Exchange rates between currencies vary over time, reflecting supply and demand considerations for each currency. For example, the demand for British pounds comes from a number of sources, which include foreign buyers of British exports who must pay for their purchases in pounds, foreign investors who desire to make investments in physical or financial assets in Britain, and speculators who expect British pounds to increase in value relative to other currencies. The British government may also be a source of demand if it attempts to keep the value of the pound (relative to other currencies) from falling by using its supply of foreign currencies or gold to purchase pounds in the market.
Sources of supply include British importers who need to convert their pounds into foreign currency to pay for purchases, British investors who desire to make investments in foreign countries, and speculators who expect British pounds to decrease in value relative to other currencies.
Exchange rates are also affected by economic and political conditions that influence the supply of, or demand for, a country’s currency. Some of these conditions include differential inflation and interest rates among countries, the government’s trade policies, and the government’s political stability. A high rate of inflation within a country tends to lower the value of its currency with respect to the currencies of other countries experiencing lower rates of inflation. The exchange rate will tend to decline as holders sell or exchange the country’s currency for other currencies whose purchasing power is not declining at as high a rate. In contrast, relatively high interest rates within a country tend to increase the exchange rate as foreign investors seek to convert their currencies and purchase these higheryielding securities.
Government trade policies that limit imports—such as the imposition of tariffs, import quotas, and restrictions on foreign exchange transactions—reduce the supply of the country’s currency in the foreign exchange market. This, in turn, tends to increase the value of the country’s currency with respect to other currencies and thus to increase exchange rates. Finally, the political stability of the government affects the risks perceived by foreign investors and companies doing business in the country. These risks include the possible expropriation of investments or restrictions on the amount of funds (such as returns from investments) that may be taken out of the country.
In the following sections, we develop the important relationships among spot rates, forward rates, interest rates, and inflation rates as they impact foreign currency exchange rates.
Covered Interest Arbitrage and Interest Rate Parity
There is a close relationship between the interest rates in two countries and the forward exchange rate premium or discount.Consider a U.S. investor with $1.2 million to invest who notes that the interest rate on 90-day certificates of deposit (CDs) available at Swiss banks is 4 percent for 90 days.At the same time, the 90-day CD rate in the United States is only 2 percent. The spot rate of the Swiss franc (CHF) is $0.60/CHF and the 90-day forward rate is also $0.60. As an investor, you know that you can immediately convert $1.2 million into CHF2 million at today’s spot rate of $0.60 with no risk. You can also lock in the 4 percent Swiss interest rate for 90 days by purchasing a Swiss CD with your CHF2 million. However, there is risk regarding the exchange rate at which you will be able to convert CHF back to dollars at the end of 90 days. You can guarantee this rate by selling 2 million CHF (plus the interest you will receive on your Swiss CD) in the 90-day forward market at today’s forward rate of $0.60. This transaction will guarantee you a risk-free profit. Consider the following steps in this transaction:
This risk-free transaction enabled you to earn an additional return of $24,000 over what would be available by investing in the United States. Because there are virtually no barriers to prevent individuals from engaging in this transaction called covered interest arbitrage, it can be expected that opportunities to earn risk-free additional returns such as these will not persist very long. The demand by American investors for CHF will put upward pressure on the spot price of CHF, to a price greater than $0.60/CHF. At the same time, as American investors sell CHF forward to cover their position, this will put downward pressure on the forward rate of the CHF to a price less than $0.60. Furthermore, as funds leave the United States for Switzerland, the reduced supply of funds will tend to increase U.S. interest rates.
The increased supply of funds in Switzerland, on the other hand, will tend to lower Swiss interest rates. The net effect of these transactions and market pressures will be an equilibrium condition where covered interest arbitrage transactions are not possible. This relationship is called interest rate parity (IRP).When IRP exists, the forward rate will differ from the spot rate by just enough to offset the interest rate differential between the two currencies. The IRP condition states that the home (or domestic) interest rate must be higher (lower) than the foreign interest rate by an amount equal to the forward discount (premium) on the home currency.
In other words, the forward premium or discount for a currency quoted in terms of another currency is approximately equal to the difference in interest rates prevailing between the two countries. Thus, if interest rates in Switzerland are higher than interest rates in the United States, then the IRP condition indicates that the dollar can be expected to increase in value relative to the CHF. The exact IRP relationship is
where ih is the home (U.S.) interest rate, if is the comparable foreign (Swiss) interest rate, F is the direct quote forward rate, and S0 is the direct quote spot rate.2 (Note that the interest rates in Equation 22.1 are the interest rates for the same period of time as the number of days in the forward price, not necessarily annualized interest rates.) The relationship in Equation can be simplified to
An approximation of the IRP relationship is
equation indicates that when interest rate parity exists, differences in interest rates between two countries will be (approximately) offset by changes in the relative value of the two currencies.
To illustrate, assume that the 90-day interest rate is 1.5 percent in the United States and 2.5 percent in Switzerland, and the current spot exchange rate between dollars and CHF is $0.60. If IRP holds, what will the 90-day forward rate be (using the exact relationship in)?
In this case, the dollar has increased in value relative to the CHF (i.e., it takes fewer dollars to buy each CHF).Why do you think this should occur?
Purchasing Power Parity
When there are no significant costs or other barriers associated with moving goods or services between markets, then the price of each product should be the same in each market.
In economics, this is known as the law of one price. When the different markets represent different countries, the law of one price says that prices will be the same in each country after making the appropriate conversion from one currency to another. Alternatively, one can say that exchange rates between two currencies will equal the ratio of the price indexes between the countries. In international finance and trade, this relationship is known as the absolute version of purchasing power parity.
In reality, we know that this relationship does not hold because of the costs of moving goods and services and the existence of tariffs and other trade barriers. For example, The Economist, in a lighthearted look at the law of one price, regularly reports on the price of Big Mac hamburgers in various countries. When the price of a Big Mac was $2.20 in the United States, it cost (after converting currencies) $2.06 in Germany, $1.21 in the Czech Republic, $1.14 in Hong Kong, $1.21 in Russia, $2.44 in Japan, and $3.04 in Switzerland.It is obviously not possible to buy Big Macs in Hong Kong and ship them to New York for sale, for example. Hence the law of one price does not hold for Big Macs. On the other hand, for goods that are standardized and somewhat easier to move and store, such as gold or crude oil, one would expect only minor violations of the law of one price.
A less restrictive form of the law of one price is known as relative purchasing power parity (PPP). The relative PPP principle states that in comparison to a period when exchange rates between two countries are in equilibrium, changes in the differential rates of inflation between two countries will be offset by equal but opposite changes in the future spot exchange rate. For example, if prices in the United States rise by 4 percent per year and prices in Switzerland rise by 6 percent per year, then relative PPP holds if the Swiss franc (CHF) weakens relative to the U.S. dollar by approximately 2 percent.
where S1 is the expected future (direct quote) spot rate at time period 1, S0 is the current (direct quote) spot rate, ph is the expected home country (U.S.) inflation rate, and pfis the expected foreign country inflation rate. This relationship can be simplified to
Using the previous example, if U.S. prices are expected to rise by 4 percent over the coming year, prices in Switzerland are expected to rise by 6 percent during the same time, and the current spot exchange rate (S0) is $0.60/CHF, then the expected spot rate in one year (S1), will be
The higher Swiss inflation rate can be expected to result in a decline in the future spot value of the CHF relative to the dollar by 1.89 percent. The market forces that support the relative PPP relationship operate in the following way. If one nation has a higher inflation rate than another, its goods and services will become relatively more expensive, making its exports less price competitive and imports more price competitive. The resulting deficit in foreign trade will place downward pressure on the currency value of the high inflation country until a new, lower equilibrium value is established. The opposite will be true for the country with the lower inflation rate. For example, if the United States has a lower inflation rate than its major trading partners, relative PPP indicates that the value of the dollar can be expected to increase relative to the value of the currencies of these other trading partners.
Tests of relative PPP indicate that the relationship holds up reasonably well over long periods, but it is a less accurate indicator of short-term currency value changes.Also, the relative PPP relationship is stronger for those countries experiencing high rates of inflation.
Tests of the strength of the PPP relationship are hampered by the use of noncomparable price indexes between countries and government interference in commodity and currency markets. Nevertheless, the general relationship between inflation rates and currency values is widely accepted, even if it is difficult to measure properly.
Expectations Theory and Forward Exchange Rates
If foreign currency markets are efficient, the forward rate should reflect what market participants expect the future spot rate for a currency to be. For example, if market participants expected the 1-year future spot rate (S1) for CHF to be $0.58, then what would the 1-year forward rate (F1) have to be? It would also have to be $0.58. If the forward rate were lower than this amount, market participants would want to buy CHF forward, thereby placing upward price pressure on the CHF until an equilibrium is reached where the forward rate equals the expected future spot rate.
If the expected future spot rate is equivalent to the forward rate, we can say that the forward rate is an unbiased estimator of the future spot rate. It is important to recognize that this does not mean that the forward rate will always be equal to the actual future spot rate. Rather, it means that the estimates of the future spot rate provided by the forward rate will not systematically overshoot or undershoot the actual future spot rate, but will equal it on average. Evidence regarding the expectations theory of forward exchange rates indicates that, in general, the forward rate is an unbiased estimate of expected future spot rates, if risk in the currency markets is ignored. There is some evidence, however, that when the forward rate implies a large change from the current spot rate, these forecasts tend to overshoot the actual future spot rate.
Forward rates as unbiased estimates of expected future spot rates have important implications for managers. First, managers should not spend the firm’s resources to buy forecasts of future exchange rates since unbiased forecasts are provided free in the marketplace. Second, managers will find that hedging their future foreign currency risk by making use of the forward market should be a cost-effective way of limiting this risk exposure. In the following sections, some of these hedging techniques are considered.
The International Fisher Effect
The final piece in the international currency market puzzle is the relationship between interest rates and future spot currency rates. In his 1930 book, The Theory of Interest, Irving Fisher established that in equilibrium lenders will receive a nominal rate of interest equal to a real interest rate plus an amount sufficient to offset the effects of expected inflation. Nominal interest rates are market rates stated in current, not real, terms, such as the rates quoted in financial publications like The Wall Street Journal. Real rates of return are not directly observable.
The real rate of return is the rate at which borrowing and lending in the financial markets are in equilibrium. The real rate of return is equal to the real rate of growth in the economy, and it reflects the time preference of market participants between present and future consumption. The relationship between nominal (risk-free) rates of return, real rates of return, and expected inflation is
where i is the nominal (and risk-free) rate of interest, iR is the real rate of return, and p is the expected inflation rate. This relationship is often referred to as the Fisher effect.7 For example, if the annual real rate of return in Hong Kong was 3 percent and the expected annual inflation rate was 8 percent, the nominal interest rate would bei = 0.03 + 0.08 + (0.03)(0.08) = 0.1124 or 11.24%
Fisher argues that in the absence of government interference and holding risk constant, real rates of return across countries will be equalized through a process of arbitrage. If real rates of return are higher in the United States than in Japan, for example, capital will flow to the United States from Japan until an equilibrium is reached. The assumption of equal real rates of return across countries ignores differences in risk and attitudes toward risk that may exist in different cultures. Also, to the extent that there are barriers to the movement of capital between countries, real rates of return may be different between countries. In spite of these limitations, the assumption of equal real returns is useful because (1) it is a reasonable representation of reality among the major industrialized countries and (2) as capital markets become increasingly internationalized and barriers to capital flows fall, differences in real rates of return can be expected to decrease.
If real rates of return tend to be equalized across countries, it follows that differences in observed nominal rates between countries must be due primarily to different inflation expectations. Incorporating the equilibrium condition for real interest rates with relative PPP leads to what has been called theinternational Fisher effect (IFE). The IFE states that differences in interest rates between two countries should be offset by equal but opposite changes in the future spot exchange rate. For example, if 1-year nominal interest rates are 10 percent in the United States and 7 percent in Hong Kong, then IFE predicts that the Hong Kong Dollar (HKD) should increase in value relative to the U.S. dollar by approximately 3 percent.
The exact IFE relationship is
where S1 is the expected future (direct quote) spot rate at time period 1, S0 is the current (direct quote) spot rate, ih is the home country (U.S.) nominal interest rate, and if is the foreign country nominal interest rate.8 This relationship can be simplified to
Using the previous example, if 1-year U.S. nominal interest rates are 10 percent, 1-year Hong Kong nominal interest rates are 7 percent, and the current spot exchange rate, S0, is $0.16/HKD, then the expected spot rate in one year, S1, will beS1/$0.16 = (1 + 0.10) / (1 + 0.07)
The lower nominal Hong Kong interest rate results in an expected increase in the value of the HKD (decrease in the value of the $) of 2.80 percent.
An Integrative Look at International Parity Relationships
provides an integrative look at international parity relationships. Beginning with the lower box in the figure, suppose one observes that the 1-year nominal interest rate is 10 percent in the United States and 5 percent in Switzerland. This implies, according to the Fisher effect, that the difference in expected inflation rates between the United States and Switzerland is also 5 percent because real rates of return are assumed to be equal between the United States and Switzerland. The 5 percent inflation differential means that the 1-year future spot rate of exchange between dollars and CHF can be expected to change such that the dollar will weaken by 5 percent relative to the CHF. This condition is expected from the purchasing power parity relationship.
International Parity Conditions: An Integrative Look
The 5 percent differential in interest rates also implies that the dollar will sell at a 5 percent discount in the 1-year forward market relative to the CHF. This expectation arises from the interest rate parity relationship. If the forward rate is an unbiased estimator of future spot rates, then the 1-year future spot rate of exchange between dollars and CHF can be expected to change such that the dollar will weaken by 5 percent relative to the CHF. Finally, the international Fisher effect implies that if 1-year nominal interest rates are 5 percent higher in the United States than in Switzerland, then the 1-year future spot rate of exchange between the dollar and the CHF will change such that the dollar will weaken by 5 percent relative to the CHF.
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