Question

Stock Y has a beta of 1.0 and an expected return of 12.4%. Stock Z has a beta of .6 and an expected return of 8.2%.

What would the risk-free rate have to be for the two stocks to be correctly priced? (Do
not round intermediate calculations and enter your answer as a percent rounded to 2
decimal places, e.g., 32.16.)

Answer 1

Answer: 1.9%

Step-by-step explanation:

The Capital Asset Pricing Model can be used to solve for this.

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

From the formula, it is shown that we first need to find the Market return. We will use the same formula:

Using stock Y:

12.4% = Risk free rate + 1.0 * (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%