Question

Assume both portfolios A and B are well diversified, that E(r_A) = 14.4% and E(r_B) = 16.0%. If the economy has only one factor, and β_A = 1 while β_B = 1.2, what must be the risk-free rate? (Do not round intermediate calculations. Round your answer to 1 decimal place.)

Answer 1

E (r) = Rf+ B(Rm-Rf)
E (r) = Rf+ B(Rp)
E (r) = Expected return
f = risk free rate
B = beta
Rp = Risk premium = (Rm - Rf)
Let us solve using equation
Equation for portfolio 1
14.4% = Rf +1 Rp
Equation for portfolio 2
16% = Rf + 1.2 Rp
On solving equation 1 and 2
Rp = 8%
And Rf would be
14.4% = Rf+1*8
Rf =14.4 - 8
Rf =6.4%
Risk free rate = 6.4%