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rpeso(real) = “1= “ 1 = .044, or 4.4%
E(1 + ipeso) 1.20
In the United States, where the nominal interest rate is about 6 percent and the expected
inflation rate is about 2 percent,
1 + r$ 1.06
r$(real) = “1= “ 1 = .039, or 3.9%
E(1 + i$) 1.02
The real interest rate is higher in Mexico than in the United States, but the difference in
the real rates is much smaller than the difference in nominal rates.


How similar are real interest rates around the world? It is hard to say, because we can-
not directly observe expected inflation. In Figure 6.3 we have plotted the average interest
FIGURE 6.3
Countries with the highest 40
interest rates generally have
the highest subsequent 35
Average interest rate, percent (1994“1998)




inflation rates. In this
diagram, each point 30
represents a different country.
25


20


15


10


5


0
0 10 20 30 40
Average inflation, percent (1994“1998)
608 SECTION SIX


rate in each of 40 countries against the inflation that in fact occurred. You can see that the
countries with the highest interest rates generally had the highest inflation rates.


American investors can invest $1,000 at an interest rate of 6.0 percent. Alternatively,
Self-Test 5
they can convert those funds to 306,675 drachma at the current exchange rate and in-
vest at 8.5 percent in Greece. If the expected inflation rate in the United States is 2 per-
cent, what must be investors™ forecast of the inflation rate in Greece?


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 — 1.06 = $1,060,000.
• Peso loan: The current rate of exchange (from Table 6.5) is peso9.438/$. Therefore,
for $1 million, you can buy 1,000,000 — 9.438 = peso9,438,000. The rate of interest
on a 1-year peso loan is 25.25 percent. So at the end of the year, you get
peso9,438,000 — 1.2525 = peso11,821,000. Of course, you don™t know what the ex-
change rate will be at the end of the year. But that doesn™t matter. You can nail down
the price at which you sell your pesos. The 1-year forward rate is peso11.153/$.
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
1 + rpeso 1.2525
= = 1.1816
1 + r$ 1.06
International Financial Management 609


and the differential between the forward and spot exchange rates is virtually identical:
fpeso/$ 11.153
= = 1.1817
speso/$ 9.438
Interest rate parity theory says that the interest rate differential must equal the dif-
INTEREST RATE
ferential between the forward and spot exchange rates. Thus
PARITY Theory that
forward premium equals
interest rate differential. Difference in Difference between
interest rates forward and spot rates
equals
1 + rpeso fpeso/$
1 + r$ speso/$




What Happens If Interest Rate Parity
EXAMPLE 4
Theory 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 — 1.06 = $112,312. Of course, this is not money to spend because you must
repay your peso loan. The amount that you need to repay is 1,000,000 — 1.2525 =
peso1,252,500. If you buy these pesos forward, you can fix in advance the number of
dollars that you will need to lay out. With a forward rate of peso12.00/$, 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 “ $104,375 = $7,937. It is a pity that in prac-
tice interest rate parity almost always holds and the opportunities for such easy profits
are rare.



Look at the exchange rates in Table 6.5. Does the Swiss franc sell at a forward
Self-Test 6
premium or discount on the dollar? Does this suggest that the interest rate in Switzer-
land is higher or lower than in the United States? Use the interest rate parity relation-
ship to estimate the 1-year interest rate in Switzerland. Assume the U.S. interest rate is
6 percent.



THE FORWARD RATE AND THE
EXPECTED SPOT RATE
If you buy pesos forward, you get more pesos for your dollar than if you buy them spot.
So the peso is selling at a forward discount. Now let us think how this discount is re-
lated to expected changes in spot rates of exchange.
The 1-year forward rate for the peso is peso11.153/$. Would you sell pesos at this
rate if you expected the peso to rise in value? Probably not. You would be tempted to
610 SECTION SIX


wait until the end of the year and get a better price for your pesos in the spot market. If
other traders felt the same way, nobody would sell pesos forward and everybody would
want to buy. The result would be that the number of pesos that you could get for your
dollar in the forward market would fall. Similarly, if traders expected the peso to fall
sharply in value, they might be reluctant to buy forward and, in order to attract buyers,
the number of pesos that you could buy for a dollar in the forward market would need
to rise.4
This is the reasoning behind the expectations theory of exchange rates, which pre-
EXPECTATIONS
dicts that the forward rate equals the expected future spot exchange rate: fpeso/$ =
THEORY OF EXCHANGE
E(speso/$). Equivalently, we can say that the percentage difference between the forward
RATES Theory that
rate and today™s spot rate is equal to the expected percentage change in the spot rate:
expected spot exchange rate
equals the forward rate.


Difference between Expected change in
forward and spot rates spot exchange rate
equals
fpeso/$ E(speso/$)
speso/$ speso/$

This is the final leg of our quadrilateral in Figure 6.1.

The expectations theory of forward rates does not imply that managers are
perfect forecasters. Sometimes the actual future spot rate will turn out to be
above the previous forward rate. Sometimes it will fall below. But if the theory
is correct, we should find that on the average the forward rate is equal to the
future spot rate.

The theory passes this simple test reasonably well. This is important news for the fi-
nancial manager; it means that a company which always covers its foreign exchange
commitments by buying or selling currency in the forward market does not have to pay
a premium to avoid exchange rate risk: on average, the forward price at which it agrees
to exchange currency will equal the eventual spot exchange rate, no better but no worse.
We should, however, warn you that the forward rate does not tell you very much
about the future spot rate. For example, when the forward rate appears to suggest that
the spot rate is likely to appreciate, you will find that the spot rate is about equally likely
to head off in the opposite direction.


SOME IMPLICATIONS
Our four simple relationships ignore many of the complexities of interest rates and ex-
change rates. But they capture the more important features and emphasize that interna-
tional capital markets and currency markets function well and offer no free lunches.
When managers forget this, it can be costly. For example, in the late 1980s, several Aus-
tralian banks observed that interest rates in Switzerland were about 8 percentage points
lower than those in Australia and advised their clients to borrow Swiss francs. Was this
advice correct? According to the international Fisher effect, the lower Swiss interest

4 Thisreasoning ignores risk. If a forward purchase reduces your risk sufficiently, you might be prepared to
buy forward even if you expected to pay more as a result. Similarly, if a forward sale reduces risk, you might
be prepared to sell forward even if you expected to receive less as a result.
International Financial Management 611


rate indicated that investors were expecting a lower inflation rate in Switzerland than in
Australia and this in turn would result in an appreciation of the Swiss franc relative to
the Australian dollar. Thus it was likely that the advantage of the low Swiss interest rate
would be offset by the fact that it would cost the borrowers more Australian dollars to
repay the loan. As it turned out, the Swiss franc appreciated very rapidly, the Australian
banks found that they had a number of very irate clients and agreed to compensate them
for the losses they had incurred. Moral: Don™t assume automatically that it is cheaper
to borrow in a currency with a low nominal rate of interest.


In October 1998 Stellar Corporation borrowed 100 million Japanese yen at an attractive
Self-Test 7
interest rate of 2 percent, when the exchange rate between the yen and U.S. dollar was
¥123.97/$. One year later when Stellar came to repay its loan, the exchange rate was
¥107.52/$. Calculate in U.S. dollars the amount that Stellar borrowed and the amounts
that it paid in interest and principal (assume annual interest payments). What was the
effective U.S. dollar interest rate on the loan?


Here is another case where our simple relationships can stop you from falling into a
trap. Managers sometimes talk as if you make money simply by buying currencies that
go up in value and selling those that go down. But if investors anticipate the change in
the exchange rate, then it will be reflected in the interest rate differential; therefore, what
you gain on the currency you will lose in terms of interest income. You make money
from currency speculation only if you can predict whether the exchange rate will change
by more or less than the interest rate differential. In other words, you must be able to pre-
dict whether the exchange rate will change by more or less than the forward premium.


Measuring Currency Gains
EXAMPLE 5
The financial manager of Universal Waffle is proud of his acumen. Instead of keeping
his cash in U.S. dollars, he for many years invested it in German deutschemark deposits.
He calculates that between the end of 1980 and 1998, the deutschemark increased in
value by nearly 47 percent, or about 2.1 percent a year. But did the manager really gain
from investing in foreign currency? Let™s check.
The compound rate of interest on dollar deposits during the period was 9.0 percent,
while the compound rate of interest on deutschemark deposits was only 6.9 percent. So
the 2.1 percent a year appreciation in the value of the deutschemark was almost exactly
offset by the lower rate of interest on deutschemark deposits.
The interest rate differential (which by interest rate parity is equal to the forward pre-
mium) is a measure of the market™s expectation of the change in the value of the cur-
rency. The difference between the German and United States interest rates during this
period suggests that the market was expecting the deutschemark to appreciate by just
over 2 percent a year,5 and that is almost exactly what happened.



5 Ifthe interest rate is 9.0 percent on dollar deposits and 6.9 percent on deutschemark deposits, our simple re-
lationship implies that the expected change in the value of the deutschemark was (1 + r$)/(1 + rDM) “ 1 =
1.090/1.069 “ 1 = .020, or 2.0 percent per year.
612 SECTION SIX



Hedging Exchange Rate Risk
Firms with international operations are subject to exchange rate risk. As exchange rates
fluctuate, the dollar value of the firm™s revenues or expenses also fluctuates. It helps to
distinguish two types of exchange rate risk: contractual and noncontractual. By con-

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