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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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