國際財務管理Eun7e-Ch-006-PPT課件

1、International Parity Relationships and Forecasting Exchange RatesChapter SixCopyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved.Chapter OutlineInterest Rate ParityCovered Interest ArbitrageIRP and Exchange Rate DeterminationCurrency Carry TradeReasons for Deviations from IRPPurchas

2、ing Power ParityPPP Deviations and the Real Exchange RateEvidence on Purchasing Power ParityThe Fisher EffectsForecasting Exchange RatesEfficient Market ApproachFundamental ApproachTechnical ApproachPerformance of the ForecastersCopyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved.6

3、-2IRP 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 timeInteres

4、t Rate Parity DefinedCopyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved.6-3Interest 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 pounds

5、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 tha

6、t the 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.6-4Interest Rate Parity Examplei = 5%; i = 15%S0(/) = 0110,000 invest at i = 5%10,000 (1.05) = 1

7、0,500 Buy 8,000 at spotAlternatively 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=0.801.001.1551.050.881.00F1(/) = Copyright 2014 by the McGraw-Hill Companies, Inc. All rights reserv

8、ed.6-5Why IRP Holds: Part 1Suppose that the one-year forward rate was a tiny bit too low at 0.8799/ An astute trader would move quickly toBorrow 1,000,000 at i = 5%Trade 1,000,000 for 800,000 at the spot ratesInvest 800,000 at i = 15%Enter into a short position in a one-year forward contract on 924,

9、000 at 0.8799/ In one year he 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.6-6Why IRP Holds: Part 1011,000,000 At T = 0 borrow at i = 5% & sell 924,000 forward1

10、m(1.05) = 1,050,000 Buy 800,000 at spot1m 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 924,0

11、00 per forward contract924,000 0.87991.00= 1,050,119.33 Copyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved.6-7Why IRP Holds: Part 2Suppose that the one-year forward rate was a tiny bit too high at 0.8801/ An astute trader would move quickly toBorrow 800,000 at i = 15%.Trade 800,00

12、0 for 1,000,000 at spot ratesInvest 1,000,000 at 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 Compa

13、nies, Inc. All rights reserved.6-8Why IRP Holds: Part 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

14、 contract Buy 924,000 at 0.8801/Repay loan with 924,000 The easy money 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

15、Multi-Year Interest Rate ParitySo far weve computed the no-arbitrage 1-year.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

16、F2(/) =1,067,2201,102,500 F1(/) =0.8800/F2(/) =0.9680/012F2(/) =1.00(1+ i)21.25(1+ i)2Copyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved.6-10IRP Even More Carefully DefinedInterest Rate Parity is a “no arbitrage” condition that suggests that forward exchange rates are defined by t

17、odays spot exchange rates grossed up and down by the future value interest factors:In our 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

18、i and the euro in the spot rate by i to find the forward rate. Copyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved.6-11Currency Carry TradeCurrency carry trade involves buying a currency that has a high rate of interest and funding the purchase by borrowing in a currency with low r

19、ates of interest, without any hedging.The carry trade is profitable as long as the interest rate 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.6-12Currency Carry Trade Exampl

20、eSuppose the 1-year borrowing rate in dollars is 1%.The 1-year lending rate in pounds is 2%.The 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 640,6

21、25.The currency carry trade will be profitable if the spot bid rate prevailing in one year is high enough that his 640,625 will sell for at least $1,010,000 (enough to repay his debt).No less expensive than:S360($/) = $1,010,000640,625$1.57661.00=bCopyright 2014 by the McGraw-Hill Companies, Inc. Al

22、l rights reserved.6-13Carry trade loses moneyCarry trade makes moneywhen interest rate spread exchange rate changeInterest Rate Spreads and Exchange Rate Changes Australian Dollar vs. Japanese YenCopyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved.6-14Reasons for Deviations from IR

23、PTransactions CostsThe interest rate available to an arbitrageur for borrowing, ib, may exceed the rate he can 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 ControlsGovernments sometimes restrict import and export of money through taxes or

24、 outright bans.Copyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved.6-15IRP with Transactions Costsexploitable arbitrage opportunity i$ i IRP lineUnprofitable arbitrageF1($/) S0($/) S0($/)Unprofitable “arbitrage” opportunityCopyright 2014 by the McGraw-Hill Companies, Inc. All right

25、s reserved.6-16Transactions Costs ExampleWill an arbitrageur facing the following prices be able to make money?BorrowingLending$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(

26、$/) =aCopyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved.6-1701IRPNo 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$1m(1+i$)bBorrow $1m at i$Step 1binvest at il$1m S0($/)a1(1+i)lStep 3(A

27、ll transactions at retail prices.)F1($/) =b (1+i$)bS0($/)a1(1+i)l (1+i$)b (1+i)lS0($/)a= $1.4431/Copyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved.6-1801buy at forward askStep 4sell 1m at spot bidStep 2:1m S0($/)blend at i$Step 3:lIRP1m(1+i)b1m S0($/) (1+i$) F1($/) =bla1m(1+i)b1m

28、Step 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$) blCopyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved.6-19Why This May Seem ConfusingOn the last two slides we found “no arbitrage.”Fo

29、rward 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 profit.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

30、 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.6-20Setting Dealer Forward Bid and AskDealer stands ready to be on the opposite side of every trade.Dealer buys foreign currency at the bid price

31、.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.BorrowingLending$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 =

32、5.5%.bbCopyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved.6-21Setting Dealer Forward Bid PriceOur dealer is indifferent between buying euros today at the spot bid price and buying euros in 1 year at the forward bid price.spot bidHe is willing to spend $1m today and receive $1m S0(

33、$/)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, Inc. All rights reserved.6-22Setting Dealer Forward Ask PriceOur dealer is indifferent between selling euros tod

34、ay 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($/)aHe is also willing to buy atspot askHe is willing to spend 1m today and receive 1m S0($/)b1m1m S0($/)bInvest at i$b(1+i$)b1m S0($/)bCopyright 2014 by the McGraw

35、-Hill Companies, Inc. All rights reserved.6-23PPP and Exchange Rate DeterminationThe exchange rate between two currencies should equal the ratio of the countries price levels:S($/) =PP$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 o

36、f 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 exchange rate in one year should be $1.25(1.03) = 1.00(1.05).Copyright 2014 by the McGraw-Hill

37、Companies, Inc. All rights reserved.6-24The 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 exchange rate is equal to differences in the rates of inflationroughly 2%.PPP and Ex

38、change Rate DeterminationCopyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved.6-25PPP and IRPNotice that our two big equations equal each other:= = F($/)S($/)1 + $1 + PPP1 + i1 + i$=F($/)S($/)IRPCopyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved.6-26Expected Rate

39、of Change in Exchange Rate as Inflation DifferentialWe 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 the McGraw-Hill Companies, Inc. All rights r

40、eserved.6-27Expected Rate of Change in Exchange Rate as Interest Rate Differential= F($/) S($/)S($/)i$ i1 + iE(e) = i$ iGiven the difficulty in measuring expected inflation, managers often use a “quick and dirty” shortcut: i$ i$ Copyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved.6

41、-28PPP Deviations and the Real Exchange RateCopyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved.6-29Evidence on PPPPPP 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 the developing world.Film, on

42、 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 Companies, Inc. All rights rese

43、rved.6-30Evidence on PPPBig Mac pricesImpliedActual dollarUnder or overIn localPPPa ofexchange ratevaluation againstcurrencyIn 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

44、.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 6.56.561.520.9952Copyright 2014 by the McG

45、raw-Hill Companies, Inc. All rights reserved.6-31A Guide to World Prices: March 2013LocationHamburger(1 unit)Aspirin(20 units)Mans Haircut(1 unit)Movie Ticket(1 unit)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 Angeles$3.57

46、$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$4.82$4.15$46.89

47、$12.48Copyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved.6-32Approximate Equilibrium Exchange Rate RelationshipsE($ ) IRP PPP FE FRPPP IFE FEPSF SE(e) (i$ i)Copyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved.6-33The Exact Fisher EffectsAn increase (decrease) in

48、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 t

49、he equilibrium expected nominal U.S. interest rate.Copyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved.6-34International 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

50、are the same in each country, $ = then we get the International Fisher Effect:E(1 + )E(1 + $)1 + i$1 + i=Copyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved.6-35International Fisher EffectIf the International Fisher Effect holds, then forward rate PPP holds:E(1 + )E(1 + $)1 + i$1 +

51、 i=and if IRP also holds,1 + i$1 + iS/$ F/$ =E(1 + )E(1 + $)=S/$ F/$ Copyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved.6-36PPPFRPPPFEFEPIFEExact Equilibrium Exchange Rate RelationshipsIRPE(1 + )E(1 + $)1 + i$1 + iCopyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved.6-37How Large is Indias Economy?Copyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved.6-38Forecasting Exchange Rates: Efficient Markets ApproachFinancial markets are efficient if prices reflect all a