Linear Regression Project:
On Testing the Empirical Validity of CAPM
Spring 2018 Dr. H. Fahmy
Instructions:
• Due Thursday, July 12, 2018 at the beginning of class sharp!
• Late submissions are not acceptable under any circumstances.
• The work that you will submit should be your own. Do not, under any circumstances, attempt to copy
or use other students’ results.
• You should submit your report with a cover page indicating clearly your first and last name and your
student ID. The cover page should be printed. For the content, feel free to print or write your answer.
Please note that unstapled parts or parts without cover pages will not be accepted.
• Do not just copy and paste your R code. You need to present your estimation results in standard
report form. The R code should be attached in an Appendix.
Preliminaries: The Universe
In this project, the universe is a Canadian common stocks market. In particular, we will focus on the top 60
stocks listed on the Standard Poor Toronto Stock Exchange (SPTSX). The market index, which we will
denote by SPTSX60, is taken to be the value-weighted portfolio of the top 60 traded stocks in the SPTSX
such that the weight of asset i in the market portfolio is
Explain how can you estimate such an equation empirically. In other words, describe step-by-step
how would you fit a linear model that describes this equation explaining the types of variables or
transformations of variables necessary to specify the equation and how would you go about the relevant
data? In particular, refer to the specification step of the linear regression modelling procedure. (Hint:
Think of the specification step of the linear regression modelling procedure, where you specify a model
and collect the necessary data. Your answer, for instance, could begin with something like this: Step
where the regressand Yt
is time t’s rate of return of the stock in excess of the risk-free rate, the regressor
Xt
is time t’s market rate of return in excess of the risk-free rate, eu
it
is a white noise error term, and
T is the total number of monthly observations between June 1989 and April 2014 (including both
months). Note that the workable number of observations in this case is T −1.
(a) Take i =AEM and estimate the regression equation using the lm function on R. Report your
results in a standard form. and comment on the validity of your estimation. (Hint: use the four
decision criteria)
(b) Explain the meaning of the estimated coe¢cients. Sketch the estimated relation.
(c) Construct an ANOVA table and compute TSS,ESS,andRSS.
(d) Find an estimate for σ
2
, the variance of the unobserved true error term.
(e) Compute the adjusted coe¢cient of determination and explain why it is preferred over the coef-
ficient of determination as a measure of goodness of fit.
(f) Jensen (1968) was the first to note that the relation between expected return and market beta
implies the time series regression above. A valid CAPM described by this regression implies that
Jensen’s alpha,theintercepttermintheregression,iszeroforanyasset.Testthishypothesis
using the likelihood ratio test.
(g) Since you are using time-series data, you suspect the existence of serial correlation of order 1.
Test the presence of serial correlation using Durbin-Watson test.
(h) Run White test to detect the presence of heteroskedasticity. Report your estimation and test
results properly and attach your R code in the Appendix.
(i) Given all your previous estimation results and tests, what can you say about the empirical validity
of CAPM? Explain.