Chapter 7
International Parity Conditions
? Questions
1. Purchasing Power Parity. Define the following terms:
a. The law of one price. The law of one price states that if identical products or services can be
sold in two different countries, and no restrictions exist on the sale or transportation costs of moving the product between the countries, the product’s price should be the same in both countries. Comparing prices across countries requires only a conversion from one currency to the other. For example,
P $ ? S ? P ￡
where the price of the product in U.S. dollars (P $ ), multiplied by the spot exchange rate (S, pounds sterling per U.S. dollar), equals the price of the product in British pounds (P ￡).
b. Absolute purchasing power parity. If the law of one price were true for all goods and services,
the purchasing power parity exchange rate could be found from any individual set of prices. By comparing the prices of identical products denominated in different currencies, one could determine the “real” or PPP exchange rate which should exist if markets were efficient. This is the absolute version of the theory of purchasing power parity. Absolute PPP states that the spot exchange rate is determined by the relative prices of similar baskets of goods.
c. Relative purchasing power parity. If the assumptions of the absolute version of PPP theory
are relaxed a bit more, we observe what is termed relative purchasing power parity. This more general idea is that PPP is not particularly helpful in determining what the spot rate is today, but that the relative change in prices between two countries over a period of time determines the
change in the exchange rate over that period. More specifically, if the spot exchange rate between two countries starts in equilibrium, any change in the differential rate of inflation between them tends to be offset over the long run by an equal but opposite change in the spot exchange rate.
2. Nominal Effective Exchange Rate Index. Explain how a nominal effective exchange rate index
is constructed. An exchange rate index is an index that measures the value of a given country’s exchange rate against
all other exchange rates in order to determine if that currency is overvalued or undervalued. A nominal effective exchange rate index is based on a weighted average of actual exchange rates over a period of time. It is unrelated to PPP and simply measures changes in the exchange rate (i.e., currency value) relative to some arbitrary base period. It is used in calculating the real effective exchange rate index. 3. Real Effective Exchange Rate Index. What formula is used to convert a nominal effective exchange
rate index into a real effective exchange rate index? A real effective exchange rate index adjusts the nominal effective exchange rate index to reflect
differences in inflation. The adjustment is achieved by multiplying the nominal index by the ratio of domestic costs to foreign costs. The real index measures deviations from purchasing power parity, and consequently pressures on a country’s current account and foreign exchange rate.
28 Moffett/Stonehill/Eiteman ? Fundamentals of Multinational Finance, Fourth Edition
$ The real effective exchange rate index for the U.S. dollar, ER,is found by multiplying the nominal
$effective exchange rate index,EN,by the ratio of U.S. dollar costs, C$, over foreign currency costs, C FC, both in index form:
C$E?E?FC.
C$R$N 4. Real Effective Exchange Rates: Japan and the United States. Exhibit 7.3 compares the real
effective exchange rates for the United States and Japan. If the comparative real effective exchange rate was the main determinant, does the United States or Japan have a competitive advantage in exporting? Which of the two has an advantage in importing? Explain why. Exhibit 7.3 shows that the real effective exchange rate of the dollar, yen, and euro have changed over
the past three decades and the data lend some support to the concept that PPP may hold over the long run. The dollar’s index value was substantially above 100 in the 1980s (overvalued), but has remained below 100 (undervalued) since the late 1980s (it did rise slightly above 100 briefly in 1995–1996 and again in 2001–2002). The Japanese yen’s real effective rate has remained above 100 for nearly the entire 1980 to 2006 period (overvalued). In theory, a country with an undervalued currency should have a relative advantage in exporting over
those countries suffering an overvalued currency. Similarly, an overvalued currency should result in increased purchasing power for imports. 5. Exchange Rate Pass-Through. Incomplete exchange rate pass-through is one reason that a country’s
real effective exchange rate can deviate for lengthy periods from its purchasing power equilibrium level of 100. What is meant by the term exchange rate pass-through? Incomplete exchange rate pass-through refers to the degree to which the prices of imported and
exported goods change as a result of exchange rate changes. Although PPP implies that all exchange rate changes are passed through by equivalent changes in prices to trading partners, empirical research in the 1980s questioned this long-held assumption. For example, sizeable current account deficits of the United States in the 1980s and 1990s did not respond to changes in the value of the dollar. 6. The Fisher Effect. Define the Fisher effect. To what extent do empirical tests confirm that the Fisher
effect exists in practice? The Fisher effect, named after economist Irving Fisher, states that nominal interest rates in each
country are equal to the required real rate of return plus compensation for expected inflation. More formally, this is derived from (1 ? r)(1 ? ?) – 1:
i?r???r?
where i is the nominal rate of interest, r is the real rate of interest, and ? is the expected rate of
inflation over the period of time for which funds are to be lent. The final compound term, r ? ?, is frequently dropped from consideration due to its relatively minor value. The Fisher effect then reduces to (approximate form):
i?r??.
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Chapter 7 International Parity Conditions 29
To empirically test the Fisher effect, forecasts of future rates of inflation are needed (not what
inflation has been). Predicting the future can be difficult. Empirical tests using ex-post national inflation rates have shown that the Fisher effect usually exists for short-maturity government
securities such as Treasury bills and notes. Comparisons based on longer maturities suffer from the increased financial risk inherent in fluctuations of the market value of the bonds prior to maturity. Comparisons of private sector securities are influenced by unequal creditworthiness of the issuers. All the tests are inconclusive to the extent that recent past rates of inflation are not a correct measure of future expected inflation. 7. The International Fisher Effect. Define the international Fisher effect. To what extent do empirical
tests confirm that the international Fisher effect exists in practice? Irving Fisher stated that the real return in different countries should be the same, so that if one
country has a higher nominal interest rate, the gain from investing in that currency will be lost by a deterioration of its exchange rate. The relationship between the percentage change in the spot
exchange rate over time and the differential between comparable interest rates in different national capital markets is known as the international Fisher effect. “Fisher-open,” as it is often termed, states that the spot exchange rate should change in an equal amount but in the opposite direction to the difference in interest rates between two countries. More formally:
S1?S2?100?i$?i?, S2 where i$ and i￥ are the respective national interest rates, and S is the spot exchange rate using indirect
quotes (an indirect quote on the dollar is, for example, ￥/$) at the beginning of the period (S1) and the end of the period (S2). This is the approximation form commonly used in industry. The precise formulation is:
S1?S2i$?i??. S21?i￥ Empirical tests lend some support to the relationship postulated by the international Fisher effect,
although considerable short-run deviations occur. A more serious criticism has been posed, however, by recent studies that suggest the existence of a foreign exchange risk premium for most major
currencies. Also, speculation in uncovered interest arbitrage creates distortions in currency markets. Thus, the expected change in exchange rates might consistently be more than the difference in interest rates. 8. Interest Rate Parity. Define interest rate parity. What is the relationship between interest rate parity
and forward rates? The theory of interest rate parity (IRP) provides the linkage between the foreign exchange markets
and the international money markets. The theory states: The difference in the national interest rates for securities of similar risk and maturity should be equal to, but opposite in sign to, the forward rate discount or premium for the foreign currency, except for transaction costs.
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30 Moffett/Stonehill/Eiteman ? Fundamentals of Multinational Finance, Fourth Edition
9. Covered Interest Arbitrage. Define the terms covered interest arbitrage and uncovered interest
arbitrage. What is the difference between these two transactions? The spot and forward exchange markets are not constantly in the state of equilibrium described by
interest rate parity. When the market is not in equilibrium, the potential for “riskless” or arbitrage profits exists. The arbitrager who recognizes such an imbalance will move to take advantage of the disequilibrium by investing in whichever currency offers the higher return on a covered basis. This is called covered interest arbitrage (CIA). CIA is possible when interest rate parity does not hold. An example of a basic CIA strategy would be to 1) convert dollars at the current spot into a foreign currency, 2) invest the foreign currency in a risk-free investment in the foreign country, 3) simultaneously sell the future proceeds of the foreign risk-free investment in the forward market, and finally 4) calculate the opportunity cost of the funds at the U.S. risk-free interest rate. When done correctly, the difference between the revenue in step 2 should exceed the cash-outflows in steps 3 and 4. A deviation from covered interest arbitrage is uncovered interest arbitrage (UIA), wherein investors
borrow in countries and currencies exhibiting relatively low interest rates and convert the proceeds into currencies that offer much higher interest rates. The transaction is “uncovered” because the investor does not sell the higher yielding currency proceeds forward, choosing to remain uncovered and accept the currency risk of exchanging the higher yield currency into the lower yielding currency at the end of the period. Uncovered interest arbitrage is not truly arbitrage, since it is not a riskless proposition. 10. Forward Rate as an Unbiased Predictor of the Future Spot Rate. Some forecasters believe that
foreign exchange markets for the major floating currencies are “efficient” and forward exchange rates are unbiased predictors of future spot exchange rates. What is meant by “unbiased predictor” in terms of how the forward rate performs in estimating future spot exchange rates? An “unbiased predictor” means that the distribution of possible actual spot rates in the future is
centered on the forward rate. The fact that it is an unbiased predictor, however, does not mean that the future spot rate will actually be equal to what the forward rate predicts. Unbiased prediction simply means that the forward rate will, on average, overestimate and underestimate the actual future spot rate in equal frequency and degree. The forward rate may, in fact, never actually equal the future spot rate. The rationale for this relationship is based on the hypothesis that the foreign exchange market is
reasonably efficient. Market efficiency assumes that 1) all relevant information is quickly reflected in both the spot and forward exchange markets; 2) transaction costs are low; and 3) instruments denominated in different currencies are perfect substitutes for one another. Empirical studies of the efficient foreign exchange market hypothesis have yielded conflicting results. Nevertheless, a consensus is developing that rejects the efficient market hypothesis. It appears that the forward rate is not an unbiased predictor of the future spot rate and that it does pay to use resources to attempt to forecast exchange rates.
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