McMaster University
DeGroote School of Business
MFIN 701
Assignment 1
Due Feb. 15, 5pm.
Hand in a pdf copy of your computer output and a separate write-up of the answers
to the following questions to Avenue, Assignment 1 by 5pm Feb 15. 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 = α + βRMt + γSMBt + δHMLt + ut, ut ∼ NID(0, σ2). (1)
Answer the following questions.
1. Estimate this model by OLS and report estimates, standard errors and t-statistics
for α, β, γ, δ, σ2. Which variables are significantly different than 0?
2. Report a 95% confidence interval for δ. What is the interpretation of this interval?
What is the probability it contains the true value of δ?
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 ∈ {RMt, SMBt, HMLt}, 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.
7. Prove that the OLS estimator is unbiased.
8. Assume θˆ is an unbiased estimator for θ.
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.
1
(a) Is 5θˆ an unbiased estimator for 5θ?
(b) Is 1/θˆ and unbiased estimator for 1/θ?
9. For the general linear model with k regressors show that the fitted model goes
through the sample mean of y and the sample mean of the regressors X1, ..., Xk.
10. How does the OLS estimator change if the dependent variable y is scaled by 100?
How would it change if y and all regressors X are scaled by 100?
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