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INTEREST RATES AND EXCHANGE RATES

You are an investor with $1 million to invest for 1 year. The interest rate in Mexico is 25.25 percent and in the United States it is 6 percent. Is it better to make a peso loan or a dollar loan?

The answer seems obvious: Isn`t it better to earn an interest rate of 25.25 percent than 6 percent? But appearances may be deceptive. If you lend in Mexico, you first need to convert your $1 million into pesos. When the loan is repaid at the end of the year, you need to convert your pesos back into dollars. Of course you don`t know what the exchange rate will be at the end of the year but you can fix the future value of your pesos by selling them forward. If the forward rate of exchange is sufficiently low, you may do just as well keeping your money in the United States.

Let`s use the data from Table 6.5 to check which loan is the better deal:

Dollar loan: The rate of interest on a dollar loan is 6 percent. Therefore, at the end of the year you get 1,000,000 ГЧ 1.06 = $1,060,000.

Peso loan: The current rate of exchange (from Table 6.5) is peso9.438/$. Therefore, for $1 million, you can buy 1,000,000 ГЧ 9.438 = peso9,438,000. The rate of interest on a 1-year peso loan is 25.25 percent. So at the end of the year, you get peso9,438,000 ГЧ 1.2525 = peso11,821,000. Of course, you don`t know what the exchange rate will be at the end of the year. But that doesn`t matter. You can nail down the price at which you sell your pesos. The 1-year forward rate is peso11.153/$.

Therefore, by selling the peso11,821,000 forward, you make sure that you will get 11,821,000/11.153 = $1,059,900.

Thus the two investments offer almost exactly the same rate of return. They have to ¤ they are both risk-free. If the domestic interest rate were different from the ¬covered ­ foreign rate, you would have a money machine: you could borrow in the market with the lower rate and lend in the market with the higher rate.

A difference in interest rates must be offset by a difference between spot and forward exchange rates. If the risk-free interest rate in country X is higher than in country Y, then country X`s currency will buy less of Y`s in a forward transaction than in a spot transaction.

When you make a peso loan, you gain because you get a higher interest rate. But you lose because you sell the pesos forward at a lower price than you have to pay for them today. The interest rate differential is and the differential between the forward and spot exchange rates is virtually identical: Interest rate parity theory says that the interest rate differential must equal the differential between the forward and spot exchange rates.

What Happens If Interest Rate ParityTheory Does Not Hold?

Suppose that the forward rate on the peso is not peso11.153/$ but peso12.00/$. Here is what you do. Borrow 1 million pesos at an interest rate of 25.25 percent and change these pesos into dollars at the spot exchange rate of peso9.438/$. This gives you $105,954, which you invest for a year at 6 percent. At the end of the year you will have 105,954 ГЧ 1.06 = $112,312. Of course, this is not money to spend because you must repay your peso loan. The amount that you need to repay is 1,000,000 ГЧ 1.2525 = peso1,252,500. If you buy these pesos forward, you can fix in advance the number of dollars that you will need to lay out. With a forward rate of peso12.00/$, you need to set aside 1,252,500/12.00 = $104,375. Thus, after paying off your peso loan, you walk away with a risk-free profit of $112,312 Ј $104,375 = $7,937. It is a pity that in practice interest rate parity almost always holds and the opportunities for such easy profits are rare.

INTEREST RATE PARITY Theory that forward premium equals interest rate differential.