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.)

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%

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