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7 International Arbitrage And Interest Rate Parity

 Explain the conditions that will result in various forms of

international arbitrage and the realignments that will occur in

response

 Explain the concept of interest rate parity

 Explain the variation in forward rate premiums across maturities

and over time

Chapter Objectives

International Arbitrage

 Defined as capitalizing on a discrepancy in quoted prices by making a riskless profit.

 Arbitrage will cause prices to realign.

 Three forms of arbitrage: Locational arbitrage

 Triangular arbitrage

 Covered interest arbitrage

Locational Arbitrage

1. Defined as the process of buying a currency at the location where it is priced cheap and immediately selling it at another location where it is priced higher. (See Exhibit 7.1)

2. Gains from locational arbitrage are based on the amount of money used and the size of the discrepancy. (See Exhibit 7.2)

3. Realignment due to locational arbitrage drives prices to adjust in different locations so as to eliminate discrepancies.

Exhibit 7.1 Currency Quotes for LocationalArbitrage Example

Exhibit 7.2 Locational Arbitrage

Triangular Arbitrage

1. Defined as currency transactions in the spot market to capitalize on discrepancies in the cross exchange rates between two currencies. (See Exhibits 7.3, & 7.5)

2. Accounting for the Bid/Ask Spread: Transaction costs (bid/ask spread) can reduce or even eliminate the gains from triangular arbitrage.

3. Realignment due to triangular arbitrage forces exchange rates back into equilibrium. (See Exhibit 7.6)

Exhibit 7.3 Example of Triangular Arbitrage

Exhibit 7.5 Example of Triangular Arbitrage Accounting for Bid/Ask Spreads

Exhibit 7.6 Impact of Triangular Arbitrage

Covered Interest Arbitrage

1. Defined as the process of capitalizing on the interest rate differential between two countries while covering your exchange rate risk with a forward contract.

2. Consists of two parts: (See Exhibit 7.7)a. Interest arbitrage: the process of capitalizing on the

difference between interest rates between two countries.b. Covered: hedging the position against interest rate risk.

3. Realignment: due to covered interest arbitrage causes market realignment.

4. Timing of realignment may require several transactions before realignment is completed.

Exhibit 7.7 Example of Covered Interest Arbitrage

Comparison of Arbitrage Effects

1. The threat of locational arbitrage ensures that quoted exchange rates are similar across banks in different locations.

2. The threat of triangular arbitrage ensures that cross exchange rates are properly set.

3. The threat of covered interest arbitrage ensures that forward exchange rates are properly set. Any discrepancy will trigger arbitrage, which should eliminate the discrepancy.

4. Thus, arbitrage tends to allow for a more orderly foreign exchange market.

Exhibit 7.8 Comparing Arbitrage Strategies

Interest Rate Parity

1. Interest Rate Parity (IRP) is a theory that says the difference between the interest rates of two countries is equal based on the difference calculated by using the forward exchange rate and the spot exchange rate techniques.

1. Interpretation of Interest Rate ParityInterest rate parity does not imply that investors from different countries will earn the same returns. Interest rate parity brings together interest rates, spot exchange rates, and foreign exchange rates.

Considerations When Assessing Interest Rate Parity

1. Transaction costsThe actual point reflecting the interest rate differential and forward rate premium must be farther from the IRP line to make covered interest arbitrage worthwhile. (See Exhibit 7.10)

2. Political riskA crisis in the foreign country could cause its government to restrict any exchange of the local currency for other currencies.

3. Differential tax lawsCovered interest arbitrage might be feasible when considering before-tax returns but not necessarily when considering after-tax returns.

Variation in Forward Premiums

1. Forward Premiums across MaturitiesThe annualized interest rate differential between two countries can vary among debt maturities, and so will the annualized forward premiums.(See Exhibit 7.11)

2. Changes in Forward Premiums over TimeExhibit 7.12 illustrates the relationship between interest rate differentials and the forward premium over time, when interest rate parity holds. The forward premium must adjust to existing interest rate conditions if interest rate parity holds.

3. Explaining Changes in the Forward RateThe forward rate is indirectly affected by all the factors that can affect the spot rate (S) over time, including inflation differentials, interest rate differentials, etc. The change in the forward rate can also be due to a change in the premium.

Exhibit 7.11 Quoted Interest Rates for Various Times to Maturity

Exhibit 7.12 Relationship between the Interest Rate Differential and the Forward Premium

SUMMARY

 Locational arbitrage may occur if foreign exchange quotations differ among banks. The act of locational arbitrage should force the foreign exchange quotations of banks to become realigned, and locational arbitrage will no longer be possible.

 Triangular arbitrage is related to cross exchange rates. A cross exchange rate between two currencies is determined by the values of these two currencies with respect to a third currency. If the actual cross exchange rate of these two currencies differs from the rate that should exist, triangular arbitrage is possible. The act of triangular arbitrage should force cross exchange rates to become realigned, at which time triangular arbitrage will no longer be possible.

SUMMARY (Cont.)

 Covered interest arbitrage is based on the relationship between the forward rate premium and the interest rate differential. The size of the premium or discount exhibited by the forward rate of a currency should be about the same as the differential between the interest rates of the two countries of concern. In general terms, the forward rate of the foreign currency will contain a discount (premium) if its interest rate is higher (lower) than the U.S. interest rate.

 If the forward premium deviates substantially from the interest rate differential, covered interest arbitrage is possible. In this type of arbitrage, a foreign short term investment in a foreign currency is covered by a forward sale of that foreign currency in the future. In this manner, the investor is not exposed to fluctuation in the foreign currency’s value.

SUMMARY (Cont.)

 Interest rate parity (IRP) is a theory that states that the size of the forward premium (or discount) should be equal to the interest rate differential between the two countries of concern. When IRP exists, covered interest arbitrage is not feasible because any interest rate advantage in the foreign country will be offset by the discount on the forward rate. Thus, the act of covered interest arbitrage would generate a return that is no higher than what would be generated by a domestic investment.

SUMMARY (Cont.)

 Because the forward premium of a currency from a U.S. perspective is influenced by the interest rate of that currency and the U.S. interest rate and because those interest rates change over time, the forward premium changes over time. Thus the forward premium may be large and positive in one period when the interest rate of that currency is relatively low, but it could become negative (reflecting a discount) if that interest rate rises above the U.S. interest rate.

8Relationships among Inflation, Interest Rates and Exchange Rates

 Explain the purchasing power parity (PPP) theory and its implications for exchange rate changes

 Explain the International Fisher effect (IFE) theory and its implications for exchange rate changes

 Compare the PPP theory, the IFE theory, and the theory of interest rate parity (IRP), which was introduced in the previous chapter

Chapter Objectives

Purchasing Power Parity (PPP)

Interpretations of Purchasing Power Parity Absolute Form of PPP: without international barriers,

consumers shift their demand to wherever prices are lower. Prices of the same basket of products in two different countries should be equal when measured in common currency.

 Relative Form of PPP: Due to market imperfections, prices of the same basket of products in different countries will not necessarily be the same, but the rate of change in prices should be similar when measured in common currency

Rational Behind Relative PPP Theory

 Exchange rate adjustment is necessary for the relative purchasing power to be the same whether buying products locally or from another country.

 If the purchasing power is not equal, consumers will shift purchases to wherever products are cheaper until the purchasing power is equal.

Using PPP to Estimate Exchange Rate Effects

 The relative form of PPP can be used to estimate how an exchange rate will change in response to differential inflation rates between countries.

 International trade is the mechanism by which the inflation differential affects the exchange rate according to this theory (Exhibit 8.1)

Exhibit 8.1 Summary of Purchasing Power Parity

Why Purchasing Power Parity Does Not Occur

1. Confounding effectsA change in a country’s spot rate is driven by more than the inflation differential between two countries:

Since the exchange rate movement is not driven solely by ΔINF, the

Why Purchasing Power Parity Does Not Occur (Cont.)

2. No Substitutes for Traded GoodsIf substitute goods are not available domestically, consumers may not stop buying imported goods.

International Fisher Effect (IFE)

1. The Fisher effect suggests that the nominal interest rate contain two components:a. Expected inflation rateb. Real interest rate

2. The real rate of interest represents the return on the investment to savers after accounting for expected inflation.

Implications of the International Fisher Effect

1. The international Fisher effect (IFE) theory suggests that currencies with high interest rates will have high expected inflation (due to the Fisher effect) and the relatively high inflation will cause the currencies to depreciate (due to the PPP effect).

2. Implications of the IFE for Foreign Investors The implications are similar for foreign investors who attempt to capitalize on relatively high U.S. interest rates. The foreign investors will be adversely affected by the effects of a relatively high U.S. inflation rate if they try to capitalize on the high U.S. interest rates.

3. Implications of the IFE for Two Non-U.S. Currencies The IFE theory can be applied to any exchange rate, even exchange rates that involve two non-U.S. currencies.

Exhibit 8.5 Illustration of the International Fisher Effect (IFE) from Various Investor Perspectives

Exhibit 8.6 Summary of International Fisher Effect

Limitations of the IFE

The IFE theory relies on the Fisher effect and PPP1. Limitation of the Fisher Effect

The difference between the nominal interest rate and actual inflation rate is not consistent. Thus, while the Fisher effect can effectively use nominal interest rates to estimate the market’s expected inflation over a particular period, the market may be wrong.

2. Limitation of PPP Other country characteristics besides inflation (income levels, government controls) can affect exchange rate movements. Even if the expected inflation derived from the Fisher effect properly reflects the actual inflation rate over the period, relying solely on inflation to forecast the future exchange rate is subject to error.

IFE Theory versus Reality

1. The IFE theory contradicts how a country with a high interest rate can attract more capital flows and therefore cause the local currency’s value to strengthen (Ch 4).

2. IFE theory also contradicts how central banks may purposely try to raise interest rates in order to attract funds and strengthen the value of their local currencies (Ch 6).

3. Whether the IFE holds in reality is dependent on the countries involved and the period assessed.

4. The IFE theory may be especially meaningful to situations in which the MNCs and large investors consider investing in countries where the prevailing interest rates are very high.

Comparison of the IRP, PPP, and IFE

Although all three theories relate to the determination of exchange rates, they have different implications.

 IRP focuses on why the forward rate differs from the spot rate and on the degree of difference that should exist. It relates to a specific point in time.

 PPP and IFE focus on how a currency’s spot rate will change over time.

 Whereas PPP suggests that the spot rate will change in accordance with inflation differentials, IFE suggests that it will change in accordance with interest rate differentials.

 PPP is related to IFE because expected inflation differentials influence the nominal interest rate differentials between two countries.

Exhibit 8.9 Comparison of the IRP, PPP, and IFE Theories

SUMMARY

 Purchasing power parity (PPP) theory specifies a precise relationship between relative inflation rates of two countries and their exchange rate. In inexact terms, PPP theory suggests that the equilibrium exchange rate will adjust by the same magnitude as the differential in inflation rates between two countries. Though PPP continues to be a valuable concept, there is evidence of sizable deviations from the theory in the real world.

SUMMARY (Cont.)

 The international Fisher effect (IFE) specifies a precise relationship between relative interest rates of two countries and their exchange rates. It suggests that an investor who periodically invests in foreign interest-bearing securities will, on average, achieve a return similar to what is possible domestically. This implies that the exchange rate of the country with high interest rates will depreciate to offset the interest rate advantage achieved by foreign investments. However, there is evidence that during some periods the IFE does not hold. Thus, investment in foreign short-term securities may achieve a higher return than what is possible domestically.

SUMMARY (Cont.)

 The PPP theory focuses on the relationship between the inflation rate differential and future exchange rate movements. The IFE focuses on the interest rate differential and future exchange rate movements. The theory of interest rate parity (IRP) focuses on the relationship between the interest rate differential and the forward rate premium (or discount) at a given point in time.