Question

Suppose that the treasurer of IBM has chance to borrow of $10,000,000 (or its equivalent in other currency) and to invest for three months. Monthly interest rate in the USA - 1.3% per month, in Germany - 0.6% per month, in London - 0.9% per month. The treasurer of IBM does not wish to bear any exchange risk.

Current spot exchange rate: 0.8045 €/$ and 1.8095 $/£

Three-month forward exchange rate: 0.8098 €/$ and 1.8028 $/£

a. Determine whether the interest rate parity (IRP) is currently holding.

b. If the IRP is not holding, how would you carry out covered interest arbitrage? Show all the steps and determine the arbitrage profit.

c. Explain how the IRP will be restored as a result of covered arbitrage activities.

Answer 1

First we convert the Euro rate, to the correct expression: Dollar / Euro = 1/0.8045 = 1.243008

Then we use the following formular to calculate CIP forward rates and compare them with the actual forward rates

Forward exchange rate =

Spot exchange rate * (1+local interest rate) / (1+foreign interest rate)

Calculations

	Per Euro	Per Pound
Spot (Dollars per)	1.24300808	1.8095
Local interest rate for 3 months	1.039509197	1.039509197
Foreign interest for 3 months	1.018108216	1.027243729
CIP Forward rate	1.269136532	1.831105743
CIP Forward rate (reverse)	0.78793729	0.546118106
Actual 3-month forward rate	0.8098	1.8028

a. We wee that CIP is not holding since the forward rates in the market are different from what the CIP model predicts

b. We can make some money by doing arbitrage as follows:

	Euro	Dollar	Formula
Borrow Euros worth $10M at today's spot rate	8045000		10M * 0.8045
Will need to repay @ 0.6% per month	8190680.598		8045000 * (1.006^3)
Covert these into Dollars		10000000
Lend $10M for 3 months @ 1.3% per month	10000000
Buy 8190680.6 Euro in forward today @ 0.8098 (so it will be worth Dollars)	10114448.75	8190680.6 / 0.8098
Get delivery of Euro 3 months later to repay the loan	8190680.598
Get back the $10M incl. interest		10395091.97	10M * 1.013^3
Profit		280643.2172

c. When a lot of traders start making money as above, there will be more demand for Euros and more supply of Dollars for 3 month loans which will either equalize their interest rates or bring their forward rates in line with teh CIP predicted ones. The same mechanism will work on Pound/Dollar as well