CHAPTER 7
THE CAPITAL ASSET PRICING MODEL
1.
E(r
P
) = r
f
+
β
P
[E(r
M
) – r
f
]
18 = 6 +
β
(14 – 6)
β
P
= 12/8 = 1.5
2.
If the covariance of the security doubles, then so will its beta and its risk premium.
The current
risk premium is 14 – 6 = 8%, so 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 /.14
D = 50
×
.14 = $7.00
At the new discount rate of 22%, the stock would be worth only $7/.22 = $31.82.
The increase
in stock risk has lowered its value by 36.36%.
13.
Since the stock's beta is equal to 1.2, its expected rate of return is 6 + 1.2(16 – 6) = 18%
E(r) =
and
.18 =
so
P
1
= $53
15.
Using the SML: 4 = 6 +
β
(16 – 6)
so
β
= –2/10 = –.2
17. a.
Since the market portfolio by definition has a beta of 1, its expected rate of return is 12%.
b.
β
= 0 means no systematic risk.
Hence, the portfolio's expected rate of return in market
equilibrium is the riskfree rate, 5%.
c.
Using the SML, the
fair
expected rate of return of a stock with
β
= –0.5 is:
E(r) = 5 + (–.5)(12 – 5) = 1.5%
The
actually
expected rate of return, using the expected price and dividend for next year is:
E(r) = 44/40 – 1 = .10 or 10%
Because the actually expected return exceeds the fair return, the stock is underpriced.
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 Fall '11
 Stapleton
 Capital Asset Pricing Model, Modern portfolio theory

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