国际金融英文课件-2

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 Outli

2、neInterest Rate ParityPurchasing Power ParityThe Fisher EffectsForecasting Exchange RatesInterest Rate ParityCovered Interest ArbitrageIRP and Exchange Rate DeterminationReasons for Deviations from IRPPurchasing Power ParityThe Fisher EffectsForecasting Exchange RatesInterest Rate ParityPurchasing P

3、ower ParityPPP Deviations and the Real Exchange RateEvidence on Purchasing Power ParityThe Fisher EffectsForecasting Exchange RatesInterest Rate ParityPurchasing Power ParityThe Fisher EffectsForecasting Exchange RatesInterest Rate ParityPurchasing Power ParityThe Fisher EffectsForecasting Exchange

4、RatesEfficient Market ApproachFundamental ApproachTechnical ApproachPerformance of the Forecasters5.1 Interest Rate Parity5.2 Purchasing Power Parity5.3 The Fisher Effects5.4 Forecasting Foreign Exchange Rates5-15.1 Interest Rate Parity5.1.1 Interest Rate Parity Defined5.1.2 Covered Interest Arbitra

5、ge (抵补套利)5.1.3 Reasons for Deviations from Interest Rate Parity 5-2almost all of the time!5.1.1 Interest Rate Parity DefinedIRP is an “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.S

6、ince 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 $1,000: Invest in the U.S. at i$. Future value = $1,000 (1

7、+ i$) 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 (o

8、therwise 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,

9、000(1 + i$) Alternative 2:Send your $ on a round trip to BritainStep 2: $1,000S$/ (1+ i) F$/ $1,000S$/ (1+ i)=IRP5-5Interest Rate Parity DefinedThe 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

10、approximated as i$ iSF S1 + i$1 + iS$/F$/=5-7Interest Rate Parity Carefully DefinedNo matter how you quote the exchange rate ($ 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

11、wrong.1 + i$1 + iF$/ = S$/ or1 + i$1 + iF/$ = S/$ 5-8Interest Rate Parity Carefully DefinedWhen 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.

12、Otherwise, nobody would hold dollar-denominated securities.When the 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.

13、 Sell 512.45 for dollars, if Fb($/) = $2.30/, then 512.45 will be $1178.635, which is enough 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)

14、 = $2.30/ , 512.45 will be $1,178, which is enough to repay your dollar obligation of $1,030. The excess is your profit.Step 1: borrow $1,000Step 2:buy poundsStep 3:Step 5: Repay your dollar loan with $1,030.512.45More than $1,0305-15How Long Will This Arbitrage Last?The interest rate, i$, will rise

15、 in the Unites States.The pound will appreciate in the spot market since lots of purchase of pounds and sale of dollars in the spot market. Then, S($/) will be increased.The interest rate, i, will fall in the U.K.The pound will depreciate in the forward market since lots of sale of pounds and purcha

16、se of dollars in the forward market. Then, F($/) will be decreased.5-16Arbitrage Strategy II F360($/) F(real)Borrow 800,000 in Germany. Repayment in three months will be 810,000=800,000 x1.0125Buy $1,000,000 spot using 800,000 .Invest $1,000,000 in the United States. Then, the maturity value will be

17、 $1,020,000 after three months.5-22Example 5.2 -continuedBuy euro and sell dollar by forward exchange rate for 815,348 = ($1,020,000)/($1.2510/)The 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. doll

18、ar 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 receivable. 4. Repay your dollar-denominated loan with $x (1 + i$)T.5-24Money Market Hedge: ExampleA U.S.based importer of Italian bicyclesIn one year owes 100,000

19、 to an Italian supplier.The spot exchange rate is $1.50 = 1.00The one-year interest rate is i = 4% in Italy, i$ = 3% in USA $1.501.00Dollar cost today = $144,230.77 = 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 maturit

20、y, he will have 100,000 = 96,153.85 (1.04)5-25A Money Market Hedge$148,557.69 = $144,230.77 (1.03)With this money market hedge, we have redenominated a one-year 100,000 payable into a $144,230.77 payable due today.If the U.S. interest rate is i$ = 3% we could borrow the $144,230.77 today and owe in

21、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 spot FX rate as follows:5-27Determination of FX rateIn addition to relative interest rates, the forward FX rate

22、 is an important factor in spot FX rate determination.The forward FX rate can be viewed as the expected future spot FX rate on all related information being available now.S = (1+i)/(1+i$) x E(St+1 | It)First, expectation play a key role in spot FX rate determination; Second, behavior of FX rate will

23、 be driven by new events5-28Determination of FX rateWhen the forward FX rate F is replaced by the expected future spot FX rate, E(St+1);(i$ - i) = (F S)/S = E(St+1) St/St = E(e)The interest rate differential between a pair of countries is approximately equal to the expected rate of change in FX rate

24、. This relationship is called uncovered interest rate parity (非抵补利率平价).If i$=5%, i=8%, the pound will depreciate again dollar by about 3%, that is, E(e)-3%5-29Currency carry trade (货币利差交易)Currency carry trade involves buying a currency that has a high rate of interest and funding the purchase by bor

25、rowing in a currency with low rates 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.Currency Carry Trade ExampleSuppose the 1-year borrowing rate in dolla

26、rs 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 625,000.5-315-31625,000 invested for one year at 2% yields 640,625.The currency carry trade will be

27、 profitable if the Forward bid rate prevailing in one year is high enough that his 640,625 will sell for at least $1,010,000 (enough to repay his debt).No less expensive than:Currency Carry Trade ExampleS360($/) = $1,010,000640,625$1.57661.00=bCarry trade loses moneyCarry trade makes moneywhen inter

28、est rate spread exchange rate changeInterest Rate Spreads and Exchange Rate Changes Australian Dollar vs. Japanese Yen6-335.1.3 Reasons for Deviations from IRPTransactions CostsThe interest rate available to an arbitrageur for borrowing, ib may exceed the rate he can lend at, il.There may be bid-ask

29、 spreads to overcome, Fb/Sa F/S Thus (borrowing dollars as an example)(Fb/Sa)(1 + il) (1 + i$b) 0Capital ControlsGovernments sometimes restrict import and export of money through taxes or outright bans.5-34IRP with Transactions Costsexploitable arbitrage opportunity i$ i IRP lineUnprofitable arbitra

30、geF1($/) S0($/) S0($/)Unprofitable “arbitrage” opportunity6-35Transactions 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

31、+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$1m(1+i$)bBorrow $1m at i$Step 1binvest at il$1m S0($/)a1(1+i)lStep 3(All transactions at reta

32、il 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 1borrow 1m at ib(All transactions at retail prices.)No arbitrage forward ask price:F1($/)

33、=a (1+i$)l (1+i)bS0($/)b= $1.4065/1m S0($/) (1+i$) bl5-38On the last two slides we found “no arbitrage”Forward bid prices of $1.4500/ and Forward ask prices of $1.4065/Normally the dealer sets the ask price above the bidrecall that this difference is his profit.But the prices on the last two slides

34、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.Why This Seems ConfusingSetting Dealer Forward Bid and AskDealer stands ready to be on opposite side of every tradeDe

35、aler buys foreign currency at the bid priceDealer sells foreign currency at the ask priceDealer borrows (from customer) at the lending rates Dealer lends to his customer at the borrowing rateBorrowingLending$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

36、.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 and receive $1m S0($/)b1$1m$1m S0($/)b1Invest at i$b$1m(1+i$)bInvest

37、 at ib(1+i)b$1m S0($/)b1forward bidF1($/) =b (1+i$)b (1+i)bS0($/)bHe is also willing to buy at5-41Setting Dealer Forward Ask PriceOur dealer is indifferent between selling euro today at spot ask price and selling euro in 1 year at forward ask price.Invest at ib1m(1+i)bforward askF1($/) =a (1+i$)b (1

38、+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%) / (1 + 5.5%) = 1.4132= 1.45 x (1 + 5%) / (1 + 5.5%) =

39、1.44315-435.2 Purchasing Power Parity5.2.1 Purchasing Power Parity (PPP) and FX Rate Determination5.2.2 PPP Deviations and the Real FX Rate5.2.3 Evidence on PPP5-445.2.1 Purchasing Power ParityThe exchange rate between two currencies should equal the ratio of the countries price levels:S($/) =PP$S($

40、/) =PP$150$300= $2/ 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 and elsewhere.In July 2009, a Big M

41、ac 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 ofexchange ratevaluation againstcur

42、rencyIn 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 162.643.706.07-39Euro area 3.584.341.21

43、e1.21e0JapanYen 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 DeterminationSuppose the spot exchange rate is $1.25 = 1.00If the inflation rate in the U.S. is expected to be 3% in the next year

44、 and 5% in the euro zone,Then 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 DeterminationThe 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 + $1 + = = 5-49Pu

45、rchasing Power Parity and Interest Rate ParityNotice 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 DifferentialWe could also reformulate our equations as inflation or interest rate differentials:

46、= 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

47、expected to be 6% in the next 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 CutGiven the difficulty in measuring expected inflation, managers often use i$ i$ 5-53= F($/) S($/)S($/)i$ i1 + iE(e) = i$ i= F

48、($/) S($/)S($/)$ 1 + E(e) = $ PPP DeviationsThe real exchange rate, q, which measures deviations from PPP, can be defined as follows:q = (1 + $) /(1 + e) x (1 + )Appreciation of dollar: e Depreciation of dollars: +eWhen q=1, then (1 + e) = (1 + $)/(1 + ). It implies that PPP holdsq=1: Competitivenes

49、s of the domestic country unalteredq1: Competitiveness of the domestic country worsens5-54PPP Deviations - exampleSuppose 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 rat

50、e? q = (1.05)/(1+0.045) x (1.035) = 0.97The dollar depreciated by more than is warranted by PPP, strengthening the competitiveness of US industries in the world market.5-555.2.3 Evidence on PPPPPP probably doesnt hold precisely in the real world for a variety of reasons.Haircuts cost 10 times as muc

51、h in the developed world as in the 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.5-56Lo

52、cationHamburger(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$2.72$27.33$11.90Madrid$5.40$5.76$20.43$9.87Mexico City$4.02$0.91$21.72$4.72Munich$4.7

53、1$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$12.48A Guide to World Prices: (March 2013)5.3 The Exact Fisher EffectsAn increase (de

54、crease) 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 + $)i$ $ + E($)Where $ is the equilibrium expected “real” interest rateE($) is the expected rate of inflati

55、oni$ is the equilibrium expected nominal interest rate5-58International 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 get the International Fisher

56、 Effect:E(1 + )E(1 + $)1 + i$1 + i=5-59International Fisher EffectIf the International Fisher Effect holds, then forward rate PPP holds:E(1 + )E(1 + $)1 + i$1 + i=and if IRP also holds1 + i$1 + iS/$ F/$ =E(1 + )E(1 + $)=S/$ F/$ 5-60PPPFRPPPFEFEPIFEExact Equilibrium Exchange Rate RelationshipsIRPE(1

57、+ )E(1 + $)1 + i$1 + i5-61How Large is Chinas Economy?5.4 Forecasting Exchange Rates5.4.1 Efficient Markets Approach5.4.2 Fundamental Approach5.4.3 Technical Approach5.4.4 Performance of the Forecasters5-635.4.1 Efficient Markets ApproachFX Markets are efficient if current FX prices reflect all avai

58、lable and relevant information.If this is so, exchange rates will only change when new information arrives. Since news is unpredictable, the exchange rate will change randomly over time.If the exchange rate indeed follows a random walk, the future exchange rate is expected to be the same as the current exchange rate.St = ESt+1-(A)5-64Efficient Markets ApproachIf FX markets are efficient, the current forward exchange rate can be viewed as the markets expect of the future exchange rate based on the available information.Ft = ESt+1| It-(B)In efficient market hypothesis