ECN603
ECN603 TURN OVER 1
** SAMPLE EXAM **
Data Provided: Statistics tables, Formula sheet
DEPARTMENT OF ECONOMICS
ECN603 Asset Pricing
Maximum 1500 words excluding equations
Answer ALL questions. The marks shown within each question indicate the
weighting given to component sections.
The answers to the questions must be type-written. The preference is that
symbols and equations should be inserted into the document using the
equation editor in Word. Alternatively, they can be scanned and inserted as an
image (providing it is clear and readable).
You MUST submit your answers through Blackboard using Turnitin. The
submission file MUST include the coversheet (provided on Blackboard); please
do not alter the formatting (margins, font, font size nor line spacing).
Enter your SRN (student registration number) as the submission title.
Please submit in Word format and check your file is under the 40MB size limit.
ECN603
ECN603 CONTINUED 2
Question 1 [15 marks]
A price on a non-dividend paying stock is currently £50. Over each of the next two
six-month periods the stock is expected to go up by 5% or down by 10%. The risk-
free interest rate is 3% per annum with continuous compounding.
(a) What is the value of a one-year European call option with a strike price of £48?
[5 marks]
(b) What is the value of a one-year American call option with a strike price of £48?
[5 marks]
(c) Discuss how your answer to (b) would change if the stock instead actually did pay
cash dividend? [5 marks]
Question 2 [20 marks]
A non-dividend paying stock costs £100 at the end of today. You estimate that this
stock has an expected return of 20% per year and a volatility of 50% per year.
Assume that the stock return follows a Geometric Brownian motion. Consider that a
year is made up of 250 trading days.
(a) Calculate the expected value of the stock price and standard deviation of the
change in stock price at the end of the next trading day. [5 marks]
(b) Calculate the 99% confidence interval for the stock price at the end of the next
trading day. Calculate the 99% confidence interval for the stock price at the end
of the next calendar day, i.e. consider that a year is made up of 365 calendar
days. [5 marks]
(c) Comment on the difference in your answer to (b) versus (c) [5 marks]
(d) Consider the likelihood of observing a stock price below £92 the next day.
[5 marks]
Question 3 [15 marks]
It is July 16. A company has a portfolio of stocks worth £30 million. The beta of the
portfolio is 1.0. The company would like to use the December futures contract on a
stock index to change beta of the portfolio to zero during the period July 16 to
November 16. The index is currently 1,250, and each contract is on £250 times the
index.
(a) What position should the company take? [5 marks]
(b) If the company instead wants to increase its portfolio beta from 1 to 2, what
position in futures contracts should it take? [5 marks]
Do the positions in (a) and (b) contain basis risk? [5 marks]
Question 4 [20 marks]
A trader owns 55,000 units of a particular asset and decides to hedge the value of
her position with futures contracts on another related asset. Each futures contract is
on 5,000 units. The spot price of the asset that is owned is £28 and the standard
deviation of the change in this price over the life of the hedge is estimated to be
£0.43. The futures price of the related asset is £27 and the standard deviation of the
change in this over the life of the hedge is £0.40. The coefficient of correlation
between the spot price change and futures price change is 0.95.
(a) What is the minimum variance hedge ratio? [5 marks]
(b) Should the hedger take a long or short futures position? [5 marks]
(c) What is the optimal number of futures contracts with no tailing of the hedge?
[5 marks]
ECN603
ECN603 … 3
(d) What is the optimal number of futures contracts with tailing of the hedge?
5 marks]
Question 5 [15 marks]
The 6-month, 12-month, 18-month, and 24-month zero rates are 2%, 2.5%, 2.75%,
and 3% with semiannual compounding.
(a) What are the rates with continuous compounding? [5 marks]
(b) What is the forward rate for the six-month period beginning in 18 months?
[5 marks]
(c) What is the value of an FRA that promises to pay you 4% (compounded
semiannually) on a principal of £1 million for the six-month period starting in 18
months? [5 marks]
Question 6 [15 marks]
A stock price is currently £40. The stock pays no dividend. Over each of the next two
three-month periods it is expected to go up by 10% or down by 10%. The risk-free
interest rate is 12% per annum with continuous compounding.
(a) What is the value of a six-month European put option with a strike price of £42?
[5 marks]
(b) What is the value of a six-month American put option with a strike price of £42?
[5 marks]
(c) Explain why you get different answers in (a) and (b). How would you answer
differ if the stock paid dividend during the next 6 months? [5 marks]
END OF QUESTION PAPER