School for Business and Society


Module Code: MAN00134M

Module Title: Quantitative Methods for Finance

Module Leader: Lewis Ramsden

Open/Closed Assessment: Open

Maximum Word Count: 1,500

Release Date: July 2025

Submission Deadline: 11am, Monday 11th August 2025

Weighting: 50%


Important information

A penalty of five marks will be deducted for late submissions that are made within the
first hour after the deadline. Submissions that are more than one hour late but within the
first 24 hours of the deadline will incur a penalty of ten marks. After the first 24 hours
have passed, ten marks will be deducted for every 24 hours (or part thereof) that the
submission is late for a total of 5 days. After 5 days it is treated as a non-submission
and given a mark of zero. The consequences of non-submission are serious and can
include de-registration from the University.

If you are unable to complete your open assessment by the submission date indicated
above because of Exceptional Circumstances you can apply for an extension. If
unforeseeable and exceptional circumstances do occur, you must seek support and
provide evidence as soon as possible at the time of the occurrence. Applications must
be made before the deadline to be considered.

Full details of the Exceptional Circumstances Policy and claim form can be found here:
https://www.york.ac.uk/students/studying/progress/exceptional-circumstances

If you submit your open assessment on time but feel that your performance has been
affected by Exceptional Circumstances you may submit an Exceptional Circumstances
Affecting Assessment claim form by 7 days from the published assessment submission
deadline. If you do not submit by the deadline indicated without good reason your claim
will not be considered.

Please take proper precautions to safeguard your work and remember to make
backup copies of your data. The University provides all its students with storage
space on the University server and you should save and back up any work in
progress on this server on a regular basis. Computer failure and theft of your
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equipment or storage media are not considered exceptional circumstances and
extensions cannot be granted for work lost for these reasons.

The University has guidance on the use of AI in assessments available here. This
details appropriate and inappropriate use of digital tools. Inappropriate use will
be considered academic misconduct, and penalised accordingly

Word count requirements

The word count for this assignment is 1,500 words.

You must state on the front of your assignment the number of words used and this will
be checked.

The main text for this assignment must be word-processed in Arial, font 12, double
spacing, minimum 2cm margins all around.

You must observe the word count specified in this assignment brief. The School has a
policy of accepting variations to the recommended word count of plus or minus 5%.

What does this mean for you?

Markers will mark your work up to the word count maximum plus 5% and then will stop
marking; therefore all words which are in excess of the word count plus 5% will not be
marked.

Where your word count is more than 5% below that specified, it is likely that this will
result in a lack of analytical depth or relevant content, which will be reflected in the mark
assigned.


What is in the word count?

The word count includes:

- the main text, including in-text reference citations and quotations.

The word count does not include:

- Appendices. These may be used to include supporting data, which may be too
detailed or complex to include as a Table. They are not a device to incorporate
material, which would otherwise cause you to exceed the word limit.

- Title page
- Contents page
- Abstract/executive summary
- Tables, figures, legends
- Reference lists
- Acknowledgements


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Assignment:

For this assessment, you are tasked with applying your knowledge, skills and expertise
to analyse financial data and provide statistically informed insights and
recommendations to a client. The assessment is split into TWO parts: Part 1 concerns
returns on different index funds, whilst Part 2 considers the (possible) linear
relationship(s) between a company’s “Sales” and advertising strategy.

Your final solution should be in the form of a 1,500 word written report. Mathematical
formulae do not count towards your word limit. Within your report, you should include a
response to ALL of the questions provided below but could also include any additional
analyses you believe relevant to the problem. To ensure a thorough report, you should
include details of any model assumptions, limitations and considerations used within
your analysis.

Part 1 (Analysis of returns):

You work for a hedge fund company and have been tasked with analysing the returns
on different assets from different asset classes. More specifically, the returns from
GLOBAL UK, YORKTECH LTD and GREENFOODS INC stocks.

Below you will find summary statistics for the daily log-returns for these three assets,
as well as an equally weighted portfolio, over the last 5 years:


















Note: This data is based on 1235 observations over a 5 year period (247 trading days
per year).

Your line manager would like you to analyse these different assets as in possible
investment opportunities and provide a summary of your findings. Your manager has
provided a list of specific tasks and questions for you to include in your analysis:

1) For each of the funds above (GLOBAL UK, YORKTECH LTD, GREENFOODS
INC and Portfolio), calculate the daily Sharpe ratios assuming a risk free rate of
4% per annum over the same 5 year period.
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[6 marks]

2) Using the summary statistics provided in the table above, and your answer to
part 1), provide a general summary of the FOUR different assets. Explain which
you think would be the best investment and why.
[8 marks]

3) It is assumed that the daily-log returns for GLOBAL UK are independent and
normally distributed with unknown mean and unknown variance . Using the µ σ2
sample data, determine (unbiased) point estimates for the parameters and . µ σ2

[4 marks]

4) Using your results from part 3), estimate the probability that GLOBAL UK stock
will produce a daily-log return between 0% and 0.02%.

[6 marks]

5) Based on the sample data provided, comment on the assumption of normally
distributed log-returns for GLOBAL UK.

[3 marks]

6) The daily-log returns of YORKTECH LTD, denoted are assumed to {
1
, ... ,

}
be independent but NOT necessarily normally distributed. Using the sample of
data provided, test the hypothesis that the population mean is equal to 0.00025
at the 5% significance level.
[6 marks]

7) Given that the true population mean is actually 0.00027, calculate the power of
the hypothesis test conducted in part 6). What does the power of the test
represent?

[7 marks]



Part 2 (Regression Modelling):


It is believed that the sales made in a company (in thousands of GBP) is linearly related
to the amount of money spent on advertising (in thousands of GBP). That is

,

= β
1
+ β
2


+



where and represent the amount of sales and money spent on advertising for



company , respectively, and are unknown parameters and are β
1
β
2


∼ (0, σ2)
normally distributed errors.

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The above regression model has been fitted to a sample of data from 200 companies
across the UK and the results are given in the output below:




Analyse the above model by answering each of the following questions and provide
your expert opinion on the validity of this model and the linear relationship between the
sales and money spent on advertising:

1) Using the output provided, determine the value of the correlation coefficient
between “Sales” and “Money Spent on Advertising”. What does this value tell us
about the type of correlation between these two variables?
[5 marks]

2) The coefficient estimates for parameters and are calculated via the method β
1
β
2
of Ordinary Least Squares (OLS). Explain, in words, the OLS method for
estimating these unknown parameters in the context of this model.

[5 marks]

3) Interpret the estimated parameter values for and . What do the values β
1
β
2
represent in the context of this model?
[6 marks]

4) Comment on the ‘quality of fit’ of this linear regression model.
[5 marks]

5) Explain the difference between an estimator and an estimate in the context of
this model.

[4 marks]

6) State the distribution of the OLS estimator for , including all parameters of the β
2
distribution.

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[4 marks]

7) Hence, determine the 99% confidence interval for . β
2
[6 marks]

8) Comment on the significance of “Money Spent on Advertising” on “Sales”. Justify
your answer.
[6 marks]

9) Explain the purpose of the error variables, , in a linear regression model.

[5 marks]

10) Given the fitted model, estimate the average “Sales” of a company given that
they spend £110,000 in advertising.

[4 marks]

After some further investigation it is now believed that the relationship between “Sales”
and “Money Spent on Advertising” is NOT linear but instead logarithmic. Moreover, it is
believed that the “Advertising Type” (Social Media, TV or Radio), also has an effect on
“Sales”.

11) Write down a normal regression model for the relationship between “Sales” and
the proposed explanatory variables “Money Spent on Advertising” and
“Advertising Type” (assume each company only uses one form of advertising
type). Define every variable and parameter included and explain what the
individual parameters represent in context to the model.

[10 marks]


[Total = 100 marks]



















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before upload

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specified otherwise.

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If yes;


Please insert here any assessment specific matrix - these need to be approved by BoS
before use.

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Finally;


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head of group will be able to let you know who your internal moderator is
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