стр. 87 
10 0.3 3

25 0.4 13 169 67.6
10


12 U* = 181
P= 
Since U* = 181, U = f i= 13.45%.
Return and Measures of Risk. Stocks A and B have the following probability distributions of
7.2
possible future returns:
B (Yo)
Probability (pi) A (%)
15 20
0.1
10
0.2 0
5
0.4 20
30
0.2 10
50
0.1 25
( a ) Calculate the expected rate of return for each stock and the standard deviation of returns
for each stock. ( b ) Calculate the coefficient of variation. (c) Which stock is less risky?
Explain.
SOLUTION
For stock A:
(a)
i)2p,(oh)
(r, F)("/O)
rgl(%) (r, F)2
pt
rd%) (rf
15 1.5 20
0.1 400 40
0 0.2 5
0 25 5
5 0.4 2 0 0 0
10 0.2 2 5
5 25
 40

25 0.1 2.5 20 400
 u2= 90
P = 5.0

Since o2= 90, o = fi= 9.5%.
For stock B:
92P,(o/o)
(rf F()
)% (rf i)2
rd0/.) rpl(%)
pi (4
20 0.1 2 39 1,521 152.1
10 0.2 2 9 16.2
81
20 8
0.4 1 1 0.4
30 0.2 6 11 121 24.2
 
5
0.1 31 961
50 96.1
19
P= u2= 289

Since u2= 289, U = v289 = 17%.
RISK, RETURN, AND VALUATION
186 [CHAP. 7
(b) The coefficient of variation is d?.
Thus, for stock A:
For stock B:
17.0%
= 0.89
19%
( c ) Stock B is less risky than stock A since the coefficient of variation (a measure of relative risk) is smaller
for stock B.
Absolute and Relative Risk. Ken Parker must decide which of two securities is best for him. By
73
.
using probability estimates, he computed the following statistics:
Security Y
Statistic Security X
Expected return ( f ) 8%
12%
Standard deviation (a) 20Yo 10%
( a ) Compute the coefficient of variation for each security, and (b) explain why the standard
deviation and coefficient of variation give different rankings of risk. Which method is superior
and why?
SOLUTION
For the X coefficient of variation (df)is 20112 = 1.67. For Y it is 1018 = 1.25.
(a)
(b) Unlike the standard deviation, the coefficient of variation considers the standard deviation of
securities relative to their average return. The coefficient of variation is therefore the more useful
measure of relative risk. The lower the coefficient of variation, the less risky the security relative to
the expected return. Thus, in this problem, security Y is relatively less risky than security X.
Diversification Effects. The securities of firms A and B have the expected return and standard
7.4
deviations given below; the expected correlation between the two stocks (pAB)is 0.1.
F U
A 14% 20%
B 9% 30%
Compute the return and risk for each of the following portfolios: ( a ) 100percent A; (6) 100
percent B; (c) 60 percent A 4 0 percent B; and ( d ) 50 percent A50 percent B.
SOLUTION
100 percent A: P = 14%; U = 20%; u/p=  = 1.43
(4 2o
14
30
= 3.33
100 percent B: P = 9%; U = 30%; ulf =
(b) 9
(c) 60 percent A  40 percent B:
+ (O.4)(9%) = 12%
rp = w A ˜ A W B ˜ B (O.6)(14%)
= 4
+ 2wA WB PAB C A u B
= d w iui + W i 0:
up
= d(0.6)2(0.2)2 + (0.4)2(0.3)2 + 2(0.6)(0.4)pA, (0.2)(0.3)
= ˜ 0 . 0 1 4 4 0.0144 + 0.0288pAB = d0.0288 + 0.0288(0.1)
+ = = 0.1780 = 17.8%
187
RISK, RETURN, AND VALUATION
стр. 87 