Question
In: Economics
Suppose that the treasurer of IBM has chance to borrow of $10,000,000 (or its equivalent in...
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.
Solutions
Expert Solution
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
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