The Power of Arbitrage — Purchasing Power and Interest Rate Parities 83
Chapter Eight
The Power of Arbitrage — Purchasing Power and
Interest Rate Parities
I. Fundamental Issues
1. What does the concept of absolute purchasing power parity imply about the value of the real exchange rate?
2. What is relative purchasing power parity, and is it useful as a guide to movements in exchange rates?
3. What are the covered and uncovered interest parity conditions?
4. What is the distinction between adaptive and rational expectations?
5. What is foreign exchange market efficiency?
6. Under what conditions does real interest parity hold, and why is it a useful indicator of international integration?
II. Chapter Outline
1. Law of One Price and Absolute Purchasing Power Parity
a. Arbitrage and the Law of One Price
b. Absolute Purchasing Power Parity
c. Online Globalization: Increasing the Scope for International Arbitrage via Multicurrency Payment Processing
2. Relative Purchasing Power Parity
a. Proportionate Price Changes and Relative Purchasing Power Parity
b. Purchasing Power Parity as a Long-Run Determinant of Exchange Rates
c. Management Notebook: Sandwiching Currency Values in a Sesame Seed Bun—The Big Mac Index
3. International Interest Rate Parity
a. The Forward Exchange Market and Covered Interest Parity
b. Uncovered Interest Arbitrage
c. Visualizing Global Economic Issues: Why Covered Interest Parity Is Often Satisfied
4. Are Foreign Exchange Markets Efficient?
a. Adaptive Versus Rational Expectations
b. Foreign Exchange Market Efficiency
5. Revisiting Global Integration of the Real and Financial Sectors
a. Real Interest Rate Parity
b. Real Interest Rate Parity As an Indicator of International Integration
6. Questions and Problems
III. Chapter in Perspective
This chapter covers the major parity conditions of international commerce. The parity conditions are the linkages between prices in different national markets that should hold due to the arbitrage profits that could otherwise be earned among free markets. Parity conditions do not generally hold as well for goods and services as they do for financial assets. This is mainly true because arbitrage is more difficult and costly for most goods and services than for financial assets. The major parity conditions are absolute purchasing power parity, relative purchasing power parity, covered interest parity, uncovered interest rate parity, and real interest parity.
IV. Teaching Notes
1. Law of One Price and Absolute Purchasing Power Parity
a. Arbitrage and the Law of One Price
Arbitrage is the basis for all of the parity conditions. Arbitrage is buying an item market and selling it at a higher price in another market.
The law of one price implies that a good selling in a foreign country should sell for the same price, measured in the same currency, as a good sold domestically. In competitive markets with numerous buyers and sellers having low cost, equal access to information, the process of arbitrage will require that prices, after adjusting for exchange rate differences, will be the same in different countries. Likewise, risk-adjusted expected real returns on financial assets in different markets should be equal. On a basic level, this makes sense because similar things should provide similar benefits and be priced similarly. Because tangible goods are services are likely to be more different between countries, harder, more costly and riskier to transport, and because they are likely to be valued differently in different cultures, the law of one price is less likely to hold for tangible goods and services than for financial assets.
b. Absolute Purchasing Power Parity
Whereas the law of one price applies to a single good, absolute purchasing power parity (absolute PPP) is a theory that applies to all goods and services in two countries. According to absolute PPP, the exchange rate S (expressed in units of home currency per unit of foreign currency), and the price levels in the two countries under considerations P should be related such that S = P / P*, where P = domestic price level and P* = the foreign price level.
Example 1: Absolute PPP Example:
The law of one price (absolute PPP applied to one good) states that if the U.S. price of a digital camera is $300 in the United States and the exchange rate S is $0.10 per peso, the price of the camera in Mexico should be 3,000 pesos ($0.10 = $300 / Mexican price). Otherwise profitable arbitrage would be possible. Suppose for example the camera costs 2500 pesos in Mexico. As entrepreneurs purchased cameras in Mexico, the price will begin to rise on increased demand. The cameras will be transported to the U.S. and sold there, increasing a rise in the U.S. supply, and causing the price to decline. If this occurs for enough goods and services, the demand for the peso would also rise, thereby increasing the value exchange of the peso.
Extending this example to all goods and services implies that S = Index of average prices in the U.S. / Index of average prices in Mexico, or S = P / P*. If the Mexican price level is 1800 and the U.S. price level is 180 then the exchange rate should be S = 180 / 1800 = $0.10.
Problems with Absolute PPP:
Absolute PPP is unlikely to hold for two countries because of the restrictive assumptions implied:
· Transportation costs, time to ship, and the riskiness of shipping goods internationally are all ignored. These are not particularly serious problems because relaxing these assumptions implies that parity will still hold within a band of the parity level (parity level plus or minus these costs).
· Taxes, tariffs, quotas and other non-tariff barriers are ignored.
· Entities in the two countries do not consume the same basket of goods and services and do not value the baskets equally. For this reason especially absolute PPP is not likely to hold.
Teaching Tip:
It would be interesting to examine the number of goods for which absolute PPP holds on a case-by-case basis. As the global markets become more integrated and open we would expect PPP to hold in more cases.
Tests of Absolute PPP:
If absolute PPP holds, then the real exchange rate has to always equal 1. This yields a testable hypothesis, which can be easily shown to be false. The Big Mac index in the Economist is a light-hearted way to show students that absolute PPP does not hold.
c. Online Globalization: Increasing the Scope for International Arbitrage via Multicurrency Payment Processing
For Critical Analysis: If the yen value of the U.S. dollar rises considerably just before a Japanese customer is about to submit an order on a site using a system such as the one operated by Planet Payment, thereby changing the terms of the transaction with a U.S. seller, will the Japanese customer be more, or less, likely to click on the “order submit” button?
As the dollar becomes worth more yen, the Japanese customers will be faced with a higher yen price, making them less likely to buy the good. This brings up another relevant question. As a courtesy to buyers, many sellers post price quotations, in a given currency, that are fixed for certain time period such as 30 days. This provides a competitive advantage over other firms that do not post fixed prices. You may wish to ask your students the following related discussion question: In the example above who bears the currency risk, the buyer or the seller? Although the seller does not bear any transaction currency risk, the seller does bear operational risk. The foreign buyer is less likely to buy from him or her if the dollar appreciates against the buyer’s home currency. Similarly, the foreign buyer will not be able to buy as much if their home currency depreciates. We need to realize that foreign exchange exposure is broader than transaction exposure. Moreover, Planet Payment has a transaction exposure. In this example, the seller receives dollars now and the buyer pays yen over time as he or she pays down their credit card. Planet Payment is exposed to a decline in the yen against the dollar.
2. Relative Purchasing Power Parity
a. Proportionate Price Changes and Relative Purchasing Power Parity
Relative PPP avoids the problem of having different baskets of goods and services consumed in different countries. It also addresses an unrealistic implication of absolute PPP, which is that the real exchange rate, S ´ (P* / P), always equals 1, since with S = P / P*, the real exchange rate must be (P / P*) ´ (P* / P) = 1. This is unlikely to be true if people in different countries consume goods and services in different proportions. According to relative PPP, %DS = %DP - %DP*, so that the percentage change in a rate of exchange for two countries’ currencies equals the difference between the two nations’ inflation rates. All that is required for this relative PPP condition to hold true is for the real exchange rate to be stable over time.
Teaching Tip:
Explain to students that businesspeople can use relative PPP to do “back-of-the-envelope” predictions of the likely direction of exchange-rate movements. If a businessperson anticipates, for instance, that the inflation rate in Mexico will be 7 percent next year while the U.S. inflation rate will be 2 percent, the relative PPP condition indicates that the Mexican peso will depreciate by 5 percent relative to the U.S. dollar. Even if relative PPP fails to hold exactly, its implication could still prove useful for making general predictions about the likely direction of the movement in the peso’s value relative to the dollar.
b. Purchasing Power Parity as a Long-Run Determinant of Exchange Rates
Studies indicate that persistent inflation differentials lead to currency changes in line with the PPP predictions. Short-term (year-to-year) fluctuations in inflation rates, however, are generally not perfectly priced out by exchange rate changes. In other words, relative PPP does not hold well in the short run, but appears to have validity in the long run. Some studies indicate that when an event that moves a real exchange rate away from its parity level, it takes 3 to 7 years to get halfway back. During periods of hyperinflation however, PPP does hold very well even in the short run. In this case, the inflation effects, not surprisingly, dominate all others.
Teaching Tip:
What all this tells us is that in the short-run variables other than inflation affect nominal and real exchange rates. Consumption patterns only change slowly over time in response to exchange rate changes. The elasticities of supply and demand certainly affects responses to varied price levels. People’s perception of the persistence of the exchange rate change and various trade barriers also distort the relationship. Nevertheless, with growing openness to trade we would expect parity to hold more in the future than it has in the past, at least over long time periods.
Teaching Tip:
It matters quite a lot to businesses whether relative PPP holds. If it holds most of the time then hedging exchange rate risk is probably not very important. The amount of hedging done by corporations varies quite a lot depending on degree of international involvement, firm size and sophistication. Almost no firms attempt to hedge all their exchange risk, but a growing number hedge some risk. Most managers seem to believe that much of their exchange rate risk is minimized by diversification resulting from having operations in various countries. As the global economy becomes more integrated, does this imply that exchange rate risk will become less diversifiable?
c. Management Notebook: Sandwiching Currency Values in a Sesame Seed Bun — The Big Mac Index
For Critical Analysis: Studies have found that the Big Mac index is closely related to several other more elaborate measures of purchasing power parities, so some economists have concluded that the Big Mac index is a surprisingly good longer-term indicator of PPP valuations of exchange rates. What does the predictive performance of the Big Mac index imply about the likely usefulness of absolute PPP as a shorter-term measure of currency under- or overvaluation?
Because PPP appears to hold only in the long run, using the Big Mac index to predict short -un (year-to-year) exchange rate changes is a dubious practice at best. Because the Big Mac index deals in a non-tradable good, its value in the long run is also questionable. Nevertheless, it is unlikely that absolute PPP will provide a good measure of a currency’s under- or overvaluation in the short run since absolute PPP does not appear to hold in the short run.
3. International Interest Rate Parity
a. The Forward Exchange Market and Covered Interest Parity
Large capital flows between economies are now the norm. This implies the possibility that financial markets are becoming integrated, and arbitrage among the various markets should then result in parity conditions in international financial markets.
The covered interest parity condition states that R = R* + (F - S)/S, where R is the domestic interest rate, R* is the foreign interest rate, F is the forward exchange rate in units of domestic currency per unit of foreign currency, and S is the spot exchange rate in units of domestic currency per unit of foreign currency. The quantity (F - S)/S is the forward premium or discount, so the covered interest parity condition states that the interest rate on a domestic bond should approximately equal the interest rate on a foreign bond plus the forward premium or discount.
If covered interest parity did not hold, then the return from holding a domestic bond would differ from the domestic-currency-denominated return, covered from risk by a transaction in the forward exchange market, on a foreign bond. In that case, opportunities for riskless profit would exist simply from a choice of one bond over the other.
Teaching Tip:
Students often wonder about whether there is evidence in support of international interest parity conditions. In the case of covered interest parity, a very interesting, nontechnical study by Mark Taylor (Economica, 1987, pp. 429-438) can easily be discussed in class. Taylor recorded data on spot dollar-pound and dollar-mark exchange rates and corresponding forward exchange rates at one-, three-, six-, and twelve-month maturities, plus interest rates for those maturities every 10 minutes over a three-day period in the London foreign exchange market. This yielded 144 data points for each of the four maturities with six different borrowing-lending arbitrage combinations to consider, for a total of 3,456 potential arbitrage combinations. Out of all these possibilities, he only found one case in which a profitable arbitrage might have been feasible.