EFN426
Assignment 1
Linear regression, inference, diagnostics
Due: Thursday 26.March
Data Go to Kenneth French’s Homepage, and get data for analyzing CAPM and Factor
description: Models. Under “U.S. Research Returns Data”, you can find Fama/French 3 Factors, which
reports market excess return, the two F-F factors, as well as risk free rate. Under the
section “Sorts involving prior returns”, you’ll find the momentum factor. You then have to
choose a portfolio to analyse. For example, under “Bivariate sorts of size, B/M, OP, and
Inv” you could pick a portfolio representing particular size and B/M ratio. As another
example, under “Industry portfolios” you could pick a portfolio representing a particular
industry section.
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/index.html
Submission: Report, Do-file and the data file AllData.xlsx (see end of this document for details)
All the analysis must be replicable using your submitted do-file and the AllData.xlsx data file.
Setting up the Excel data file: Get the three data sets (FACTORS, MOMENTUM, PORTFOLIO) in monthly
frequency and in csv format. Place the data in an Excel file, each data set on a separate worksheet. (See
Note 4.) Rename the worksheets using names FACTORS, MOMENTUM, PORTFOLIO (in capital letters).
Label the first column on each worksheet as Date. Save this file as AllData.xlsx.
Starting the do-file: [12 marks]
At the top of the do-file, you will need to read in and prepare the data for the analysis. The do-file must
utilise the Excel file directly. Do not save any further changes to the AllData.xlsx – all modifications to the
data will be part of your do-file code. Read a worksheet FACTORS into Stata:
import excel using "AllData.xlsx", sheet("FACTORS") firstrow clear
The Date has been saved in numeric format (e.g. 199701 for January 1997). First convert this to a string
using tostring Date – then create a new Ddate variable that converts the string Date into a daily date
using date(Date,”YM”) – then extract the month of the daily date using mofd(Ddate)– store these
into a variable Mdate, and finally format this monthly date to look like a monthly date using %tm. Delete
the date and Ddate variables. Save the data file as FACTORS.dta. Then repeat for MOMENTUM and
PORTFOLIO. You should now have three data sets in dta format, each with the Mdate variable storing the
date of the observations. To merge them together, first pick one to be the “master” data set. Read it into
Stata in the usual way. Then bring in the other data sets:
merge 1:1 commondatevariable using datafile.dta, nogenerate
Clean up (drop variables you will not use), set time series, and adjust the sample period to your liking.
CAPM = + + . [27 marks]
In this model, there are two quantities that can be seen as measurements of how closely the portfolio
tracks the market. One of them is the alpha, α, measuring the risk-adjusted performance relative to a
market benchmark. Another is the beta, β, the systematic risk, or volatility, in comparison to the market.
Investigate these risk measurements with regards to the portfolio’s market tracking capabilities,
separately and jointly. The portfolio performance and risk may have changed over time. Investigate the
stability of the CAPM parameters, by suggesting a plausible breakpoint and carrying out a formal test.
Relate your findings to the above discussion of market tracking.
(a) Estimate CAPM over the whole sample period. [NC]
(b) Test whether = 0. Then test whether = 1. Finally test the two hypotheses jointly.
(c) Suggest a plausible break point for the time series. Estimate CAPM for the time before and after
your choice of break point using dummy variables. Test whether has changed over time.
Fama-French 2-Factor Model = + + 2 + 3 + [10 marks]
Investigate whether the 2-Factor Model is preferred over the CAPM. There are two approaches to
consider. One is based on comparing how well the two models fit the data set. The other is based on a
formal test of 2-Factor Model parameters.
(d) Estimate Fama-French 2-Factor Model over the whole sample period. [NC]
(e) Compare the fit of the CAPM and 2-Factor Model.
(f) Test which one is preferred, CAPM or 2-Factor Model.
Fama-French 3-Factor Model = + + 2 + 3 + 4+ [51 marks]
Assess the individual explanatory variables in this model, and comment on their significance. From here,
form your preferred model in which all factors are statistically significant. Examine the residuals from your
preferred model, paying special attention to heteroskedasticity and autocorrelation. Relate your findings
to the OLS method you have used to estimate the model.
(g) Estimate the 3-Factor Model over the whole sample period. [NC]
(h) Assess individual explanatory variables, and comment on their significance at 1% level. Remove
insignificant variables (one at a time). Show and comment all details.
(i) Save the residuals from the final model from previous part. [NC]
(j) Test the residuals for autocorrelation. Illustrate and comment appropriately.
(k) Test the residuals for heteroskedasticity. Illustrate and comment appropriately.
(l) Test if the residuals are normally distributed. Illustrate and comment appropriately.
NOTE 1: and are excess return on portfolio and market, respectively, and SMB is the F-F size
factor, HML is the F-F B/M factor, and MOM is the momentum factor.
NOTE 2: All tests must include a clear statement of the null and alternative hypotheses, and in statistical
terms motivated conclusion, as well as interpretation of the conclusion.
NOTE 3: [NC] at the end of the task means that the particular task does not require comments.
NOTE 4: The downloaded CSV files have the data you need at the start of the file, followed by annual
factors and copyright notices. When forming the AllData.xlsx, copy over ONLY the data you need,
with variable names in the top row. Delete all other data and comments – failing this will result
in an argument with Stata.
NOTE 5: Before adjusting the time period, have a look at the line graphs of the portfolio and market
returns. Aim to have a few hundred observations in the sample. Look at task (c) – do you see /
can you think of a reason for an interesting break point somewhere? Include this around the
middle of your sample. You may not get the sample selection right the first time, and so you may
need to try a few ideas. Remember to code the sample selection as part of the do-file
commands.
SUBMIT
• Report (Word document)
a. use the question numbers as section headings
b. list the contributing group members’ names at the top
c. name the file as YourGroupName_A1.docx
• Your data file (AllData.xlsx)
a. Name the file as YourGroupName_AllData.xlsx
• Do-file (that directly utilises the AllData.xlsx file and does all the analysis)
a. Name the file as YourGroupName_A1.do