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FIN2028 Assignment 2 (25%)
Tripti Sharma

Empirically testing the Capital Asset Pricing Model

1. Capital Asset Pricing Model (CAPM)
The CAPM is a theoretical model derived under a set of simplifying assumptions that explains
what expected returns for assets will be given their risk. Let be the return for asset , the
return for the market portfolio and the risk-free rate of interest. Under the CAPM
assumptions, it can be shown that the risk premium for asset , () − is given by the
product of the risk premium for the market portfolio and the asset’s beta,
=
( , )

2
where
2 denotes the variance of the return for the market portfolio. This result is summarised
in the following equation,
() − = [() − ].
Therefore, the CAPM tells us that investors are rewarded for bearing systematic risk, where
an asset’s systematic risk is measured by its contribution to the risk of the market portfolio, as
measured by its beta (). Sollis (2012) explains the CAPM in detail. Gujarati and Porter (2009)
also have examples based on the CAPM.
2. Aim
In this project, you are required to carry out a simple two-step regression-based empirical test
of the CAPM.
The analysis must be conducted in the following manner –
Step (i)
a) Using the sample of time series data on returns for a large sample of stocks as
assigned to your group, the market portfolio (FTSEAll-Share) and the risk-free rate
(UK 3-month Treasury bills), generate time series for excess returns for each asset
(, − ,) and time series for market excess returns (, − ,).
b) Estimate the parameters of the security characteristic line for each stock using ordinary
least squares,
, − , = + [, − ,] + ,
where and , represent the intercept and slope coefficients, respectively, for each
asset .
These are called ‘first-pass regressions’.
For each regression, record ̂ and ̂
2 in a new dataset. ̂
2 is the estimated error
variance.
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Step (ii)
a) Calculate the sample mean excess returns ̅ − ̅ for each stock and add these to your
new dataset.
b) Graph the sample mean excess returns ̅ − ̅ versus ̂. This is known as the ‘security
market line’. Does the relationship seem broadly linear?
c) Run a second cross-sectional regression of the sample mean excess returns for the
stocks on the estimated betas from the first-pass regressions
̅ − ̅ = 0 + 1̂ + ,
d) This is called the ‘second-pass regression’. Comment on the model’s explanatory
power.
e) The CAPM implies that 0: 0 = 0 and that 0: 1 = ̅̅̅ − ̅. Test these two hypotheses
individually. State the alternate hypothesis for each of these tests.
An extended version of this approach can be used to test the null hypothesis that non-
systematic risk is not priced (as the CAPM predicts). This involves including the estimated
error variance ̂
2 from Step (i), as a regressor in the second pass-regression to capture non-
systematic risk,
̅ − ̅ = 0 + 1̂ + 2̂
2 +
Test 0: 2 = 0 using a t-test. If 2 > 0 it suggests that investors earn a risk premium for
bearing non-systematic risk. Are your results still supportive of the CAPM? Is this model an
improvement over the model in Step (ii)?
3. Data
This project requires using a sample of time series data on returns for a large sample of stocks,
market portfolio returns and risk-free rate . The proxy of market portfolio and risk-free
rates are FTSEAll-Share index and UK 3-month Treasury bill respectively. Samples of large
stocks were randomly selected from the UK FTSE350 index. These datasets were obtained
from Bloomberg Terminal for the period January 2009 to December 2019. The table below
describes data files available on Canvas.
Table 1: Data
Variable .csv file Description
,
A.csv, B.csv, …,
H.csv
Each .csv file contains a unique sample of monthly time series data on
stock returns. There are 100 time series for a sample of stocks randomly
selected from the UK FTSE350 index in each file. Stock names are
highlighted in the first row of the file. These returns are in per cent (%).
Each group is required to use the sample of stocks assigned to
them. Please check your name and group number against a dataset
in “Groups” file in “Assignment 2” folder on Canvas.
, RMRF.csv
Column heading "FTSEALLShare" provides monthly time series of
returns on FTSEAll-Share index. These returns are in per cent (%).
, RMRF.csv
Column heading “UK3mTBill” contains UK 3-month Treasury bill
yields, quoted per annum and in per cent (%).


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4. Criteria
Your task is to test the CAPM as outlined above and write a report. The report forms the basis
of your marks, and it must include the following –
• an introduction section comprising a brief description of the CAPM in your own words,
your question (what is it that you are doing here) and why must a reader be interested
in your report,
• presentation and discussion of the results of the model
• conclusions drawn based on the analysis and any suggestions for further work.
Marks will be given for a coherent description of the theory, the clarity of the processes in
econometric work and most importantly the quality of interpretation of all findings. You can
easily fill a word document with a 1500-word description of the numbers or by simply saying
that a null hypothesis is rejected or not rejected. However, that would undermine the task.
Instead, demonstrate your understanding of what your results mean in relation to the CAPM.
For example, if the null hypotheses 0: 0 = 0 and 0: 1 = ̅̅̅ − ̅ are not rejected, then the
CAPM holds. This implies that investors are rewarded for bearing the market risk. However,
you may find varying results leading to different interpretations and conclusions.
Marks will be deducted for any results provided with no interpretation. Marks will also be
deducted for late submission.
The body of the report should not exceed the word limit of 1500 words in any case.
The deadline for submission in Canvas is Week 10, 1st April 2022 by 17:00.
5. Report
The project should be typed in 12-point font size, double spaced, and should not exceed 1500
words in length (excluding graphs, tables, equations, R-script commands, and bibliographical
references). The project should contain a cover page with the following information:
• Title
• Full name
• Student ID numbers
• Group number
• Name of the stocks’ dataset assigned to the group (A, B, and so on).
Each project should have a References (Bibliography) section for cited works. The submission
types are restricted to word files with .doc or .docx extensions.
6. The R Script
The working R script must be appended to your work. The project will be considered
incomplete if you do not append the R codes to your report. You will then be asked to resubmit
the project, and the relevant penalty for late submission will be applied. The project will also
be considered incomplete if any code is omitted.
Therefore, you need to copy and paste the R file commands into your Word file containing
your project write-up at the end of this project. The code text does not count towards the word
count.

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7. Groups
This is a group assignment. You have been assigned into a group based on your tutorial group
in Canvas. This is done randomly, so you cannot choose you group mates. It is your
responsibility to contact and connect with your group members. I recommend that the first time
you meet you specify the roles and responsibilities of each group member. You will need to
complete the “FIN2028 Coursework submission form” and append this to your final report.
This won’t count towards the word limit.
8. A few tips
Stock returns and market returns are monthly, whereas UK 3-month Treasury bills are quoted
on a per annum basis. It is crucial that all time series are measured consistently – either all of
them are monthly rates or annualised figures.
For coding, I would create an R object consisting of time series of excess returns on stocks
only. I would use “for loop” for estimating the parameters of the first-pass regressions and
simultaneously recording ̂ and ̂
2 for each first-pass regression and the sample mean
excess returns ̅ − ̅.
9. An indicative timeline
It is completely up to you and your group mates how you want to proceed with the project. I
have mapped out a rough schedule for you to monitor the progress of the project. This is only
a suggestion – you can work as you wish.
Table 2: Timeline
Tasks completed By the end of Week
Understand the project
Meet/contact group members
Specify roles and responsibilities
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Literature review of the CAPM
Coding
Data analysis
Map out sections of the report
Start writing
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First draft of the report
Circulate amongst group members for comments
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Incorporate feedback from group members
proofread and submit the report
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10. Note on plagiarism
• Please cite references properly and include them in Bibliography.
• Each group member must understand the difference between plagiarism and
referencing.
• This is a group work. The marks for the entire group will suffer if plagiarism is detected.
In the most blatant situation, the group will be referred to academic affairs.
References
Gujarati, D. & Porter, D. (2009), Basic Econometrics, Mc-Graw-Hill (look under Capital Asset Pricing
Model in index).
Sollis, R. (2012), Empirical Finance for finance and banking, Wiley (Chapter 5).