BFW2751 S1, 2021 Week 2 Tutorial Suggested Solutions
Topic: Mechanics of Future Contracts
Question 1.
a) Outline the differences between a forward contract and a futures contract
b) Explain how the clearinghouse operates to protect the futures market.
c) Explain how margins protect investors against the possibility of default
a) Differences between futures and forwards can be summarized by the following table:
Buyer-seller interaction
Contract specification
Delivery date
Settlement
Closing out of contract
Credit risk/counterparty risk
FORWARD
Private contract between 2 parties
Non-standard contract
Usually 1 specified delivery date
Settled at end of contract
By delivery or final cash settlement
Some credit risk
FUTURES
Exchange traded
Standard contract
Range of delivery dates
Settled daily
Prior to maturity
Virtually no credit risk
b) The clearinghouse intervenes in each contract, guaranteeing to the buyer that the seller's losses will be
covered and guaranteeing to the seller that the buyer's losses will be covered. This allows a trader to
enter into a transaction without having to check the creditworthiness of the other party. In turn, to protect
themselves against risk of default by futures parties, the clearinghouse requires that each trader
maintain a margin account to cover losses. Daily marking to market is performed to prevent loss from
accumulating. The clearinghouse also maintains a cash reserve to cover losses in the event of a failure
to cover a loss by a trader or firm.
c) A margin is money deposited by an investor with their broker. It acts as a guarantee that the investor
can cover any losses on the futures contract. The balance in the margin account is adjusted daily to
reflect gains and losses on the futures contract. If losses are above a certain level, the investor is
required to deposit a further margin. This system makes it unlikely that the investor will default. A similar
system of margins makes it unlikely that the investor’s broker will default on the contract it has with the
clearinghouse member and unlikely that the clearinghouse member will default with the clearinghouse.
Question 2.
Suppose now you enter into a short position in September futures contract to sell Silver for
$17.20 per ounce. The contract size is 5,000 ounces. The initial margin is $4,000, and the
maintenance margin is $3,000. What change in the futures price will lead to a margin call? What
happens if you do not meet the margin call?
Answer:
There will be a margin call when $1,000 has been lost from the margin account. This will occur
when the price of silver increases by 1,000/5,000 = $0.20. The price of silver must therefore rise
to $17.40 per ounce for there to be a margin call. If the margin call is not met, your broker closes
out your position.
Question 3.
Suppose that you buy a stock index futures contract at the opening price of 452.25 on
July 1. The multiplier on the contract is 500 times, so the contract value at inception is
$500(452.25) = $226,125. You hold the position open until selling it on July 10 at a
settlement price of $451.45.The initial margin requirement is $9000 and the maintenance
margin is $6000. Assume that you deposit the initial margin and do not withdraw the
excess on any given day. Complete the table below and explain any additional funds deposited
Settlement
Price
Total Contract
Value
Daily Gain/ (Loss)
Cumulative.
Gain/Loss
Margin Balance
Margin Call
(index Point)
($)
($)
($)
($)
($)
01-Jul
453.95
226,975
850
850
9,850
No
02-Jul
454.5
227,250
275
1,125
10,125
No
03-Jul
452
226,000
-1,250
-125
8,875
No
07-Jul
441.62
220,810
-5,190
-5,315
3,685
5,315
Day
9,000
08-Jul
455.25
227,625
6,815
1,500
15,815
No
09-Jul
452.65
226,325
-1,300
200
14,515
No
10-Jul
451.45
225,725
-600
-400
13,915
No
Explanation of additional Funds deposited
 1/7: Initial margin deposit of $9,000
 8/7: Balance on 7/7 was $3,685 which is below $6,000 maintenance margin.
 Required to deposit $5,315 to replenish the margin balance to initial margin of $9,000
 Therefore, on 1st July the contract value was $226,125 and the close out was $225,725
 225,725 – 226,125 = -$400
 Final margin balance =$13,915 – Initial Margin $9000 = $4,915 less Margin call $5,315 = -$400
Question 4.
Show that, if the futures price of a commodity is higher than the spot price during the delivery
period, then there is an arbitrage opportunity. Does an arbitrage opportunity exist if the futures
price is less than the spot price? Explain your answer.
Answer:
If the futures price is greater than the spot price during the delivery period, an arbitrageur buys the asset,
shorts a futures contract, and makes delivery for an immediate profit.
If the futures price is less than the spot price during the delivery period, there is no similar perfect arbitrage
strategy. An arbitrageur can take a long futures position but cannot force immediate delivery of the asset.
The decision on when delivery will be made is made by the party with the short position. Nevertheless
companies interested in acquiring the asset may find it attractive to enter into a long futures contract and
wait for delivery to be made.
Question 5.
A trader enters into a short cotton futures contract when the futures price is 50 cents per pound.
The contract is for the delivery of 50,000 pounds. How much does the trader gain or lose if the
cotton price at the end of the contract is (a) 48.20 cents per pound; (b) 51.30 cent s per pound?
Answer:
(a) The trader sells for 50 cents per pound and buys back the same for 48.20 cents per pound.
Gain ($0.5000 - $0.4820) x 50 000 = $900
(b) The trader sells for 50 cents per pound and buys back the same for 51.30 cents per pound.
Loss ($0.5000 - $0.5130) x 50 000 = ($650)
Question 6.
Explain carefully the difference between hedging, speculation, and arbitrage.
Answer:
A trader is hedging when he/she has an exposure to the price of an asset and takes a position in a derivative
to offset the exposure.
In a speculation, the trader has no exposure to offset. He / She is betting on the future movements in the
price of the underlying asset.
Arbitrage involves taking a position in two or more different markets to lock in a guaranteed profit.
Question 7
Explain why a futures contract can be used for either speculation or hedging.
Answer:
If an investor has an exposure to the price of an asset, he or she can hedge with futures contracts.
1) If the investor will buy the asset, he will gain when the price decreases and lose when the price increases;
a long futures position will hedge the risk.
2) If the investor will sell the asset, he will lose when the price decreases and gain when the price increase;
a short position will hedge the risk
If the investor has no exposure to the price of the underlying asset, entering into a futures contract is
speculation.
1) If the investor takes a long position, he or she gains when the asset’s price increases and loses when it
decreases.
2) If the investor takes a short position, he or she loses when the asset’s price increases and gains when it
decreases.
Question 8
Explain how margins protect investors against the possibility of default.
Answer:
A margin is a sum of money deposited by an investor with his or her broker. It acts as a collateral/guarantee
that the investor can cover any losses on the futures contract.
The balance in the margin account is adjusted daily to reflect gains and losses on the futures contract. If
losses are above a certain level, the investor is required to deposit a further margin. This system makes it
unlikely that the investor will default.
[END OF TUTORIAL WEEK 2]