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50 percent A50 percent B:
(if)
+ (0.5)(9%) = 11.5%
rp = (O.5)(14%)
+
up= d(0.5)2(0.2)2+ (0.5)2(0.3)2 2(0.5)(0.5)pAB(0.2)(0.3)
= dO.01 + 0.0225 + 0.03pAB= d0.0325 + O.03pAB
= d0.0325 + 0.03(0.1) = = 0.1884 = 18.84%
DiversificationEffects. Use the same facts as for Problem 7.4, except for this problem assume the
7.5
expected correlation between the two stocks (pAB)= 1.0.
SOLUTION
The answers are the same as in Problem 7.4.
( a ) and (b)
rp = 12%
(4
fi= 0%
up= d0.0288 + 0.0288(1.0) =
(4 rp = 11.5%
up= 40.0325 + 0.03( 1.0) = 5%
= 0.05 =
Beta and Expected Return. Assume that the riskfree rate of return is 8 percent, the required
7.6
rate of return on the market is 13 percent, and stock X has a beta coefficient of 1.5. ( a ) What is
stock X's required rate of return? ( b )What if the beta increases to 2? (c) What if the riskfree
rate decreases to 6 percent, assuming the beta is still 1.5?
SOLUTION
r = r, + b(r,,,  r,)
r = 8% + 1.5(135%0 8%) = 8% + 1.5(5%) = 15.5%

r = 8% + 2(130/,  8%) = 8% + 10% = 18%
r = 6% + 1.5(130/,  6%) = 6% + 10.5 = 16.5%
Required Rate of Return and Beta. Moe Corporation is considering several securities. The rate
7.7
on Treasury bills is currently 8.25 percent, and the expected return for the market is 11.5percent.
What should be the required rates of return for each security?
Beta
Security
A 1.15
0.85
B
1.oo
C
D 1S O
SOLUTION
(1.15)(11.5  8.25)
' A 8.25 11.9875
(0.85)(11.5  8.25)
8.25 11.0125
B
(l.OO)(llS  8.25)
C 8.25 11.5
D 8.25 (1.50)(11.5  8.25) 13.125
188 RISK, RETURN, AND VALUATION [CHAP. 7
CAPM.If Treasury bills yield 10 percent, and Alpha Companyâ€™s expected return for next year
7.8
is 18 percent and its beta is 2, what is the marketâ€™s expected return for next year? Assume the
capital asset pricing model (CAPM) applies and everything is in equilibrium.
SOLUTION
r = rf+ b(rm rf)
18% = 10% + 2(rm 10%)
0.18 = 0.1 + 2rm 0.2
0.28 = 2r,
Beta. Assuming the CAPM applies, if the marketâ€™s expected return is 13 percent, the riskfree
7.9
rate is 8 percent, and stock Aâ€™s required rate of return is 16 percent, what is the stockâ€™s beta
coefficient?
SOLUTION
rf+ b(rm â€˜j)
=
16% = 8% + b(130/,  8%)
0.16 = 0.08 + b(0.05)
0.08 = b(0.05)
b = 1.6
Security Market Line (SML).The riskfree rate is 7 percent, and the expected return on the
71
.0
market portfolio is 12 percent. ( a ) What is the equation for the security market line (SML)? (b)
Graph the SML.
SOLUTION
( a ) The SML equation is:
+ b(5%)
r = rf + b(rnt rf) = 7% + b(12Y0  7%) = 7%
( b ) See Fig.72.
71
.1 CAPM. Assume the following: the riskfree rate is 8 percent, and the market portfolio expected
return is 12 percent.
189
RISK, RETURN, AND VALUATION
CHAP. 71
Portfolio Beta
06
.
A
B 1.o
C 14
.
( a ) Calculate for each of the three portfolios the expected return consistent with the capital
asset pricing model. ( b )Show graphically the expected portfolio returns in (a). ( c ) Indicate what
would happen to the capital market line if the expected return on the market portfolio were 10
percent. (CFA, adapted.)
SOLUTION
Portfolio A: r = 8%+ 0.6(12%  8%) = 10.4%
Portfolio B: r = 8% + 1.0(12%  8%) = 12.0%
Portfolio C: r = 8% + 1.4(12% 8%) = 13.6%
( b ) See Fig. 73.
4%)
13.6
12.0
10.4
r, = 8.0
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