Stock Y has a beta of .9 and an expected return of 11.2 percent. Stock Z has a beta of .5 and an expected return of 7.2 percent.

Problem 13-19 Reward-to-Risk Ratios [LO4]

Stock Y has a beta of .9 and an expected return of 11.2 percent. Stock Z has a beta of .5 and an expected return of 7.2 percent.

  

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

  

Risk-free rate

%

 

Explanation:

We need to set the reward-to-risk ratios of the two assets equal to each other, which is:

(.112 – Rf) / .9 = (.072 – Rf) / .5

We can cross multiply to get:

.5(.112 – Rf) = .9(.072 – Rf)

Solving for the risk-free rate, we find:

.0560 – .5Rf = .0648 – .9Rf

Rf = .0220, or 2.20%