Exchange Rates and Interest Rates: Levels and Changes of the Price of Foreign Currency

Transcription

1 Exchange Raes and Ineres Raes: Levels and Changes of he Price of Foreign Currency Charles Engel Universiy of Wisconsin Conference in Honor of James Hamilon, Federal Reserve Bank of San Francisco, Sepember 8-9, 204. Paper formerly called The Real Exchange Rae, Real Ineres Raes and he Risk Premium.

2 There are wo well-known puzzles concerning exchange raes and ineres raes:. The Fama puzzle: he foreign exchange risk premium on a counry s shor erm ineres bearing asses covaries posiively wih is ineres rae. 2. The excess volailiy in levels of he exchange rae: When a counry s ineres rae rises, is currency appreciaes, bu much more han can be accouned for in Dornbusch-syle models ha assume uncovered ineres pariy (i.e., no risk premium.) These wo puzzles boh involve he foreign exchange risk premium and is relaionship o ineres raes. Are hey really capuring he same phenomenon? 2

3 The answer is NO. They say, in a sense, he opposie. Wha has been hereofore unnoiced is ha we have a puzzle squared: he soluions pu forh o accoun for one of he puzzles go in he wrong direcion for he oher puzzle. This paper:. Documens he wo puzzles in a simple unified framework 2. Explains why our models of he Fama puzzle don explain he volailiy puzzle (and really canno be easily modified so hey will.) 3. Skeches a simple model ha can accoun for boh based on he unmeasured liquidiy reurn o shor-erm asses 3

4 Fama puzzle: Define he excess reurn on foreign shor-erm deposis (in his sudy, home is he U.S. and foreign are he oher G7 counries): ρ + i + s + s i We end o hink of he deposi raes as riskless. The risk is from he foreign exchange rae. Fama puzzle: ( r r ) cov ρ +, > 0 Tha is, whaever is driving he risk from foreign exchange (covariance risk, e.g.) covaries wih whaever drives he ineres differenial. Like a covariance of covariances. Noe ha I use r r. All of he heories call for real ineres raes 4

5 Recen Models of he Fama Puzzle I has been hard o explain, hough recen work has offered explanaions based on () non-sandard preferences, or on (2) raional inaenion. Models of risk premiums wih sandard expeced uiliy don work: Bekaer e. al. (997); Backus e. al. (200) () Models based on Campbell-Cochrane preferences or Epsein-Zin-Weil preferences: Verdelhan (200); Colacio and Croce (20); Bansal and Shaliasovich (203); Lusig, Roussanov, Verdelhan (20) (2) Models based on delayed overshooing : Froo and Thaler (990); Eichenbaum and Evans (995); Bacchea and van Wincoop (200) 5

6 Excess Volailiy T Le s be he ransiory (in Beveridge-Nelson sense) componen of he exchange rae. IP j= 0 ( ) ( ) s = E i i i i -- he ineres pariy level of he saionary T IP componen of he exchange rae. Tha is, if ineres pariy held, s = s. T IP In Dornbusch-syle models, ( s s r r ) T IP We find ( s s r r ) cov, > 0 cov ( = ), > 0 Tha is, exchange rae comoves in he righ direcion bu is excessively volaile. 6

7 ++ j j= 0 T IP s s = E ( ρ ρ). So, he excess volailiy puzzle can be expressed as: ( ) ( ) T IP s s r r E ρ 0 ++ j r r cov, = cov, < 0 The high-ineres rae currency is less risky Bu he Fama puzzle was: ( r r ) cov ρ +, > 0 The high-ineres rae is more risky For some j > 0, cov ( ρ ++ j, ) our models. E r r swiches sign. Tha is he challenge for 7

8 Daa U.S., Canada, France, Germany, Ialy, Japan, U.K., and G6 G6, a weighed average of he six non-u.s. counries, smoohs ou some of he idiosyncraic movemens Exchange raes las day of monh (noon buy raes, NY) Prices consumer price indexes Ineres raes 30-day Eurodeposi raes (las day of monh) Monhly, June 979 Ocober

9 Fama Regressions: ρ = ζ + β ( i i ) + u 979:6-2009:0 + s s s, + Counry βˆs 90% c.i.( βˆs ) Canada 2.27 (.86,3.355) France.26 (-0.7,2.603) Germany 2.09 (0.599,3.583) Ialy (-0.680,.359) Japan 3.73 (2.390,5.036) U.K (.70,5.225) G (0.769,4.64) 9

10 Empirical procedure Esimae a VECM in nominal exchange raes, relaive prices and relaive ineres raes: 3 0 R j j j R = + ( ( )) j+ 2 j+ 3 j j= 3 R 0 R ( j j j R ) = c + g2( s ( p p )) + g23i + c2 s j+ c22π j+ c23 i j j= ( π ) s s c g s p p g i c s c c i π 3 R R 0 R j j j R = + 3( ( )) j+ 32 j+ 33 j j= ( π ) i i c g s p p g i c s c c i 0

11 Firs, is real exchange rae saionary? Tes of g g 2 < 0 : Esimae and boosrap criical values: Counry g g 2 Criical value 5% Criical value 0% Canada France Germany Ialy Japan U.K G Null rejecions are always sronger for G6 in his sudy. 2. I is ineresing ha including ineres raes as a covariae increases power of es for uni roo in real exchange rae.

12 Using sandard projecion mehods, we can calculae esimaes of r ++ j j= 0 and E ( ρ ρ). There are wo senses in which we measure error: r r r and E ( ρ ρ) wih ++ j j= 0. Esimaion error (for VECM coefficiens.) To handle his, I boosrap all sandard errors. 2. The VECM does no conain all informaion ha markes use in forming expecaions. a. There is no way o eliminae his problem. For robusness, I add variables o VECMs ha conain informaion (sock reurns, gold price, oil price, long-erm bond yields.) b. Also, ry longer lags in VECM (hough AIC and BIC argue for very shor lags.) 2

13 Fama Regression in Real Terms: ρ = ζ + β ( rˆ rˆ) + u 979:6-2009:0 + s s s, + Counry βˆs 90% c.i.( βˆs ) Canada (-0.670,2.665) France.482 (0.076,3.004) Germany.733 (0.643,4.53) Ialy 0.43 (-0.88,2.227) Japan (0.985,4.320) U.K..850 (0.654,3.77) G6.983 (0.644,3.969). G6 average is significan. 2. All coefficien esimaes for individual counries are negaive. Join boosrap es of null hey are all 0 is srongly rejeced. 3

14 Regression E ˆ ( ρ ρ) = β + β (ˆ r rˆ) + u ++ j 0 + j= 0 979:6-2009:0 Counry βˆs 90% c.i.( βˆs ) Canada ( , -5.44) France ( , 0.200) Germany ( , -0.62) Ialy ( , ) Japan (-37.67, -2.77) U.K (-27.30,.060) G ( , ). Confidence inervals are wide, reflecing mosly serial correlaion in residual. 2. G6 average is significan. 3. All coefficien esimaes for individual counries are posiive. Join boosrap es of null hey are all 0 is srongly rejeced. 4

15 Slope coefficiens and 90% confidence inerval of he regression: ˆ j E ( ρ + ) = ζ + β rˆ rˆ + u ( ) j j j 5

16 Slope coefficiens and 90% confidence inerval of he regression: ˆ j E ( ρ + ) = ζ + β i i + u ( ) j j j 6

17 Slope coefficiens and 90% confidence inerval of he regression: j ρ + = ζ + β ˆ ˆ j j j r r + u ( ) 7

18 Slope coefficiens and 90% confidence inerval of he regression: j ρ + j = ζ j + βj i i + u ( ) 8

19 Slope coefficiens and 90% confidence inerval of he regression: ˆ j E ( ρ + ) = ζ + β rˆ rˆ + u ( ) j j j 2-lag VECM 9

20 Slope coefficiens and 90% confidence inerval of he regression: ˆ j E ( ρ + ) = ζ + β rˆ rˆ + u ( ) j j j Sock prices, gold price, oil price, long-erm bond yields in VECM 20

21 An inuiive explanaion of why he models buil o explain he Fama puzzle canno explain he excess volailiy puzzle: The key economic behavior in he models is underreacion. When rises, invesors buy foreign asses, bu hey underreac. r r In he risk premium sory, hey underreac because he foreign exchange risk has increased for home invesors. In he raional inaenion sory, hey underreac because no everyone rebalances heir porfolio. T IP Bu he volailiy puzzle, ( s s r r) cov, > 0, calls for overreacion. When r r rises, he exchange rae ends o rise more han i would under ineres pariy. The sories for he volailiy puzzle necessarily ge hings wrong for he level of he exchange rae. 2

22 Some algebraic inuiion Models of he Fama puzzle, ( ) swich in sign for ( cov E ) j, r r cov ρ +, r r > 0, are no able o explain a ρ ++ as j increases. Why no? They have a single economic facor driving ρ + and economic logic of he models dicaes hose covary posiively. Bu cov ( E ) ( ) ρ++ j, r r cov Eρ+, r j r j =. r r. The Unless he single facor driving r r has some funky dynamics, if ( ρ + r r ) > hen we will also have ( Eρ + r j r j) cov, 0 cov, > 0. 22

23 Review of foreign exchange risk premium m, m + + are logs of home, foreign sochasic discoun facors Under complee markes, ( ) s + p p s + p p = m m Since r = + var ( ) Em 2 m + and = r + var ( ) Em 2 m + Then r r = E ( m m ) + (var m var m ) E (var m var m ) ρ + =

24 . Campbell-Cochrane preferences (Verdelhan, 200) 2. EZ preferences, idenical preferences (Bansal and Shaliasovich, 203) 3. EZ preferences, asymmeric preferences (Lusig, e. al. 20) I will use (2) as an example. The ohers are similar. 24

25 Under EZ preferences, le θ be he coefficien of RRA. Assume θ >. Le ε be he ineremporal rae of subsiuion, >0. H F g +, g + are innovaions o growh raes of consumpion. i Assume var( ) g + is AR() wih serial correlaion of η i and muually ind. ( ( H ) ( F )) E ρ = 2θ var g var g ( ( ) ) ( H ) ( F θ + θ / ε ) + r + ( ) r r = 2 var g va g ( ) 2( ( ) ) ( H ρ ) 4θ θ θ ε ( ) ( ( F )) cov, r r = + / var var g + var var g Bu ( ) 2( ( ) ) ( ) 4 ( ) ( ( )) cov ρ, r r = θ θ + θ / ε η var var g + η var var g j H j F ++ j H + F + Obviously, here is no change in sign. 25

26 Wih delayed overshooing here is a moneary conracion in, for example, he foreign counry. r r rises. IP The home currency should depreciae, so s should rise. Some invesors are inaenive, so s does no rise as much as i should. We can expec furher depreciaion of home currency. In essence, because invesors are inaenive, when r r rises, i akes ime for invesors o shif o he foreign asse. As his shifing occurs over ime, he value of he foreign asse keeps being driven up, and holders of he foreign asse receive an excess reurn. When all he invesors have shifed, he excess reurn disappears. Bu i never reverses. Tha is, ( ρ + r r ) > and also ( E j r r) cov, 0 cov ρ ++, 0. 26

27 A skech of a model ha migh work The key is ha here mus be some wo economic forces, one ha leads o an underreacion and one o an overreacion. If he former force is more volaile in he shor run, i can accoun for he Fama puzzle. If he laer is more persisen, i can accoun for he volailiy puzzle. Incorporaing a liquidiy reurn seems like a naural candidae. Cerainly recenly he demand for shor erm dollar asses, valued for heir liquidiy (usable as collaeral, e.g.) seems o have had a role in driving he exchange rae. I is also naural o hink ha here are facors ha give he ex ane excess reurn and ineres raes differen correlaions. The paper lays ou a simple model in which a liquidiy premium is incorporaed in a very sandard New Keynesian open-economy model. 27

28 On he one hand, a he margin when he Fed raises he ineres rae, liquid asses are more valuable on he margin. Dollar asses earn a liquidiy reurn which appears as a smaller pecuniary reurn. This can accoun for he excess volailiy when ineres raes rise. The dollar is sronger boh because of persisen ineres rae increases and because of higher liquidiy value. Bu also, ineres raes may respond endogenously o liquidiy shocks. Suppose here is a shock o he financial sysem ha reduces he liquidiy value of foreign asses. There is a drop in demand for hose asses, leading o a depreciaion of he foreign currency. This increases inflaionary pressure in he foreign counry, leading he cenral bank o increase he ineres rae. As in he risk-premium and delayed overshooing sories, he desirabiliy of he asse is lower from non-pecuniary facors when he ineres rae is high. 28

29 Conclusions The wo puzzles concerning ineres raes and exchange raes are no plausibly explained by a single economic force. I propose an example of a model ha could work, bu here are oher possibiliies (peso problem, bandwagon effecs, ), possibly in conjuncion wih he models of he Fama puzzle. These puzzles have implicaions beyond inernaional finance. The currency is he perhaps he only naional asse. Is pricing is deermined only by aggregae facors, and so may be imporan in undersanding how aggregae shocks affec asse prices. 29