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ECON90033 Semester 2, 2025 Assignment 1
ECON90033 – QUANTITATIVE ANALYSIS OF FINANCE I
Second Semester, 2025
Assignment 1
Due date and time: Friday 5 September, 11:00AM
Please read the following instructions carefully before starting to work on the
assignment.
 There is a total of 50 marks for this assignment. It is worth 15% of the final
grade for QAF1.
 This assignment must be submitted online via the LMS by 11:00AM on
Friday 5 September. Any assignment not submitted by the due date and time
will incur a penalty of the available marks: namely, 10% penalty for 1-60
minutes late, 20% penalty for 61-120 minutes late, 30% penalty for 121-180
minutes late, etc., until zero mark.
 Students may work alone and submit their own assignment answers if they
wish to do so, or they can work on the assignment in pairs. In the latter case,
each assignment pair must submit only one set of assignment answers, and
both students of the pair will receive the same mark for their assignment. It
is not allowed to form assignment groups of more than two students.
 Please note that the assignment submission process has two stages:
1. Registering your assignment group (only if you work in a pair), and
2. Submitting the assignment online via the LMS.
Students who intend to work on the assignment in pairs must register their
groups. To do so, click the “People” link and then the Groups tab in the
Canvas course navigation menu. The group names (set by default) are A1
Group 1, A1 Group 2, A1 Group 3, etc. Every assignment pair MUST register
as one of these created groups for submitting the assignment and not create
a new group. The deadline for registering your group is 5:00PM on Friday 22
August. If a pair fails to register their group before the deadline for group
registration, both students will need to make an individual, i.e., sufficiently
different, submission.
Students making individual submissions do not need to register.
 Answer the assignment questions using Microsoft Word or some other word
processing software (WordPerfect Office, LaTeX, R markdown, Scientific
Work, etc.). Make sure to include a cover page in the document with the
student ID, the name, and the tutorial group of each group member.
 If a task involves some manual calculations, use your calculator (not R,
Excel, or any other software), the relevant statistical table(s), and show the
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ECON90033 Semester 2, 2025 Assignment 1
major steps, including the formulas in the document. Otherwise, use only R
/ RStudio and paste your scripts, screenshots, and printouts (graphs, output
tables, etc.) into the document.
 Once you complete the assignment, convert the whole file to PDF before
submitting it online via the LMS. Please note that only PDF files can be
uploaded to the LMS.
 Do not forget to preview your assignment after uploading it on the LMS to
ensure that you have indeed uploaded the correct and complete assignment
and that its formatting is in order as in the original document. Submissions
that are late because of formatting issues or because a version is
incomplete, will not be accepted.
Assignment Tasks and Questions
Download the a1e1.xlsx and a1e3.xlsx files. There are three exercises in this
assignment, each consisting of several parts. Every exercise and part is
compulsory. For every test you are asked to perform and comment on, state the
hypotheses, make a statistical decision with explanation, and state your
conclusion. Be precise and explain your statements and answers.
Exercise 1 (3 + 17 = 20 marks)
The a1e1.xlsx Excel workfile has three sheets that contain daily, weekly, and monthly
prices (Price), respectively, of the S&P/ASX 200 index1 from the beginning of January
2000 to the end of June 2025.
a) Launch RStudio, create a new project and script, and name both a1e1. Import the
Price data from the daily, weekly, and monthly sheets of the a1e1.xlsx file to
RStudio, and save them as a1e1.RData. Attach this data set to your R project.
From the three Price series create three xts objects, and name them Price.d,
Price.w, Price.m, respectively. Take a screenshot of the two panels on the right
side of your RStudio window and insert it in your report.2
b) Compute logarithmic returns (expressed as decimals) from all three Price series,
and name them r.d, r.w and r.m. Using these log returns and the lm() function,
estimate the following regression for each frequency:
1 The S&P/ASX 200 index is a market-capitalisation weighted index of the 200 largest stocks listed on
the Australian Securities Exchange
2 On a Windows PC you can use the Snipping Tool to take a picture of the two right-side panels of your
RStudio window. Do not take a picture of your whole screen because it will be impossible to see the
details of the RStudio window.
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ECON90033 Semester 2, 2025 Assignment 1
0 1 1t t tr r    
where r = {r.d, r.w, r.m}.
Briefly evaluate and compare the three regressions in terms of the quality of the
fit to the data and overall significance. Does it seem to matter whether the
frequency of the log returns is daily, weekly or monthly?
In week 1 you learnt that although the simple and logarithmic returns are not the same,
the logarithmic return is often favoured in practice because (i) it makes easier to
calculate multi-period returns, and (ii) it is approximately equal to the simple return as
long as the simple return is not too large3.
Although by definition the one-period simple and logarithmic returns (Rt and rt) satisfy
the following equation
ln(1 )t tr R  (1)
Hudson and Gregoriou (2015)4 show that the relationship between their sample means
depends on the sample variance of the simple return. In particular, the following
approximate relationship holds:
20.5
tt t R
r R s  (2)
According to this formula, (i) the sample mean of the log returns is smaller than the
sample mean of the corresponding simple returns, unless the simple returns are
constant and thus their sample variance is zero, and (ii) the larger the sample variance
of the simple returns, the greater the difference between the sample means of the two
returns.
Using daily data on the Dow Jones Index from 2 January 1897 to 23 March 2009,
Hudson and Gregoriou (2015) illustrate that this approximation is pretty accurate in
practice. Namely, they find that the ratio of the mean log return to the ‘expected’ mean
log return, given by the expression on the right side of eq. (2), is 0.99913.
But is this approximation reasonably accurate in general? It has been derived from
the Taylor expansion of the log return
2 3 4
1
1
ln(1 ) ... ( 1)
2 3 4
i
it t t t
t t
i
R R R RR R
i



       
3 See Exercise 5 of Tutorial 2.
4 Hudson and Gregoriou (2015): Calculating and Comparing Security Returns is Harder than you Think:
A Comparison between Logarithmic and Simple Returns, International Review of Financial Analysis,
vol. 38, pp. 151-162.
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ECON90033 Semester 2, 2025 Assignment 1
assuming that for every t the cubic and higher order terms (i.e. i  3) are so small that
they can be neglected. If this is untrue, eq. (2) can be quite inaccurate.
In the next exercise you are going to check the accuracy of this approximation by
applying it to the daily S&P/ASX 200 index.
Exercise 2 (3 + 4 = 7 marks)
a) Launch RStudio, create a new project and script, and name both a1e2. Import the
data again from the daily sheet of the a1e1.xlsx file to RStudio, save them as
a1e2.RData, attach them to your R project, and create the Price.d xts object. From
Price.d calculate the simple and the logarithmic returns (R.d, r.d). How do their
sample means compare to each other? Do they support the first conclusion drawn
from eq (2)?
b) Calculate the ratio of mean log return to the ‘expected’ mean log return, given by
the expression on the right side of eq. (2). What do you conclude from this ratio?
Exercise 3 (2 + 7 + 6 + 8 = 23 marks)
The a1e3.xlsx file contains seasonally unadjusted monthly observations from January
2006 to June 2025 on the following variables:
USDI: nominal US dollar index5 (Jan 2006 = 100).
INFR: US annual inflation rate (percent, all items in U.S. city average, all urban
consumers).
INTR: US 1-year real interest rate (percent).
a) Given these variables, consider the following population regression model:
0 1 2t t t tUSDI INFR INTR      
What prior expectations do you have about the logical signs of the two slope
parameters?
b) Launch RStudio, create a new project and script, and name both a1e3. Import the
data from the a1e3.xlsx file to RStudio, save them as a1e3.RData, and attach this
data set to your R project. Create ts objects from the data on the three variables.
Estimate the regression model in part (a). Write out the sample regression
5 The U.S. dollar index is a measure of the value of the dollar against the basket of the euro, the Swiss
franc, the Japanese yen, the Canadian dollar, the British pound, and the Swedish krona.
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ECON90033 Semester 2, 2025 Assignment 1
equation. Do the signs of the slope estimates meet your expectations? Interpret
the slope estimates. Is the estimate of the y-intercept meaningful this time?
c) Comment on the adjusted R2 statistic and on the F-test for the overall significance.
Are the coefficients significant individually at the 1% level? In the light of your
answer in part (a), are the coefficients significant individually in the expected
directions at the 1% level?
d) Conduct residual analyses by performing (i) the White test for heteroskedasticity,
(ii) the Breusch-Godfrey LM test for autocorrelation of order 1 to 4, (iii) the Jarque-
Bera test for normality, and (iv) the Ramsey regression specification error test with
a 3rd degree polynomial. Perform each test at the 5% significance level.

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