MFIN703 Assignment #1
Winter 2021
1
MFIN703 – OPTIONS & FUTURES
ASSIGNMENT #1 - SOLUTIONS (CHAPTERS 1, 2, 3, 4, 5, 10, 11)
WINTER 2021 - MCMASTER UNIVERSITY

Answer all of the following questions. For quantitative questions, show your work to earn the full marks
allocated. The final answer is only worth one mark. Questions requiring a qualitative response may be
written in point form.

Total Marks: 135

1. Explain the difference between hedging, speculation and arbitrage. (5 marks)

2. A trader obtains the following fx quotes. Identify the arbitrage opportunities. (20 marks)

CHF/USD
Spot 0.8868 Strike Cost
30-day forward 0.8700 30-day put 0.8750 0.0115
60-day forward 0.8875 60-day call 0.8750 0.0120

3. A US company corporate treasurer expects to receive GBP 5 million at the end of July, which is 4
months from today. She would like to ensure that the funds can be converted into USD at a
minimum of \$1.30 per GBP. She does not think the exchange rate will rise above \$1.34 per GBP
and is willing to forego the risk of it rising above this level. If the exchange rate is between \$1.30
and \$1.34, she will settle for the exchange rate on that day i.e. the spot rate. How could you use
options to meet the treasurer’s requirements? (10 marks)

4. On January 6, 202x, a company sells three April 202x oil futures contract @101.00. Each
contract represents 1,000 barrels of oil. It closes out its position on January 18, 202x. For each
contract, initial margin is \$5,000 and maintenance margin is \$4,100. The futures prices during this
period are as follows:

Date Closing price
Jan 6 101.00
Jan 7 101.50
Jan 8 102.30
Jan 9 104.50
Jan 10 105.00
Jan 13 103.00
Jan 14 102.50
Jan 15 102.00
Jan 16 103.10
Jan 17 104.00
Jan 18 103.50

MFIN703 Assignment #1
Winter 2021
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a. What are the margin implications for the company? (10 marks)
b. What was the gain/loss on the futures position? (2 marks)
c. If the company had initiated the futures position as a hedge in the prior fiscal year, what is
company’s taxable position at the end of the previous fiscal year? (3 marks)

5. Two traders enter into the following contracts:

Trader A: long 1 futures contract to buy EUR 3 million for USD 3.54 million in 3 months
Trader B: long 1 forward contract to buy EUR 3 million for USD 3.54 million in 3 months

During the first two months of the contract, the exchange rate increases sharply (ie. USD
depreciates). At the end of the third month, the exchange rate closes at 1.130.

a. What is the profit for each trader? (4 marks)
b. Differentiate how the profits realized? (6 marks)

6. A bank’s derivatives transactions with a counterparty are worth +\$10 million to the bank and are
cleared bilaterally. The counterparty has posted \$10 million of cash collateral. Describe the credit
exposure of the bank. (10 marks)

7. When is a forward exchange rate an unbiased predictor of future exchange rates? (5 marks)

8. The following data is for a 6-month long forward contract:

current price of stock: \$55 (non-dividend paying)
risk-free rate of interest: 3% (with continuous compounding)

a. What are the 6-mo forward price and initial value of the forward contract? (5 marks)
b. Three months later, the price of the stock is \$60 and the risk-free rate is unchanged. At this time,
what are the forward price and value of the forward contract? (5 marks)
c. If the stock underlying the 6-mo forward contract pays a dividend of \$1, what is the 6-mo forward
price? (5 marks)

9. A trader owns 55,000 units of an asset and decides to hedge the value of the position with futures
contract. Each futures contract is on 5,000 units.
Spot price of asset today: \$28
Futures price of asset: \$27
Spot price of asset on Nov 30, 20xx: \$30

a. Explain whether the hedger should take a long or short position? (3 marks)
b. What is the optimal number of futures contracts? (2 marks)
c. What is the profit or loss on the contract on Nov 30, 20xx? (5 marks)

10. The following table gives the prices of bonds. Half the stated coupon is paid every 6-mos.

Bond principal Time to Maturity (yrs) Annual coupon (%) Bond price (\$)
MFIN703 Assignment #1
Winter 2021
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100 0.5 - 98.0
100 1.0 - 96.5
100 1.5 4.5 101.3
100 2.0 5.0 103.0
100 2.5 5.5 105.1
100 3.0 5.9 107.0

a. Calculate the zero rate for each bond. (15 marks)
b. Calculate the forward rate for each period. (10 marks)

11. Calculate the payoff for the following option positions. Ignore any option premium paid or earned.
(10 marks)

Option Position S0 K
Long call 45 40
Short put 41 45
Short call 25 31
Long put 17 15

END OF ASSIGNMENT