C7-,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,International Arbitrage AndInterest Rate Parity,7,Chapter,South-Western/Thomson Learning 2003,See,c7.xls,for spreadsheets to accompany this chapter.,Chapter Objectives,To explain the conditions that will result in various forms of international arbitrage,along with the realignments that will occur in response;and,To explain the concept of interest rate parity,and how it prevents arbitrage opportunities.,International Arbitrage,Arbitrage,can be loosely defined as capitalizing on a discrepancy in quoted prices.Often,the funds invested are not tied up and no risk is involved.,In response to the imbalance in demand and supply resulting from arbitrage activity,prices will realign very quickly,such that no further risk-free profits can be made.,Locational arbitrage,is possible when a banks buying price(bid price)is higher than another banks selling price(ask price)for the same currency.,Example:,Bank CBidAskBank DBidAsk,NZ$.635$.640NZ$.645$.650,Buy NZ$from Bank C$.640,and sell it to Bank D$.645.Profit=$.005/NZ$.,International Arbitrage,Triangular arbitrage,is possible when a cross exchange rate quote differs from the rate calculated from spot rates.,Example:,Bid,Ask,British pound()$1.60$1.61,Malaysian ringgit(MYR)$.200$.202,MYR8.1MYR8.2,Buy$1.61,convert MYR8.1/,then sell MYR$.200.Profit=$.01/.,(8.1,.2=1.62),International Arbitrage,When the exchange rates of the currencies are not in equilibrium,triangular arbitrage will force them back into equilibrium.,International Arbitrage,$,MYR,Value of in$,Value of,MYR in$,Value of,in MYR,Covered interest arbitrage,is the process of capitalizing on the interest rate differential between two countries,while covering for exchange rate risk.,Covered interest arbitrage,tends to force a relationship between forward rate premiums and interest rate differentials.,International Arbitrage,Example:,spot rate=90-day forward rate=$1.60,U.S.90-day interest rate=2%,U.K.90-day interest rate=2%,Borrow$at 3%,or use existing funds which are earning interest at 2%.Convert$to at$1.60/and engage in a 90-day forward contract to sell at$1.60/.Lend at 4%.,International Arbitrage,Spot exchange rates can be found online at :/sonnet-financial /rates/full.asp,while forward rates can be found at :/bmo /economic/regular/fxrates.html,and interest rates at :/federalreserve.gov/releases/H15/update/.,Online Application,Locational arbitrage ensures that quoted exchange rates are similar across banks in different locations.,Triangular arbitrage ensures that cross exchange rates are set properly.,Covered interest arbitrage ensures that forward exchange rates are set properly.,International Arbitrage,Any discrepancy will trigger arbitrage,which will then eliminate the discrepancy.Arbitrage thus makes the foreign exchange market more orderly.,International Arbitrage,Interest Rate Parity(IRP),Market forces cause the forward rate to differ from the spot rate by an amount that is sufficient to offset the interest rate differential between the two currencies.,Then,covered interest arbitrage is no longer feasible,and the equilibrium state achieved is referred to as,interest rate parity(IRP),.,Derivation of IRP,When IRP exists,the rate of return achieved from covered interest arbitrage should equal the rate of return available in the home country.,End-value of a$1 investment in covered interest arbitrage=(1/S),(1+,i,F,),F,=(1/S),(1+,i,F,),S,(1+p),=(1+,i,F,),(1+p),where p is the forward premium.,Derivation of IRP,End-value of a$1 investment in the home country=1+,i,H,Equating the two and rearranging terms:,p=,(1+,i,H,),1,(1+,i,F,),i.e.,forward,=,(1+home interest rate),1,premium (1+foreign interest rate),Determining the Forward Premium,Example:,Suppose 6-month,i,peso,=6%,i,$,=5%.,From the U.S.investors perspective,forward premium=1.05/1.06 1,-,.0094,If S=$.10/peso,then,6-month forward rate=S,(1+p),.10,(1,_,.0094),$.09906/peso,Determining the Forward Premium,Note that the IRP relationship can be rewritten as follows:,F S,=,S(1+p)S,=p=,(1+,i,H,),1=,(,i,H,i,F,),S S,(1+,i,F,)(1+,i,F,),The approximated form,p,i,H,i,F,provides a reasonable estimate when the interest rate differential is small.,Graphic Analysis of Interest Rate Parity,Interest Rate Differential(%),home interest rate,foreign interest rate,Forward,Premium(%),Forward,Discount(%),-,2,-,4,2,4,1,3,-,1,-,3,IRP line,Graphic Analysis of Interest Rate Parity,Interest Rate Differential(%),home interest rate,foreign interest rate,Forward,Premium(%),Forward,Discount(%),-,2,-,4,2,4,1,3,-,1,-,3,IRP line,Zone of potential covered interest arbitrage by local investors,Zone of potential covered interest arbitrage by foreign investors,Test for the Existence of IRP,To test whether IRP exists,collect the actual interest rate differentials and forward premiums for various currencies.Pair up data that occur at the same point in time and that involve the same curr