Assume both portfolios A and B are well diversified, that E ( r A ) = 13.8% and

Question

Assume both portfolios A and B are well diversified, that E(rA) = 13.8% and E(rB) = 15.6%. If the economy has only one risk factor, and A = 1 while B = 1.2, what must be the risk-free rate? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 1 decimal places.)

Assume both portfolios A and B are well diversified, that E(rA) = 13.8% and E(rB) = 15.6%. If the economy has only one risk factor, and A = 1 while B = 1.2, what must be the risk-free rate? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 1 decimal places.)

Explanation / Answer

We know that as per CAPM theory

Er = Rf + x (Rm- Rf)

Therefore

Er(a) = Rf + A x (Rm- Rf) -----------------(1)

Er(b) = Rf + B x (Rm-Rf) ------------------- (2)

By substracting equation (1) from equation (2) we get

Er(b)- Er(a) = Rm-Rf (B- A)

15.6-13.8 = Rm-Rf (1.2-1)

1.8 = 0.2 (Rm-Rf)

Rm-Rf = 9

Rm = 9 + Rf

Now by putting this value in equation (1) we get

13.8 = Rf + (9 + Rf –Rf)

Rf = 4.8 %

Hence Risk free rate of return = 4.8 %

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