Question

Stock Y has a beta of 1.0 and an expected return of 12.4 percent. Stock Z has a beta of .6 and an expected return of 8.2 percent.
What would the risk free rate have to be for the two stocks to be correctly priced?

Answer 1

Answer: 1.9%

Explanation:

First derive the Market return as this is needed in the Capital Asset Pricing Model by using the same model:

Required return = Risk free rate + Beta * ( market return - Risk free rate)

Using stock Y:

12.4% = Risk free rate + 1 * (market return - Risk free rate)

12.4% = Rf + market return - Rf

Market return = 12.4%

Use this to calculate the Risk free rate:

Stock Z:

8.2% = Rf + 0.6 * (12.4% - Rf)

8.2% = Rf + 7.44% - 0.6Rf

Rf - 0.6Rf = 8.2% - 7.44%

0.4Rf = 0.76%

Rf = 0.76% / 0.4

= 1.9%