汇率决定与国际平价条件

1、第一章第一章汇率决定与国际平价条件汇率决定与国际平价条件 基本内容基本内容n有关外汇与汇率的基本知识（有关外汇与汇率的基本知识（reference to chapter four)n汇率变化幅度的测定汇率变化幅度的测定n汇率变化的影响因素汇率变化的影响因素n购买力平价购买力平价n利率平价利率平价n国际费雪效应国际费雪效应n汇率预测汇率预测Foreign exchange (fx) marketsnAn exchange rate measures the value of one currency in units of another currency.nMarkets-Spot marke

2、tTrade in cash with delivery in two business days-Forward marketTrade at a pre-specified price and on a pre-specified future datenVolume-$1.2 trillion average daily volume during 2001-75% of trade is in the interbank market（75%的交易是银行之间的外汇交易，其日均交易额达1.2trillion 美元）Swiss franc, 6%Canadian $, 5%Australi

3、an $, 4%Swedish krona, 3%Hong Kong $, 2%Singapore $, 1%Other, 10%Euro, 38%U.S. $, 90%Japanese Yen, 23%British Pound, 13%Emerging mkts, 5% FX turnover by currency Source: Bank for International Settlements (), March 2002.Percentages sum to 200 because two currencies are involved in each tr

4、ansaction.Participants in the fx marketnWholesale market-Dealers (or market makers)Buy and sell at quoted bid and offer prices-BrokersServe as matchmakers, without putting their own money at risk nRetail market-Governments-Corporations-Smaller financial institutions-IndividualsTwo rules for multinat

5、ional financenRule #1 Keep track of your units （注意货币单位）nRule #2 Always buy or sell the currency in the denominator of a foreign exchange quote（买卖的货币是指外汇标价中处于分母的货币）Rule #1 Keep track of your unitsA bottle of Georges de Bouef merlotBuy 1 bottle of wine P= 40/btlSpot exchange rate S$/= $0.80/ S/$= 1/S$

6、/= 1.25/$How much is this in dollars?P$= PS$/= (40/btl) ($0.80/)= $32/btl= P/S/$= (40/btl) / (1.25/$)= $32/btlRule #1 Keep track of your unitsA bottle of Georges de Bouef merlotBuy 1 bottle of wine P= 40/btlSpot exchange rate S$/= $0.80/ S/$= 1/S$/= 1.25/$How much is this in dollars?P$= P S/$= (40/b

7、tl) (1.25/$)= 250 / (btl$) 这是什么?因此，因此，Keep track of your currency units!Rule #2 Think of buying or sellingthe asset in the denominator先从商品买卖说起，先从商品买卖说起，Buying and selling a bottle of wineBuy a bottle at 40/btl and sell at 50/btl 10/btl profit。在这里买卖的对象是分母中的wine。Buying or selling a foreign currency is

8、 like buying or selling any other asset.Buying and selling eurosBuy s at $0.80/ and sell at $1.00/Buy s at $0.80/ Sell $s at 1.25/$ Sell s at $1.00/ Buy $s at 1.00/$ $0.20/ profit 0.25/$ profitAn example of what can go wrong如果买卖价格弄错了，即如果Buy $s at $0.80/ and sell $s at $1.00/，结果会如何呢？Buy $s at $0.80/

9、Sell s at 1.25/$ Sell $s at $1.00/ Buy s at 1.00/$ $0.20/ loss 0.25/$ lossSo, Always think of buying or sellingthe currency in the denominator!FX quotation conventions (汇率报价惯例）nEuropean/American quotes for the $nEuropean quotes are convenient for a European because they place the foreign currency (t

10、he $) in the denominator（银行间报价多为欧式报价，即单位美元的外（银行间报价多为欧式报价，即单位美元的外国货币汇率，因为美元是最经常交易的货币。）国货币汇率，因为美元是最经常交易的货币。）欧式标价欧式标价法对当地人很方便。法对当地人很方便。e.g. 1.25/$nAmerican quotes are convenient for an American because they place the foreign currency (the ) in the denominator美式标价法对美国人很方便。e.g. $0.80/FX quotation convent

11、ions(汇率报价惯例）nDirect/indirect quotes for foreign currency fnDirect quotes are convenient for a domestic resident because they place the foreign currency in the denominator (d/f); e.g. 110.95/ for a resident of JapannIndirect quotes are inconvenient for a domestic resident because they place the forei

12、gn currency in the numerator (f/d);e.g. 110.95/ for a resident of Europe 汇率变动幅度的测定汇率变动幅度的测定nWhen a currency declines in value, it is said to depreciate. When it increases in value, it is said to appreciate.n外国货币相对于本国货币的变动百分比外国货币相对于本国货币的变动百分比The percentage change (% D)D) in the value of a foreign cur

13、rency is computed as:A positive % D D represents appreciation of the foreign currency, while a negative % D D represents depreciation.本国货币相对于外国货币汇率的变动百分比本国货币相对于外国货币汇率的变动百分比11tttSSS11tttSSS人民币兑美元汇率变动例如：人民币兑美元汇率例如：人民币兑美元汇率:2005年年7月月21日日:$1=8.1100RMB2010年年3月月4日日:$1=6.8265RMB请计算美元相对于人民币的变化率和人民币相对于美请计算美元

14、相对于人民币的变化率和人民币相对于美元的变化率？元的变化率？美元相对于人民币的汇率变动率美元相对于人民币的汇率变动率 =（6.8265-8.1100）/8.1100 = -15.8%人民币相对于美元的汇率变动率人民币相对于美元的汇率变动率 =（8.1100-6.8265)/6.8265 =18.8%人民币兑欧元汇率变动例如：人民币兑欧元汇率例如：人民币兑欧元汇率:2005年年7月月21日日: 1=10.0641RMB2010年年3月月4日日: 1=9.3482RMB欧元相对于人民币的汇率变动率欧元相对于人民币的汇率变动率 =（9.3482-10.0641）/10.0641 = -7.1%人民币

15、相对于欧元的汇率变动率人民币相对于欧元的汇率变动率 =（10.0641-9.3482)/9.3482 =7.7%RMB/$Quantity of $S0D0r0RMB. inflation 中国对美国商品的需求增加中国对美国商品的需求增加,因而外汇需求也增加因而外汇需求也增加美国对中国商品的需求减少美国对中国商品的需求减少,因而美元外汇供应减少因而美元外汇供应减少D1r1S1影响汇率变化的因素影响汇率变化的因素1.Relative Inflation RatesRMB/$Quantity of $r0S0D0S1D1r1RMB. interest rates 人民币对美元存款的需求减人民币对美

16、元存款的需求减少少,因而外汇需求下降因而外汇需求下降美元对人民币存款的需求增美元对人民币存款的需求增加加,因而外汇供给增加因而外汇供给增加 影响汇率变化的因素影响汇率变化的因素2.Relative Interest RatesRMB/$Quantity of $S0D0r0RMB. income level 人民币对美国商品需求增加人民币对美国商品需求增加,因而外汇需求上升因而外汇需求上升对外汇供给的影响不无法预对外汇供给的影响不无法预测测D1r1影响汇率变化的因素3.Relative Income Levels,S14.Government Controlsnimposing foreign

17、 exchange barriers（设置外汇交易障碍）,nimposing foreign trade barriers（设置贸易障碍）,nintervening in the foreign exchange market（干预外汇市场）, naffecting macro variables such as inflation, interest rates, and income levels.（影响宏观变量）影响汇率变化的因素影响汇率变化的因素5.ExpectationsnForeign exchange markets react to any news that may have

18、 a future effect.n当市场预计某种货币趋跌时，交易者会大量抛售该货币，造成该货币汇率下浮的事实；反之，当人们预计某种货币趋于坚挺时，又会大量买进该种货币，使其汇率上扬。由于公众预期具有投机性和分散性的特点，加剧了汇率短期波动的振荡。影响汇率变化的因素影响汇率变化的因素 ExpectationsFed chairman suggests Fed isStrengthenedunlikely to cut U.S. interest ratesA possible decline in GermanStrengthenedinterest ratesCentral banks ex

19、pected toWeakenedintervene to boost the euro SignalImpact on $Poor U.S. economic indicatorsWeakened影响汇率变化的因素影响汇率变化的因素6.Speculating自自1973年实行浮动汇率制以来，外汇市场的投机活年实行浮动汇率制以来，外汇市场的投机活动越演越烈，投机者往往拥有雄厚的实力，可以在动越演越烈，投机者往往拥有雄厚的实力，可以在外汇市场上推波助澜，使汇率的变动远远偏离其均外汇市场上推波助澜，使汇率的变动远远偏离其均衡水平。衡水平。 投机的关键内容是低价买入、高价卖出，或者是高价投机的关键内

20、容是低价买入、高价卖出，或者是高价卖出、低价买入。卖出、低价买入。Purchasing Power Parity, or PPP1.绝对购买力平价的基本内容绝对购买力平价的基本内容nThe absolute form of PPP, or the “law of one price”（Equivalent assets sell for the same price.n） suggests that similar products in different countries should be equally priced when measured in the same currenc

21、y.n这就是绝对购买力的基本公式n即，汇率取决于以不同货币衡量的可贸易商品的价格水平之比，也就是不同货币对可贸易商品的购买力之比。niniiiiiPeP00*niiiniiiPPe00*PPe The Law of One PriceEquivalent assets sell for the same price(also called purchasing power parity, or PPP)nSeldom holds for nontraded assetsnCant compare assets that vary in qualitynMay not hold precisel

22、y when there are market frictionsAn example: The world price of goldSupposeP= 250/oz in London P = 400/oz in BerlinThe law of one price requires:Pt = Pt St/ 250/oz = (400/oz) St/即St/ 0.6250/ or 1/(0.6250/) = 1.6000/Purchasing Power Parity, or PPP2.相对购买力平价的基本内容相对购买力平价的基本内容nThe relative form of PPP 认为

23、，即期汇率应根据两国预期的认为，即期汇率应根据两国预期的通货膨胀率进行调整。即通货膨胀率进行调整。即EStd/f= S0d/f(1+Epd/(1+E(pf)tn即即RPPP将汇率的涨落归因于物价或货币购买力的变动。将汇率的涨落归因于物价或货币购买力的变动。nRPPP states that the expected appreciation or depreciation of the spot rate is determined by the expected inflation differential.nIf inflation is a known constant in each

24、currency, then RPPP can be stated as EStd/f= S0d/f(1+pd/(1+pft Arbitrage Arbitrage n If PPP does not hold, then there is an opportunity to lock in a riskless arbitrage profit.有些书上将有些书上将arbitrage 指为指为speculative positions，但是，但是，arbitrage is more strictly defined as a profitable position obtained with

25、: No net investment and No risk因此，套利利润是指无净投资和无风险情况下的利润。因此，套利利润是指无净投资和无风险情况下的利润。考虑交易成本，在不存在市场摩擦的情况下，如果一价定律不成立，则存在无风考虑交易成本，在不存在市场摩擦的情况下，如果一价定律不成立，则存在无风险套利机会。险套利机会。nEg,X银行：银行：Bid A$0.5838/ ;Offer A$0.5841/ n Y银行：银行：Bid A$0.5842/ ;Offer A$0.5845/ 套利者可以从套利者可以从X银行买进欧元，与此同时，再卖给银行买进欧元，与此同时，再卖给Y银行，即可赚取无风险利润。

26、银行，即可赚取无风险利润。因为汇率比为：因为汇率比为：(Y银行银行)0.5842/(X银行银行)0.5841=1.00017121，套利收益，套利收益率为率为0.01712%The No-Arbitrage ConditionThe No-Arbitrage ConditionPPPPPP意味着：即期汇率由本国货币资产价格与相同资产意味着：即期汇率由本国货币资产价格与相同资产的外国货币价格之比决定。如果的外国货币价格之比决定。如果PPPPPP不成立，则价格不成立，则价格差异会使套利有利可图。差异会使套利有利可图。P Pd d/P/Pf f=S=Sd/fd/f P Pd d=P=Pf fS Sd

27、/fd/fnThe No-Arbitrage Condition The No-Arbitrage Condition 非套利条件，即非套利条件，即PPPPPP成成立。立。n双边套汇的汇率均衡条件双边套汇的汇率均衡条件SXd/f/ SYd/f =1 即即SXd/f =SYd/fn交叉交叉三角套汇情况下的均衡汇率：三角套汇情况下的均衡汇率：Sd/e Se/f Sf/d = 1 An example with transactions costsGold dealer AGold dealer B401.40/oz Offer401.00/oz Bid250.25/oz Offer250.00/o

28、z BidBuy low from ASell high to BFX dealer1.599/ bid1.601/ askArbitrage profitPay 250.25 million to buy 1 million oz from A Sell 1 million oz to B for 401 million Buy s with s at the spot rate +1 million oz oz -250,250,000 -1 million oz +250,468,500 +401,000,000 -401,000,000 Arbitrage profit 218,500

29、 Cross exchange rates and triangular arbitrageIf Sd/eSe/fSf/d 1, then either Sd/e, Se/f or Sf/d must fall（说明说明分母货币相对于分子货币价格较高，有下降的可能）分母货币相对于分子货币价格较高，有下降的可能） For each spot rate, sell the currency in the denominator （分母）for the currency in the numerator： 即出售分母货币，购买分子货币即出售分母货币，购买分子货币Cross exchange rate

30、s and triangular arbitrageSupposeSRbl/$= Rbl 5.000/$S$/Rbl= $0.2000/RblS$/= $0.01000/S/$ = 100.0/$S/Rbl= 20.20/RblSRbl/ Rbl 0.04950/SRbl/$ S$/ S/Rbl= (Rbl 5/$)($.01/)(20.20/Rbl) = 1.01 1Cross exchange rates and triangular arbitrageSRbl/$ S$/ S/Rbl = 1.01 1Currencies in the denominators (分母分母)are too

31、 high relative to the numerators（分子）（分子）,（出售分母货币以购买分子货币）：（出售分母货币以购买分子货币）：nsell dollars and buy rubles ：Sell $1 million and buy Rbl 5 millionnsell rubles and buy yen： Sell Rbl 5 million and buy 101 million（520.20）nsell yen and buy dollars：Sell 101 million yen and buy $1.01 million（1010.01）nProfit of

32、$1 million n= ($1.01-$1) million =0.01 million =10000$n or 1% of the initial amount(利润率为利润率为1%）nAn example of triangular arbitragen反之也成立。检验过程：根据汇率折算方式，有下式成立：反之也成立。检验过程：根据汇率折算方式，有下式成立：（SRbl/$ S$/ S/Rbl）-1 S$/Rbl S￥/$ SRbl/￥ 由于由于S$/Rbl S￥/$ SRbl/￥0.21000.049500.99 1n却从买进分母货币入手，这样的套利结果是：却从买进分母货币入手，这样的套

33、利结果是：n仍以仍以100万美元出发，就是卖出美元买进日元、然后万美元出发，就是卖出美元买进日元、然后卖出日元买进卢布，最后卖出卢布买进美元，则有：卖出日元买进卢布，最后卖出卢布买进美元，则有：n$100万万1/0.011/20.201/5=99.01n亏损：亏损：99.011000.99万美元。万美元。PPP的图示的图示: Which way do you go?Inflation Rate Differential (%)home inflation rate foreign inflation rate% D D in the foreign currencys spot rate- 2

34、- 42413- 1- 3PPP line外国商品的外国商品的购买力上升购买力上升外国商品的外国商品的购买力下降购买力下降CD PPP的图示的图示: Which way do you go?n例如,D点,表示国内通货膨胀比国外低3%,但是,外币只贬值了2%,因此,出现了购买力差别,外国商品的购买力低于本国商品的购买力.nPPP理论表明在这个例子中外币应该贬值3%,以便完全抵销3%的通货膨胀差额.n由于外币没有疲软到这种程度,本国消费者不再继续购买外国的商品,外币需求下降,使外币疲软到PPP理论所预计的水平,因此,D点应移向PPP线nPPP线右边或下面的所有点表示对本国商品的购买力大于对外国商品

35、的购买力PPP的图示：的图示： Which way do you go?n例如,C点,表示国内通货膨胀比国外高4%,但是,外币只升值了1%,因此,出现了购买力差别,外国商品的购买力高于本国商品的购买力.nPPP理论表明在这个例子中外币应该升值4%,以便完全抵销4%的通货膨胀差额.n由于外币没有坚挺到这种程度,本国消费者不再继续购买本国的商品,而是转而购买外国商品,外币需求上升,使外币坚挺到PPP理论所预计的水平,因此,C点应移向PPP线nPPP线左边或上面的所有点表示对外国商品的购买力大于对本国商品的购买力.四、四、 Interest Rate Parity, or IRPCovered In

36、terest Arbitrage Unconered Interest Arbitrage Ftd/f / S0d/f= (1+id)/(1+if)t= EStd/f / S0d/f = (1+pd)/(1+pf)t where S0d/f = todays spot exchange rate EStd/f= expected future spot rate Ftd/f= forward rate for time t exchange i= a countrys nominal interest rate p= a countrys inflation rate Forward prem

37、iums and discounts are entirely determined by interest rate differentials.(远期升贴水几乎完全由利率差异所决定)Interest rate parity:Which way do you go? Which currency do we borrow and which currency do we lend in order to take advantage of a market disequilibrium? If Ftd/f/S0d/f (1+id)/(1+if)t then so.Ftd/f must fal

38、lSell f at Ftd/fS0d/f must riseBuy f at S0d/fid must riseBorrow at id if must fall Lend at ifIf Ftd/f/S0d/f (1+i$) / (1+i) 1.041667 1.038835The fx and Eurocurrency markets are not in equilibrium.Covered interest arbitrage1. Borrow $1,000,000 at i$ = 7%2. Convert $s to s at S0$/ = $1.20/3. Invest s a

39、t i = 3% 4. Convert s to $s at F1$/ = $1.25/5. Take your profit: $1,072,920$1,070,000 = $2,920+$1,000,000+833,333-$1,000,000-833,333-$1,070,000+858,333+$1,072,920-858,333 RulesnIf If Ftd/f/S0d/f (1+id)/(1+if)t ,then borrow at id, buy S0d/f ,lend at id, and sell Fd/fnIf If Ftd/f/S0d/f (1+id)/(1+if)t

40、,then borrow at if, sell Sd/f, lend at id,and buy F0d/f .Forward rates as predictors of future spot ratesnFtd/f = EStd/f that is :Forward rates are unbiased estimates of future spot rates.nFtd/f / S0d/f = EStd/f / S0d/f that is: forward premiums reflect the expected change in the spot exchange rate.

41、nForward rates are not good predictors of future spot rates over short forecasting horizons.nAt the very least, the long time holds.Exchange rate Timet 2 t 3 t 4 t 1 S1S2S3S4F1F2F3ErrorErrorErrort 2 t 3 t 4 t 1 The forward rate available today (Ft,t+1), time t, for delivery at future time t+1, is us

42、ed as a “predictor” of the spot rate that will exist at that day in the future. Therefore, the forecast spot rate for time St2 is F1; the actual spotrate turns out to be S2. The vertical distance between the prediction and the actual spot rate is the forecast error.When the forward rate is termed an

43、 “unbiased predictor of the future spot rate,” it means that the forward rateover or underestimates the future spot rate with relatively equal frequency and amount. It therefore “misses the mark” in a regular and orderly manner. The sum of the errors equals zero. Forward Rate as an Unbiased Predicto

44、r for Future Spot RateIRP的图示： Which way do you go?Interest Rate Differential (%)home interest rate foreign interest rateForwardPremium (%)ForwardDiscount (%)- 2- 42413- 1- 3IRP lineABXY4ZWiH-iF=2%P=4%本国投资者本国投资者到外国投资到外国投资有利有利iH-iF=-3%P=-1%本国投资者本国投资者到外国投资到外国投资有利有利iH-iF=3%P=-2%外国投资者外国投资者到本国投资到本国投资有利有利i

45、H-iF=-1%P=-3%外国投资者外国投资者到本国投资到本国投资有利有利Managing for Value: How IRP Affects IBMs HedgenIBM has some foreign subsidiaries based in Brazil. nIBM considers hedging any funds that its Brazilian subsidiaries plan to remit to the parent.nForward contracts con be used to hedge the future transactions in which

46、 the Brazilian real will be converted into dollars.nDue to IRP, however, the forward rate of the Brazilian real is unfavorable relative to its spot rate.nSince the Brazilian interest rate is higher than the U.S. interest rate, IRP forces the forward rate of Brazilian real to exhibit a discount.nThis

47、 exchange rate may not be as favorable as the prevailing spot rate at that future time, even if todays spot rate declines over time.International Fisher relation (Fisher Open hypothesis)Recall the Fisher relation: (1+i) = (1+)(1+p)If real rates of interest are equal across currencies, from the IRP,

48、then(1+id)/(1+if)t= (1+d)(1+pd)t / (1+f)(1+pf)t= (1+pd)/(1+pf)tThis relation is called the international Fisher relation. International Fisher relation (Fisher Open hypothesis)(1+id)/(1+if)t = (1+pd)/(1+pf)t Speculators will force this relation to hold on averagenIf real rates of interest are equal

49、across countries (d = f ), then interest rate differentials merely reflect inflation differentialsnThis relation is unlikely to hold at any point in time, but should hold in the long runIFE的图示： Which way do you go?Interest Rate Differential (%)home interest rate foreign interest rate- 2- 42413- 1- 3

50、IFE line% D D in the foreign currencys spot rateBA投资外国取得投资外国取得高的回报率高的回报率投资外国取得投资外国取得较低的回报率较低的回报率亚洲金融危机期间亚洲金融危机期间IFE的运用的运用n根据根据IFE,在亚洲危机前夕在亚洲危机前夕,高利率将不会吸引高利率将不会吸引外国投资外国投资,因为高利率意味着汇率的下降因为高利率意味着汇率的下降.n但是但是,由于一些国家中央银行实行的是固定汇由于一些国家中央银行实行的是固定汇率度率度,仍然吸引了大量的外国投资仍然吸引了大量的外国投资.n不幸的是不幸的是,中央银行的这种努力被市场力量所中央银行的这种努

51、力被市场力量所淹没了淹没了. n结果结果,东南亚国家贬值东南亚国家贬值 彻底消灭了高利率的收彻底消灭了高利率的收益益. Summary: Intl parity conditionsInterest rates(1+id)/(1+if)tInflation rates(1+pd)/(1+pf)tEStd/f / S0d/fExpected changein the spot rateFtd/f / S0d/fForward-spotdifferentialInterestrate parityRelativePPPInternational Fisher relationForward rat

52、es as predictorsof future spot ratesExchange Rate ForecastingnNumerous foreign exchange forecasting services exist, many of which are provided by banks and independent consultants.nSome multinational firms have their own in-house forecasting capabilities.nPredictions can be based on elaborate econom

53、etric models, technical analysis of charts and trends, intuition, and a certain measure of gall.Exchange Rate ForecastingA. Market-Based ForecastingExchange rate forecasts are provide by several of the international parity conditions.nEStd/f=Ftd/f forward paritynEStd/f=S0d/f(1+id)/(1+if)t a combinat

54、ion of forward and interest rate paritynEStd/f=S0d/f(1+pd)/(1+pf)t relative PPPMarket-Based ForecastingnThe beauty of market-based forecasts is that anyone with access to a financial newspaper can make them.基于市场的预测法看起来很美！基于市场的预测法看起来很美！nUnfortunately,一方面，一方面，它在短期预测上效果差。它在短期预测上效果差。 these forecasts do

55、not work well in the short term.nThe international parity conditions provide a signal as to which direction a currency should change in equilibrium. 相对于每天汇率的波动而言，相对于每天汇率的波动而言， this signal is weak。因此，它可用于一年以上的汇率。因此，它可用于一年以上的汇率预测。预测。Market-Based Forecastingn另一方面，国际平价条件对于长期名义汇率的预测也许另一方面，国际平价条件对于长期名义汇率的

56、预测也许有是用的，但对于实际汇率的预测却是少有帮助的。有是用的，但对于实际汇率的预测却是少有帮助的。Although the international parity conditions are useful for forecasting long-term trends in nominal exchange rate, they are less helpful in forecasting real exchange rates because real exchange rates are assumed to be constant in the international parity relations.因为在平价条件因为在平价条件中假定实际汇率是不变的。中假定实际汇率是不变的。n而而实际汇率预测在管理经营外汇风险中至关重要实际汇率预测在管理经营外汇风险中至关重要。The real exchange ratenThe real exchange rate is the nominal exchange rate adju