Principles of Corporate Finance_ 12th Edition

710 Part Eight Risk Management

bre44380_ch27_707-731.indd 710 10/08/15 10:08 AM

Interest Rates and Exchange Rates

Suppose that you have $1,000 to invest for one year. U.S. dollar deposits are offering an inter-

est rate of 5%; Ruritanian peso deposits are offering (an attractive?) 15.5%. Where should you

put your money? Does the answer sound obvious? Let’s check:

• Dollar loan. The rate of interest on one-year dollar deposits is 5%. Therefore, at the end
  of the year you get 1,000 × 1.05 = USD1,050.


• Peso loan. The current exchange rate is RUP50/USD1. Therefore, for $1,000, you can
  buy 1,000 × 50 = RUP50,000. The rate of interest on a one-year peso deposit is 15.5%.
  Therefore, at the end of the year you get 50,000 × 1.155 = RUP57,750. Of course, you
  don’t know what the exchange rate is going to be in one year’s time. But that doesn’t mat-
  ter. You can fix today the price at which you sell your pesos. The one-year forward rate
  is RUP55/USD1. Therefore, by selling forward, you can make sure that you will receive
  57,750/55 = $1,050 at the end of the year.
  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.
  When you make the peso loan, you receive a higher interest rate. But you get an offsetting
  loss because you sell pesos forward at a lower price than you pay for them today. The interest
  rate differential is

1 + Ruritanian interest rate______________________

1 + U.S. interest rate

And the differential between the forward and spot exchange rates is

Forward peso exchange rate

___

Current peso spot rate

Interest rate parity theory says that the difference in interest rates must equal the difference

between the forward and spot exchange rates:

equals

Difference in

interest rates

1 + Ruritanian

interest rate

Difference between

forward and spot rates

Forward peso

exchange rate

1 + U.S.

interest rate

Current peso

spot rate

In our example,

_____ 1.155

1.05

= ___^55

50

The Forward Premium and Changes in Spot Rates

Now let’s consider how the forward premium is related to changes in spot rates of

exchange. If people didn’t care about risk, the forward rate of exchange would depend

solely on what people expected the spot rate to be. For example, if the one-year forward

rate on pesos is RUP55/USD1, that could only be because traders expect the spot rate in

one year’s time to be RUP55/USD1. If they expected it to be, say, RUP60/USD1, nobody

would be willing to buy pesos forward. They could get more pesos for their dollar by

waiting and buying spot.