The answer to the question is highlighted in red. Explanations are highlighted in green.
8. Susan has an investment portfolio that contains the following two stocks:
Stock Amount Invested Beta
A $40,000 2.5
B 60,000 0.5
If the risk-free rate is 4 percent and the market rate is 10 percent, what return should Susan’s portfolio earn?
a. 11.8%
b. 10.0%
c. 14.4%
d. 17.0%
e. None of the above is correct.
Solution
Weight A = 40,000/(40,000 + 60,000) = 0.4, Weight B =
60,000(40,000 + 60,000) = 0.6
Alternative 1: (a)
Compute the beta for the portfolio; βP = 0.4(2.5) + 0.6(0.5) =
1.3
(b) Compute the return using the CAPM; r = 4 + (10 – 4)1.3
= 11.8%
Alternative 2: (a)
Compute the return for each stock; rA = 4
+ (10 – 4)2.5 = 19.0, rB
= 4 + (10 – 4)0.5 = 7.0
(b) Compute the weighted average return for the portfolio; rP = 0.4(19.0%) + 0.6(7.0%) = 11.8%