Question

4. Currently, the spot exchange rate is $0.85/AS and the one-year forward exchange rate is $0.81/A$. One-year interest is 3.5% in the United States and 4.2% in Australia. You may borrow up to $1,000,000 or A$1,176,471, which is equivalent to $1,000,0oo at the current spot rate. a. Determine if IRP is holding between Australia and the United States. b. If IRP is not holding, explain in detail how you would realize certain profit in U.S. dollar terms. Explain how IRP will be restored as a result of arbitrage transactions you carry out above. c.

Answer 1

(a) Current Spot Rate = $ 0.85 / A $, US Interest Rate = 3.5 % and Australian Interest Rate = 4.2 %

If IRP holds, then one-year forward exchange rate = 0.85 x [(1.035) / (1.042)] = $ 0.844 / A $

However, the actual forward rate is $ 0.81 / A $, thereby indicating that IFE does not hold

(b) As is observed in part (a), the IRP does not hold thereby providing an opportunity to earn arbitrage profit. The same can be executed as described below:

- Borrow 1176471 A $ at the Australian Interest Rate of 4.2 %. Borrowing creates repayment liability worth (1176471 x 1.042) = A $ 1225882.78 after one year

- Convert the borrowing into $ at the current spot rate of $ 0.85 / A $ to yield = (1176471 / 0.85) ~ $ 1000000

- Invest the converted $ amount at the US interest rate of 3.5 % for one year to yield = 1000000 x 1.035 = $ 1035000

- After one year convert the investment yield of $ 1035000 into A $ at the forward rate of $ 0.81 / A $ tp yield = 1035000 / 0.81 = A $ 1277778.22

- Arbitrage Profit = 1277778.22 - 1225882.78 = A $ 51895.44 or (51895.44 x 0.81) = $ 42035.31

(c) The arbitrage process involves borrowing A $ and converting them into $, followed by investing the latter. As more and more people realize the opportunity of making arbitrage profits, more people would borrow A $ and convert the same into $. This would increase the demand for A $ relative to $ thereby strengthening A $ relative to $ and pushing the exchange rate towards the IRP.