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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 related 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 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.

This is the reasoning behind the expectations theory of exchange rates, which predicts that the forward rate equals the expected future spot exchange rate: fpeso/$ = E(speso/$). Equivalently, we can say that the percentage difference between the forward rate and today`s spot rate is equal to the expected percentage change in the spot rate:

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

The theory passes this simple test reasonably well. This is important news for the financial 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 exchange rates. But they capture the more important features and emphasize that international 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 Australian 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 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.

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 predict whether the exchange rate will change by more or less than the forward premium.

Measuring Currency Gains

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 premium) is a measure of the market`s expectation of the change in the value of the currency. 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.

EXPECTATIONS THEORY OF EXCHANGE RATES Theory that expected spot exchange rate equals the forward rate.