C323 Risk Management: Principles and Applications Session Three 2015
Assignment Two
In this assignment you will develop options strategies in relation to the
stock of Royal Dutch Shell plc, the Anglo-Dutch multinational oil and
gas company. In Question 1, you will suppose it is February 2014, and
you will form trading strategies based on information available up to 4
February 2014. In Question 2, you will jump forward to 3 February 2015,
and assess the profit from your options strategies, based on the stock
price at this later date. In your answer, use European options on nondividend-paying
stock.
Explain and illustrate your answers to these questions, which are based on Units 5–
6, in no more than 2,500 words. This limit includes tables and captions but excludes
footnotes, endnotes, tables of figures and references. Answers that exceed this limit
will result in a loss of marks. Full details of penalties for late submission, exceeding the
word limit and other information can be found at the end of this assignment.
Your assignment should be submitted via the Virtual Learning Environment (VLE)
hosted on Moodle to The Centre for Financial and Management Studies no later than
26th May 2015. Full instructions are available on the VLE.
Question 1
Using daily data on the share price of Royal Dutch Shell plc (share price in GB pence,
B shares, source https://uk.finance.yahoo.com), the daily logged return has been calculated
for the year 4 February 2013 to 3 February 2014, where the return is calculated
as
1
ln i
i
i
S
u
S ?
? ? ? ? ? ? ?
Using the methods described on pp 304-305 in Hull, the estimated volatility per annum
is calculated as 15% (or 0.15). The Shell stock price on 4 February 2014 is
2094.41 pence. The 12 month sterling interbank lending rate for 4 February 2014 is
0.84% (or 0.0084) (source: www.bankofengland.co.uk).
1(a) Suppose you have a long position in the stock on 4 February 2014. How
would you hedge against price declines for a one-year period, using puts,
calls, and combinations of options? [30% of total marks]
1(b) Suppose you have a short position in the stock on 4 February 2014 (for example,
you are obliged to purchase the stock in one year). How would you
hedge against price increases for a one-year period, using puts, calls, and
combinations of options? [30% of total marks]
C323 Risk Management: Principles and Applications Session Three 2015
Question 2
On 3 February 2015 the price of Shell stock is 2268.50 pence. Calculate the payoffs
for the strategies you chose in Q1a combined with the long position in the stock, and
the strategies you chose in Q1b combined with the short position in the stock. Comment
on your results. [40% of total marks]
Student Assignment Guidelines
There is no single right way to answer these questions; rather there are a number of
approaches, and different students will have their own view of what is expected and
how much weight to give any particular element. Whatever your approach, you will
need to plan your answers carefully, in order to provide a focused and succinct answer
to the questions, within the word limit.
In your answers you should demonstrate your knowledge of and ability to explain and
apply economic and financial models. You must justify any conclusion you reach on
the basis of evidence provided by you by reference to, or quotation from, the course
notes, textbooks, other course readings, or any other source you choose to use. As
long as your essay gives a good justification for the answer and demonstrates your
reasoning ability and your knowledge, you can obtain a good grade.
This assignment is based on material studied in Units 5 and 6. Please note the mark
weightings. At all stages you should explain your reasoning in a way that shows your
understanding of the theory and empirical studies of Units 5 and 6. You can also introduce
knowledge you have gained from other parts of the course, where appropriate,
or from other courses, or elsewhere. But remember that the assignment is designed to
focus on the subjects you studied in Units 5 and 6.
Your answer should be written in an academic manner, presenting your view carefully,
justifying your view with rigour and discussion. When you present a relevant theory
in your justification it is good, where possible, to demonstrate your understanding of it
by using a simple equation or diagram. In presenting your argument you should also
comment on possible weaknesses and limitations.
In your assignment you could include a brief outline of options, explain a method for
pricing options, and how options can be used for hedging. You should use the example
presented in the question to demonstrate your points. Particular guidance on Q1
and Q2 is given below. You might also choose to comment on the strengths and
weaknesses of the approach you have used.
Question 1
For question 1 you will need to devise relevant options strategies for the situations
described. Therefore you will need to calculate the price of the required call and put
options, and of the overall strategy, as required. You might find it useful to calculate
by hand the prices of the options using the Black-Scholes-Merton equations in the
first instance, and then check your calculations with DerivaGem. For simplicity, use
European options on non-dividend-paying stock.
For each option strategy you should explain carefully what the strategy is attempting
to achieve, including an indication, in general terms, of what the payoffs from the
C323 Risk Management: Principles and Applications Session Three 2015
strategy might be (in terms of stock price increases and decreases). You should base
your analysis on the information provided up to 4 February 2014, and form strategies
for the year to 3 February 2015. You do not need to conduct additional research on
Shell to write your assignment. You should state the initial payments or receipts in
respect of each strategy.
(For Question 1 you need to assume it is 4 February 2014, and you do not know the
price of the stock in one year’s time. Of course, you could find and use information on
stock prices for the year 4 February 2014 to 3 February 2015, and form your options
strategies with the benefit of hindsight. However, for the purpose of this question, imagine
it is 4 February 2014, and you do not know what is about to happen in the coming
year.)
You can choose any kind of options strategies you like, as long as you explain the
strategies clearly. The following suggestions are provided for guidance. To hedge
against price decreases you could consider using a long position in a put option on the
stock; or you could use a short call. For these options, you will need to decide on a
strike price. As a guide, you could use the stock price at 4 February 2014, 0 S , as the
strike price. For strategies using a combination of options you could consider a bear
put spread. In this case, you will need to choose two strike prices. For the lower strike
price you could use the minimum stock price reached in the year 4 February 2013 to 3
February 2014, which would give K1 ? 1955.77. For the higher strike price you could
use the stock price on 4 February 2014, so K2 ? 2094.41.
To hedge against price increases, you could consider a long call, or a short put. What
strike price will you choose in each case? Again, you could choose a strike price equal
to the stock price on 4 February 2014. For a strategy using a combination of options,
you could use a bull call spread; in this case you will need to choose two strike prices.
As a suggestion, you could choose the lower strike price to be the stock price on 4
February 2014; and for the higher strike price you could choose the maximum stock
price in the year 4 February 2013 to 3 February 2014, which is 2200.73.
Question 2
It is now 3 February 2015. The price of Royal Dutch Shell B shares is 2268.50 pence.
You will need to calculate the payoffs for the option strategies you chose in Q1, combined
with the relevant positions in the stock, described in Q1a and Q1b. You should
provide some comment on the results. You could explain why the payoffs are as they
are. You might choose to compare the payoffs for a variety of options strategies. Or
you could suggest alternative strategies that would have provided a better performance.
Or there may be elements of the option-pricing model you have used which
you would like to comment on.
Your assignment must be properly referenced. Further information on referencing
(ie the Harvard system) is available in the Studying at a Distance textbook by Talbot
and on the Virtual Learning Environment in the Study Skills area.
C323 Risk Management: Principles and Applications Session Three 2015
Plagiarism
All assignments submitted must be your own work and written in your own words.
Where you have used quoted material, you must make full reference to it. You must
cite all references used throughout your work at the end of your assignment. Advice
on what is classified as plagiarism and the action taken against this can be found in
the University of London Regulations and on the Virtual Learning Environment in the
Study Skills area.
Submitting Assignments
Students are required to submit their assignment in one place only on the Virtual
Learning Environment using TurnItIn, the plagiarism detection software. A video tutorial
and step-by-step instructions on how to do this can be found on the Virtual
Learning Environment on your module assignment page.
Please see the information below for the current policy on penalties.
IMPORTANT INFORMATION
Late Submission
Assignments submitted after the published deadline will be penalised:
Marks will be deducted at a rate of two marks per working day (ie Mon-Fri, and a maximum
of 10 marks for up to one week after the deadline). Assignments will not be accepted beyond
one week after the deadline, and a mark of zero will be awarded to assignments submitted
beyond one week late. There is no procedure for extensions.
Penalties for late submission of assignments (ie up to one week after the deadline) may be
waived if all the following conditions are met:
• immediate, unexpected or unforeseen difficulties. Such difficulties may include:
illness, bereavement, impact of disability, sudden and severe change in personal
circumstances.
• The impact of such difficulties will be of a significant and unavoidable nature
• The request must be accompanied by relevant documentation (eg. medical
certification)
Word count & Over length Assignments
The specified word count for the assignment includes tables and captions but excludes
footnotes, endnotes, tables of figures, and references.
Over length assignments will be penalised as follows:
Up to and including 10% - 5 marks.
Between 10% & 20% - 10 marks,
Between 20% & 30% - 15 marks.
Over 30%. The assignment will not be marked but will be given a grade of 0.
In the case of assignments that are not essays, alternative but commensurate limits and
penalties will be applied to over-length submissions
Referencing and Citation
Students are expected to use the Harvard system of referencing. Incorrect referencing can
lead to penalties and if a student is found to have plagiarised other work it is an examination
offence. For this reason, all assignments must be submitted to TurnItIn which checks your
work against existing books, journals and other student assignments.
The penalties for plagiarism are set by the University of London. Please see the Study Skills
resources on Referencing and Citation for detailed examples of how to reference correctly to
avoid unnecessary deductions.
Eligibility for examination
Should a student sit an examination without having submitted the required number of
assignments, the examination entry and/or examination result will be declared invalid.