Question

Assuming £1.00 = $1.45 and €1.00 = $1.25, the interest rate in the UK is 6.50% and the interest rate in Germany is 5.45%, determine the forward rate of the   £ / € if interest rate parity (IRP) holds. What does this imply about future forward rates? Explain how you can engage in covered interest arbitrage if the spot rate remains the same, and the interest rate in the UK is still 6.50%, and the forward rate is .868 £ / € .

Answer 1

According to Interest rate parity, there would be no arbitrage opportunity if an investor invests in his country at the interest rate his country offers or decides to convert his local currency into a foreign currency, and deposit it in that country receiving a different interest rate, and then, after a certain period converting that foreign currency back to local currency at a rate locked in while making the investment, using a forward contract.

Since the interest rate in the UK is higher than that in Germany, the interest rate parity suggests that the forward rate for euro per pound will be lower, that is pound value is lower in the forward rate.

There is a discrepancy in the interest rate parity in the above question and can be exploited as follows.

Let's say that an investor has 10,000 euros to invest. He converts the euros into pound at the spot rate

euro per pound = dollar per pound/ dollar per euro = 1.45/1.25 = 1.16 euros per pound = Spot rate

At the same time, he will get 0.868 pounds per euro,

pounds per euros = 1/ (euros per pounds) = 1/0.868 = 1.152073

At the spot rate he will get,

amount in euros / euro per pounds spot rate

10,000 / 1.16 = 8,620.6896 pounds

Now, he can invest these pounds and receive an interest rate of 6.5%.

After the end of the period, he will get

pounds invested at the start of the period * (1 + interest rate in UK)

8,620.6896 * 1.065 = 9,181.03448 pounds.

Now, he can convert it back into euros at 1.152073 per pound

pounds at the end of the period * fixed forward currency rate

9,181.03448 * 1.152073= 10,577.23 euros.

If he had invested the same 10,000 euros at the German interest rate, he would have got,

principal amount in euros * (1 + interest rate in germany)

10,000 * 1.0545 = 10,545 euros

As a result, he made 22.23 euros more by using covered interest arbitrage.