Answer:
The risk free rate (Rf) is 28,2%
Explanation:
We will substituting the portfolio expected return (Er) and the betas of the portfolio in the expected return & beta relationship, that is:
E[r] = Rf + Beta * (Risk Premium)
On doing this we get 2 equations in which the risk free rate (Rf) and the risk premium [P] are not known to use:
12% = Rf + 1 * (P - Rf)
9% = Rf + 1.2 * (P - Rf)
On solving first equation (of Portfolio A) for P(risk premium), we get:
12% = Rf + 1 * (P - Rf)
12% = Rf + P - Rf
(Rf and Rf cancels each other)
P = 12%
Now, on using the value of P in second equation (of Portfolio B), and solving for Rf (risk free rate), we get:
9% = Rf + 1.2 * (12.2% - Rf)
9% = Rf + 14.64% -1.2Rf
1.2Rf - Rf = 14.64% - 9%
0.2Rf = 5,64%
Rf = 5.64% / 0.2
Rf = 28,2%
So, the risk free rate (Rf) is 28,2%
