Question

The market return is 10% and the risk free rate is 3%. Rascals Inc. has a market beta of 1.0, a SMB beta of −.60, and a HML beta of −0.85. If the risk premium on HML and SMB are both 2%, using the Fama-French Three Factor Model, what is the expected Return on Rascal Inc. stock?

Answer 1

Solution :

The formula for calculating the expected return of a stock using the Fama-French Three Factor Model is

Expected Return = R_F + ( β_M * ( R_M - R_F ) ) + ( β_HML * Risk premium of HML ) + ( β_SMB * Risk premium of SMB )

Where

R_F = Risk free rate ; β_M = Beta of the market ;   R_M = Market Return ; β_HML = Beta of HML ; β_SMB = Beta of SMB

As per the information given in the question we have

R_F =        3 % ; β_M = 1.0 ; R_M = 10 % ; β_HML = - 0.85 ; Risk premium of HML = 2 % ; β_SMB = - 0.60 ; Risk premium of SMB = 2 %

Applying the above information in the formula we have the expected return as

= 3 % + ( 1.0 * ( 10 % - 3 % ) ) + ( - 0.85 * 2 % ) + ( - 0.60 * 2 % )

= 3 % + ( 1.0 * 7 % ) + ( - 0.85 * 2 % ) + ( - 0.60 * 2 % )

= 3 % + 7 % - 1.70 % - 1.20 %

= 7.1 %

Thus the expected Return on Rascal Inc. stock using the Fama-French Three Factor Model = 7.1 %