Assume both portfolios A and B are well diversified, that E (rA) = 13.4% and E (rB) = 15.0%. If the economy has only one factor, and βA = 1 while βB = 1.2, what must be the risk-free rate? (Do not round intermediate calculations. Round your answer to 1 decimal place.)

The answer is risk free rate should be 5.4%

Explanation:

We apply the CAMP model to solve the risk free rate: E (r) = Risk free rate + Beta x (Market return - Risk free rate).

Denote X as risk free rate; y is market risk premium (that is market return minus risk free rate)

We have:

For portfolio A: x + 1 * y = 13.4%;

For portfolio B: x + 1.2 * y = 15%

Solving the two equation above, we have: y = 8%; x = 5.4%

So, the risk free rate should be 5.4%.

5.4%

Explanation:

To calculate the risk free rate apply the CAPM equation

Risk free rate = expected rate - beta * (market risk premium)

for portfolio A

Risk free rate = 13.4% - 1 * MRP

for portfolio B

Risk free rate = 15.0% - 1.2 * MRP

To calculate the risk free rate equate both equations

Risk free rate = 13.4% - 1*MRP = 15.0% - 1.2*MRP

= 1.2 * MRP - 1*MRP = 15.0% - 13.4%

= 0.2 MRP = 1.6% therefore MRP = 1.6 % / 0.2 = 8%

Insert the MRP into equation for portfolio A

Risk free ratio = 13.4% - 1 * 8% = 5.4%