Stock X has a beta of .87 and an expected return of 9.8 percent. Stock Y has a beta of 1.2 and an expected return of 13.1 percent. What is the risk-free rate of return assuming that both stock X and stock Y are correctly priced?
A) 1.10 percent
B) 1.20 percent
C) 2.07 percent
D) 3.30 percent
E) 3.50 percent

Question

Quizplus · Accepted Answer

The Capital Asset Pricing Model (CAPM) states that the expected return on a stock is equal to the risk-free rate plus a risk premium. The risk premium is equal to the beta of the stock multiplied by the market risk premium. The market risk premium is the difference between the expected return on the market and the risk-free rate.In this case, we are given the expected return on two stocks, X and Y, and their betas. We can use the CAPM to solve for the risk-free rate.For stock X, we have:Expected return = Risk-free rate + Beta * Market risk premium9.8% = Risk-free rate + 0.87 * Market risk premiumFor stock Y, we have:Expected return = Risk-free rate + Beta * Market risk premium13.1% = Risk-free rate + 1.2 * Market risk premiumSubtracting the first equation from the second equation, we get:3.3% = 0.33 * Market risk premiumMarket risk premium = 10%Substituting this value back into the first equation, we get:9.8% = Risk-free rate + 0.87 * 10%Risk-free rate = 1.1%Therefore, the risk-free rate of return is 1.1%.

Stock X Has a Beta of