Question

Suppose that the current spot exchange rate of the EUR is USD 1.25 / EUR and the 3-month forward exchange rate is USD $1.10 / EUR. The 3-month interest rate is 4% per annum in the US and 3% per annum in Germany. Assume that you can borrow EUR 1,000,000 or USD 1,000,000.

Determine whether interest rate parity is currently holding.

If IRP is no holding, how would you carry out covered interest arbitrage (CIA)? Show all the steps and determine the arbitrage profit. Assume you choose to keep your profits in US dollars.

Do the problem again, assuming that you choose to keep your profits in euros.

Answer 1

Spot Exchange Rate = S = 1.25 USD/EUR, US Interest Rate = rd = 4% per annum or 1% per quarter (3 months), European Interest Rate = rf = 3% per annum or 0.75% per quarter.

Also the exchange rate is quoted in the direct format which states the amount of domestic curreny purchasable for a unit of the foreign currency. Obviously, USD is considered domestic and EUR is considered foreign currency in this examples.

Let the IRP compliant forward rate be Fi

Using IRP

(Fi / S) = (1+rd) / (1+rf)

Fi / 1.25 = (1.01) / (1.0075)

Fi = 1.2531 USD /EUR

Actual Foward Rate = Fa = 1.1 USD /EUR

Therefore, the forward rate is not IRP compliant thereby giving the opportunity of an arbitrage.

Let us consider EUR as the asset and USD as the currency used to purchase the asset.

Arbitrage Strategy:

- Borrow 1 million EUR and sell them at the spot price to obtain 1.25 million USD. Sell a EUR forward contract simultaneously.

- Lend these USDs at the 3 month interest rate of 1%.

- Lending Proceeds received after 3 month = 1.25 x (1.01) = 1.2625 million USD

- Borrowing proceeds payable after 1 month = 1 million x (1.0075) = 1.0075 million EUR

- Convert Borrowing proceeds into USD by exercising the forward contract at the actual (and not IRP calculated) forward rate of 1.1 USD / EUR.

- Borrowing Proceeds become = 1.0075 x 1.1 = 1.10825 million USD

- Abritrage Profits = Investment Proceeds - Borrowing Proceeds = 1.2625 - 1.10825 = 0.15425 million USD.

For profits in EUR, convert the USD investment proceeds into EUR at the forward rate of 1.1 USD / EUR, though purchase of a forward contract at the beginning.

- Convert Investment proceeds of 1.2625 million USD into EUR at the forward rate of 1.1 USD / EUR

- Investment Proceeds in EUR = 1.2625 / 1.1 = 1.1477 million EUR

- Arbitrage Profit = Investment Proceeds - Borrowing Proceeds = 1.1477 - 1.0075 = 0.14023 million EUR