Question

1. Suppose that the annual interest rate is 5% in the U.S. and 8% in the U.K. The spot exchange rate is $1.80/£. Assume that the arbitrager can borrow up to $1,000,000 or £555,556. If the one-year forward rate is $1.72/£.

1. What is the no arbitrage one-year forward rate implied by Interest Rate Parity (IRP)?
2. What transactions will the arbitrager carry out? How much profit can the arbitrager make in terms of dollar?
3. Discuss how IRP will be restored in this case

Answer 1

(a) UK Interest Rate = 8% and USD Interest Rate = 5 %, Current Spot Rate = $ 1.8 / £

IRP Predicted 1-Year Forward Rate = 1.8 x [(1.05) / (1.08)] = $ 1.75 / £

(b) An arbitrage can be executed as described below:

- Borrow £ 555556 and convert the borrowing into $ at the current spot rate of $ 1.8 / £ to yield $ 1000000

- The borrowing creates a repayment liability worth 555556 x (1.08) = £ 600000

- Invest the $ yield at the US Interest Rate of 5% to yield = 1000000 x (1.05) = $ 1050000.84

- Convert the $ investment yield into £ at the forward rate of $ 1.72 / £ to yield (1050000.84 / 1,72) = £ 610465.6047

- Arbitrage Profit = £ Investment Yield - £ Repayment Liability = 610465.6047 - 600000 = £ 10465.12

(c) The actual forward rate is $ 1.72 / £ whereas the no-arbitrage forward rate should be $ 1.75 / £. This implies that the £ is cheaper than it should be as per the no-arbitrage condition. As more and more people identify the aforementioned arbitrage opportunity, the demand for £ with respect to the $ will increase, thereby making the £ costlier and pushing the actual forward rate towards the no-arbitrage predicted forward rate.