Question

1. You are about to regress the historical monthly excess returns of Google (RGooge) on the three Fama-French factors – Excess S&P 500 returns (Rme), SMB factor returns (SMB), and HML factor returns (HML). In other words, in each month t in your sample, you will run the following OLS regression:

   RGoog,,te = α + β1Rm,te + β2SMBt + β3HMLt + εt , where εt is an error term in month t.

   What are the expected signs (+ or -) of the regression parameters α, β1, β2, and β3? Briefly explain.

Answer 1

Answer:-

a) See here our mutiple linear regression model is .

RGoog,,te = α + β1Rm,te + β2SMBt + β3HMLt + εt

Let RGoog,,te = x ,  Rm,te=x₁ ,  SMBt = x₂ ,  HMLt=x₃ .

b) Then our equation can be written as  

In matrix form we can write we can write it as

x is matrix of

c) Estimated value of is

d) So for to decide the sign of , we have to solve equation (1 ) and finally we get the sign of these regression coefficient .

e) We cannot able to estimate or predict the sign of   , without solving equation (1) . For to solve equation (1) we need observation on each variable    without knowing these values no one can predict the sign of ,

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