FIN4400- Futures & Options
Ch1 homework solution
1. What is the difference between a long forward position and a short forward position?
Long forward position (aka buying a forward) is an agreement to buy an asset at a certain future
time for a certain price. Short forward position (aka selling a forward) is an agreement to sell an
asset at a certain future time for a certain price.
2. An investor enters into a short forward contract to sell 100,000 British pounds (GBP) for U.S. dollars
at an exchange rate of 1.5000 USD per pound. If the contract is held to expiration how much does
the investor gain or lose if the exchange rate at the end of the contract is (a) 1.49000 and (b)
1.5200?
By shorting the forward the investor has agreed to sell 1 GBP for $1.50. If at expiration the exchange
rate declines to $1.49/GBP the investor would make a profit of $0.01/GBP since he is able to sell
each pound for $1.50 instead of the market rate of $1.49 at expiration. The total profit for the
contract would be GBP 100,000 x $0.01/GBP = $1,000.
Conversely, if at expiration the exchange rate increases to $1.52/GBP the investor would make a loss
of $0.02/GBP since he has to sell each pound for $1.50 instead of the market rate of $1.52 at
expiration. The total loss for the contract would be GBP 100,000 x $0.02/GBP = $2,000.
Notice shorting (or selling a forward) is like betting the underlying asset (in this case the $/GBP
exchange rate) will decline in value.
3. 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. If held until expiration 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 and (b) 51.30
cents per pound?
By shorting cotton futures the trader has agreed to sell cotton at $0.50/lbs. If at expiration the price
of cotton declines to $0.482/lbs the trader would make a profit of $0.018/lbs since he is able to sell
cotton at $0.50 vs. the market rate at expiration of $0.482/lbs. The total profit on the contract
would be 50,000 lbs x $0.018/lbs = $900.
Conversely, if at expiration the price of cotton increases to $0.513/lbs the trader would make a loss
of $0.013/lbs sine he has to sell cotton at $0.50 vs the market rate at expiration of $0.513/lbs. The
total loss on the contract would be 50,000 lbs x $0.013/lbs = $650.
4. A company knows that it is due to receive a certain amount of a foreign currency in 4 months. What
type of derivative contract is appropriate for hedging?
If a company is due to receive foreign currency in the future it would benefit if the foreign currency
appreciated in the future. Conversely it would lose money if the foreign currency depreciated in the
future. Therefore, in order to hedge, it would look to gain on its forward contract in the event of a
depreciation of the foreign currency. This would be done by short (or selling) forward contract(s) in
the foreign currency.
FIN4400- Futures & Options
Ch1 homework solution
If using options, the company can buy put options on the foreign currency. This way if the currency
depreciated the gain from the put options would offset the loss from the depreciation of the foreign
currency.
5. A U.S. company expects to have to pay 1 million Canadian dollars in 6 months. Explain how the
exchange rate risk can be hedged using a forward contract.
If a U.S. company has to pay 1 million Canadian dollars in 6 months it wants to hedge against the
Canadian dollar appreciating in the future. To hedge against this outcome it would go long (or buy)
Canadian dollar forward contract(s). This way, if the Canadian dollar appreciated, any l oss would be
mitigated by the profit from the forward contract(s).
