1、International Parity Relationships and Forecasting Exchange RatesChapter SixCopyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.Chapter Outline Interest Rate Parity Covered Interest Arbitrage IRP and Exchange Rate Determination Currency Carry Trade Reasons for Deviations from IRP Pur
2、chasing Power Parity PPP Deviations and the Real Exchange Rate Evidence on Purchasing Power Parity The Fisher Effects Forecasting Exchange Rates Efficient Market Approach Fundamental Approach Technical Approach Performance of the ForecastersCopyright 2014 by the McGraw-Hill Companies,Inc.All rights
3、reserved.6-2 IRP is a“no arbitrage”condition.If IRP did not hold,then it would be possible for an astute trader to make unlimited amounts of money exploiting the arbitrage opportunity.Since we dont typically observe persistent arbitrage conditions,we can safely assume that IRP holds.Most of the time
4、Interest Rate Parity DefinedCopyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-3 Interest Rate Parity ExampleConsider an investor with 10,000 who faces an interest rate in the euro zone of i=5%He could invest in Europe and have 10,500 in one year.Or he could trade his euro for pou
5、nds sterling at the spot exchange rate and invest in the United Kingdom at i=15%The spot exchange rates are 1.00=$1.50 and 1.00=$1.20If he invests in Britain,he prudently hedges his exchange rate risk with a short position in a forward contract on the 9,240 his investment will grow toIRP says that t
6、he forward exchange rate must be 0.8800/=$1.501.01.0$1.201.251.009,240=10,000 1.155 1.251.00F1(/)=9,240 10,500=0.8800/=S0(/)Copyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-4 Interest Rate Parity Examplei=5%;i =15%S0(/)=0110,000 invest at i=5%10,000 (1.05)=10,500 Buy 8,000 at sp
7、otAlternatively 10,000 1.00$1.20$1.501.00=8,000invest at i=15%9,2409,240=10,500 IRP says that the 1-year forward rate must be 0.88/=9,24010,500=1.00$1.50$1.201.000.801.00=0.801.001.1551.050.881.00 F1(/)=Copyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-5 Why IRP Holds:Part 1 Supp
8、ose that the one-year forward rate was a tiny bit too low at 0.8799/An astute trader would move quickly to1.Borrow 1,000,000 at i=5%2.Trade 1,000,000 for 800,000 at the spot rates3.Invest 800,000 at i=15%4.Enter into a short position in a one-year forward contract on 924,000 at 0.8799/In one year he
9、 has a cash inflow of 1,050,119.33 from the forward contract and owes 1,050,000 Risk-free arbitrage profit of 119.33Copyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-6 Why IRP Holds:Part 1011,000,000 At T=0 borrow at i=5%&sell 924,000 forward1m(1.05)=1,050,000 Buy 800,000 at spot
10、1m 1.00$1.20$1.501.00=800,000invest at i=15%924,000At T=1,owe 1.05m:You are short in a forward contract Sell 924,000 for 1,050,119.33 Repay loan with 1,050,000 The easy profit of 119.33 will attract trades that will force prices back into line.Sell 924,000 per forward contract924,000 0.87991.00=1,05
11、0,119.33 Copyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-7 Why IRP Holds:Part 2 Suppose that the one-year forward rate was a tiny bit too high at 0.8801/An astute trader would move quickly to Borrow 800,000 at i=15%.Trade 800,000 for 1,000,000 at spot rates Invest 1,000,000 at
12、i=5%Enter into a long position in a one-year forward contract on 924,000 at 0.8801/In one year he has a cash outflow of 1,050,000 from the forward contract and owes 924,000 Risk-free arbitrage profit of 119.31Copyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-8 Why IRP Holds:Part
13、2011,000,000 Invest at i=5%10,000(1.05)=1,050,000 At T=0 Sell 800,000 for 1m at spot;go long in forward contract on 924,000 at 0.8801/1m=1.00$1.20$1.501.00 800,000At T=0,Borrow 800,000 at i=15%924,000receiveYou are long in a forward contract Buy 924,000 at 0.8801/Repay loan with 924,000 The easy mon
14、ey will attract traders who will force prices back into line.this will only cost 1,049,880.70 Buy 924,000 forwardT=1 oweRisk-free arbitrage profit of 119.31Copyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-9 Multi-Year Interest Rate ParitySo far weve computed the no-arbitrage 1-y
15、ear.forward rateTo calculate the two-year forward rate compound the interest for 2 years:=$1.501.001.00$1.201.251.00spoti=15%.924,000 i=15%.1,067,220800,000 1,000,000 i=5%1,050,000 i=5%1,102,500 F1(/)=924,000 1,050,000 F2(/)=1,067,2201,102,500 F1(/)=0.8800/F2(/)=0.9680/012F2(/)=1.00(1+i)21.25(1+i)2C
16、opyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-10 IRP Even More Carefully Defined Interest Rate Parity is a“no arbitrage”condition that suggests that forward exchange rates are defined by todays spot exchange rates grossed up and down by the future value interest factors:In our
17、 example with a spot rate of 1.25/,interest rate parity says that the N-year future exchange rate that prevails today must be:FN(/)=1.00(1+i)N1.25(1+i)NNotice that we increase the pounds in the spot rate at i and the euro in the spot rate by i to find the forward rate.Copyright 2014 by the McGraw-Hi
18、ll Companies,Inc.All rights reserved.6-11 Currency Carry Trade Currency 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.The carry trade is profitable as long as the interest rat
19、e differential is greater than the appreciation of the funding currency against the investment currency.Copyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-12 Currency Carry Trade ExampleSuppose the 1-year borrowing rate in dollars is 1%.The 1-year lending rate in pounds is 2%.The
20、direct spot ask exchange rate is$1.60/.A trader who borrows$1m will owe$1,010,000 in one year.Trading$1m for pounds today at the spot generates 625,000.625,000 invested for one year at 2%yields 640,625.The currency carry trade will be profitable if the spot bid rate prevailing in one year is high en
21、ough that his 640,625 will sell for at least$1,010,000(enough to repay his debt).No less expensive than:S360($/)=$1,010,000640,625$1.57661.00=bCopyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-13 Carry trade loses moneyCarry trade makes moneywhen interest rate spread exchange rat
22、e changeInterest Rate Spreads and Exchange Rate Changes Australian Dollar vs.Japanese YenCopyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-14 Reasons for Deviations from IRP Transactions Costs The interest rate available to an arbitrageur for borrowing,ib,may exceed the rate he c
23、an lend at,il.There may be bid-ask spreads to overcome,Fb/Sa F/S.Thus,(Fb/Sa)(1+il)(1+i b)0.Capital Controls Governments sometimes restrict import and export of money through taxes or outright bans.Copyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-15 IRP with Transactions Costsex
24、ploitable arbitrage opportunity i$i IRP lineUnprofitable arbitrageF1($/)S0($/)S0($/)Unprofitable“arbitrage”opportunityCopyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-16 Transactions Costs Example Will an arbitrageur facing the following prices be able to make money?BorrowingLen
25、ding$5.0%4.50%5.5%5.0%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($/)bF1($/)=aCopyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-17 01IRPNo arbitrage forward bid price(for customer):Buy at spot a
26、sk$1m S0($/)a1Step 2Sell at forward bidStep 4$1m S0($/)a1(1+i)lF1($/)=b$1m(1+i$)b$1m$1m(1+i$)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=$1.4431/Copyright 2014 by the McGraw-Hill Companies,Inc.All
27、 rights reserved.6-18 01buy at forward askStep 4sell 1m at spot bidStep 2:1m S0($/)blend at i$Step 3:lIRP1m(1+i)b1m S0($/)(1+i$)F1($/)=bla1m(1+i)b1mStep 1:borrow 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$)blCopyrig
28、ht 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-19 Why This May Seem Confusing On the last two slides we found“no arbitrage.”Forward bid prices of$1.4431/.Forward ask prices of$1.4065/.Normally the dealer sets the ask price above the bidrecall that this difference is his expected prof
29、it.But the prices on the last two slides are the prices of indifference for the customer,NOT the dealer.At these forward bid and ask prices the customer is indifferent between a forward market hedge and a money market hedge.Copyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-20 Set
30、ting Dealer Forward Bid and AskDealer stands ready to be on the opposite side of every trade.Dealer buys foreign currency at the bid price.Dealer sells foreign currency at the ask price.Dealer borrows(from customer)at the lending rates.Dealer lends to his customer at the posted borrowing rates.Borro
31、wingLending$5.0%4.50%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%i$=5.0%,i=5.5%.bbCopyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-21 Setting Dealer Forward Bid PriceOur dealer is indifferent between buying euros today at the spot bid pr
32、ice and buying euros in 1 year at the forward bid price.spot bidHe is willing to spend$1m today and 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($/)bHe is also willing to buy atCopyright 2014 by the McGraw-Hill Companies,
33、Inc.All rights reserved.6-22 Setting Dealer Forward Ask PriceOur dealer is indifferent between selling euros today at the spot ask price and selling euros in 1 year at the forward ask price.Invest at ib1m(1+i)bforward askF1($/)=a (1+i$)b (1+i)bS0($/)aHe is also willing to buy atspot askHe is willing
34、 to spend 1m today and receive 1m S0($/)b1m1m S0($/)bInvest at i$b(1+i$)b1m S0($/)bCopyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-23 PPP and Exchange Rate Determination The exchange rate between two currencies should equal the ratio of the countries price levels:S($/)=PP$For e
35、xample,if an ounce of gold costs$300 in the U.S.and 150 in the U.K.,then the price of one pound in terms of dollars should be:S($/)=PP$150$300=$2/Suppose the spot exchange rate is$1.25=1.00.If the inflation rate in the U.S.is expected to be 3%in the next year and 5%in the euro zone,then the expected
36、 exchange rate in one year should be$1.25(1.03)=1.00(1.05).Copyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-24 The euro will trade at a 1.90%discount in the forward market:$1.251.00=F($/)S($/)$1.25(1.03)1.00(1.05)1.031.051+$1+=Relative PPP states that the rate of change in the e
37、xchange rate is equal to differences in the rates of inflationroughly 2%.PPP and Exchange Rate DeterminationCopyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-25 PPP and IRP Notice that our two big equations equal each other:=F($/)S($/)1+$1+PPP1+i1+i$=F($/)S($/)IRPCopyright 2014 b
38、y the McGraw-Hill Companies,Inc.All rights reserved.6-26 Expected Rate of Change in Exchange Rate as Inflation Differential We could also reformulate our equations as inflation or interest rate differentials:=F($/)S($/)S($/)1+$1+1=1+$1+1+1+=F($/)S($/)1+$1+=F($/)S($/)S($/)$1+E(e)=$Copyright 2014 by t
39、he McGraw-Hill Companies,Inc.All rights reserved.6-27 Expected Rate of Change in Exchange Rate as Interest Rate Differential=F($/)S($/)S($/)i$i1+iE(e)=i$i Given the difficulty in measuring expected inflation,managers often use a“quick and dirty”shortcut:i$i$Copyright 2014 by the McGraw-Hill Companie
40、s,Inc.All rights reserved.6-28 PPP Deviations and the Real Exchange RateCopyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-29 Evidence on PPP PPP probably doesnt hold precisely in the real world for a variety of reasons.Haircuts cost 10 times as much in the developed world as in t
41、he developing world.Film,on the other hand,is a highly standardized commodity that is actively traded across borders.Shipping costs,as well as tariffs and quotas,can lead to deviations from PPP.PPP-determined exchange rates still provide a valuable benchmark.Copyright 2014 by the McGraw-Hill Compani
42、es,Inc.All rights reserved.6-30 Evidence on PPPBig Mac pricesImpliedActual dollarUnder or overIn localPPPa ofexchange 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
43、.0414Britain 2.694.161.61c1.55c-4CanadaC$3.893.820.901.02-12ChinaYuan 15.652.453.626.39-43EgyptPound 162.643.706.07-39Euro 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 6.56.561.520.9952Copy
44、right 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-31 A Guide to World Prices:March 2013LocationHamburger(1unit)Aspirin(20units)MansHaircut(1unit)MovieTicket(1unit)Athens$3.81$2.09$58.72$13.24Copenhagen$7.00$4.86$55.50$13.82Hong Kong$2.82$2.39$80.13$9.62London$5.71$1.39$56.60$20.49Los
45、 Angeles$3.57$2.72$27.33$11.90Madrid$5.40$5.76$20.43$9.87Mexico City$4.02$0.91$21.72$4.72Munich$4.71$5.01$17.25$10.70Paris$5.97$3.70$68.49$12.63Rio de Janeiro$5.56$5.63$44.70$10.64Rome$5.14$7.99$42.19$9.64Sydney$5.38$4.34$53.77$16.29Tokyo$3.29$8.24$77.00$18.91Toronto$5.32$2.20$40.28$12.20Average$4.8
46、2$4.15$46.89$12.48Copyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-32 Approximate Equilibrium Exchange Rate RelationshipsE($)IRP PPP FE FRPPP IFE FEPSF SE(e)(i$i)Copyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-33 The Exact Fisher Effects An increase(decreas
47、e)in the expected rate of inflation will cause a proportionate increase(decrease)in the interest rate in the country.For the U.S.,the Fisher effect is written as:1+i$=(1+$)E(1+$)Where:$is the equilibrium expected“real”U.S.interest rate.E($)is the expected rate of U.S.inflation.i$is the equilibrium e
48、xpected nominal U.S.interest rate.Copyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-34 International Fisher EffectIf the Fisher effect holds in the U.S.,1+i$=(1+$)E(1+$)and the Fisher effect holds in Japan,1+i=(1+)E(1+)and if the real rates are the same in each country,$=then we
49、get the International Fisher Effect:E(1+)E(1+$)1+i$1+i=Copyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-35 International Fisher EffectIf the International Fisher Effect holds,then forward rate PPP holds:E(1+)E(1+$)1+i$1+i=and if IRP also holds,1+i$1+iS/$F/$=E(1+)E(1+$)=S/$F/$Cop
50、yright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-36 PPPFRPPPFEFEPIFEExact Equilibrium Exchange Rate Relationships$/$/)(SSE$/$/SFIRPE(1+)E(1+$)1+i$1+iCopyright 2014 by the McGraw-Hill Companies,Inc.All rights reserved.6-37 How Large is Indias Economy?Copyright 2014 by the McGraw-Hil
