Introduction to Econometrics, MFIN 701
Assignment 1
Hand in a copy of your computer output and a separate write-up of the answers to
the following questions. Each student’s write-up should be done independently. The
data set is ass1.out and is posted on the class website. It consists of: column number;
date; monthly excess returns on GE (RGEt); monthly excess returns on the market
(RMt) and two portfolio factors SMBt and HMLt constructed from Fama and French
(1993).1 SMB is the average return on the three small portfolios minus the average
return on the three big portfolios. HML is the return on two value portfolios minus the
average return on the two growth portfolios. For statistical tests always report a p-value
when possible.
Consider the following model for GE excess returns
RGEt = + RMt + SMBt + HMLt +ut; ut NID(0; 2): (1)
Answer the following questions.
1. Estimate this model by OLS and report estimates, standard errors and t-statistics
for ; ; ; ; 2. Which variables are signi cantly di erent than 0?
2. Report a 95% con dence interval for . What is the interpretation of this interval?
What is the probability it contains the true value of ?
3. Provide a test that all slope regressors do not belong in the model. What are your
conclusions? Test if SMBt and HMLt do not belong in the model.
4. What is the R2 for this model? Do the regressors explain much of the movements
in GE excess returns?
5. Suppose you create a new regressor Vt SMBt HMLt and add it to the model
above. When you estimate this model what happens and why?
6. Add each of the possible cross products Wt = X1t X2t terms from the regressors
Xit 2fRMt;SMBt;HMLtg, i = 1;2 to the model. Estimate this model and
perform. an F-test to see if the cross product regressors belong in the model.
1Eugene F. Fama, Kenneth R. French, Common risk factors in the returns on stocks and bonds,
Journal of Financial Economics, Volume 33, Issue 1, February 1993, Pages 3-56.