ETF5930 Financial Econometrics
Semester 1, 2023
Assignment 1
Due Date: Friday 28 April 2023 (Week 8)
Due by 11.55pm Melbourne time
When performing a hypothesis test, use = 0:05. This is an individual assignment. Unless
otherwise speci?ed, feel free to report any decimal places you like when presenting your
answers. Please include EViews outputs in your answers. In this assessment, you must not
use generative arti?cial intelligence (AI) to generate any materials or content in relation to
the assessment task.
This assignment will be marked out of 50 marks and this mark will be converted to a mark
out of 15 for the purpose of establishing a ?nal mark for you in this unit.
You are required to complete your answers in a Word document and then upload your
completed ?le in PDF through Moodle submission. Your assignment can be either (i)
entirely handwritten or (ii) entirely typed or (iii) a mixture of handwritten and typed answers.
You may take photos of handwritten answers and paste them on a Word document.
If you prefer not to use Word, feel free to use apps such as Camscanner or Microsoft Lens:
PDF Scanner (available on iPhones and Android) to convert photos of your handwritten
answers into PDF. This app can combine multiple pages into one PDF document.
You can access Microsoft Word via the MoVE website https://move.monash.edu/
Please save your Word document as PDF with its ?le name as your name and student ID.
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Short Extensions (https://www.monash.edu/students/admin/exams/cant-complete)
You may be eligible for a short extension of ?ve calendar days or less if you can?t complete
your assessment on time due to short-term exceptional circumstances, such as: illness, carer
responsibilities, car accident, testing positive for COVID-19. You can request a short exten-
sion by emailing your Chief Examiner, Kew (email: hsein.kew@monash.edu), before the day
that your assessment is due. Make sure that you explain why you need an extension and for
how long. No need to provide supporting documents.
Long Extensions
If you can?t receive a short extension, or you need more than ?ve calendar days, you can
apply for a long extension of 10 calendar days or less by submitting a Special Consideration
Application form, as long as you can provide the required supporting documents, via the
link here:
https://www.monash.edu/students/admin/exams/cant-complete/extend#tabs__3092628
Answer Preparation Tip:
It is very simple to copy output from EViews and paste it directly into a Word document for
writing up your assignment answers. To copy the EViews output, on your computer keyboard
you press PrtScn. Or you can use "snipping tool" to capture screenshots on your Windows
10 - see this website: https://support.microsoft.com/en-au/help/4027213/windows-10-open-
snipping-tool-and-take-a-screenshot. Or you can take "screenshot" on your Mac - see this
website: https://support.apple.com/en-au/HT201361.
Question 1 [1+1+1+1+1+1+3+3 = 12 marks]
Go to the Yahoo Finance website. Pick your favourite U.S. stock and download itsmonthly
data from January 2011 to December 2022. Perform your analysis on the monthly adjusted
closing prices.
If you are having issues accessing the yahoo ?nance website, feel free to use the following two
Excel ?les: (i) tsla.csv and (ii) r3000.csv. The tsla.csv ?le contains monthly adjusted closing
prices of Tesla (ticker symbol TSLA) in column B. Tesla manufactures electric cars and is, as
of 2023, the world?s most valuable car-maker. Feel free to use Tesla as your favourite stock.
The r3000.csv ?le contains the R3000 index (see part (f) below) in column B.
(a) What is your favourite stock? Write down its ticker symbol1. Plot the price data of
your stock. Write down the values for the ?rst three observations of your price data.
(b) Compute simple returns of your stock. Express the simple returns as percentages and
then plot the simple returns. Write down the values for the ?rst three observations of
your simple returns in percentage terms.
1For example, the ticker symbol for the Tesla stock is "TSLA".
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(c) Compute log returns of your stock. Express the log returns as percentages and then
plot the log returns. Write down the values for the ?rst three observations of your log
returns in percentage terms.
(d) Based on the time plots in parts (a) to (c), do any of them look like a stationary process?
Explain.
(e) Plot the simple returns and log returns on the same graph and compare the two returns.
(f) Download monthly data for the Russell 3000 Index (or simply the R3000) ticker symbol
^RUA, for the same time period as your stock. Compute log returns of this R3000
index. Express the log returns as percentages and then plot the log returns. (For your
information, R3000 is a benchmark of the entire U.S. stock market because it is based
on the performance of the 3,000 largest publicly held U.S. companies.)
(g) Report the sample mean and sample standard deviation for (i) the log return of your
stock in percentage, and (ii) the log returns of the R3000 index in percentage. Brie?y
comment on these statistics and compare your stock with the R3000 index.
(h) For your favourite stock, estimate the CAPM regression model
rjt rft = 0 + 1 (rmt rft) + et
where rjt is the monthly log return of your stock in percentage, rft is the monthly
risk-free rate in percentage, where you will use the 3-month Treasury Bill rate (tb3ms)
as the risk-free asset and rmt is the monthly log return on a market index portfolio in
percentage, where you will use the R3000 index as the market index portfolio. The
Excel ?le tb3ms.csv (see Week 5 tutorial question 1) contains tb3ms in column B from
January 1934 to January 2023. Interpret the estimated beta risk ^1 of your favourite
stock. What is the percentage of market risk? What is the percentage of ?rm-speci?c
risk?
TESLA....the future is "electric cars" and not
"petrol cars"
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Question 2 [4 marks]
Jane has been o¤ered a choice between two portfolios of ?nancial assets. Each portfolio is
made up of shares in only two companies. The ?rst portfolio consists of shares in company A
and company B, both weighted equally. The second portfolio consists of shares in company C
and company D, both weighted equally. Jane is told that the expected value of the returns of
the two portfolios is exactly the same. So the choice between the two portfolios will depend
solely upon whether one is more risky than the other. Jane has been told that the variance
of returns for company A is the same as that for company C and that the variance of returns
for company B is the same as that for company D. Jane has also been told that returns
for company A and for company B are perfectly and negatively correlated (AB = 1 in
this case) while the returns for company C and for company D are perfectly and positively
correlated (CD = 1 in this case). If Jane is risk averse (ie, prefers less risk to more risk), is
it possible to tell which portfolio will she choose? Why or why not?
Question 3 [1+1+2+2 = 6 marks]
One general belief held by observers of the business ?nance world is that taller men earn
more money than shorter men. In a study reported in the Wall Street Journal published
on 18 March 20122, 30 Master of Finance graduates were surveyed and asked to report their
annual incomes (in dollars) and their heights (in centimetres). This information is recorded
in the EViews work?le earn_more.wf1.
(a) In EViews, draw a scatter diagram of income (y-axis) versus height (x-axis). What do
you see?
(b) Use EViews to perform a regression analysis where the dependent variable is income.
Write down the sample regression line.
2For those who are interested, the link is https://www.wsj.com/articles/
SB10001424052702304459804577285710102760818. You need to subscribe to continue reading. However
reading this article will NOT at all help you to answer the questions.
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(c) Interpret the estimated slope coe￠ cient.
(d) Predict the income of a man 175 centimetres tall.
Question 4 [1+4+1+(3+3+3)+5+8 = 28 marks]
The EViews data?le ?rm_size.wf1 contains monthly data from January 1941 to January
2021. The work?le (downloaded from Ken French?s website) contains 961 observations for
the following variables3:
ret_large = monthly log return on a portfolio of large sized ?rms in percentage
ret_medium = monthly log return on a portfolio of medium sized ?rms in percentage
ret_small = monthly log return on a portfolio of small sized ?rms in percentage
ret_market = monthly log return on a market index portfolio in percentage
rf = monthly risk-free rate in percentage
SMB = measures the ?size?factor in percentage
HML = measures the ?value?factor in percentage
Consider estimating the CAPM as a regression model for a portfolio j as
rjt rft = 0 + 1 (rmt rft) + et (1)
where rjt is the monthly log return on a portfolio j (either large sized ?rms or medium sized
?rms or small sized ?rms) in percentage, rft is the monthly risk-free rate in percentage,
where we use the 3-month Treasury Bill rate as the risk-free asset and rmt is the monthly log
return on a market index portfolio in percentage, where we use the value-weighted portfolio
of all ?rms listed on the NYSE, AMEX, or NASDAQ as the market index portfolio.
When answering the following question, you may ?nd the following information useful: the
t-test
t =
^j j
Std. Error
for j = 0; 1; and z0:025 = 1:96 and z0:05 = 1:645:
(a) For each of the three portfolios (large sized, medium sized, small sized) estimate the
regression model in equation (1). Write down the three sample regression lines.
(b) You are employed as a ?nancial analyst by an investment ?rm in Melbourne. Liz (your
manager) says that the CAPM predicts that large sized ?rms command a higher return
than the market portfolio. Is Liz correct in saying this? Explain.
(c) Report the R2 for the three regression models in part (a)?
3Sometimes large sized, medium sized and small sized ?rms are called large-cap, mid-cap and small-cap
?rms. Large-cap ?rms have a market capitalisation of more than $10b while small-cap ?rms have a market
capitalisation of less than $2b.
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(d) Use = 0:05.
(i) For the large sized ?rms portfolio, test the following hypothesis
H0 : 1 = 1
HA : 1 < 1
by using EViews.
(ii) For the medium sized ?rms portfolio, test the following hypothesis
H0 : 1 = 1
HA : 1 6= 1
by using the p-value approach.
(iii) For the small sized ?rms portfolio, test the following hypothesis
H0 : 1 = 1
HA : 1 > 1
by calculating the t-test by hand.
(e) For each of the three portfolios (large sized, medium sized, small sized), estimate the
FF3F CAPM regression:
rjt rft = 0 + 1 (rmt rft) + 2SMBt + 3HMLt + et
Write down the three sample regression lines. For each of the three estimated regression
models, can you reject the null hypothesis that 2 = 3 = 0? Explain. Use = 0:05.
(f) Liz wants you to write a brief summary in which you will summarise your ?ndings (based
on your answers to parts (a) to (e)) about the relation between systematic risk and the
size of ?rms. (Note that this question will be marked entirely on your write-up. Keep
your summary succinct, detailing only essential information. Marks will be deducted
if your summary is unclear and contains irrelevant information.)