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Parity Conditions in International Finance


We shall now examine a simple yet elegant set of equilibrium (or parity) conditions that should apply to product prices, interest rates, and spot and forward exchange rates if the markets are not impeded. These parity conditions provide the foundation for much of the theory and practice of international finance.


In competitive markets, characterized by numerous buyers and sellers having low-cost access to information, exchange-adjusted prices of identical tradeable goods and financial assets must be within transactions costs of equality worldwide. This idea, referred to as the law of one price, is enforced by international arbitrageurs who follow the profit-guaranteeing dictum of "buy low, sell high" and prevent all but trivial deviations from equality. Similarly, in the absence of market imperfections, risk-adjusted expected returns on financial assets in different markets should be equal.


Five key theoretical economic relationships, which are depicted in Exhibit F.2, result from these arbitrage activities. This framework emphasizes the links among prices, spot exchange rates, interest rates, and forward exchange rates. According to the diagram, if inflation in, say, France is expected to exceed inflation in the United States by 3 percent for the coming year, then the French franc should decline in value by about 3 percent relative to the dollar. By the same token, the one-year forward French franc should sell at a 3 percent discount relative to the U.S. dollar. Similarly, one-year interest rates in France should be about 3 percent higher than one-year interest rates on securities of comparable risk in the United States.



Exhibit F.2


Purchasing Power Parity


If international arbitrage enforces the law of one price, then the exchange rate between the home currency and domestic goods must equal the exchange rate between the home currency and foreign goods. In other words, a unit of home currency (HC) should have the same purchasing power worldwide. Thus, if a dollar buys a pound of bread in the United States, it should also buy a pound of bread in Great Britain. For this to happen, the foreign exchange rate must change by (approximately) the difference between the domestic and foreign rates of inflation. This relationship is called purchasing power parity (PPP).


Formally, if ih and if are the price level increases (rates of inflation) during a period of time for the home country and the foreign country, respectively, e0 is the dollar value of one unit of foreign currency at the beginning of the period, and e1 is the end-of-period exchange rate, then




In effect, PPP says that currencies with high rates of inflation should devalue relative to currencies with lower rates of inflation.


Empirical Evidence. Although the strictest version of purchasing power parity that all goods and financial assets obey the law of one price is demonstrably false, there is clearly a relationship between relative inflation rates and changes in exchange rates. This is shown in, Exhibit F.3, which compares the relative change in the purchasing power of 22 currencies (as measured by their relative inflation rates) with the relative change in the exchange rates for those currencies for the period 1982 through 1988. As expected, those currencies with the largest relative decline (gain) in purchasing power saw the sharpest erosion (appreciation) in their foreign exchange values. 0<3/P>



Exhibit F.3


Fisher Effect


According to the Fisher effect, introduced in Chapter 4 of the text, the nominal interest rate equals the real interest rate plus an adjustment for inflation. The generalized version of the Fisher effect asserts that real returns are equalized across countries through arbitrage. If expected real returns were higher in one currency than another, capital would flow from the second to the first currency. This process of arbitrage would continue, in the absence of government intervention, until expected real returns were equalized. In equilibrium, then, with no government interference, it should follow that the nominal interest differential will approximately equal the anticipated inflation differential, or




where rh and rf are the nominal home and foreign currency rates, respectively. In effect, the Fisher effect says that currencies with high rates of inflation should bear higher interest rates than currencies with lower rates of inflation.


Empirical Evidence. Exhibit F.4 illustrates the relationship between interest rates and subsequent inflation rates for 20 countries as of June 1998. It is evident from the graph that nations with higher inflation rates generally have higher interest rates. Thus the empirical evidence is consistent with the hypothesis that most of the variation in nominal interest rates across countries can be attributed to differences in inflationary expectations.



Exhibit F.4


International Fisher Effect


The key to understanding the impact of relative changes in nominal interest rates among countries on the foreign exchange value of a nation's currency is to recall the implications of PPP and the generalized Fisher effect. PPP implies that exchange rates will move to offset changes in inflation rate differentials. Thus, a rise in the U.S. inflation rate relative to those of other countries will be associated with a fall in the dollar's value. It will also be associated with a rise in the U.S. interest rate relative to foreign interest rates. Put these two conditions together and the result is the international Fisher effect (IFE):




In effect, the IFE says that currencies with low interest rates are expected to revalue relative to currencies with high interest rates.


Empirical Evidence. As predicted, there is a clear tendency for currencies with high interest rates (e.g., Mexico and Israel) to depreciate and for those with low interest rates (e.g., Japan and Switzerland) to appreciate. This is shown in Exhibit F.5, which graphs the nominal interest differential (relative to the U.S. interest rate) against exchange rate changes (relative to the U.S. dollar) for 21 currencies over the period 1982 to 1988. The ability of interest differentials to anticipate currency changes is also supported by several empirical studies, which indicate the long-run tendency for these differentials to offset exchange rate changes. Thus at any given time, currencies bearing higher nominal interest rates can reasonably be expected to depreciate relative to currencies bearing lower interest rates



Exhibit F.5


Interest Rate Parity Theory


The movement of short-term funds between two currencies to take advantage of interest rate differentials is also a major determinant of the spread between forward and spot rates. In fact, the forward discount or premium is closely related to the interest differential between the two currencies.


According to interest rate parity theory, the currency of the country with a lower interest rate should be at a forward premium in terms of the currency of the country with the higher rate. More specifically, in an efficient market with no transaction costs, the interest differential should be (approximately) equal to the forward differential. When this condition is met, the forward rate is said to be at interest parity, and equilibrium should prevail in the money markets. Interest parity ensures that the return on a hedged (or "covered") foreign investment will just equal the domestic interest rate on investments of identical risk, thereby eliminating the possibility of having a money machine.


Interest rate parity holds when there are no covered interest arbitrage opportunities. If f1 is the forward rate, this no-arbitrage condition can be stated as follows:




In effect, interest rate parity says that high interest rates on a currency are offset by forward discounts and that low interest rates are offset by forward premiums.


Empirical Evidence. Interest rate parity is one of the best documented relationships in international finance. In fact, in the Eurocurrency markets, the forward rate is calculated from the interest differential between the two currencies using the no-arbitrage condition. Deviations from interest parity do occur between national capital markets, however, owing to capital controls (or the threat of them), the imposition of taxes on interest payments to foreigners, and transaction costs.

Forward Rates and Expected Future Spot Rates


Our current understanding of the workings of the foreign exchange market suggests that under a system of freely floating rates, both the spot rate and the forward rate are influenced heavily by current expectations of future events, and both rates move in tandem, with the link between them based on interest differentials. New information, such as a change in interest rate differentials, is reflected almost immediately in both the spot and forward rates.


Suppose a depreciation of pounds sterling is anticipated. Recipients of sterling will begin selling sterling forward whereas sterling-area dollar earners will slow their sales of dollars in the forward market. These actions will tend to depress the price of forward sterling. At the same time, banks will probably try to even out their long (net purchaser) positions in forward sterling by selling sterling spot. In addition, sterling-area recipients of dollars will tend to delay converting dollars into sterling, and earners of sterling will speed up their collection and conversion of sterling. In this way, pressure from the forward market is transmitted to the spot market, and vice versa.


Equilibrium is achieved only when the forward differential equals the expected change in the exchange rate. At this point, there is no longer any incentive to buy or sell the currency forward.


A formal statement of the unbiased nature of the forward rate is that the forward rate should reflect the expected future spot rate on the date of settlement of the forward contract:




Where f1 is the forward rate for settlement at time 1, and _1 is the expected future ex-change rate at time 1.


Empirical Evidence. The general conclusion from early studies was that forward rates are unbiased predictors of future spot rates. But more recent studies, using more powerful econometric techniques, argue that the forward rate is a biased predictor, probably because of a risk premium. However, the premium appears to change signs--being positive at some times and negative at other times--and averages near zero. In the absence of a detailed econometric model, therefore, it would not be stretching things to treat the forward rate as an unbiased forecast of the future spot rate.