Investment and Pic
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.
6-3 kRF = 5%; RPM = 6%; kM = ?
kM = 5% + (6%)1 = 11%.
ks when b = 1.2 = ?
ks = 5% + 6%(1.2) = 12.2%.
6-4 kRF = 6%; kM = 13%; b = 0.7; ks = ?
ks = kRF + (kM - kRF)b = 6% + (13% - 6%)0.7 = 10.9%.
6-5 a. [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.
6-6 a. [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.
6-7 a. 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%.
6-8 a. ki =
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.
6-3 kRF = 5%; RPM = 6%; kM = ?
kM = 5% + (6%)1 = 11%.
ks when b = 1.2 = ?
ks = 5% + 6%(1.2) = 12.2%.
6-4 kRF = 6%; kM = 13%; b = 0.7; ks = ?
ks = kRF + (kM - kRF)b = 6% + (13% - 6%)0.7 = 10.9%.
6-5 a. [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.
6-6 a. [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.
6-7 a. 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%.
6-8 a. ki =