FM212 MT2014 Problem Set Solutions
Class 6
16. CAPM
a.
b. Market risk premium = r
m
– r
f
= 0.12 – 0.04 = 0.08 = 8.0%.
c. Use the security market line:
r = r
f
+ β(r
m
– r
f
)
r = 0.04 + [1.5 × (0.12 – 0.04)] = 0.16 = 16.0%
d. For any investment, we can find the opportunity cost of capital using the security market
line. With β = 0.8, the opportunity cost of capital is:
r = r
f
+ β(r
m
– r
f
)
r = 0.04 + [0.8 × (0.12 – 0.04)] = 0.104 = 10.4%
The opportunity cost of capital is 10.4% and the investment is expected to earn 9.8%.
Therefore, the investment has a negative NPV.
e. Again, we use the security market line:
r = r
f
+ β(r
m
– r
f
)
0.112 = 0.04 + β(0.12 – 0.04) ⇒ β = 0.9
17.
a. If the two stocks are perfectly negatively correlated, they fluctuate due to the same risks,
but in opposite directions. Because Intel is twice as volatile as Coke, we will need to
hold twice as much Coke stock as Intel in order to offset Intel’s risk. That is, our
portfolio should be 2/3 Coke and 1/3 Intel.
We can check this:
2 2 2 2
P Coke Intel Coke Intel Coke Intel
2 2 2 2
Var(R ) (2 /3) SD(R ) (1/3) SD(R ) 2(2/3)(1/3)Cor
r(R ,R )SD(R )SD(R )
(2 /3) (0.25 ) (1/3) (0.50 ) 2(2 / 3)(1/ 3)( 1)(.25)(.50)
0
= + +
= + + −
=
b. The expect return of the portfolio is
P Coke Intel
E[R ] (2/ 3)E[R ] (1/3)E[R ]
(2/3)6% (1/ 3)26%
12.67%
= +
= +
=
Because this portfolio has no risk, the risk-free interest rate must also be 12.67%.
0
5
10
15
20
0 0.5 1 1.5 2
Beta
Expected Return
