5Chapter 8 CFIN5
Chapter 8 Solutions
8-1 a.
r
ˆ
= (0.2)(19%) + (0.7)(9%) + (0.1)(4%) = 10.5%
b.
2 2 2
= (0.2)(19 – 10.5 + (0.7)(9 – 10.5 + (0.1)(4 – 10.5 20.25 4.5%
) ) )
s = =
c.
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accessible website, in whole or in part.
4.5%
= = 0.429
CV 10.5%
Solutions
8-2 a.
r
ˆ
= (0.45)(32%) + (0.35)(-4%) + (0.2)(-20%) = 9.0%
b.
2 2 2
= (0.45)(32 – 9 + (0.35)( 4 9 + (0.2)( 20 9 465.4 21.573%
) ) )
s – – – – = =
c.
2
21.573%
= = 2.397
CV 9%
Chapter 8 CFIN5
8-3 a.
A
ˆ
r
= (0.3)(30%) + (0.2)(10%) + (0.5)(-2%) = 10%
= (0.3)(5%) + (0.2)(15%) + (0.5)(25%) = 17%
b.
2 2 2
A
= (0.3)(30 – 10 + (0.2)(10 10 + (0.5)( 2 10 192 13.856%
) ) )
s – – – = =
2 2 2
B = (0.3)(5 -17 + (0.2)(15 17 + (0.5)(25 17 76 8.718%
) ) )
s – – = =
c.
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accessible website, in whole or in part.
A
13.865%
= = 1.386
CV 10%
ˆ
r
Stock M 6.0% 4.0% 0.667 = 4%/6%
Stock N 18.0 12.0 0.667 = 12%/18%
Stock O 12.0 7.0 0.583 = 7%/12%
According to the CV measure, Stock O has the best risk/return relationship; its risk per unit of return is
the lowest at 0.583.
8-5 To answer the question, the coefficient of variation for each investment must be computed.
Investment
ˆ
r
CV
F 16.0% 7.0% 0.438 = 7%/16%
8-6 $9,000 invested in one stock with an 18 percent expected return
Chapter 8 CFIN5
8-8 Portfolio beta:
Investment Weight Beta Portfolio beta
(1) (2) (3) (4) = (2) x (3)
$ 350,000 0.35 = $350,000/$1,000,000 1.0 0.35
Alternative solution: First compute the return for each stock using the CAPM equation
[rRF + (rM – rRF)βj], and then compute the weighted average of these returns.
1.00 11.40%
rp = 9.0%(0.35) + 4.2%(0.25) + 18.0%(0.40) = 11.4%.
8-9 a.
ABC
ˆ
r
= (0.1)(22%) + (0.6)(12%) + (0.3)(2%) = 10.0%
RST
ˆ
r
= (0.1)(-2%) + (0.6)(12%) + (0.3)(30%) = 16.0%
b.
2 2 2
ABC
= (0.1)(22 -10 + (0.6)(12 10 + (0.3)(2 10 36 6.000%
) ) )
s – – = =
2 2 2
RST = (0.1)( 2 16 + (0.6)(12 16 + (0.3)(30 16 100.8 10.040%
) ) )
s – – – – = =
c. Compute the expected return of the portfolio
Probability rABC rRST Portfolio Return: 60% ABC; 40% RST
0.1 22.0% -2.0% 12.4% = 0.6(22%) + 0.4(–2%)
0.6 12.0 12.0 12.0 = 0.6(12%) + 0.4(12%)
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accessible website, in whole or in part.
Chapter 8 CFIN5
8-13 Information that is given:
Total current value $200,000
8-14 rRF = 3%
RRM = 6%
8-15 rRF = 4%
rM = 12%
8-16 rRF = ?
rM = 12.5%
β = 0.8
rZR = 11%
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accessible website, in whole or in part.
Chapter 8 CFIN5
8-17 rRF = 5%
rM = 11%
βV = 2.0
βW = 0.5
8-18 Original information:
rQ = 11%
rRF = 4%
rM = 9%
Based on this information, we can compute the stock’s beta coefficient:
8-19 Given information:
rRF = 3.5%
RPM = 7%
βU = 0.9
P0 = $28
D0 = $1.75
g = 4%
Chapter 8 CFIN5