Question

1. Assume that spot rate is GBP/USD 1.22, and annual interest rate is 1% in USA and 6% in England.
   1. What should be the one-year forward rate GBP/USD per interest rate parity condition? (10 points)
   2. Show that there is no arbitrage opportunity based on the forward rate that you computed in part a. Pick any initial borrowing amount of your choice. (15 points)
   3. Compute arbitrage profit if one-year forward rate is GBP/USD 1.38. Pick any initial borrowing amount of your choice. (15 points)

Answer 1

a. Forward rate = Spot rate * (1 + foreign rate of interest) / (1 + domestic rate of interest)

Spot rate: USD 1.22 / GBP

Forward rate: 1.22 * (1+1%) / (1+6%) = 1.162453

b. Let's assume we borrow GBP 1000 @ 6%, so we need to return GBP 1060 at the end of one year

Today, we use this to buy USD, we get 1000X1.22 = 1220 USD, which we would invest at 1% and get 1220X1.01 = 1232.2 USD at the end of one year

After one year, we use this USD 1232.2 to buy GBP so that we can repay our GBP loan

We get USD 1232.2 / 1.162453 (since we had booked a forward contract)

which is GBP 1060 which is exactly equal to the loan amount we need to repay

Hence there is no arbitrage opportunity

c. Assuming that teh one year forward rate is USD 1.38 / GBP [we see based on a. that this is undervaluing USD]

Hence we will borrow USD 1000 @ 1% so that our liability is to repay USD 1010 at the end of one year

Today, we use this USD 1000 to buy GBP @ 1.22, we get 1000 / 1.22 = GBP 819.6721

We invest this @6% for one year, and get GBP 819.6721 X 1.06 = GBP 868.8525 at teh end of one year

We use this to buy USD at 1.38 (since we had booked a forward contract) and get 868.8525 X 1.38 = USD 1199.016

After repaying USD 1010 loan, we are left with a cool profit of USD 189.016