Question

Assume both portfolios A and B are well diversified, that E(rA) = 15.0% and E(rB) = 16.8%. If the economy has only one factor, and βA = 1 while βB = 1.2, what must be the risk-free rate?

Answer 1

Answer:

6%

Explanation:

Given that,

Assume both portfolios A and B are well diversified,

E(rA) = 15.0%

E(rB) = 16.8%

βA = 1

βB = 1.2

Therefore, the risk-free rate is calculated as follows:

$\frac{E(rA)-rf}{\beta A} =\frac{E(rB)-rf}{\beta B }$

$\frac{0.15-rf}{1} =\frac{0.168-rf}{1.2}$

1.2 × (0.15 - rf) = 1 × (0.168 - rf)

0.18 - 1.2rf = 0.168 - rf

0.18 - 0.168 = 1.2rf - rf

0.012 = 0.2rf

0.06 or 6% = rf

Hence, the risk-free rate is 6 percent.