $18.09
The internal rate of return (IRR) for the project is 35.73%. Recall from your
introductory finance class that NPV is positive if IRR > discount rate (or, equivalently,
hurdle rate). The highest value that beta can take before the hurdle rate exceeds the IRR
is determined by:
35.73 = 8 +
β
(16 – 8)
⇒
β
= 27.73/8 = 3.47
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92
Chapter 09  The Capital Asset Pricing Model
93
5.
a.
Call the aggressive stock A and the defensive stock D. Beta is the sensitivity of the
stock’s return to the market return, i.e., the change in the stock return per unit
change in the market return. Therefore, we compute each stock’s beta by
calculating the difference in its return across the two scenarios divided by the
difference in the market return:
00
.
2
25
5
38
2
A
=
−
−
−
=
β
30
.
0
25
5
12
6
D
=
−
−
=
β
b.
With the two scenarios equally likely, the expected return is an average of the two
possible outcomes:
E(r
A
) = 0.5
×
(–2 + 38) = 18%
E(r
D
) = 0.5
×
(6 + 12) = 9%
c.
The SML is determined by the market expected return of [0.5(25 + 5)] = 15%,
with a beta of 1, and the Tbill return of 6% with a beta of zero. See the following
graph.
Expected Return  Beta Relationship
0
5
10
15
20
25
30
35
40
0
0.5
1
1.5
2
2.5
3
Beta
Expected Return
SML
DM
A
α
A
The equation for the security market line is:
E(r) = 6 +
β
(15 – 6)
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94
d.
Based on its risk, the aggressive stock has a required expected return of:
E(r
A
) = 6 + 2.0(15 – 6) = 24%
The analyst’s forecast of expected return is only 18%. Thus the stock’s alpha is:
α
A
= actually expected return – required return (given risk)
= 18% – 24% = –6%
Similarly, the required return for the defensive stock is:
E(r
D
) = 6 + 0.3(15 – 6) = 8.7%
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This note was uploaded on 11/13/2009 for the course BUSINESS A buscom taught by Professor Caglarsenel during the Spring '09 term at Marmara Üniversitesi.
 Spring '09
 caglarsenel
 Pricing, Capital Asset Pricing Model

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