Module Title: Quantitative Finance
Module Code: NBS-7047B
Part A: Diversification (500 words)
What do we mean by ‘diversification’ and why is it important for investors? (20 marks)
Part B: Optimal Capital Allocation (2,500 words)
You are an investment analyst in a large financial institution. A client enquires about a potential investment in
Apple Inc. and Amazon.com Inc. Her investment budget is $1,000,000 and her utility (U) has the form:
𝑈 = 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑅𝑒𝑡𝑢𝑟𝑛 −
∙ 𝑅𝑖𝑠𝑘 𝐴𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟 ∙ 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒
Using a profile investment questionnaire, you determine that the client is conservative with respect to risk
since her risk-aversion factor (A) is equal to 10. You are required to undertake a thorough investment analysis
in order to propose the optimal capital allocation for the client. Your analysis, along with your final
recommendation, should be presented in a comprehensive report.
Section 1: Download from Yahoo! Finance (https://uk.finance.yahoo.com/) the monthly dividend-adjusted
prices for Apple Inc. (Symbol: AAPL) and Amazon.com Inc. (Symbol: AMZN) for the most recent 5-year period
(i.e., 60 monthly observations). Plot the stock price evolution for both firms on the same graph and comment
on each firm’s performance (Figure 1). Calculate the monthly period returns for both stocks; plot them on the
same graph and comment on each firm’s risk (Figure 2). Plot the scatter diagram of the two stock returns, add
the trend line and display its equation on the graph (Figure 3). What can you infer with respect to the
relationship between the two stock returns? Calculate for both return series descriptive statistics (mean,
median, skewness, kurtosis, variance and standard deviation), their covariance and correlation factors (Table
1). What is their meaning from both a statistical and financial perspective? (20 marks)
Section 2: Construct the investment opportunity set for the two stocks using 1% weight increments and plot
the efficient frontier (Figure 4). Assuming an annual T-Bill rate of 10% calculate also the Sharpe ratio for each
weight combination (Table 2). What is approximately the weight combination for the minimum-variance
portfolio and what for the optimal risky portfolio? (20 marks)
Section 3: Using the ‘Solver’ add-in in Microsoft Excel find the exact weight combination for the minimumvariance portfolio and the optimal risky portfolio. Indicate the position of both portfolios on the efficient
frontier; draw the minimum-variance capital allocation line (CAL) and the optimal CAL, add their trend lines
and display their equations on the graph (Figure 5). What is the key difference between these two CALs? For
what kind of investor will you propose the minimum-variance CAL? What is the slope of the optimal CAL? What
is the intercept of both CALs? (20 marks)
Section 4: Using the ‘Solver’ add-in in Microsoft Excel find the exact optimal capital allocation and identify the
complete portfolio on the optimal CAL (Figure 6). If the risk-aversion factor for your client was 20 instead of
10, would the optimal capital allocation portfolio ‘move’ towards the left or towards the right relative to the
current position on the optimal CAL? According to your analysis, what is the proportion of your client’s
investment budget (in both % and $) that should be allocated in T-Bills, Apple’s stock and Amazon’s stock
(Table 3)? (20 marks)
The report should be typed in Microsoft Word using Times New Roman font with a size of 12 points;
use normal margins (2.5cm on top, bottom, left and right); line spacing must be 1.5 lines with an extra
line between paragraphs and headings; alignment must be justified. All sections, tables and figures
must be clearly titled and sequentially numbered. All tables and figures should be self-explanatory and
should include necessary axis definitions and legends. Numbers in the text, tables and figures should
have a reasonable number of decimal points in order to allow an accurate representation and
comparisons (usually between 2 and 4 decimal points).
The report should not exceed 3,000 words in total (500 words for Part A and 2,500 words for Part B)
and should be structured following the parts and sections above.
For Part B, each section should include details about the data used and of your calculations (e.g.
formulas used). Also, you should include as a minimum the figures and tables suggested in the
description of each section above. Moreover, all calculations should be performed using Microsoft
Excel in a single workbook with multiple worksheets. You should upload the Excel file along with the
Word (or pdf) file containing your report with your submission. You will lose 40 marks for not
uploading the Excel file.
Include at least 5 references to articles in credible professional magazines, academic journals and/or
textbooks. Do not include articles that you do not cite within your report or that you have not at least
partly read. Do not use material that exists exclusively on the Internet (e.g., websites and blogs) or
module lecture notes/slides as sources in your references.
Word Length: 3,000
The deadline for submission for all reassessment coursework is 15:00 on 10 September 2020.
The assignment will be submitted electronically via e:Vision or Blackboard; there will not be an option to
submit a hard copy. Even late assignments, or those that have extensions, should be submitted electronically
rather than in paper format. Work uploaded after 15:00 on the specified deadline day will incur a late penalty
unless there is an approved extension. Students are advised not to leave it to the last few minutes before
15:00 to upload work, just in case they encounter any upload problems.
Electronic submission will be by PDF and for those submitted via e:Vision, printing will be in black and white
unless your Module Organiser has indicated otherwise. As part of the upload process, a coversheet will be
automatically attached to your work before the work is printed out.
Students will need to fill in the following on the e-cover sheet:
1. Add in the marker’s name where they have been asked by their lecturer to do so.
2. Students should add in the Word Count for their piece of work, including the footnotes and
endnotes, references (in the main text), tables and illustrations and if applicable the abstract, title
page and contents page. Any appendicised material and the bibliography or reference list should
not be included in the word count.
3. Students should also apply their Specific Learning Difficulty (SpLD) e-sticker, if appropriate
Where your module is being marked via Blackboard, please go to the module Blackboard site and submit your
work via Reassessment 19-20, in the left hand column. General instructions regarding Blackboard submissions
can be found here.
How will you know where to submit your work?
Your coursework submission page on the portal will tell you. If there is a link to submit directly from the page,
this means you are submitting via e:Vision. If there is an instruction beside the assessment item saying ‘work
to be submitted via Blackboard’, then you must go to the module Blackboard site. If in doubt, please contact
your hub immediately to check.
University Policy on Plagiarism and Collusion
It is important that all students familiarise themselves with the rules and regulations regarding plagiarism and
collusion. Understanding these rules will help you to avoid plagiarism and to maintain the quality of your
The current rules and regulations can be found here.
Information and support on how to avoid plagiarism can be found in http://www.uea.ac.uk/plagiarism
Individual study skills support and advice on referencing is also provided by the Learning Enhancement Service
at the Dean of Students Office.
You may be requested to provide a digital copy of your coursework (after an initial examination of the hard
copy by the coursework assessors) for use with plagiarism detection software. Instances where plagiarism is
suspected will be investigated. Students who are found to have plagiarised will be penalised.
In proven cases offenders will be punished and the punishment may extend to degree failure, temporary
suspension or expulsion from further study if the case comes before a Discipline Committee of the University.
All reassessment coursework must be submitted by 15:00 on 10th September 2020. Failure to submit on time
without an approved extension will result in a penalty for late submission.
Please note that the deadline represents the last time that a piece of work can be submitted, and not a target.
You are advised to plan ahead, and submit work well in advance of the deadline. This will help to ensure that
any last minute delays do not result in late submission.
Extensions to Coursework Deadlines
In exceptional circumstances, you may be entitled to request an extension to a deadline for the submission of
work required for assessment. Requests for coursework extensions should be applied for online via eVision
together with appropriate supporting evidence.
Extension requests can be submitted on the following grounds:
Medical (subject to a doctor’s note)
Serious personal issues (subject to supporting evidence)
Extension requests cannot be considered for the following:
Poor time management
Transport or parking delays
IT problems (unless evidence can be provided from an IT technician)
Medical or personal circumstances that are not accompanied by supporting evidence
You should plan your work so that minor delays do not prevent submission on time. In all cases, you should
ensure that you make regular backup copies of all coursework in progress.
Where extenuating circumstances prevented you from applying for an extension in advance of the deadline,
work submitted after the deadline should be accompanied by an online extension application. Allowance will
be given for acceptable extenuating circumstances and in such cases penalties for late submission will not be
Extension requests will be considered by the Coordinator in those instances where acceptable extenuating
circumstances exist and the request is submitted before the deadline. The designated member of academic
staff in the School will consider all other requests.
Penalties for Late Submission
If you submit coursework after the published deadline, without an approved extension, the following penalties
Work submitted Marks deducted
After 15:00 on the due date and before 15:00 on the
day following the due date. (Up to 24 hours)
After 15:00 on the second day after the due date
and before 15:00 on the third day after the due
date. (Up to 72 hrs)
After 15:00 on the third day after the due date and
before 15:00 on the 20th day after the due date.
(Over 72 hrs)
All the marks the work merits if submitted on time (i.e.
no marks awarded.)
After 20 working days Work will not be marked and a mark of zero will be
Late submission of pass/fail marked work for assessment in the absence of acceptable extenuating
circumstances will be awarded a fail mark.
Saturdays & Sundays will not be taken into account for the purposes of calculating marks deducted.