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ECON3107 { Economics of Finance
Assignment 2
T1, 2020 School of Economics
Instruction (Please read carefully.)
The purpose of this assignment is to give you practice in applying the knowledge delivered
in classes, analyse real world questions, and present your results in a professional way.
The assignment simulates the research and teamwork you will encounter in your daily
life. The assignment is not a project to leave until the last minute so a suggested time
line is provided below to help to plan your research and writing.
The Deadline. This assignment counts for 30% of the final mark. A submission channel
will be opened close to the deadline. The only way to submit is via the submission
channel. Email submissions will not be considered. The deadline for submission
is 23:59 on Sunday April 26 (end of Week 10). Late submission will not be
considered. Early submission is allowed after the submission channel opens, but please
submit once only. No revision will be accepted after submission.
The Teamwork and Project Charter. Teamwork is an essential part of the assignment.
The team project charter, attached underneath this document, is a project planning and
management tool. Your team will be working together on planning, analysing, developing, writing up, proofreading and editing your project report ready for submission. You
are also jointly responsible for allocating relevant tasks including research, logistical and
organisational duties. Each team member is expected to have a similar level of involvement and contribution to the assessment process and product. Each group will need to
submit a charter, signed off by each team member, by 23:59, Sunday, April 5.
Peer Review Marking. After submission, we will give each group one overall mark, call it
M, if you like. Alongside the assignment submission, each member will submit a mark
which indicates the satisfaction level, out of 100%, for her/his group mate, or each of the
group mates, if the group has 3 members. Call this “S”, for satisfaction. Each individual
member’s mark then will be: M × S. In case of 3 member groups, S will be the average
satisfaction mark. In case of large discrepancy in the peer review marking, the team will
need to present the completed project charter to the lecture, and trigger a dispute. The
lecture will then make a final decision based on the charter.
Plagiarism vs. Discussing. All assignments will be checked for plagiarism. See notes on
Plagiarism here. While discussing the assignments is encouraged, do not lend your assignment to another group. When an assignment is copied, it is difficult for the instructor
to determine who the copier is and you may be penalised heavily. It is in your interest
to do the assignment independently.
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be removed from this material.
Time line. Week 6 Assignment released. Carefully read the assignment. Consider the
method you will use, the information you will need and where to get it. A team discussion
about all relevant aspects is expected. Break down the tasks and discuss with your team
mate about potential options. Each team member is expected to do some part of each
question. Draft a preliminary version of your team charter.
Week 7 Carry out a comprehensive study about relevant topics. Carefully consider
each sub-question. Examine thoroughly the relevant information. Consider your presentation. It will be useful to draft a format template for everyone in the group to work on
it. Keep a record of your progress and each individual’s contribution faithfully. Submit
your team charter before the deadline.
Week 8 Demonstrate your ability solve the questions using the knowledge you learnt
from the course to explain/understand the topics. Pin-point your calculation results/insights,
and think of how your part of the question will fit in the big picture. Discuss with your
team mate(s) about the structure/organization of your project. Do NOT cite articles or
graphs without acknowledgment. Do NOT assume the reader will understand a piece of
Matlab code with no instruction. Keep a record of your progress and each individual’s
contribution faithfully.
Week 9 & 10 Draft your assignment. Carefully address each sub-question, and
organize in a logical-coherent way. Paragraph your answer. Do not be reluctant to use
full-stop. Read each sentence again. Make sure each sentence has a purpose, and it is
clearly understandable. If time allows, do not be reluctant to polish your assignment
again. Submit your assignment before the deadline.
Submission Format. The assignment needs to be typed, and the pdf file needs to be
submitted before the deadline through online submission channel.
Cover Page Each submission should contain a cover page. The cover page should
specify names and IDs of all the members of the group. Title the submission as
“ECON3107/5106 Assignment 2”, if you like.
Body Text The submission should be divided into individual questions. The text
should be in either 1.5 or double-spaced typescript. The font size should be no less than
11 point (use 10 point for footnotes) in a legible font. Use A4 (297mm x 210mm) paper.
Number pages consecutively. The margins on each page should not be less than 30mm
on the left-hand side, 30mm on the right-hand side, 30mm at the top and 20mm at the
bottom. Diagrams, charts and tables should be presented within the text when possible.
DO NOT INCLUDE CODING OR LENGTHY CALCULATION IN THE BODY TEXT.
Coding and lengthy calculations should be contained in appendix. You may wish to insert
a indicator in the body text to direct your reader. For example, “please refer to appendix
I, part ii for Matlab coding” will look like a nice indicator.
Appendix Appendix includes reference, Matlab coding, and medium steps of mathematical calculations. Faithfully reference the literature you have reviewed during your
study. All matlab codings need to be included in appendix. Organize your coding and
calculations in chronological order. Make captions for your coding and calculations for
each section. Make sure content of your coding and calculations match with the caption
and the indicators in the body text.
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be removed from this material.
Question 1, Option pricing (6 marks)
BHP Billiton (BHP), the leading Australian iron ore mining giant, is listed on New York
Stock Exchange. The iron ore prices have almost doubled from $67.87 on 3 August 2018
to $123.16 on 3 July 2019. The following table shows the BHP’s stock prices in USD and
the annualised historical volatility (Vol. for short) of BHP on NYSE, VIX Index, the iron
ore prices in USD at given dates below.
Table 1

A European call option with underlying stock BHP’s strike price of $65 is traded at
$1.46 on 3 July 2019, expiring on 17 Jan 2020. A European put option with underlying
stock BHP’s strike price of $65 is traded at $8.55 on 3 July 2019, expiring on 17 Jan 2020.
The risk-free rate of interest is 2.15%.
1. Compute the implied volatility of both put and call options using the Black-Scholes
Options. Compare the implied volatilities of call and put options, and provide an
economic rational to explain the difference. (2 marks)
2. Identify if there is arbitrage opportunity. Construct an arbitrage strategy if there
is an arbitrage opportunity. (2 marks)
3. Evaluate the vega of the call option for the period based on the period from 3 June
2019 to 3 July 2019. Comment on your results. (2 marks)
Useful links: A report on surging iron ore here, and market index here.
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be removed from this material.
Question 2, Duration and Banking (8 marks)
Consider a 5-year bond with annual coupon payments. The bond that has a face value
of $100 and sells for $95. The coupon rate is 3%. Coupon rate is the ratio between the
coupon value and the face value. The face value is paid at the maturity year in addition
to the last coupon payment.
1. Calculate the the bond’s yield to maturity (YTM). (2 marks)
2. Calculate the bond’s duration using its YTM. (2 marks)
3. Suppose the bond’s YTM changes in correspondence to 5-year T-bill interest rate.
Use the bond’s duration to evaluate the percentage change in the 5-year bond’s
value if the interest rate on 5-year T-bills falls by one basis point, that is, by 0.01%.
(2 marks)
Suppose the following fixed rate part has be extracted from the balance sheet of the First
Bank of Australia:

where the fixed-rate liabilities has the average duration of 4 years.
4. How does the bank’s equity change, if the T-bill interest rate increases by 10 basis
point? (2 marks)
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be removed from this material.
Question 3, Arrow-Debreu Economy (8 marks)
Consider a world in which there are only two dates: 0 and 1. At date 1 there are three
possible states of nature: a good weather state (GW), a fair weather state (FW), and a bad
weather state (BW). Denote S1 as the set of these states, i.e., s1 2 S1 = fGW; FW; BW g.
The state at date zero is known: call it s0. Denote probability of the three states as π (·) ;
π (S1) = (0:4; 0:3; 0:3):
There is one non-storable consumption good { say apples. There are three consumers
in this economy. Their preferences over apples are exactly the same and are given by the
following expected utility function
ci
0 (s0) + β X
s12S1
π (s1) uci 1 (s1);
where subscript i = 1; 2; 3 denotes consumers. In period 0, all agents have a linear
utility while in period 1, the three consumers have the same CRRA instantaneous utility
function: u (c) = c11–γγ ; where the coefficient of RRA is γ = 0:2: The consumers’ time
discount factor, β, is 0:98.
The consumers differ in their endowments which are given in the table below:
Table 2
Endowments

Assume that Arrow-Debreu securities are traded in this economy. One unit of ’GW
security’ sells at time 0 at a price q(GW) and pays one unit of consumption at time 1
if state ’GW’ occurs and nothing otherwise. One unit of ’FW security’ sells at time 0
at a price q(FW) and pays one unit of consumption at time 1 if state ’FW’ occurs and
nothing otherwise. One unit of ’BW security’ sells at time 0 at a price q(BW) and pays
one unit of consumption in state ’BW’ only.
1. Write down the consumer’s budget constraint for all times and states, and define a
Sequential Market Equilibrium in this economy. Is there any trade of Arrow-Debreu
securities possible in this economy? (1 mark)
2. Write down the Lagrangian for the consumer’s optimisation problem, find the first
order necessary conditions, and characterise the equilibrium (i.e., find the allocation
and price defined in the equilibrium). (1 mark)
3. At the equilibrium, calculate the forward price and risk premium for each atomic
security. What do your results suggest about the consumers’ preference? Prove
your intuition, and comment on your results. (1 mark)
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be removed from this material.
(ECON3107 only) Suppose that instead of Arrow-Debreu securities there are two
securities, a (risky) bond, a riskless bond, and a stock, available for trade in this economy.
The risky bond pays 1 apple in GW and FW, but 0 in BW, the riskless bond pays 1 apple
in every state, while the stock pays 2, 1 and 0 apples in GW, FW and BW, respectively.
Each trader is able to commit to their claim.
4. Write down the budget constraint for each consumer. (1 mark)
5. Write down the Lagrangian for the consumer’s optimisation problem, find the first
order necessary conditions, and characterise the equilibrium (i.e., find the allocation
and price defined in the equilibrium). (2 marks)
6. What is the price for risky bond, riskless bond and stock? What are the risk
premia/discount for these securities? (1 mark)
7. Compare your results with part 3. and comment on your results in light of the
arbitrage-free markets.(1 mark)
(ECON5106 only) Suppose that instead of Arrow-Debreu securities there are two
securities, a (risky) bond and a stock, available for trade in this economy. The bond pays
1 apple in GW and FW, but 0 in BW, while the stock pays 2, 1 and 0 apples in GW, FW
and BW, respectively. Each trader is able to commit to their claim.
4. What is the competitive equilibrium now? (1 mark)
Suppose in addition to bond and stock, there exists an option based on the stock price
which only pays at one state. This option completes the market.
5. What is the type of this option (call or put)? What is the range of the strike price
of this option? Design such an option and show how it completes the market.(2
marks)
6. Characterise the competitive equilibrium with bond, stock and the security you
designed. (1 mark)
7. Explain how financial innovation affects the social desirability of the allocations in
the economy. (1 mark)(max. 200 words)
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be removed from this material.
Question 4, CAPM (8 marks)
Suppose the risk-free rate of return is 0.03. There are three securities available on the market, their returns are all normally distributed, and their variance-covariance and returns
are given as the Table below:
Table 3

There are two investors in the economy. Their instantaneous utility functions are
given by:
u(r) = 1 – e-cir; for i = 1; 2;
where c1 = 2 and c2 = 3.
1. Derive the market portfolio and Sharpe ratio. Are they related to the individual
investors’ preference? (3 marks)
2. Derive the two individual investors’ portfolios. What are the expected return of
each individual investor’s choice? (2 marks)
3. Compare the two investors’ choice. What does your results suggest? Comment on
your observations. (3 marks) (max. 200 words)
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ECON3107/5106 – Economics of Finance
MARKING GUIDE FOR ASSIGNMENT
Criteria and weighting Below expectations (F) Meets expectations (P/Cr) Exceeds expectations (D/HD)
1 Presentation: clear and precise
(10%)
• Ideas not communicated clearly,
e.g. incorrect vocabulary/ grammar
• Unprofessional presentation, little
evidence of editing (e.g. many
spelling, punctuation errors)
• Verbose, expressed in more words
than are needed.
• Ideas generally communicated
clearly although could be more
effective
• An attempt at professional
presentation and editing: only
minor spelling/ punctuation errors.
• Ideas communicated clearly and
fluently; mostly accurate
vocabulary/ grammar
• Ideas expressed concisely
• Very professional presentation –
evidence of thorough editing
(negligible errors)
2 Structure: clear and well
organised (10%)
• Difficult to follow sequence of ideas;
unclear focus
• Text not clearly structured, e.g.
paragraphs not clearly developed.
• Sufficiently clear focus
• Mostly logical sequence of ideas.
• Adequately structured
• Ideas developed logically and
coherently
• Clear focus; no irrelevant material
• Well structured
3 Teamwork: cooperation and
execution (20%)
• Poor engagement;
• Disagreement in peer review;
• Separate work without mutual
understanding;
• Lack of communication;
• Fail to submit project chart on time.
• Good engagement;
• Sufficient communication;
• Consistent submission with good
proofreading;
• General agreement on the
workflow and peer review;
• Submit project chart on time;
• Great engagement;
• Efficient communication great
coordination;
• Great project outcome;
• Well understood workflow in
project chart submission;
• Appreciating peer review.
4 Critical thinking and knowledge
applied to issues and ideas; use
of theory (60%)
• Does not clearly/correctly identify or
explain issues/problem
• Little analysis or critical evaluation of
ideas or information
• Struggles to appropriately apply
theory.
• Identifies and defines key
issues/problems but does not
convey all aspects or complexity
• Some analysis of ideas or
information and application of
theory but with limited depth
• Clearly identifies and explains all
aspects of issues/problem and
conveys complexity of issue.
• Insightful analysis and critical
evaluation of ideas or information,
using appropriate theories and
showing depth of understanding

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