International Parity Conditions

Chapter8International Parity Conditions6B. 1

Major International Finance TheoriesThe objective of International Finance theories isto understand how and why, in a system of freemarkets and flexible exchange rates, currenciesstrive to move toward equilibrium.These theories define the relationship betweenexchange rates (current spot, future spot, andforward), inflation, and nominal interest ratemovements.6B. 2

Parity Objectives To explain the concept of interest rate parity(IRP), and how parity condition preventsforeign exchange arbitrage opportunities. To explain Purchasing Power Parity (PPP)and International Fisher Effect (IFE) theories,and their implications on exchange ratechanges; and To compare and show linkage between PPP,IFE, and Interest Rate Parity (IRP) theories.6B. 3

1. Interest Rate Parity (IRP) TheoremAccording to IRP, at equilibrium, the forward rateof a foreign currency will differ (in %) from thecurrent spot rate by an amount that will equal theinterest rate differential (in%) between the homeand foreign country.6B. 4

Interest Rate Parity (IRP) As a result of market forces, the forward ratediffers from the spot rate by an amount thatsufficiently offsets the interest rate differentialbetween two currencies. Then, covered interest arbitrage is no longerfeasible, and the equilibrium state achieved isreferred to as interest rate parity (IRP).6B. 5

Derivation of IRP When IRP exists, the rate of return achievedfrom covered interest arbitrage should equalthe rate of return available in the homecountry. End-value of a 1 investment in coveredinterest arbitrage (1/S) (1 iF) F (1/S) (1 iF) [S (1 p)] (1 iF) (1 p)where p is the forward premium.6B. 6

Derivation of IRP End-value of a 1 investment in the home country 1 iH Equating the two and rearranging terms:(1 iF) (1 p) 1 iHp (1 iH)(1 iF)–1i.e.forwardpremium (1 home interest rate)(1 foreign interest rate)–16B. 7

Determining the Forward PremiumExample Suppose 6-month ipeso 6%, i 5%. From the U.S. investor’s perspective,forward premium (1.05/1.06) – 1 - .0094 If spot rate, S .10/peso, then6-month forward rate S (1 p) .10 (1.0094) .09906/peso6B. 8

Determining the Forward Premium The IRP relationship can be rewritten as follows:F–SS S(1 p) – SS p (1 iH)(1 iF)–1 (iH–iF)(1 iF) The approximated form, p iH – iF, provides areasonable estimate when the interest ratedifferential is small.6B. 9

Graphic Analysis of Interest Rate ParityInterest Rate Differential (%)home interest rate – foreign interest rate4IRP line2ForwardDiscount ofFC (%) Y-3B 1-1AWZX3 ForwardPremium ofFC(%)-2-46B. 10

Graphic Analysis of Interest Rate ParityInterest Rate Differential (%)home interest rate – foreign interest rate4IRP lineZone of potentialcovered interestarbitrage byforeign investorsForward-3Discount ofFC (%)2-113 ForwardPremium ofFC (%)-2-4Zone of potentialcovered interestarbitrage bylocal investors6B. 11

Test for the Existence of IRP To test whether IRP exists, collect actualinterest rate differentials (assets of similar riskand maturity) and forward premiums/discountsfor various currencies, and plot them on agraph. IRP holds when covered interest arbitrage isnot possible or worthwhile.6B. 12

Interpretation of IRP When IRP exists, it does not mean that bothlocal and foreign investors will earn the samereturns. What it means is that investors cannot usecovered interest arbitrage to achieve higherreturns than those achievable in theirrespective home countries.6B. 13

Does IRP Hold?Forward RatePremiums andInterest RateDifferentials forSeven Currencies6B. 14

Does IRP Hold? Various empirical studies indicate that IRPgenerally holds. While there are deviations from IRP, they areoften not large enough to make coveredinterest arbitrage worthwhile. This is due to the characteristics of foreigninvestments, such as transaction costs,political risk, and differential tax laws.6B. 15

Considerations When AssessingIRPTransaction CostsiH – iFZone of potentialcovered interestarbitrage byforeign investorsZone wherecovered interestarbitrage is notfeasible due totransaction costsIRP linepZone ofpotentialcoveredinterestarbitrageby localinvestors6B. 16

Considerations When AssessingIRPPolitical Risk A crisis in a country could cause its government torestrict capital outflow and impose exchangecontrols (exchange of the local currency for reservecurrencies). Investors may also perceive a higher default risk onforeign investments.Differential Tax Laws If tax laws vary, after-tax returns should beconsidered instead of before-tax returns.6B. 17

Changes in Forward Premiums6B. 18

PPP and IFE Theories Purchasing Power Parity (PPP): At equilibrium,the future spot rate of a foreign currency will differ(in %) from the current spot rate by an amountthat equals (in %) the inflation differential betweenthe home and foreign countries. International Fisher Effect (IFE): At equilibrium,the future spot rate of a foreign currency will differ(in %) from the current spot rate by an amountthat equals (in %) the nominal interest ratedifferential between the home and foreigncountries6B. 19

2. Purchasing Power Parity(PPP) When a country’s inflation rate rises relative tothat of another country, decreased exports andincreased imports depress the high-inflationcountry’s currency because of worsening tradeand current account balances. Purchasing Power Parity (PPP) theoryattempts to quantify this inflation – exchangerate relationship.6B. 20

Interpretations of PPP The absolute form of PPP is an extension ofthe law of one price. It suggests that the pricesof the same products in different countriesshould be equal when measured in a commoncurrency. The relative form of PPP accounts for marketdistortions like transportation costs, laborcosts, tariffs, taxes, and quotas. It states thatthe rate of price changes should be similar.6B. 21

Rationale behind PPP TheorySuppose U.S. inflation U.K. inflation. U.S. imports from U.K. and U.S. exports to U.K., and U.S. current account Downward pressure (depreciation) is placed on the This shift in consumption and the ’s depreciation willcontinue until in the U.S.: priceU.K. goods priceU.S. goods in the U.K.: priceU.S. goods priceU.K. goods6B. 22

Derivation of PPPAssume that PPP holds.Over time, as inflation occurs exchange rates adjusts tomaintain PPP:Ph1 Ph0 (1 Ih )Where Ph1 home country’s price index, year-1 endIh home country’s inflation rate for the yearPf1 Pf0 (1 If ) (1 ef )wherePf foreign country’s price indexIf foreign country’s inflation rateef foreign currency’s % in value6B. 23

Derivation of PPPIf PPP holds Ph1 Pf1 andPh0 (1 Ih ) Pf0 (1 If ) (1 ef )Solving for ef (1 Ih ) – 1(1 If )Ih If ef 0 i.e. foreign currency appreciatesIh If ef 0 i.e. foreign currency depreciatesExample: Suppose IU.S. 9% and IU.K. 5% .Then e (1 .09 ) – 1 3.81% (1 .05 )6B. 24

Simplified PPP RelationshipWhen the inflation differential is small, the PPP relationship canbe simplified asef Ih – IfExample:Suppose IU.S. 9% and IU.K. 5% .Then e 9 – 5 4%U.S. consumers:U.K. consumers: PU.S. IU.S. 9% PU.K. IU.K. e 9% PU.K. IU.K. 5% PU.S. IU.S. – e 5%6B. 25

Graphic Analysis of Purchasing PowerParityInflation Rate Differential (%)home inflation rate – foreign inflation rate4PPP lineIncreasedCpurchasingpower ofA2foreigngoods-3-11-2BD3Decreasedpurchasingpower offoreigngoods% in theforeigncurrency’sspot rate-46B. 26

Testing the PPP TheoryConceptual Test Plot actual inflation differentials and spotexchange rate changes for two or morecountries on a graph. If the points deviate significantly from the PPPline over time, then PPP does not hold.6B. 27

Testing the PPP TheoryStatistical Test Apply regression analysis to historical exchange ratesand inflation differentials:ef a0 a1 [ (1 Ih)/(1 If) – 1 ] µ Then apply t-tests to the regression coefficients. (Testfor a0 0 and a1 1.) If any coefficient differs significantly from what wasexpected, PPP does not hold.6B. 28

Testing the PPP Theory Empirical studies indicate that the relationshipbetween inflation differentials and exchangerates is not perfect even in the long run. However, the use of inflation differentials toforecast long-run movements in exchange ratesis supported. A limitation in the tests is that the choice of thebase period will affect the result.6B. 29

Why PPP Does Not OccurPPP does not occur consistently due to: confounding effects Exchange rates are also affected by differences ininflation, interest rates, income levels, governmentcontrols and expectations of future rates. a lack of substitutes for some non traded goods6B. 30

PPP in the Long Run PPP can be tested by assessing a “real”exchange rate over time (e.g., crawlingpegs). The real exchange rate is the actual exchangerate adjusted for inflationary effects in the twocountries of concern. If the real exchange rate follows a randomwalk, it cannot be viewed as being a constantin the long run. Then PPP does not hold.6B. 31

The Big Mac IndexThe Big Mac Index was invented by The Economist in1986 as a lighthearted guide to whether currencies are attheir “correct” level. It is based on the theory ofpurchasing-power parity (PPP), the notion that in the longrun exchange rates should move towards the rate thatwould equalize the prices of an identical basket of goodsand services (in this case, a burger) in any two countries.For example, the average price of a Big Mac in Americain July 2017 was 5.30; in China it was only 2.92 atmarket exchange rates. So the "raw" Big Mac index saysthat the yuan was undervalued by some 45% at that x6B. 32

3. International Fisher Effect (IFE) According to the Fisher Effect, nominal risk-freeinterest rates contain a real rate of return andanticipated inflationin ir inflation If all investors require the same real return onassets of similar risk and maturity, thendifferentials in interest rates may be due todifferentials in expected inflation. Recall that PPP theory suggests that exchangerate movements are caused by inflation ratedifferentials.6B. 33

International Fisher Effect (IFE) The International Fisher Effect (IFE) theorysuggests that currencies with higher interestrates will depreciate because the highernominal rates reflect higher expected inflation. Hence, investors hoping to capitalize on ahigher foreign interest rate should earn areturn no higher than what they would haveearned domestically.6B. 34

International Fisher Effect (IFE)Investors Attempt toResiding in Invest inIh IfefifJapanJapanU.S.Canada3% 3%363 110 % aJapanU.S.Canada1111113611850Return inHomeCurrencyIhRealReturnEarned5%553%332 %22581388866622258131313131111112226B. 35

Derivation of the IFE According to the IFE, E(rf ), the expectedeffective return on a foreign money marketinvestment, should equal rh , the effective returnon a domestic investment. rf (1 if ) (1 ef ) – 1if interest rate in the foreign countryef % change in the foreign currency’svalue rh ih interest rate in the home country6B. 36

Derivation of the IFE Setting rf rh : (1 if ) (1 ef ) – 1 ih Solving for ef :ef (1 ih ) 1(1 if ) ih if ef 0i.e. foreign currency appreciates ih if ef 0 i.e. foreign currency depreciatesExample:Suppose iU.S. 11% and iU.K. 12% .TheneU.K. (1 .11 ) – 1 –.89% .(1 .12 )This will make rf rh .6B. 37

Derivation of the IFE When the interest rate differential is small, the IFErelationship can be simplified asef ihif If the British rate on 6-month deposits were2% above the U.S. interest rate, the shoulddepreciate by approximately 2% over 6months. Then U.S. investors would earn aboutthe same return on British deposits as theywould on U.S. deposits.6B. 38

Graphic Analysis of theInternational Fisher Effect6B. 39

Tests of the IFE If actual interest rates and exchange ratechanges are plotted over time on a graph, wecan see whether the points are evenlyscattered on both sides of the IFE line. Empirical studies indicate that the IFE theoryholds during some time frames. However,there is also evidence that it does not holdconsistently.6B. 40

Tests of the International FisherEffect6B. 41