Question

Stock X has a beta of 1.6 and an expected return of 18.2 percent. Stock Y has a beta of 1.19 and an expected return of 15.49 percent. What is the risk-free rate if these securities both plot on the security market line?

Answer 1

Per CAPM, we have

18.20 = rf+1.60*p ------Eq 1 and

15.49 = rf+1.19*p ------Eq 2

where, rf = risk free rate and p = market risk premium

Solving for p,

Subtracting Eq 2 from Eq 1

2.71 = 0.41*p

p = 2.71/0.41 = 6.61

Now from Eq 1

18.20 = rf+1.60*6.61

rf = 18.20-(1.60*6.61) = 7.62

Answer: risk free rate = 7.62%

Check:

7.62+1.19*6.61 = 15.49%