Question

You expect to receive a payment of £1,000,000 in British pounds after six months. The pound is currently worth $1.60 (i.e., £1 $1.60), but the six-month futures price is $1.56 (i.e., £1 5 $1.56). You expect the price of the pound to decline (i.e., the value of the dollar to rise). If this expectation is fulfilled, you will suffer a loss when the pounds are converted into dollars when you receive them six months in the future.

a) Given the current price, what is the expected payment in dollars?
b) Given the futures price, how much would you receive in dollars?
c) if, after six months, the pound is worth $1.35, what is your loss from the decline in the value of the pound?
d) To avoid this potential loss, you decide to hedge and sell a contract for the future delivery of pounds at the going futures price of $1.56. What is the cost to you of this protection from the possible decline in the value of the pound?
e) if, after hedging, the price of the pound falls to $1.35, what is the maximum amount that you lose? Why is your answer different from your answer to part (c)?
f) if, after hedging, the price of the pound rises to $1.80, how much do you gain from your position? g) how would your answer to part (f) be different if you had not hedged and the price of the pound

Answer 1

a) Expected payment in dollars is $1,600,000

b) $1,560,000

c) Loss is -$250,000

d) Loss would be $40,000

e) If after hedging the price falls to $1.35, the contract amount would still not change.

f) If after hedging the price rises to $1.80, the contract amount would still not change.

g) Loss would be $200,000

Step-by-step explanation:

You expect to receive a payment of £1,000,000 in British pounds after six months.

The pound is currently worth $1.60, i.e., £1 = $1.60

Six-month future price is $1.56, i.e., £1 = $1.56

a) At £1 = $1.60 current price, expected payment of £1,000,000 in dollars

= £1,000,000 × $1.60 = $1,600,000

b) At £1 = $1.56 future price, expected payment of £1,000,000 in dollars

= £1,000,000 × $1.56 = $1,560,000

c) If after six months, £1 = $1.35, expected payment of £1,000,000 in dollars

= £1,000,000 × $1.35 = $1,350,000

Therefore, loss = $1,350,000 - $1,600,000 = -$250,000

d) Present price at $1.60 delivery = $1,600,000

Future price at $1.56 delivery = $1,560,000

Loss = $1,600,000 - $1,560,000 = $40,000

g) Present price at $1.60 delivery = $1,600,000

Future price at $1.80 = $1,800,000

Loss = $1,800,000 - $1,600,000 = $200,000