Question

UVW, a U.S. company, will be paid £1.30 million by a British company next month. It wishes to protect the payment against a drop in the value of the British pound. To achieve this goal, UVW can either enter into a 30-day short futures position to sell the British pound at a price of $1.6512/£, or it can buy pound put options with a strike price of $1.6610/£at an option premium of $0.02/£. The spot price of the British pound is currently $1.6560/£, and the pound is expected to trade in the range of $1.6200 to 1.7000. UVW’s treasure believes that the most likely price for the British pound in 30 days will be $1.6400. Suppose the futures contract and options contract are of the same size of £65,000.

a) (4 points) How many futures contracts will UVW need to protect its receipts? How many options contracts?

b) (10 points) Tabulate UVW’s profit and loss associated with the put option position and the futures position for the following pound prices at expiration: $1.6200, $1.6400, $1.6512, $1.6610, and $1.7000. Ignore transaction costs and margins.

c) (9 points) Tabulate the total cash flow to UVW using the options and futures contracts, as well as the unhedged position for the following pound prices at expiration: $1.6200, $1.6400, $1.6512, $1.6610, and $1.7000.

d) (4 points) What is UVW’s break-even point of future spot price on the futures contract? On the options contract?

e) (3 points) Compare the two strategies.

Answer 1

a)since size of futures contract and options contract is same and equal to GBP65000, so no of futures and options contract needed will be same = total GBP amount to be protected/contract size = 1.3 million/65000 = 20

b) and c) - Answer in Table below

Unhedged position = amount hedges * final price

Final cash flow (option case) = (MAX(put strike,final price)-option premium)*contract size*no. of contracts

Profit and loss (options case) = Final cash flow (option case) - Unhedged position

Final cash flow (futures case) = Futures Strike Price - Unhedged Position

Profit and loss (futures case) = Final cash flow (futures case) - Unhedged Position

Amount hedged (in GBP)	Contract Size (in GBP)	No. of contracts	Spot Price	Put Strike Price	Put option premium (IN USD)	Futures Strike Price	Final Price	Unhedged Position	Final cash flow (option case)	Profit and loss (options case)	Final cash flow (futures case)	Profit and loss (futures case)
1300000	65000	20	1.6560	1.6610	0.0200	1.6512	1.6200	2106000	2133300	27300	2146560	40560
1300000	65000	20	1.6560	1.6610	0.0200	1.6512	1.6400	2132000	2133300	1300	2146560	14560
1300000	65000	20	1.6560	1.6610	0.0200	1.6512	1.6512	2146560	2133300	-13260	2146560	0
1300000	65000	20	1.6560	1.6610	0.0200	1.6512	1.6610	2159300	2133300	-26000	2146560	-12740
1300000	65000	20	1.6560	1.6610	0.0200	1.6512	1.7000	2210000	2184000	-26000	2146560	-63440