1、Chapter Objective:This chapter examines several key international parity relationships,such as interest rate parity(IRP)and purchasing power parity(PPP).5Chapter FiveInternational Parity Conditions and Exchange Rate Determination5-0=F($/)S($/)1+$1+PPP1+i1+i$=F($/)S($/)IRPChapter OutlinelInterest Rat
2、e ParitylPurchasing Power ParitylThe Fisher EffectslForecasting Exchange RateslInterest Rate ParitylCovered Interest ArbitragelIRP and Exchange Rate DeterminationlReasons for Deviations from IRPlPurchasing Power ParitylThe Fisher EffectslForecasting Exchange RateslInterest Rate ParitylPurchasing Pow
3、er ParitylPPP Deviations and the Real Exchange RatelEvidence on Purchasing Power ParitylThe Fisher EffectslForecasting Exchange RateslInterest Rate ParitylPurchasing Power ParitylThe Fisher EffectslForecasting Exchange RateslInterest Rate ParitylPurchasing Power ParitylThe Fisher EffectslForecasting
4、 Exchange RateslEfficient Market ApproachlFundamental ApproachlTechnical ApproachlPerformance of the Forecastersl5.1 Interest Rate Parityl5.2 Purchasing Power Parityl5.3 The Fisher Effectsl5.4 Forecasting Foreign Exchange Rates5-15.1 Interest Rate Parityl5.1.1 Interest Rate Parity Definedl5.1.2 Cove
5、red Interest Arbitrage (抵补套利)l5.1.3 Reasons for Deviations from Interest Rate Parity 5-2almost all of the time!5.1.1 Interest Rate Parity DefinedlIRP is an“no arbitrage”condition.lIf IRP did not hold,then it would be possible for an astute trader to make unlimited amounts of money exploiting the arb
6、itrage opportunity.lSince we dont typically observe persistent arbitrage conditions,we can safely assume that IRP holds.5-3S$/F$/=(1+i)(1+i$)Interest Rate Parity Carefully DefinedConsider that there are two alternative ways for one-year investments about$1,000:1.Invest in the U.S.at i$.Future value=
7、$1,000 (1+i$)2.Trade your$for at the spot rate,invest$1,000/S$/in Britain at i while eliminating any exchange rate risk by selling the future value of the British investment forward.S$/F$/Future value=$1,000 x(1+i)Since these investments have the same risk,they must have the same future value(otherw
8、ise an arbitrage would exist)5-4IRPInvest those pounds at i$1,000 S$/$1,000Future Value=Step 3:repatriate future value to the U.S.A.Since both of these investments have the same risk,they must have the same future valueotherwise an arbitrage would existAlternative 1:invest$1,000 at i$1,000(1+i$)Alte
9、rnative 2:Send your$on a round trip to BritainStep 2:$1,000S$/(1+i)F$/$1,000S$/(1+i)=IRP5-5Interest Rate Parity DefinedlThe scale of the project is unimportant(1+i$)F$/S$/(1+i)=$1,000(1+i$)$1,000S$/(1+i)F$/=5-6Interest Rate Parity DefinedFormally,IRP is sometimes approximated as i$iSF S1+i$1+iS$/F$/
10、=5-7Interest Rate Parity Carefully DefinedlNo matter how you quote the exchange rate($per or per$)to find a forward rate,increase the foreign currency by the foreign currency rate and increase the dollars by the dollar rate:be carefulits easy to get this wrong.1+i$1+iF$/=S$/or1+i$1+iF/$=S/$5-8Intere
11、st Rate Parity Carefully DefinedlWhen the dollar(the pound)is at a forward discount(premium)that is,F S,then interest rate will be higher in the United States than in the U.K.to compensate for the expected depreciation of the dollars.Otherwise,nobody would hold dollar-denominated securities.lWhen th
12、e dollars is at a forward premium,that is,F$2.01/If F360($/)=$2.30/i.Borrow$1,000 at t=0 at i$=3%.ii.Sell$1,000 for 500 at the prevailing spot rate Sa($/),then invest 500 at 2.49%(i)for one year to achieve 512.45iii.Sell 512.45 for dollars,if Fb($/)=$2.30/,then 512.45 will be$1178.635,which is enoug
13、h to repay your debt of$1,030.5-14Arbitrage IInvest 500 at i=2.49%$1,000500500=$1,000$2.001In one year 500 will be worth 512.45=500(1+i)$1,178=512.45 1F(360)Step 4:repatriate to the U.S.A.If F(360)=$2.30/,512.45 will be$1,178,which is enough to repay your dollar obligation of$1,030.The excess is you
14、r profit.Step 1:borrow$1,000Step 2:buy poundsStep 3:Step 5:Repay your dollar loan with$1,030.512.45More than$1,0305-15How Long Will This Arbitrage Last?lThe interest rate,i$,will rise in the Unites States.lThe pound will appreciate in the spot market since lots of purchase of pounds and sale of doll
15、ars in the spot market.Then,S($/)will be increased.lThe interest rate,i,will fall in the U.K.lThe pound will depreciate in the forward market since lots of sale of pounds and purchase of dollars in the forward market.Then,F($/)will be decreased.5-16Arbitrage Strategy II F360($/)F(real)lBorrow 800,00
16、0 in Germany.Repayment in three months will be 810,000=800,000 x1.0125lBuy$1,000,000 spot using 800,000.lInvest$1,000,000 in the United States.Then,the maturity value will be$1,020,000 after three months.5-22Example 5.2-continuedlBuy euro and sell dollar by forward exchange rate for 815,348=($1,020,
17、000)/($1.2510/)lThe arbitrage profit will be 5,348=815,348-810,0005-23Generic Money Market Hedge1.Calculate the present value of y at i y(1+i)T2.Borrow the U.S.dollar value of receivable at the spot rate.$x=S($/)y(1+i)T Exchange for y(1+i)T3.At maturity your pound sterling investment pays your recei
18、vable.4.Repay your dollar-denominated loan with$x(1+i$)T.5-24Money Market Hedge:ExampleA U.S.based importer of Italian bicycleslIn one year owes 100,000 to an Italian supplier.lThe spot exchange rate is$1.50=1.00lThe one-year interest rate is i=4%in Italy,i$=3%in USA$1.501.00Dollar cost today=$144,2
19、30.77=96,153.85 100,0001.0496,153.85=Can hedge this payable by buyingtoday and investing 96,153.85 at 4%in Italy for one year.At maturity,he will have 100,000=96,153.85 (1.04)5-25A Money Market Hedge$148,557.69=$144,230.77 (1.03)lWith this money market hedge,we have redenominated a one-year 100,000
20、payable into a$144,230.77 payable due today.lIf the U.S.interest rate is i$=3%we could borrow the$144,230.77 today and owe in one year$148,557.69=100,000(1+i)T(1+i$)TS($/)5-26Determination of FX rate1+i1+i$=F($/)S($/)IRPS($/)=(1+i)x F($/)/(1+i$)Let us reformulate the IRP relationship in term of the
21、spot FX rate as follows:5-27Determination of FX ratelIn addition to relative interest rates,the forward FX rate is an important factor in spot FX rate determination.lThe forward FX rate can be viewed as the expected future spot FX rate on all related information being available now.lS=(1+i)/(1+i$)x
22、E(St+1|It)lFirst,expectation play a key role in spot FX rate determination;Second,behavior of FX rate will be driven by new events5-28Determination of FX ratelWhen the forward FX rate F is replaced by the expected future spot FX rate,E(St+1);l(i$-i)=(F S)/S=E(St+1)St/St=E(e)lThe interest rate differ
23、ential between a pair of countries is approximately equal to the expected rate of change in FX rate.This relationship is called uncovered interest rate parity(非抵补利率平价).lIf i$=5%,i=8%,the pound will depreciate again dollar by about 3%,that is,E(e)-3%5-29Currency carry tradeCurrency carry trade (货币利差交
24、易货币利差交易)lCurrency carry trade involves buying a currency that has a high rate of interest and funding the purchase by borrowing in a currency with low rates of interest,without any hedging.lThe carry trade is profitable as long as the interest rate differential is greater than the appreciation of th
25、e funding currency against the investment currency.Currency Carry Trade ExamplelSuppose the 1-year borrowing rate in dollars is 1%.lThe 1-year lending rate in pounds is 2%.lThe direct spot ask exchange rate is$1.60/.lA trader who borrows$1m will owe$1,010,000 in one year.lTrading$1m for pounds today
26、 at the spot generates 625,000.5-315-31l625,000 invested for one year at 2%yields 640,625.lThe currency carry trade will be profitable if the Forward bid rate prevailing in one year is high enough that his 640,625 will sell for at least$1,010,000(enough to repay his debt).lNo less expensive than:Cur
27、rency Carry Trade ExampleS360($/)=$1,010,000640,625$1.57661.00=bCarry trade loses moneyCarry trade makes moneywhen interest rate spread exchange rate changeInterest Rate Spreads and Exchange Rate Changes Australian Dollar vs.Japanese Yen6-335.1.3 Reasons for Deviations from IRPlTransactions CostslTh
28、e interest rate available to an arbitrageur for borrowing,ib may exceed the rate he can lend at,il.lThere may be bid-ask spreads to overcome,Fb/Sa F/S lThus(borrowing dollars as an example)(Fb/Sa)(1+il)(1+i$b)0lCapital ControlslGovernments sometimes restrict import and export of money through taxes
29、or outright bans.5-34IRP with Transactions Costsexploitable arbitrage opportunity i$i IRP lineUnprofitable arbitrageF1($/)S0($/)S0($/)Unprofitable“arbitrage”opportunity6-35Transactions Costs ExamplelWill an arbitrageur facing the following prices be able to make money?BorrowingLending$5.0%4.50%5.5%5
30、.0%BidAskSpot$1.42=1.00$1.45=1,00Forward$1.415=1.00$1.445=1.00(1+i$)(1+i)F($/)=S($/)(1+i$)b (1+i)l S0($/)aF1($/)=b (1+i$)l (1+i)b S0($/)bF1($/)=a5-3601IRPNo arbitrage forward bid price(for customer):Buy at spot ask$1m S0($/)a1Step 2Sell at forward bidStep 4$1m S0($/)a1(1+i)lF1($/)=b$1m(1+i$)b$1m$1m(
31、1+i$)bBorrow$1m at i$Step 1binvest at il$1m S0($/)a1(1+i)lStep 3(All transactions at retail prices.)F1($/)=b (1+i$)bS0($/)a1(1+i)l (1+i$)b (1+i)lS0($/)a=$1.4500/5-3701buy at forward askStep 4sell 1m at spot bidStep 21m S0($/)blend at i$Step 3lIRP1m(1+i)b1m S0($/)(1+i$)F1($/)=bla1m(1+i)b1mStep 1borro
32、w 1m at ib(All transactions at retail prices.)No arbitrage forward ask price:F1($/)=a (1+i$)l (1+i)bS0($/)b=$1.4065/1m S0($/)(1+i$)bl5-38lOn the last two slides we found“no arbitrage”lForward bid prices of$1.4500/and lForward ask prices of$1.4065/lNormally the dealer sets the ask price above the bid
33、recall that this difference is his profit.lBut the prices on the last two slides are the prices of indifference for the customer NOT the dealer.lAt these forward bid and ask prices the customer is indifferent between a forward market hedge and a money market hedge.Why This Seems ConfusingSetting Dea
34、ler Forward Bid and AsklDealer stands ready to be on opposite side of every tradelDealer buys foreign currency at the bid pricelDealer sells foreign currency at the ask pricelDealer borrows(from customer)at the lending rates lDealer lends to his customer at the borrowing rate BorrowingLending$5.0%4.
35、50%5.5%5.0%BidAskSpot$1.42=1.00$1.45=1.00Forward$1.415=1.00$1.445=1.00lli$=4.5%and i=5.0%bbi$=5.0%,i=5.5%.5-40Setting Dealer Forward Bid PriceOur dealer is indifferent between buying euro today at spot bid price and buying euro in 1 year at forward bid price.spot bidHe is willing to sell$1m today an
36、d receive$1m S0($/)b1$1m$1m S0($/)b1Invest at i$b$1m(1+i$)bInvest at ib(1+i)b$1m S0($/)b1forward bidF1($/)=b (1+i$)b (1+i)bS0($/)bHe is also willing to buy at5-41Setting Dealer Forward Ask PriceOur dealer is indifferent between selling euro today at spot ask price and selling euro in 1 year at forwa
37、rd ask price.Invest at ib1m(1+i)bforward askF1($/)=a (1+i$)b (1+i)bS0($/)aHe is also willing to buy atspot askHe is willing to sell 1m today and receive 1m S0($/)a1m1m S0($/)aInvest at i$b(1+i$)b1m S0($/)a5-42Bid and Ask Spread (1+i$)b (1+i)b S0($/)bF1($/)=b (1+i$)b (1+i)b S0($/)aF1($/)=a=1.42 x(1+5
38、%)/(1+5.5%)=1.4132=1.45 x(1+5%)/(1+5.5%)=1.44315-435.2 Purchasing Power Parityl5.2.1 Purchasing Power Parity(PPP)and FX Rate Determinationl5.2.2 PPP Deviations and the Real FX Ratel5.2.3 Evidence on PPP5-445.2.1 Purchasing Power ParitylThe exchange rate between two currencies should equal the ratio
39、of the countries price levels:S($/)=PP$S($/)=PP$150$300=$2/l For example,if an ounce of gold costs$300 in the U.S.and 150 in the U.K.,then the price of one pound in terms of dollars should be:5-45Absolute PPPS($/)=PP$Big Mac PPP,the exchange rate would equalize the hamburger prices between American
40、and elsewhere.In July 2009,a Big Mac cost$4.33 in American and 15.65 yuan in China.Thus,the Big Mac PPP would be about 3.62 yuan per dollar.The actual exchange rate is 6.39 yuan per dollar,implying that yuan is vastly undervalued.5-46Big Mac pricesImpliedActual dollarUnder or overIn localPPPa ofexch
41、ange ratevaluation against currencyIn dollarsthe dollara7/13/2009the dollar,%United States$4.33 4.331.00ArgentinaPeso 194.164.394.57-4AustraliaA$4.564.681.050.978BrazilReal 10.084.942.332.0414Britain 2.694.161.61c1.55c-4CanadaC$3.893.820.901.02-12ChinaYuan 15.652.453.626.39-43EgyptPound 162.643.706.
42、07-39Euro area 3.584.341.21e1.21e0JapanYen 3204.0973.9578.22-5MexicoPeso 372.708.5513.69-38RussiaRuble 752.2917.3332.77-47SwedenSKr 48.46.9411.186.9860SwitzerlandSFr 6.56.561.520.9952Exchange Rate DeterminationlSuppose the spot exchange rate is$1.25=1.00lIf the inflation rate in the U.S.is expected
43、to be 3%in the next year and 5%in the euro zone,lThen the expected exchange rate in one year should be$1.25(1.03)/1.00(1.05)F($/)=$1.25(1.03)1.00(1.05)$1.2261.00=5-48Exchange Rate DeterminationlThe euro will trade at a discount in the forward market:$1.251.00=F($/)S($/)$1.25(1.03)1.00(1.05)1.031.051
44、+$1+=5-49Purchasing Power Parity and Interest Rate ParitylNotice that our two big equations today equal each other:=F($/)S($/)1+$1+PPP1+i1+i$=F($/)S($/)IRP5-505.2.2 Expected Rate of FX Change as Inflation DifferentiallWe could also reformulate our equations as inflation or interest rate differential
45、s:=F($/)S($/)S($/)1+$1+1=1+$1+1+1+=F($/)S($/)1+$1+=F($/)S($/)S($/)$1+E(e)=$5-51Expected Rate of FX Change as Interest Rate Differential5-52Relative PPP states that the rate of FX change is equal to differences in the rates of inflation.If the inflation rate in the U.S.is expected to be 6%in the next
46、 year and 4%in the euro zoneThen,the euro should appreciate against the dollar by about 2%,that is,E(e)is about to 2%Quick and Dirty Short CutlGiven the difficulty in measuring expected inflation,managers often use i$i$5-53=F($/)S($/)S($/)i$i1+iE(e)=i$i=F($/)S($/)S($/)$1+E(e)=$PPP DeviationslThe rea
47、l exchange rate,q,which measures deviations from PPP,can be defined as follows:lq=(1+$)/(1+e)x(1+)lAppreciation of dollar:e lDepreciation of dollars:+elWhen q=1,then(1+e)=(1+$)/(1+).It implies that PPP holdslq=1:Competitiveness of the domestic country unalteredlq1:Competitiveness of the domestic cou
48、ntry worsens5-54PPP Deviations-examplelSuppose that the annual inflation rate is 5%in the United States and 3.5%in the United Kingdom,and the pound appreciated against the dollar by 4.5%.Then what is the real exchange rate?lq=(1.05)/(1+0.045)x(1.035)=0.97lThe dollar depreciated by more than is warra
49、nted by PPP,strengthening the competitiveness of US industries in the world market.5-555.2.3 Evidence on PPPlPPP probably doesnt hold precisely in the real world for a variety of reasons.lHaircuts cost 10 times as much in the developed world as in the developing world.lFilm,on the other hand,is a hi
50、ghly standardized commodity that is actively traded across borders.lShipping costs,as well as tariffs and quotas can lead to deviations from PPP.lPPP-determined exchange rates still provide a valuable benchmark.5-56LocationHamburger(1 unit)Aspirin(20 units)Mans Haircut(1 unit)Movie Ticket(1 unit)Ath
