Investment and Pic

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Chapter 6

SOLUTIONS TO END-OF-CHAPTER PROBLEMS

6-1[pic]= (0.1)(-50%) + (0.2)(-5%) + (0.4)(16%) + (0.2)(25%) + (0.1)(60%)
= 11.40%.

(2 = (-50% - 11.40%)2(0.1) + (-5% - 11.40%)2(0.2) + (16% - 11.40%)2(0.4) + (25% - 11.40%)2(0.2) + (60% - 11.40%)2(0.1)

(2 = 712.44; ( = 26.69%.

CV = [pic] = 2.34.

6-2 Investment Beta
$35,000 0.8
40,000 1.4
Total $75,000

bp = ($35,000/$75,000)(0.8) + ($40,000/$75,000)(1.4) = 1.12.

6-3kRF = 5%; RPM = 6%; kM = ?

kM = 5% + (6%)1 = 11%.

ks when b = 1.2 = ?

ks = 5% + 6%(1.2) = 12.2%.

6-4kRF = 6%; kM = 13%; b = 0.7; ks = ?

ks= kRF + (kM - kRF)b
= 6% + (13% - 6%)0.7
= 10.9%.

6-5a.[pic] = (0.3)(15%) + (0.4)(9%) + (0.3)(18%) = 13.5%.

[pic] = (0.3)(20%) + (0.4)(5%) + (0.3)(12%) = 11.6%.

b.(M= [(0.3)(15% - 13.5%)2 + (0.4)(9% - 13.5%)2 + (0.3)(18% - 13.5%)2]1/2
= [pic] = 3.85%.

(J= [(0.3)(20% - 11.6%)2 + (0.4)(5% - 11.6%)2 + (0.3)(12% - 11.6%)2]1/2
= [pic] = 6.22%.

c.CVM = [pic] = 0.29.

CVJ = [pic] = 0.54.

6-6a.[pic].

[pic]= 0.1(-35%) + 0.2(0%) + 0.4(20%) + 0.2(25%) + 0.1(45%)
= 14% versus 12% for X.

b.( = [pic].

([pic] = (-10% - 12%)2(0.1) + (2% - 12%)2(0.2) + (12% - 12%)2(0.4) + (20% - 12%)2(0.2) + (38% - 12%)2(0.1) = 148.8%.

(X = 12.20% versus 20.35% for Y.

CVX = (X/[pic]X = 12.20%/12% = 1.02, while

CVY = 20.35%/14% = 1.45.

If Stock Y is less highly correlated with the market than X, then it might have a lower beta than Stock X, and hence be less risky in a portfolio sense.

6-7a. kA= kRF + (kM - kRF)bA
12%= 5% + (10% - 5%)bA
12%= 5% + 5%(bA)
7%= 5%(bA)
1.4= bA.

b.kA = 5% + 5%(bA)
kA = 5% + 5%(2)
kA = 15%.

6-8a.ki = kRF + (kM - kRF)bi = 9% + (14% - 9%)1.3 = 15.5%.

b.1.kRF increases to 10%:

kM increases by 1 percentage point, from 14% to 15%.

ki = kRF + (kM - kRF)bi = 10% + (15% - 10%)1.3 = 16.5%. 2.kRF decreases to 8%:

kM decreases by 1%, from 14% to 13%.

ki = kRF + (kM - kRF)bi = 8% + (13% - 8%)1.3 = 14.5%.

c.1.kM increases to 16%:

ki = kRF + (kM - kRF)bi = 9% + (16% - 9%)1.3 = 18.1%.

2.kM decreases to 13%:

ki = kRF + (kM - kRF)bi = 9% + (13% - 9%)1.3 = 14.2%.

6-9Old portfolio beta = [pic](b) + [pic](1.00)
1.12 = 0.95b + 0.05
1.07 = 0.95b
1.13 = b.

New portfolio beta = 0.95(1.13) + 0.05(1.75) = 1.16.

Alternative Solutions:

1.Old portfolio beta = 1.12 = (0.05)b1 + (0.05)b2 + ... + (0.05)b20

1.12 = [pic](0.05)
[pic]= 1.12/0.05 = 22.4.

New portfolio beta = (22.4 - 1.0 + 1.75)(0.05) = 1.1575 ( 1.16.

2.[pic] excluding the stock with the beta equal to 1.0 is 22.4 - 1.0 = 21.4, so the beta of the portfolio excluding this stock is b = 21.4/19 = 1.1263. The beta of the new portfolio is:

1.1263(0.95) + 1.75(0.05) = 1.1575 ( 1.16.

6-10Portfolio beta = [pic](1.50) + [pic](-0.50)
+ [pic](1.25) + [pic](0.75)
= (0.1)(1.5) + (0.15)(-0.50) + (0.25)(1.25) + (0.5)(0.75) = 0.15 - 0.075 + 0.3125 + 0.375 = 0.7625.

kp= kRF + (kM - kRF)(bp) = 6% + (14% - 6%)(0.7625) = 12.1%.

Alternative solution: First compute the return for each stock using the CAPM equation [kRF + (kM - kRF)b], and then compute the weighted average of these returns.

kRF = 6% and kM - kRF = 8%.

Stock Investment Beta k = kRF + (kM - kRF)b Weight A $ 400,000 1.50 18% 0.10 B...
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