Question

Assume that both portfolios A and B are well diversified, that E(r_A) = 10%, and E(r_B) = 7%. If the economy has only one factor, and β_A = 1.2, whereas β_B = 0.7, what must be the risk-free rate? (Do not round intermediate calculations. Round your answer to two decimal places.)

Answer 1

Expected return of A = 10%

Expected return of B = 7%

beta of A = 1.2

Beta of B = 0.7

When portfolio are well diversified, then their required return is equal to return as per CAPM

As per CAPM, market risk premium = Difference of expected return of stock/difference of beta

=(10%-7%)/(1.2-0.7)

=6%

Expected return of stock formula = Risk free rate + (Beta * market risk premium)

lets take any of diversified stock. We will take A

10% = Risk free rate + (1.2*6%)

10%-(1.2*6%) = risk free rate

risk free rate=2.8%

So risk free rate must be 2.8%