andUncoveredInterestRateParity(国际金融(香港

Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,53,Covered and Uncovered Interest Rate Parity,WONG Ka Fu,26th January 2000,Comparing Local and Foreign Prices,Prices within a country,Prices across countries,P (in home currency),P* (in foreign currency),1 HD = x FD = 1/e FD, i.e., e HD = 1 FD,P vs. eP*,t,t+1,Time,For example,t=January,t+1=February,Buy Asset: pay P,t,Return on home asset,Sell asset: get P,t+1,May receive dividend D,t+1,between time t and time t+1,Return = P,t+1,+D,t+1,-P,t,Rate of Return = (P,t+1,+D,t+1,- P,t,)/P,t,Return on a,home,asset,P,t+1,- P,t,dividends or any interest payments to the asset holder,D,t+1,P,t+1,- P,t,+ D,t+1,Rate of Return on a,home,asset,Return / cost of asset at time of purchase / year,Home asset in home currency,( P,t+1,+ D,t+1,- P,t,)/ P,t,= ( P,t+1,+ D,t+1,) / P,t, - 1,t,t+1,Time,For example,t=January,t+1=February,Buy Asset: pay e,t,P,t,*,Return on foreign asset,Sell asset: get e,t+1,P,t+1,*,May receive dividend D,t+1,*,between time t and time t+1,Return =,e,t+1,(P,t+1,*,+D,t+1,*,)/ -,e,t,P,t,*,Rate of Return,= ,e,t+1,(P,t+1,*,+D,t+1,*,)/ -,e,t,P,t,*,/,e,t,P,t,*,Return on a,foreign,asset,A,foreign,investor invests in a foreign asset,P,t+1,*,- P,t,*,+ D,t+1,*,= P,t+1,*,+ D,t+1,*,- P,t,*,A,home,investor invests in a foreign asset,e,t+1,(P,t+1,*,+ D,t+1,*,) - e,t,P,t,*,Rate of Return on a,foreign,asset,Foreign asset in home currency, e,t+1,( P,t+1,*,+ D,t+1,*,) - e,t,P,t,*, / ( e,t,P,t,*,),= e,t+1,( P,t+1,*,+ D,t+1,*,) / ( e,t,P,t,*,) - 1,= (,e,t+1,/ e,t,) ,( P,t+1,*,+ D,t+1,*,) / P,t,*, - 1,Expectations,Lottery 1,0.5 probability to win 1000,0.5 probability to win 0,Expect to win,0.5 1000 + 0.5 0 = 500,Expectations,Lottery 2,0.2 probability to win 1000,0.3 probability to win 500,0.5 probability to win 0,Expect to win,0.2 1000 + 0.3 500 + 0.5 0 = 350,Expectations,Lottery 3,P,i,= f(y,i,) probability to win y,i,Expect to win,E,t,(y) =,i,P,i,y,i,=,i,f(y,i,) y,i,Expectations,Lottery 4,f(y) probability to win y,Expect to win,E,t,(y) = E(y|,information available at time t,),=,y,f(y) y dy,Replacing,assets,with,deposits,greatly simplifies the algebra:,Some unknown quantities become known:,P,t+1,= 1,P,t,= 1,D,t+1,= R,t,= home interest rate,P,t+1,*,= 1,P,t,*,= 1,D,t+1,*,= R,t,*,= foreign interest rate,The only unknown at time t is e,t+1,Expected return and expected rate of return,Expected return on a home asset:,E,t,(P,t+1,+ D,t+1,- P,t,),= E,t,(P,t+1,+ D,t+1,) - P,t,Expected rate of return on a home asset:,E,t,(P,t+1,+ D,t+1,) / P,t,- 1 ,= E,t,(P,t+1,+ D,t+1,) / P,t,- 1,Rate of return of,home,deposit,E,t,(P,t+1,+ D,t+1,) / P,t,- 1,P,t+1,= 1,P,t,= 1,D,t+1,= R,t,= home interest rate,E,t,(1,+ R,t,) / 1 - 1 = R,t,Expected return and expected rate of return,Expected return on a,foreign,asset:,E,t, e,t+1,(P,t+1,*,+ D,t+1,*,) - e,t,P,t,*,= E,t, e,t+1,(P,t+1,*,+ D,t+1,*,) - e,t,P,t,*,Expected rate of return on a,foreign,asset,E,t, (e,t+1,/ e,t,) (P,t+1,*,+ D,t+1,*,) / P,t,*, - 1 ,= E,t,(,e,t+1,/ e,t,) (P,t+1,*,+ D,t+1,*,) / P,t,*,- 1,Rate of return on,foreign,deposit,E,t,(e,t+1,/ e,t,) (P,t+1,*,+ D,t+1,*,) / P,t,*,- 1,P,t+1,*,= 1,P,t,*,= 1,D,t+1,*,= R,t,*,= foreign interest rate,E,t,(e,t+1,/ e,t,) (1,+ R,t,*,) / 1 - 1,= E,t,(e,t+1,) / e,t, (1,+ R,t,*,) - 1,Rate of return on,foreign,deposit,E,t,(e,t+1,) / e,t, (1,+ R,t,*,) - 1,= (1,+ R,t,*,) E,t,(e,t+1,) - e,t, + e,t, / e,t,- 1,= E,t,(e,t+1,) - e,t, / e,t,+ 1,+ R,t,*,E,t,(e,t+1,) - e,t, / e,t,+,R,t,*,- 1,E,t,(e,t+1,) - e,t, / e,t,+ R,t,*,RHS = E,t,(e,t+1,) - e,t, / e,t,+ R,t,*,Suppose E,t,(e,t+1,) and R,t,*,fixed,larger e,t,implies,smaller RHS,Suppose e,t,and R,t,*,fixed,larger E,t,(e,t+1,) implies,larger RHS,RHS = E,t,(e,t+1,) - e,t, / e,t,+ R,t,*,Suppose E,t,(e,t+1,) and e,t,fixed,larger R,t,*,implies,larger RHS,Un,covered Interest Parity,Suppose we care only about expected return (say, we are risk neutral),Deposit in home currency,if and only if,the rate of return on the deposit in home currency is,not less than,the deposit in foreign currency,R,t,E,t,(e,t+1,) - e,t, / e,t,+ R,t,*,Equilibrium,if,R,t,= E,t,(e,t+1,) - e,t, / e,t,+ R,t,*,Uncovered Interest Parity,floating,exchange rate regime,If R,t, E,t,(e,t+1,) - e,t, / e,t,+ R,t,*,both home and foreign investors will deposit in home currency,implies,supply foreign currency and demand home currency,initially, e = y HD = 1 FD,now, e = z HD = 1 FD , z E,t,(e,t+1,) - e,t, / e,t,+ R,t,*,= R,t,*,both home and foreign investors will deposit in home currency and,supply foreign currency and demand home currency,CB is committed to a fixed exchange rate and hence has to sell home currency and buy foreign currency,official foreign reserves,increase,Uncovered Interest Parity,fixed exchange rate regime,Both home and foreign investors will deposit in home currency,I.e., larger supply of home deposit and smaller supply of foreign deposit,hence, home interest rate R,t,decreases, i.e. towards equality,R,t,*,increases, i.e. towards equality,until R,t,=,R,t,*,Effect of an increase in the,foreign,deposit interest rate,e,t,RHS,Return on home deposit has to increase,Uncovered Interest Parity,fixed exchange rate regime,Note that only interest rate will adjust to restore the equality,Can the CBs fix the interest rates at some desired level?,No. Not without restrictions on capital flow.,Under,pure fixed,exchange rate regime a CB does not have monetary policy.,Uncovered Interest Parity,floating exchange rate regime,Recall that in R,t,= E,t,(e,t+1,) - e,t, / e,t,+ R,t,*,investors faces,exchange rate risk,when invested in foreign deposits.,Investors are generally,not risk-neutral,.,In general, R,t,E,t,(e,t+1,) - e,t, / e,t,+ R,t,*,R,t,= E,t,(e,t+1,) - e,t, / e,t,+ R,t,*,+,risk premium,investors spend huge amount of money trying to,forecast,e,t+1,Forecasting e,t+1,Uncovered interest parity: R,t,= E,t,(e,t+1,) - e,t, / e,t,+ R,t,*,implies,a forecast of e,t+1,is,E,t,(e,t+1,) =e,t,(R,t,- R,t,*,)+1,Nave forecast (random walk): e,t+1,= e,t,+ u,t+1,E,t,(e,t+1,) =e,t,Forecasting e,t+1,Use linear time series models such as ARIMA,ECO3131: Applied Forecasting Methods,Use non-linear time series models,Howell Tong: Non-linear Time Series,a Dynamical System Approach,Journal of Forecasting,Uncovered Interest Parity,fixed exchange rate regime,In general, R,t,R,t,*,Why?,Because,E,t,(e,t+1,) - e,t,0,Because investors may expect the (fixed) exchange rate to change,and hence risk premium,0,Covered Interest Parity,Is there a way to avoid the exchange risk?,Yes!,By using a,forward contract,to offset your position on foreign exchange.,Hence, may replace,E,t,(e,t+1,),with,the,time t one-period ahead forward rate,f,t,1,R,t,= ,f,t,1,- e,t, / e,t,+ R,t,*,Forecasting e,t+1,Forward rate suggest: f,t,= E,t,(e,t+1,) implies,a forecast of e,t+1,is,E,t,(e,t+1,) = f,t,Empirical evidence of the interest parity,Covered interest parity: generally supported by data,Uncovered interest parity: generally not supported by data,Empirical evidence of the interest parity,Figures from Moosa and Bhatti (1997):,Uncovered interest parity:,Domestic returns and foreign returns,Figure 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),Covered interest parity:,Actual forward rate and CIP forward rate.,Figure 1.5(a), Figure 1.5(b) Figure 1.6(a), Figure 1.6(b), Figure 1.7(a), Figure 1.7(b), Figure 1.8(a), Figure 1.8(b),Uncovered interest parity is,rate of return on home deposit = rate of return on foreign deposit,R,t,= E,t,(e,t+1,) / e,t, (1,+ R,t,*,) - 1,1+R,t,= E,t,(e,t+1,) / e,t, (1,+ R,t,*,),e,t,(1+R,t,) / (1,+ R,t,*,) = E,t,(e,t+1,),ln E,t,(e,t+1,) = ln e,t,+ ln(1+R,t,) - ln(1,+ R,t,*,),E,t,(ln e,t+1,),ln e,t,+ ( R,t,- R,t,*,),ln e,t+1,ln e,t,+ ( R,t,- R,t,*,) +,t,t,= ln e,t+1,- E,t,(ln e,t+1,),ln e,t+1,- ln e,t,=, + ,( R,t,- R,t,*,) +,t,Empirical test of uncovered interest parity,ln e,t+1,- ln e,t,=, + ,( R,t,- R,t,*,) +,t,Test,=0 and =1.,Ordinary Least Squares regression 0,Test of unbiased hypothesis,E,t,(e,t+1,),=,f,t,E,t,ln e,t+1,ln f,t,ln e,t+1,ln f,t,+,t,t,= ln e,t+1,- E,t,(ln e,t+1,),ln e,t+1,- ln e,t,= ln f,t,- ln e,t,+,t,ln e,t+1,- ln e,t,=, + ,(ln f,t,- ln e,t,) +,t,Test,=0 and =1.,Reject hypothesis.,Why did the regression test fail so badly?,Poor approximation?,Risk premium?,Expectation not rational?,Monetary policy working on the short-term interest rate?,Omitted variables?,Buy and sell exchange and interest rates are different? Any arbitrage opportunities?,Dealing with assets returns directly is complicated:,Expected return on a home asset:,E,t,(P,t+1,+ D,t+1,) - P,t,Expected return on a,foreign,asset:,E,t, e,t+1,(P,t+1,*,+ D,t+1,*,) - e,t,P,t,*,= Cov,t, e,t+1,(P,t+1,*,+ D,t+1,*,) + E,t, e,t+1, E,t,P,t+1,*,+ D,t+1,*, - e,t,P,t,*,using the formula Cov(x,y)=E(xy) - E(x)E(y).,Thus, to forecast e,t+1,(E,t, e,t+1,), we would need to know E,t,P,t+1,*,+ D,t+1,*, , E,t,P,t+1,*,+ D,t+1,*, and the Cov,t, e,t+1,(P,t+1,*,+ D,t+1,*,) ,Dealing with assets returns directly is complicated:,E,t,(P,t+1,+ D,t+1,) - P,t,may depends on the economic growth, fiscal and monetary policy (interest rate) of home country.,E,t,P,t+1,*,+ D,t+1,*, may depends on the economic growth, fiscal and monetary policy (interest rate) of foreign country.,Cov,t, e,t+1,(P,t+1,*,+ D,t+1,*,) is the covariance between e,t+1,and (P,t+1,*,+ D,t+1,*,).,If they move in the same direction, Cov,t, e,t+1,(P,t+1,*,+ D,t+1,*,) is positive.,If they move in opposite directions, Cov,t, e,t+1,(P,t+1,*,+ D,t+1,*,) is negative.,Dealing with assets returns directly is complicated:,There are too many unknowns.,Solving these quantities would probably require us to build another economic model(s).,It is difficult for us to get a clear intuition and forecast of future exchange rate.,Want to know more about it?,Krugman and Obstfled,Chapter 13 for the theory,pp. 675-679 for empirical evidence,Chapter 11 of Levi,Search “interest parity” in EconLit ,165 items returned,For examples.,Want to know more about it?,Moosa, Imad A.; Bhatti, Razzaque H. (1997):,International Parity Conditions: Theory, Econometric Testing and Empirical Evidence, Macmillan Press.,Marston, Richard C. (1997): “Tests of Three Parity Conditions: Distinguishing Risk Premia and Systemic Forecast Errors,”,Journal of International Money and Finance, 16(2), pp. 285-303.,