European Bank?

This is a bit more complicated. First, you buy euros with your $100. Second, you deposit these euros in a European bank and earn interest. Third, at the end of the year, you withdraw your euros from the bank and sell them for dollars. For example, suppose that the current dollar price of euros is $1.25 and the interest rate paid on deposits in Europe is 5 percent. Suppose you also expect that the price of a dollar in euros will be EUR 0.70 in a year’s time. With the second investment strategy,

 You take your $100 and buy EUR 80.  You put these EUR 80 in the European bank for a year, giving you EUR 84 at the end of

the year.  You take these EUR 84 and use them to purchase $120.

The second strategy therefore earns you more than the first strategy. It would be better to invest in Europe compared to the United States. Moreover, a slight variation on this strategy seems like it is a money machine. Consider the following.

 Borrow $100 from a US bank for one year.  Take the $100 and use it to buy euros.  Deposit the euros in a European bank.  Wait for a year.  Withdraw the deposit and interest and use it to buy dollars.  Repay the dollar loan plus interest.

Using the same interest rates and exchange rates as previously, this transaction works as follows: you borrow $100, obtain $120 at the end of the year, pay back $110 to the bank, and end up with $10 profit. To evaluate this arbitrage possibility, you need to know (1) the current dollar price of euros, (2) the annual return on deposits in Europe, and (3) the price of a dollar in euros a year from now. Look carefully at the language we used. You need to know “the euro price of dollars a year from now.” But when we went through the example, we said “you expect that the price of dollar in euros will be EUR 0.70 in a year’s time.” As with the term structure of interest rates, there is some risk involved here. You cannot know the future exchange rate with certainty. This strategy entails a gamble about the future exchange rate. Still, if everyone has the same guess about the future exchange rate as you do, then such a situation could not last. Everyone would pursue the same strategy: borrow in the United States, buy euros, invest in Europe, and convert back in a year’s time. What would happen?

 The demand for credit would increase interest rates in the United States.  The demand for euros would increase the dollar price of euros.  The extra supply of savings in Europe would drive down the interest rate in Europe.  Investors might anticipate the extra demand for dollars in a year’s time and expect the euro price of dollars to increase. These forces would all tend to eliminate the profit opportunity.