Question

An analyst has modeled the stock of a company using the Fama-French three-factor model. The risk-free rate is 5%, the market return is 9%, the return on the SMB portfolio is 3.2%, and the return on the HML portfolio is 4.8%. If a = 0, b = 1.1, c = -0.3, and d=1.2, what is the stock’s predicted return ?

Please show your solution step by step.

Answer 1

Predicted return= ai + bi(r ̄M,t) + ci(r ̄SMB,t) + di(r ̄HML,t)

The actual formula is;

(r ̄i,t - r ̄RF,t) = ai + bi(r ̄M,t - r ̄RF,t) + ci(r ̄SMB,t) + di(r ̄HML,t)

or

r ̄i,t = r ̄RF,t + ai +bi(r ̄M ,t - r ̄RF,t) + ci(r ̄SMB,t) + di(r ̄HML,t)

So

r ̄RF = 5%,r ̄M =9%, r ̄SMB,t =3.2%, r ̄HML,t=4.8%
ai=0

bi=1.1

Ci=-0.3

di =1.2

(r ̄i,t - 5%) = 0% + 1.1(9% - 5 %) + (-0.3)(3.2%) + 1.2(4.8%)

r ̄i,t = 5 % + 0% + 1.1(9% - 5 %) + (-0.3)(3.2%) + 1.2(4.8%)

r ̄i,t = 14.2 %. ( predicted return )