andUncoveredInterestRateParity(國際金融(香港

1、1Covered and Uncovered Interest Rate ParityWONG Ka Fu26th January 20002Comparing Local and Foreign PriceszPrices within a countryzPrices across countrieszP (in home currency)zP* (in foreign currency)z1 HD = x FD = 1/e FD, i.e., e HD = 1 FDzP vs. eP*3tt+1Time For example, t=January,t+1=FebruaryBuy As

2、set: pay PtReturn on home assetSell asset: get Pt+1May receive dividend Dt+1between time t and time t+1Return = Pt+1+Dt+1 -PtRate of Return = (Pt+1+Dt+1 - Pt)/Pt4Return on a home assetzPt+1 - Ptzdividends or any interest payments to the asset holder Dt+1 zPt+1 - Pt + Dt+15Rate of Return on a home as

3、setzReturn / cost of asset at time of purchase / yearzHome asset in home currencyz( Pt+1 + Dt+1 - Pt )/ Pt = ( Pt+1 + Dt+1 ) / Pt - 16tt+1Time For example, t=January,t+1=FebruaryBuy Asset: pay etPt*Return on foreign assetSell asset: get et+1Pt+1*May receive dividend Dt+1*between time t and time t+1R

4、eturn = et+1(Pt+1* +Dt+1* )/ - etPt*Rate of Return = et+1(Pt+1* +Dt+1* )/ - etPt* / etPt*7Return on a foreign asset zA foreign investor invests in a foreign asset zPt+1* - Pt* + Dt+1* = Pt+1* + Dt+1* - Pt*zA home investor invests in a foreign assetzet+1 (Pt+1* + Dt+1* ) - etPt* 8Rate of Return on a

5、foreign assetzForeign asset in home currencyz et+1 ( Pt+1* + Dt+1* ) - etPt* / ( etPt* )= et+1 ( Pt+1* + Dt+1* ) / ( etPt* ) - 1 = (et+1 / et ) ( Pt+1* + Dt+1* ) / Pt* - 1 9ExpectationszLottery 1y0.5 probability to win 1000y0.5 probability to win 0zExpect to winy0.5 1000 + 0.5 0 = 50010Expectationsz

6、Lottery 2y0.2 probability to win 1000y0.3 probability to win 500y0.5 probability to win 0zExpect to winy0.2 1000 + 0.3 500 + 0.5 0 = 35011ExpectationszLottery 3yPi = f(yi) probability to win yizExpect to winEt(y) = i Pi yi = i f(yi) yi12ExpectationszLottery 4yf(y) probability to win yzExpect to winE

7、t(y) = E(y| information available at time t)= y f(y) y dy13Replacing assets with deposits greatly simplifies the algebra:zSome unknown quantities become known:yPt+1 = 1 yPt = 1 yDt+1 = Rt= home interest rateyPt+1*= 1 yPt* = 1 yDt+1*= Rt*= foreign interest ratezThe only unknown at time t is et+1 14Ex

8、pected return and expected rate of returnzExpected return on a home asset:zEt (Pt+1 + Dt+1 - Pt ) = Et (Pt+1 + Dt+1) - PtzExpected rate of return on a home asset:zEt (Pt+1 + Dt+1) / Pt - 1 = Et (Pt+1 + Dt+1) / Pt - 1 15Rate of return of home deposit zEt (Pt+1 + Dt+1) / Pt - 1 zPt+1 = 1 zPt = 1 zDt+1

9、 = Rt= home interest ratezEt (1 + Rt) / 1 - 1 = Rt16Expected return and expected rate of returnzExpected return on a foreign asset:zEt et+1 (Pt+1* + Dt+1* ) - etPt* = Et et+1 (Pt+1* + Dt+1* ) - etPt* zExpected rate of return on a foreign assetzEt (et+1 / et ) (Pt+1* + Dt+1* ) / Pt* - 1 = Et (et+1 /

10、et ) (Pt+1* + Dt+1* ) / Pt* - 1 17Rate of return on foreign deposit zEt (et+1 / et ) (Pt+1* + Dt+1* ) / Pt* - 1 zPt+1*= 1 zPt* = 1 zDt+1*= Rt*= foreign interest ratezEt (et+1 / et ) (1 + Rt* ) / 1 - 1 = Et (et+1 ) / et (1 + Rt* ) - 118Rate of return on foreign depositzEt (et+1 ) / et (1 + Rt* ) - 1=

11、 (1 + Rt* ) Et (et+1 ) - et + et / et - 1= Et (et+1 ) - et / et + 1 + Rt* Et (et+1 ) - et / et + Rt* - 1 Et (et+1 ) - et / et + Rt* 19RHS = Et (et+1 ) - et / et + Rt* zSuppose Et (et+1 ) and Rt* fixed, zlarger et implies zsmaller RHSzSuppose et and Rt* fixed, zlarger Et (et+1 ) implieszlarger RHS 20

12、RHS = Et (et+1 ) - et / et + Rt* zSuppose Et (et+1 ) and et fixed,zlarger Rt* implieszlarger RHS 21Uncovered Interest ParityzSuppose we care only about expected return (say, we are risk neutral)zDeposit in home currency if and only if the rate of return on the deposit in home currency is not less th

13、an the deposit in foreign currencyzRt Et (et+1 ) - et / et + Rt* zEquilibrium if Rt = Et (et+1 ) - et / et + Rt* 22Uncovered Interest Parity floating exchange rate regimezIf Rt Et (et+1 ) - et / et + Rt* zboth home and foreign investors will deposit in home currency implieszsupply foreign currency a

14、nd demand home currencyzinitially, e = y HD = 1 FDznow, e = z HD = 1 FD , z Et (et+1 ) - et / et + Rt* = Rt* zboth home and foreign investors will deposit in home currency and zsupply foreign currency and demand home currencyzCB is committed to a fixed exchange rate and hence has to sell home curren

15、cy and buy foreign currency zofficial foreign reserves increase34Uncovered Interest Parity fixed exchange rate regimezBoth home and foreign investors will deposit in home currency zI.e., larger supply of home deposit and smaller supply of foreign depositzhence, home interest rate Rt zdecreases, i.e.

16、 towards equalityzRt* increases, i.e. towards equalityzuntil Rt = Rt* 35Effect of an increase in the foreign deposit interest rateetRHSReturn on home deposit has to increase36Uncovered Interest Parity fixed exchange rate regimezNote that only interest rate will adjust to restore the equalityzCan the

17、 CBs fix the interest rates at some desired level?zNo. Not without restrictions on capital flow. zUnder pure fixed exchange rate regime a CB does not have monetary policy.37Uncovered Interest Parity floating exchange rate regimezRecall that in Rt = Et (et+1 ) - et / et + Rt* investors faces exchange

18、 rate risk when invested in foreign deposits. zInvestors are generally not risk-neutral. zIn general, Rt Et (et+1 ) - et / et + Rt* Rt = Et (et+1 ) - et / et + Rt* + risk premiumzinvestors spend huge amount of money trying to forecast et+1 38Forecasting et+1 zUncovered interest parity: Rt = Et (et+1

19、 ) - et / et + Rt* impliesza forecast of et+1 is zEt (et+1 ) =et (Rt - Rt* )+1 zNave forecast (random walk): et+1 = et + ut+1zEt (et+1 ) =et39Forecasting et+1 zUse linear time series models such as ARIMA ECO3131: Applied Forecasting MethodszUse non-linear time series modelsHowell Tong: Non-linear Ti

20、me Series a Dynamical System ApproachzJournal of Forecasting40Uncovered Interest Parity fixed exchange rate regimezIn general, Rt Rt* zWhy?zBecause Et (et+1 ) - et 0zBecause investors may expect the (fixed) exchange rate to changezand hence risk premium 041Covered Interest ParityzIs there a way to a

21、void the exchange risk?zYes! zBy using a forward contract to offset your position on foreign exchange.zHence, may replace Et (et+1 ) with the time t one-period ahead forward rate ft,1Rt = ft,1 - et / et + Rt*42Forecasting et+1 zForward rate suggest: ft = Et (et+1 ) impliesza forecast of et+1 is zEt

22、(et+1 ) = ft43Empirical evidence of the interest parityzCovered interest parity: generally supported by datazUncovered interest parity: generally not supported by data44Empirical evidence of the interest parityzFigures from Moosa and Bhatti (1997): yUncovered interest parity: xDomestic returns and f

23、oreign returnsxFigure 1.9(a), Figure 1.9(b) Figure 1.10(a), Figure 1.10(b), Figure 1.11(a), Figure 1.11(b), Figure 1.12(a), Figure 1.12(b)yCovered interest parity: xActual forward rate and CIP forward rate.xFigure 1.5(a), Figure 1.5(b) Figure 1.6(a), Figure 1.6(b), Figure 1.7(a), Figure 1.7(b), Figu

24、re 1.8(a), Figure 1.8(b)45Uncovered interest parity iszrate of return on home deposit = rate of return on foreign depositzRt = Et (et+1 ) / et (1 + Rt* ) - 1z1+Rt = Et (et+1 ) / et (1 + Rt* ) zet (1+Rt ) / (1 + Rt* ) = Et (et+1 )zln Et (et+1 ) = ln et + ln(1+Rt ) - ln(1 + Rt* )zEt (ln et+1 ) ln et +

25、 ( Rt - Rt* )zln et+1 ln et + ( Rt - Rt* ) + t t = ln et+1 - Et (ln et+1 ) zln et+1 - ln et = + ( Rt - Rt* ) + t46Empirical test of uncovered interest parityzln et+1 - ln et = + ( Rt - Rt* ) + tzTest =0 and =1.zOrdinary Least Squares regression 047Test of unbiased hypothesiszEt (et+1 ) = ft zEt ln e

26、t+1 ln ftzln et+1 ln ft + t t = ln et+1 - Et (ln et+1 ) zln et+1 - ln et = ln ft - ln et + tzln et+1 - ln et = + (ln ft - ln et ) + tzTest =0 and =1.zReject hypothesis.48Why did the regression test fail so badly?zPoor approximation?zRisk premium?zExpectation not rational?zMonetary policy working on

27、the short-term interest rate?zOmitted variables?zBuy and sell exchange and interest rates are different? Any arbitrage opportunities?49Dealing with assets returns directly is complicated:zExpected return on a home asset:Et (Pt+1 + Dt+1) - PtzExpected return on a foreign asset:Et et+1 (Pt+1* + Dt+1*

28、) - etPt* = Covt et+1 (Pt+1* + Dt+1* ) + Et et+1 Et Pt+1* + Dt+1* - etPt* using the formula Cov(x,y)=E(xy) - E(x)E(y).Thus, to forecast et+1 (Et et+1 ), we would need to know Et Pt+1* + Dt+1* , Et Pt+1* + Dt+1* and the Covt et+1 (Pt+1* + Dt+1* ) 50Dealing with assets returns directly is complicated:

29、z Et (Pt+1 + Dt+1) - Pt may depends on the economic growth, fiscal and monetary policy (interest rate) of home country.z Et Pt+1* + Dt+1* may depends on the economic growth, fiscal and monetary policy (interest rate) of foreign country.z Covt et+1 (Pt+1* + Dt+1* ) is the covariance between et+1 and (Pt+1* + Dt+1* ). yIf