程序代写案例-IB2533
时间:2022-06-10
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IB2533


UNIVERSITY OF WARWICK
Department Warwick Business School
Level 2
Module Code IB2530
Module Title Principles of Finance 1
Exam Paper Code IB2533
Exam Paper Title IB2533_ Principles of Finance 1_ Exam
Paper Summer 2021_Non-finalist exam
Duration 2 hours
Exam Paper Type Fixed time – Open Book

STUDENT INSTRUCTIONS

1. Read all instructions carefully. We recommend you read through the entire paper at least
once before writing

2. There are FIVE questions. All candidates should attempt ANY FOUR questions.

3. You should not submit answers to more than the required number of questions

4. All questions carry the same number of marks (25 marks) unless otherwise stated

5. Where handwritten answers are permitted, please ensure you write legibly, preferably in
dark blue or black ink. If you use a pencil, please ensure it is not too faint to be captured by
scan or photograph. It is your responsibility to ensure your work can be read

6. If uploading photographs or scanned copies of your work, please check for legibility
before uploading. It is your responsibility to ensure your work can be read

7. Add your student number to all uploaded files

8. You are permitted to access module materials, notes, resources, references and the
internet during the online assessment

9. You must not communicate with any other candidate during the assessment period,
unless instructed to do so as part of the assessment requirement(s)

10. By starting this assessment, you are declaring yourself fit to undertake it. You are
expected to make a reasonable attempt at the assessment by answering the questions in
the paper


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IB2533

IMPORTANT INFORMATION

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Alternative Exams Portal

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provided

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 Students with approved Alternative Exam Arrangements (Reasonable Adjustments) that
permit extra time and/or rest breaks will have this time added on to the stated duration


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IB2533
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contact eassessment@warwick.ac.uk

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Technical support will be available between 09:00 and 17:00 BST for each examination
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Academic support will normally be provided for the duration of the examination (i.e.
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Other Support

 Write to your department immediately if you cannot complete your assessment
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Your assessment starts below.



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IB2533
Further Instructions

Make any additional assumptions that you feel are necessary to answer each of the questions
that you attempt but state these assumptions clearly and explicitly.

For calculation questions you should show full workings. Full marks for calculations will only
be given for correct answers with full supporting workings.

Written explanations should be in your own words. Full marks for written explanations will
only be given for correct answers which demonstrate individual understanding of the material
and are not copied from module or other external resources.

Ensure your answers to each question follow the order the questions appear in the exam
paper. Start each new question or question part on a new page (or separate piece of paper,
where handwritten answers are required) and write the question number at the top of each
page of your answers. Please attach a cover sheet with your Student ID number, the module
code (IB2533) and the numbers of the questions you have answered.



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IB2533


ATTEMPT ANY FOUR QUESTIONS


Question 1 (25 marks)

ANSWER BOTH PARTS OF THIS QUESTION

Part A – 6 marks

Coventry plc stock is currently trading at £4.70 and has an annualised volatility of returns of
25%. Coventry plc is not expecting to pay dividends in the foreseeable future. The
continuously compounded risk-free rate is 8% per annum.

Calculate the nine-month forward price for Coventry plc stock.

If the current market nine-month forward price on Coventry plc stock is £4.80, explain
whether there is an arbitrage opportunity and, if so, explain how you would trade in order to
realise an arbitrage profit. Give the cash flows associated with your strategy now and at the
maturity of the forward contract.

[6 marks]








(Part B of question 1 continues on the next page)




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IB2533
Question 1 continued

Part B – 19 marks
Individual A has utility of wealth function
 1 exp( )
( )
a W
U W
a
  
 where W is the
individual’s wealth and a > 0. Individual A has current wealth £5,000 and faces the following
actuarially fair gamble which costs £2,000 and has the following outcomes:








Individual A’s Pratt-Arrow approximation πPA to the Markowitz risk premium πM for this
gamble is £125.

(a) Calculate the variance of the gamble. Hence deduce individual A’s current level of
absolute risk-aversion (ARA).
Derive an expression for individual A’s level of absolute risk aversion (ARA) as a
function of a and their current level of wealth W. Hence deduce that individual A’s
value of a is
0.001
8
.
[8 marks]
(b) Calculate individual A’s final wealth under each of the two outcomes of the gamble.
Hence calculate individual A’s expected utility of wealth and Certainty Equivalent
wealth if they undertake the gamble. Explain what the Certainty Equivalent wealth
represents. What can you deduce about how much individual A would be willing to
pay for insurance to avoid the gamble?
Suppose immediately after this gamble, individual A is faced with another identical
gamble. Without doing any further calculations explain whether the Pratt-Arrow
approximation πPA to the Markowitz risk premium πM for the second gamble differs
from that for the first.

[11 marks]


(Question 2 on next page)

1/3
2/3
£4000
£1000


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IB2533
Question 2 (25 marks)
ANSWER BOTH PARTS OF THIS QUESTION
Part A - 17 marks
Assume a world of certainty in which individuals can borrow and lend at the same riskless rate
of 20%. An individual currently earns and consumes Y0 this period and will earn and consume
Y1 next period. This pattern of consumption is represented by point E in the diagram below.
The individual also has the opportunity to invest in a capital project. If the individual decides
to invest and neither lends nor borrows, their new pattern of consumption is represented by
point B. Investment costs I0 and yields additional income next period of CF1. The rate of return
on the project is RP = 30%.










(a) What is the slope of line DEF? Explain what the individual must do to position
themselves between point E and point D on the line DEF.
Find the individual’s consumption this period and next period if they do not invest in the
project and neither lend nor borrow, Y0 and Y1.
What is the Net Present Value of the capital project? Explain.
Hence deduce the capital project’s investment cost I0 and the cash flows from the
project next period CF1.
(10 marks)
The individual wishes to consume the same amount in present value terms each period.
(b) Calculate the additional consumption in this period and in the next period which the
individual can obtain if they invest in the project.
Explain how the individual can achieve their desired consumption bundle assuming they
invest in the project.
(7 marks)
Part B - 8 marks
What does it mean for a market to be strong-form efficient?
Can a market be strong-form efficient all of the time? Explain.
(8 marks)

F
C
E
B
D A

160 240 250
Consumption (£’000s)
this period
Consumption (£’000s)
next period
0


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IB2533
(Question 3 on next page)
Question 3 (25 marks)
ANSWER BOTH PARTS OF THIS QUESTION
Part A – 15 marks
Assume a CAPM world and that the risk-free rate Rf = 4%.
Fund A and fund B have standard deviation of returns of σA = 20% and σB = 40% respectively.
Fund A is fully diversified and has expected return ERA = 12% and a beta of βA = 0.8. Fund B
has a beta of βB = 1.25
(a) Draw a graph of the Securities Market Line. Explain whether each of Fund A and Fund
B lies above, on or below the Securities Market Line. Calculate the slope of the
Securities Market Line and explain what it represents. What is the expected return of
Fund B?
(b) Draw a graph of the Capital Market Line. What can you say about whether each of
Fund A and Fund B lies above, on or below the Capital Market Line? Explain. Calculate
the slope of the Capital Market Line and explain what it represents.
Mark the positions of Funds A and B on each graph. Comment on your answers.
[15 marks]

(Part B of question 3 continues on the next page)




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IB2533
Question 3 continued

Part B – 10 marks
The current price of Rugby plc stock is £7.50. Rugby plc is not expected to pay dividends in
the foreseeable future. The continuously compounded risk-free rate is 2% per annum for all
maturities. A six-month European call option on Rugby plc stock with strike price £8.00 has a
Black-Scholes value of £0.42 and Delta of 0.43.
(a) Use put-call parity to calculate the value and Delta of the corresponding European put
option (i.e. a six-month European put option on Rugby plc stock with strike price
£8.00).
Without calculating any risk-neutral probabilities, explain which of the European call
or corresponding European put option has the greater risk-neutral probability of
exercise.
(b) A European straddle option combination consists of a long European put option and a
long European call option, both on the same underlying asset with the same strike
price and maturity. Calculate the value and Delta of a six-month European straddle on
Rugby plc stock with strike price £8.00.
Suppose Rugby plc stock price increases by £0.10. Without recalculating any option
values, estimate the change in value of a six-month European straddle option
combination on Rugby plc stock with strike price £8.00. Is the actual change in the
value of the European straddle option combination likely to be larger or smaller than
your estimate? Explain
[10 marks]

(Question 4 on next page)



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IB2533
Question 4 (25 marks)

An economy contains only two risky assets A and B. Let RA, RB be the rates of return on assets
A and B, respectively; A < B be the standard deviations of RA and RB; and AB be the coefficient
of correlation between RA and RB.
(a) Write down expressions for the weights wA, wB of assets A and B in the minimum-
variance portfolio G. Given the standard deviations of RA and RB, A and B, derive
constraints on the coefficient of correlation between RA and RB, AB, such that the
minimum-variance portfolio consists of long positions in both asset A and asset B.
If
ABA B A B
E[ ] 0.08, E[ ] 0.1, σ 0.24, σ 0.40, 0.6R R      , calculate the
weights wA, wB of assets A and B in the minimum-variance portfolio G. Deduce the
expected return  GE R and the standard deviation of returns G for the minimum-
variance portfolio G.
Draw a graph of E[R] vs. σ for the feasible set of portfolios consisting only of assets A and
B. Mark the location of the minimum-variance portfolio G. What is the slope of the
minimum variance frontier at G? Explain.
(13 marks)
(b) Suppose now there is also a risk-free asset in the economy with return Rf = 2%. Calculate
the Expected Sharpe Ratio of the minimum variance portfolio G. Verify that a portfolio
Q with weights wA = 0.6, wB = 0.4 has the same Expected Sharpe Ratio as the minimum
variance portfolio G. Mark the location of portfolio Q on the graph.
Mark the Capital Allocation Line and the tangency portfolio T on the graph. Without
doing any further calculations, explain how the weight of asset A in the tangency
portfolio T compares to the weight of asset A in portfolio G and the weight of asset A in
portfolio Q.
(7 marks)
(c) Portfolio Z consists of positions in assets A, B and riskless bonds. It has the highest
expected return of all portfolios with standard deviation of returns Z = G. The expected
return on Z equals 8.185%.
Mark the location of portfolio Z on the graph. Calculate the Expected Sharpe Ratio for
portfolio Z and explain how this is this related to the Expected Sharpe Ratio for the
tangency portfolio T and the minimum variance portfolio G.
(5 marks)

(Question 5 on next page)


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IB2533
Question 5 (25 marks)

The market prices of three bonds of the same credit quality which you believe to be fairly
priced are given below:

Coupon
(% of face value)
Maturity
(years)
Market
price
(% of face value)
A 10% 1 105.7692
B 7.5% 2 104.7172
C 5% 3 97.5029

a) Calculate the one-year, two-year and three-year discount factors for bonds of this
credit quality. Show full workings.
Give an expression for the T-period spot rate as a function of the T-period discount
factor TD . Hence calculate the one-year, two-year and three-year spot rates implied
by these discount factors.
Give an expression for the s-into-T period forward rate s Tf as a function of the ratio
of the T-period and s-period discount factors T
s
D
D
. Hence calculate the forward rates
1f2, 2f3 and 1f3 implied by these discount factors.
[11 marks]



(Question 5 continues on next page)




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IB2533
Question 5 continued

Bonds X and Y are bonds of the same credit quality as bonds A, B and C. Both bonds pay an
annual coupon of C%. Bond X has maturity T years and bond Y has maturity T-1 years.
b) Consider a portfolio Q which consists of a long position in bond X and a short position
in bond Y with the same face value. Calculate the cash flows to this portfolio at each
future date (as a proportion of the common face value) and give an expression for its
current value in terms of the discount factors for each future date.
Hence deduce the relationship between the coupon rate C and current forward rates
which needs to be satisfied if the current value of the portfolio is greater than zero. If
the current value of the portfolio is greater than zero, which of the two bonds should
have a higher price?
Bond E is a three-year bond of the same credit quality as bonds A, B and C with an
annual coupon of 7.5%. Without doing any further calculations, deduce whether the
current value of bond E should be higher or lower than the current value of bond B.
[Note you do not need to calculate the current value of bond E.]
[8 marks]
c) If the Pure Expectations Hypothesis holds, calculate the expected price of bond E in
two years’ time just after payment of the annual coupon.
How would your answers change if instead the Liquidity Preference Hypothesis holds?
Explain.
[6 marks]




END OF QUESTION PAPER
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