You are expected to make a payment of 4,000,000 GBP to your British client on June 15, 2022. As of today (April 11), current exchange rate GBP/USD is 1.3623. You do not want to expose yourself to a currency risk. You decided to hedge against the exchange risk by using futures contract. Assume, todays settlement price for pound futures contract is 1.3655. Please answer the following questions:

(a) In order to hedge yourself against the currency risk, what position should you take on futures contract? In other words, should you buy (long) or sell(short) futures contract?

(b) How many contract you should buy or sell to perfectly hedge? Assume you can also buy a fractions of the contract.

(c) Assume that the settlement prices of the same futures contract for next four days are 1.3659, 1.3654, 1.3658, 1.3656. Calculate the unrealised profit/loss for each day due to the your position in the futures contract.

(d) Assume that spot prices for next four days 1.3627, 1.3622, 1.3626, 1.3624. Calculate the changes in your liability each day.

(e) Using payoff graph for (c) and (d) show that the futures contract offset losses caused by the change in exchange rate, thereby providing a perfectly hedged position.