Stock Y has a beta of 1.4 and an expected return of 14.2 percent. Stock Z has a

Question

Stock Y has a beta of 1.4 and an expected return of 14.2 percent. Stock Z has a beta of 0.85 and an expected return of 10.7 percent.

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

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

Explanation / Answer

Let the risk free rate be r and expected market return be m

As per CAPM, expected return = risk free rate + Beta * (market return - risk free rate)

Thus, 14.2% = r + 1.4*(m - r)
and 10.7% = r + 0.85 *(m - r)

subtracting the 2 equations

3.5% = 1.4(m - r) - 0.85 ( m - r)

3.5% = 0.55(m - r)

m - r = 3.5%/0.55 = 6.364%

Substituting this in the first equation

14.2% = r + 1.4*6.364%

r = 14.2% - 8.91% = 5.29%

Risk free rate must be 5.29%

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