The Real Exchange Rate, Real Interest Rates, and the Risk Premium. Charles Engel University of Wisconsin

Transcription

1 The Real Exchange Rae, Real Ineres Raes, an he Risk Premium Charles Engel Universiy of Wisconsin 1

2 Define he excess reurn or risk premium on Foreign s.. bons: λ i + Es+ 1 s i = r + Eq+ 1 q r The famous Fama regression emonsraes ha as r r falls, λ falls I verify his for real raher han nominal ineres raes On he oher han, as r r falls (i.e., r r rises), Home currency appreciaes excessively more han can be explaine by expecaions of fuure ineres raes uner UIP Are hese wo finings: cov( λ, r r ) < 0 cov( q q IP, r r ) < 0 arising from he same source? 2

3 No. They seem o say he opposie. cov( λ, r r ) < 0 means when home r is high (relaive o eposis are riskier. r, relaive o average), home cov( q IP, q r r ) < 0 means when home r is high (relaive o r, relaive o average), he home currency is sronger han i woul be uner ineres pariy. Why? Because home eposis are less risky. 3

4 1. Empirical mehoology 2. Empirical resuls 3. Why finings are a puzzle no reaily explainable by complee marke risk premium moels no reaily explainable by elaye overshooing moels 4. Type of moel ha resolves puzzle. 4

5 Real ineres raes an real exchange raes. Rewrie: q E q r r r λ λ + 1 = ( ) ( ) Ierae forwar o ge: where q lim( E q + ) = R Λ j j ( + j + j ) Λ E λ+ j j= 0 j= 0 R E r r r Λ level risk premium ( λ ) We fin evience for long run purchasing power pariy: limeq + j IP q = q Λ j = q 5

6 Daa U.S., Canaa, France, Germany, Ialy, Japan, U.K., an G6 G6 is like oing panel regressions Exchange raes las ay of monh (noon buy raes, NY) Prices consumer price inexes Ineres raes 30 ay Euroeposi raes (las ay of monh) Monhly, June 1979 Ocober

7 VAR mehoology Two ifferen VAR moels: Moel 1: Moel 2: q, i i, i 1 π ( i 1 π ) q, i i, π π (Exensions inclue long erm bon yiels an sock reurns.) Esimae VAR wih 3 lags. (Exension wih 12 lags.) Use sanar projecion measures o esimae r r = i i ( Eπ + 1 Eπ + 1), an IP + j + j j= 0 Then λ is consruce as λ r + E q + 1 q r IP Λ esimae is consruce from Λ = q q q E ( r r r) + q 7

8 Fama Regression in Real Terms: q ˆ = ζ β ˆ q r q qr + uq + 1, + 1 Counry ˆβ 1 90% c.i.( 1 ˆβ ) Canaa ( 0.498,2.222) ( 0.632,2.908) ( 0.676,2.800) France ( 0.117,3.269) (0.281,3.240) ( 0.125,3.602) Germany ( 0.015,3.689) (0.687,4.458) (0.589,4.419) Ialy ( 1.336,2.056) ( 1.087,2.136) ( 1.358,2.328) Japan (0.768,3.860) (0.746,4.300) (0.621,4.441) Unie Kingom (0.854,4.042) (0.873,4.614) (1.039,4.846) G (0.318,4.548) (0.510,3.932) (0.473,4.005) 8

9 Regression of q on rˆ ˆ r : q = β + β ( rˆ r ˆ ) + u Counry ˆβ 1 90% c.i.( ˆβ 1) Canaa ( 62.15, 34.88) ( 94.06, 31.41) ( , 27.34) France ( 32.65, 8.62) ( 44.34, 1.27) ( 54.26,1.75) Germany ( ) ( 85.97, 25.35) ( , 19.38) Ialy ( 51.92, 26.28) ( 67.63, 16.36) ( 90.01, 13.70) Japan ( 29.69, 9.72) ( 42.01, 1.05) ( 46.53, 4.33) Unie Kingom ( 31.93, 5.98) ( 40.19, 3.08) ( 55.94,4.08) G ( 55.60, 32.80) ( 73.17, 23.62) ( 82.87, 21.74) 9

10 Regression of ˆ Λ on rˆ ˆ r : Λ ˆ = ˆ ˆ + β 0 + β 1( r r ) u+ 1 Counry ˆβ 1 90% c.i.( ˆβ 1) Canaa (15.12,32.10) (12.62,51. 96) (11.96,63.71) France (1.06,25.72) ( 2.56,36.25) ( 6.98,42.40) Germany (19.66,49.78) (9.34,57.59) (3.68,69.36) Ialy (17.58,37.48) (14.98,48.32) (12.51,58.54) Japan (4.76,25.66) ( 0.45,37.08) (0.91,38.87) Unie Kingom (0.33,27.86) (0.39,34.46) ( 8.70,46.45) G (20.62,43.13) (16.89,54.62) (16.78,60.89) 10

11 Implicaions: cov(, r r ) 0 λ < (Fama regression in real erms) r r Eλ j r r j= 0 cov( Λ, ) = cov( +, ) > 0 (from VAR esimaes) λ + > for some j (as in previous figure) cov( E j, r r ) 0 Explaining cov(, r r ) 0 λ < an cov( Eλ+ j, r r ) > 0 is a challenge for ris k premium moels when r r is high, he home currency is boh riskier han average an expece o be less risky han average. Noaion: + 1 = q+ 1 q 11

12 E ˆ ( ˆ ˆ λ+ k = β λ k r r ) G Monhs

13 Figure 2 plos slope coefficiens from he following regressions (Daa are monhly, ineres raes are 1 monh, en of monh. For his slie, U.S. relaive o weighe average of res of G7): q = k α + qk βqk( r + r ) β qk = cov( q + k, r r )/ var( r r ) IP q + = α + β ( r r ) β = cov( q IP +, r r )/var( r r ) k Rk Rk Rk k (Real ineres raes hemselves are esimaes) IP Difference beween q + an q + kis Λ = q q +. IP + k + k k k Λ + k: So ifference in lines is β Λ k = cov( Λ + k, r r )/var( r r ) 13

14 q = k α + qk βqk( r + r ), IP q α β + = + ( k Rk Rk r r ) G6 Levels Monhs

15 Puzzle is cov( λ, r ) < 0 bu cov( Λ, r ) > 0 Can complee markes risk premium moels explain his? m 1, m+ are logs of home, foreign sochasic iscoun facors + 1 r = E ( m m ) (var m var m ) λ = 2 m+ 1 m+ 1 (var var ) Moels are specifie o accoun for UIP puzzle. When Home relaive risk increases so λ goes up, Home precauionary saving increases sufficienly ha r goes own. These preference assumpions mus imply cov( Λ, r ) < 0. 15

16 q = k α + qk βqk( r + r ), IP q α β + = + ( k Rk Rk r r ), an Moel G6 Levels Monhs

17 Delaye overshooing o moneary shocks has been explaine in moels of elaye reacion in he foreign exchange marke Froo an Thaler (1990), Bacchea an van Wincoop (2010) The impulse response funcion for q sars off negaive, eclines for awhile, an hen increases. Moel can give us cov( λ, r ) < 0, an even cov( + 1, r ) < 0, bu implies cov( Λ, r ) < 0 The real exchange rae unerreacs o he increase in real ineres raes, raher han overreacing. 17

18 q = k α + qk βqk( r + r ), IP q α β + = + ( k Rk Rk r r ), an Moel G6 Levels Monhs

19 Moels wih a single economic variable riving r an λ : = j= 0 r aε j λ c ε j = j j j= 0 1. Single facor moels: r = k λ 2. Uniirecional moels: aj same sign j, an c j same sign j. These are common assumpions. Someimes boh are mae. Assumpion 2, especially, seems sensible. Theorem: we canno ge cov( λ, r ) < 0 an cov( Λ, r ) > 0 Nee a leas wo shocks. One mus maer in shor run an eliver cov( λ, r ) < 0. The oher mus be more persisen an have cov( E λ +, r ) > 0 in orer o ge cov( Λ, r ) > 0. j 19

20 An example of a moel ha woul work: Sanar New Keynesian, excep u.i.p. oes no hol (goo saring place because of implicaions uner u.i.p.): Open economy Phillips curve: π π = δq + βe ( π+ 1 π+ 1) Taylor rule: i i = σ ( π π) + ε, ε = ρε ε 1 + ς Liquiiy premium shor erm bons have value as collaeral λ = α i Eπ+ 1 ( i Eπ+ 1) η, α > 0 η exogenous increase in value of Foreign bons α i Eπ + 1 ( i Eπ + 1 ) Home bons are more value as collaeral uring Home moneary policy conracion 20

21 This can accoun for cov( E + 1, r ) < 0 an cov( Λ, r ) > 0 when η is more volaile bu less persisen han αε. λ = α i Eπ+ 1 ( i E π+ 1) η η Foreign asses more valuable. Foreign currency appreciaes, increasing inflaionary pressure in Home. r. This ens o give us cov( λ, r ) < 0 an cov( E + 1, r ) < 0 as in u.i.p. puzzle ε Home moneary conracion, r. Relaive liquiiy value of Home asses rises, ens o make cov( λ, r ) > 0. If η is more volaile, i ominaes shor run behavior of cov( λ, r ). If ε is sufficienly persisen, i ominaes long run behavior an eermines cov( Λ, r ). 21

22 q (1 + α)(1 ρβ) 1 ε ε = + δ (1 + α)( σ ρε ) + (1 ρεβ)(1 ρε) 1 + σδ(1 + α) η α(1 ρ β)(1 ρ ) 1 + σδ = ε ε λ ε η δ(1 + α)( σ ρε ) + (1 ρεβ)(1 ρε) 1 + σδ(1 + α) α(1 ρ β) 1 σδ ε + ε Λ = δ(1 + α)( σ ρε ) + (1 ρεβ)(1 ρ ε) 1 + σδ(1 + α) η (1 ρ β)(1 ρ ) σδ ε ε r = ε + δ (1 + α)( σ ρε ) + (1 ρεβ)(1 ρε) 1 + σδ(1 + α) η 22

23 Conclusions: A new puzzle. Our moels for he UIP puzzle on seem aequae. Visually, he fining of cov( Λ, r ) > 0 may be more imporan han he UIP puzzle, cov( λ, r ) < 0. Unersaning his maers: 1. For unersaning exchange raes 2. For unersaning macroeconomics an finance. 23

24 q = k α + qk βqk( r + r ), IP q α β + = + ( k Rk Rk r r ) G6 Levels Monhs