The market return is 11% and the risk free rate is 4%. Mammoth Inc. has a market beta of 1.2, a SMB beta of −.78, and a HML beta of −1.2. The risk premium on HML and SMB are both 3%. If the single factor model generates a regression coefficient of 1.2, using the Fama-French Three Factor Model, what is the different in returns between the Three-Factor model and the single factor model expected returns on Mammoth Inc. stock?
A) 5.66%
B) 5.94%
C) 11.3%
D) 16.3%

Question

Quizplus · Accepted Answer

Using the Fama-French Three Factor Model, the expected return is calculated as follows: Expected return = Risk-free rate + (Market beta * Market risk premium) + (SMB beta * SMB premium) + (HML beta * HML premium). Plugging in the given values: Expected return = 4% + (1.2 * (11% - 4%)) + (-.78 * 3%) + (-1.2 * 3%) = 4% + 8.4% - 2.34% - 3.6% = 6.46%. Using the single factor model (CAPM), the expected return is: Expected return = Risk-free rate + (Market beta * Market risk premium) = 4% + 1.2 * (11% - 4%) = 4% + 8.4% = 12.4%. The difference between the single factor model and the Three-Factor model expected returns is 12.4% - 6.46% = 5.94%.

The Market Return Is 11% and the Risk Free Rate