Forecasting exchange rates of major currencies with long maturity forward rates

Transcription

1 Forecasing exchange raes of major currencies wih long mauriy forward raes Zsol Darvas Bruegel, Insiue of Economics of he Hungarian Academy of Sciences and Corvinus Universiy of Budapes Zolán Schepp Universiy of Pécs 24h Annual Congress of he European Economic Associaion Barcelona, Augus 2009

2 Jus anoher ER forecasing model? There is a long sequence of aricles since Meese and Rogoff (1983 The consensus has a skepic view: A model ha forecass well for one exchange rae and ime period will end o perform badly when applied o anoher exchange rae and/or ime period. (Sarno and Taylor, 2002, p

3 Some preliminaries of our resuls The models ouperform he random walk for he mos imporan US dollar exchange raes: 9 currencies of indusrial counries are invesigaed, which represen 75% of he world forex urnover! many oher aricles wih posiive resuls used only 2 o 5 20-year long period ( for evaluaing ou of sample forecas oher aricles generally used only 3 o 5 years (a few panel models have yrs Our resuls are robus wih respec o The nine currency used Model specificaion (3 versions Daa frequency (monhly or weekly Oher aricles don' repor so universal resuls 3

4 Main characerisics of our new model Long mauriy forward exchange raes are saionary Darvas and Schepp (2009 AEL Consequenly: he spo ER and he long mauriy ineres rae differenial mus be coinegraed We can forecas a leas one of he variables wih an error correcion model (ECM ess and our resuls shows ha i is he spo ER which we can forecas We work wih raher simple (loglinear models: one can use OLS-esimaes, here are only a few (2-8 parameers, no specificaion search needed, replicaion is very easy 4

5 Ouline 1. The model 2. Hypohesis es: Boosrap 3. Daa 4. The one period regressions 5. Ou of sample forecasing resuls 6. Does saionariy maer? 7. Inerpreaion 8. Summary 9. Possible exensions 5

6 1. The Model Using Covered Ineres Pariy he forward ER (F (h is: We denoe logarihm of he ineres rae differenial as: *( ( ( 1 1 h h h h i i S F + + = 6 The logarihm of he forward rae: ( ( ( *( ( ( ~ /(1 (1 ln ~ h h h h h i h s f i i i + = + +

7 1. The Model Using Covered Ineres Pariy he forward ER (F (h is: We denoe logarihm of he ineres rae differenial as: *( ( ( 1 1 h h h h i i S F + + = 7 The logarihm of he forward rae: ( ( ( *( ( ( ~ /(1 (1 ln ~ h h h h h i h s f i i i + = + +

8 1. The modelcon d The spo exchange rae (s and he long mauriy ineres ~ ( rae differenial ( h are I (1 i (h The long mauriy forward ER ( is I (0 So he forward ER by definiion implies a coinegraing relaionship: f f ~ ( h = s + h i ( h 8

9 1. The modelcon d ( Coinegraion: a leas one of he variables (eiher s or i should be forecased using he previous period forward rae ~ h Noe: our forecas is no he forward rae iself! The forward rae consiue he coinegraion relaionship and i also converges o is saionary mean in he forecasing period 9

10 1. Model 1s specificaion EQ The simples possible error correcion model (ECM: s = f Long-horizon version: s s p ( h 1 δ + δ ( h ε = δ + δ f + ε, p = 1,..., 0 p p Only 2 parameers should be esimaed long-horizon regressions economeric problems (e.g. size disorion, biased slope esimaes and -saisics see: Berkowiz and Giorgianni (2001 RESTAT Informaion losses P 10

11 1. Model 2nd specificaion MOD Muli-sep ou of sample forecass wih a dynamic ieraion of forecass (non-overlapping samples! ( h s = δ 0+ δ1 f ε 1 + 1, ( h ( h f = φ 0+ φ1 f ε 1 + 2, Only 4 parameers mus be esimaed Avoids informaion loss drawbacks 11

12 1. Model 3rd specificaion VECM s VECM also non-overlapping samples: ξ ξ s k 1 11, j 12, j 1 1 ( h 1, ~ = + + f + h h i ( ~ ( 1 ξ ξ i ε ξ2 j= 1 21, j 22, j 1 γ 2 2, ξ γ ε If k=1 only 8 parameers Muli-sep ou of sample forecass are calculaed wih a dynamic ieraion of forecass 12

13 2. Hypohesis es: Boosrap We compare nesed models (he random walk is nesed in all models!, and calculae forecass as dynamic ieraion of one-sep ahead forecass sandard asympoic ess do no apply for esing he null hypohesis of equal forecas accuracy (Clark and Wes 2006 and 2007 C&W 2006 also find ha a boosrap es has favorable properies (size and power We adop a boosrap es similarly o relaed papers as Mark (1995, Kilian (1999 McCracken/Sepp (

14 2. Boosrap- es: a resul On he following slide we have 4 figures: The boosrap disribuions of he predicion saisics for he DEM/USD exchange rae for 4 differen forecasing horizons (1M, 1Y, 3Y, 5Y (blue Tes saisics: (models RMSPE/ RW RMSPE *100 Verical black line: he value of 100 (his means: equal predicive accuracy Verical red line: empirical RMSPE raios 14

15 DEM/USD MOD S-F5Y: boosrap disribuion of RMSPE raios monh 1 hónap év 1-year year 3 év year 5 év

16 3. Daa End of monh daa beween January 1979 and Augus 2009 USD exchange raes agains 9 currencies: DEM, GBP, JPY, CHF, CAD, AUD, NZD, NOK, SEK. Spo and forward ER-s wih 3 differen mauriies alernaively: 3Y, 5Y and 10Y so we have used 3 forward mauriies and 3 model specificaions = 9 models for all currency pairs We don aim o deermine a single opimal model our goal is he sudy of he general feaures of he nine models across he nine exchange rae series sudied 16

17 3. Daa: uni roo and saionariy ess 8 uni roo ess and 1 saionariy es Spo exchange rae: can no rejec uni roo bu can rejec saionariy Long mauriy forward raes: we can rejec he uni roo for he long forward ER-s only in 4 cases: DEM, GBP, CHF, CAD 17

18 Uni roo and saionariy ess: DEM spo 1m 3m 6m 12m 3y 5y 10y DEM / USD ADF * PP * DFGLS * -24** ERS * 24** NP MZa * ** NP MZ * -20** NP MSB * 00** NP MPT * 22** KPSS 0.69** 0.68** 0.66** 0.64** 0.60** 08**

19 3. Daa: uni roo and saionariy ess Long mauriy forward raes: we can rejec he uni roo for he long forward ER-s only in 4 cases: DEM, GBP, CHF, CAD We can no for he oher 5 (JPY, AUD, NZD, NOK, SEK Bu we esimaed our models also for his 5 currencies: (a in finie samples we never have he final word abou ime series properies (b es saisics also decline wih horizon for his 5 currencies (c i is an ineresing exercise o assume he saionariy of long mauriy forward raes for he forecasing 19

20 3. Daa: forecasing sample We are using he recursive mehod: We use he 1979M1-1989M12 sample o form an iniial esimaion, and calculae ou of sample forecas for he nex five years (1990M1-1994M12 Nex we esimae he models for 1979M1-1990M1 and calculae ou of sample forecas for 1990M2-1995M1, and so on... Noe: our longes, 5 year forecass are evaluaed on less han 4 independen (non-overlapping forecasing rounds Noe 2: Our forecass are fully ou of sample 20

21 4. The one period regression s ( h = 0+ δ1f 1 δ + ε Mauriy of forward rae DEM GBP JPY CHF CAD AUD NZD NOK SEK 1-monh δ R DW N year δ R DW N year δ R DW N year δ R DW N

22 4. The one period regression s ( h = 0+ δ1f 1 δ + ε Mauriy of forward rae DEM GBP JPY CHF CAD AUD NZD NOK SEK 1-monh δ R DW N year δ R DW N year δ R DW N year δ R DW N

23 4. The one period regression s ( h = 0+ δ1f 1 δ + ε Mauriy of forward rae DEM GBP JPY CHF CAD AUD NZD NOK SEK 1-monh δ R DW N year δ R DW N year δ R DW N year δ R DW N

24 4. The one period regression s ( h = 0+ δ1f 1 δ + ε Mauriy of forward rae DEM GBP JPY CHF CAD AUD NZD NOK SEK 1-monh δ R DW N year δ R DW N year δ R DW N year δ R DW N

25 5. Ou of sample forecasing resuls Nex slide: able showing Roo Mean Squared Predicion Error (RMSPE for DEM/USD random walk =

26 DEM/USD, RMSPE, random walk = 100 (and p-value 1M 3M 6M 12M 24M 36M 48M 60M EQ F3Y (04 (07 (04 (04 (05 (07 (04 (05 MOD S-F3Y (03 (05 (05 (05 (02 (07 (07 (06 VECM S-I3Y (00 (08 (07 (09 (09 (05 (01 (00 EQ F5Y (04 (08 (03 (01 (06 (07 (06 (02 MOD S-F5Y (05 (06 (02 (06 (04 (01 (01 (01 VECM S-I5Y (00 (01 (01 (0 (08 (05 (01 (03 EQ F10Y (04 (07 (01 (03 (08 (02 (02 (03 MOD S-F10Y (09 (00 (02 (06 (05 (04 (04 (05 VECM S-I10Y (04 (05 (09 (02 ER Forecasing (01 wih Long (07 Mauriy (00 Forward(00 Raes 26

27 DEM/USD, RMSPE, random walk = 100 (and p-value 1M 3M 6M 12M 24M 36M 48M 60M EQ F3Y (04 (07 (04 (04 (05 (07 (04 (05 MOD S-F3Y (03 (05 (05 (05 (02 (07 (07 (06 VECM S-I3Y (00 (08 (07 (09 (09 (05 (01 (00 EQ F5Y (04 (08 (03 (01 (06 (07 (06 (02 MOD S-F5Y (05 (06 (02 (06 (04 (01 (01 (01 VECM S-I5Y (00 (01 (01 (0 (08 (05 (01 (03 EQ F10Y (04 (07 (01 (03 (08 (02 (02 (03 MOD S-F10Y (09 (00 (02 (06 (05 (04 (04 (05 VECM S-I10Y (04 (05 (09 (02 ER Forecasing (01 wih Long (07 Mauriy (00 Forward(00 Raes 27

28 Sub-sample sensiiviy 3-year ahead forecass: RMSPE, random walk = 100 Full sample Two 9-year long period Six 3-year long period DEM GBP JPY CHF CAD AUD NZD NOK SEK

29 Sub-sample sensiiviy 3-year ahead forecass: RMSPE, random walk = 100 Full sample Two 9-year long period Six 3-year long period DEM GBP JPY CHF CAD AUD NZD NOK SEK

30 Sub-sample sensiiviy 3-year ahead forecass: RMSPE, random walk = 100 Full sample Two 9-year long period Six 3-year long period DEM GBP JPY CHF CAD AUD NZD NOK SEK

31 Sub-sample sensiiviy 3-year ahead forecass: RMSPE, random walk = 100 Full sample Two 9-year long period Six 3-year long period DEM GBP JPY CHF CAD AUD NZD NOK SEK

32 The acual spo exchange rae (blue and ou of sample forecass up o 5 years ahead (red he laer only for December and June USD_EUR Model = sacmod_5y

33 The acual spo exchange rae (blue and ou of sample forecass up o 5 years ahead (red he laer only for December and June USD_EUR Model = sacmod_5y

34 Figures: Exchange rae changes and forecass, DEM/USD The 6 panels on he nex slide show: The acual fuure exchange rae changes (blue circles and he forecased values (red line for six differen horizons beween 3 monhs and 5 years 34

35 DEM/USD: acual fuure ER changes (blue circles and forecas ER changes (red lines 3-monh year 2-year year year year ER Forecasing -.6 wih -.6 Long Mauriy Forward Raes

36 5. Summary of ou of sample forecasing resuls Models using he 3 year mauriy forward raes significanly ouperform he random walk for 8 ER-s a horizons from 1 o 5 years. In he 9h case (CAD p-values are beween 10-15%. Models using he 5 year mauriy forward raes significanly ouperform he random walk for 7 ER-s Models using he 10 year mauriy forward raes significanly ouperform he random walk for 3 ER-s The resuls are robus o he 3 differen model specificaions and o he daa frequency (for GBP/USD we used also weekly daa For some ER-s (e.g. GBP, AUD we have found even significan wihin year predicabiliy Alernaive models (RW wih drif, forward ER, esimaed AR generally fails o bea he random walk 36

37 6. Does saionariy maer? Long forwards help forecasing, bu is he saionariy assumpion he key reason for his? To es, we run wo models ha assume non-saionary forward raes: a simple VAR, and a VECM assuming ha spo and forward raes are coinegraed: spo and forward raes are coinegraed: = = h i i p i i i i i h e e f s b b b b b b f s 2, 1, ( 1 ( 22 ( 21 ( 12 ( ( = = h k i h i i i i i i h i f s c c c c c c f s 2, 1, ( ( ( 22 ( 21 ( 12 ( ( ~ ε ε δ δ

38 6. Does saionariy maer? Con d For all nine currencies we found ha models assuming saionariy of he long forwards forecas beer han models assuming ha long forwards are non-saionary This is even rue for hose currencies for which formal uni roo ess could no rejec he null hypohesis of uni roo 38

39 7. Inerpreaion Our finding ha forward exchange rae is less persisen han spo exchange rae is consisen wih he empirical finding of forward discoun bias Suppose a =1: i 1 = i 1 * s 1 = f 1 Suppose a =2: i 2 > i 2 * s 2 < f 2 i.e. s appreciaes more han f (because he home currency is sold a a forward discoun Consequenly, when high ineres rae currencies end o appreciae and he ineres rae differenial beween he wo counries change, he forward exchange rae will be less persisen han he spo exchange rae Shor mauriy forward exchange raes are primarily deermined by he spo exchange raes, while he ineres rae differenial has a larger role in longer mauriy forward raes 39

40 Do high ineres rae currencies end o appreciae? Reurns o carry rade agains he US dollar January 1976 April ,000 2,000 1,500 DKK NZD 1, SEK GBP Porfolio NOK AUD DEM JPY CAD CHF ER1995 Forecasing 2000 wih Long 2005 Mauriy Forward Raes 40

41 7. Inerpreaion con d The volailiy of he ER far exceeds he volailiy of any sandard measure of macro-fundamenals (Flood and Rose 1999 Differen behavior of shor versus long run expecaions (Froo and Io 1989 hey are no consisen! Encouraging resuls on long-run UIP (Chinn and Meredih, 2005 When here is a huge noise in he spo FOREX marke and shor and long run expecaions behave differenly, marke paricipans could raher keep heir long run expecaion sable and accep adjusmen in he spo exchange rae in response o a shock, when he naure of he shock (i.e. wheher i is a pure noise or somehing fundamenal is uncerain 41

42 7. Inerpreaion con d Unil now we lised argumens in favor of he saionariy of he long mauriy forward nominal exchange raes. The saionariy of acual real exchange rae has gained recenly more suppor (for an overview see: Sarno, bu, when he expeced cumulaive inflaion differenial is close o zero, hen he expeced nominal exchange rae is a good proxy for he expeced real exchange rae. Our model could be more relevan for counries wih sable moneary regimes (high credibiliy in conrolling inflaion A furher facor playing a role (in explaining some of our resuls could be relaed o he erm premia of long mauriy bond yields Final issue: why is he ER predicable and he long mauriy ineres rae differenial weakly exogenous? Our answer: Yield Pariy Approach (Darvas, Rappai and Schepp 2006, De Nederlandsche Bank Working Paper No

43 8. Summary A novel model ha has no been used before for forecasing (i.e. saionariy of long mauriy forward raes significanly (boh in saisical and economic erms ouperformed he random walk for 9 USD dollar raes (which represen 75% of he world forex urnover using a 20-year long period ( for evaluaing ou of sample forecas 43

44 9. Possible exensions Non-linear alernaives of our simple linear models Trading rule simulaions Sudy of he relaion of long mauriy ineres rae differenials o fundamenals deermining long run movemens in he exchange rae 44

45 Thank you for your aenion The paper is available a: 45

46 GBP/USD: acual fuure ER changes (blue circles and forecas ER changes (red lines 3-monh 1-year 2-year year 4-year 5-year ER Forecasing wih Long Mauriy Forward Raes 46

47 JPY/USD: acual fuure ER changes (blue circles and forecas ER changes (red lines 3-monh year.5-2-year year.6 4-year 5-year ER Forecasing -.5 wih -.8 Long Mauriy Forward Raes

48 CHF/USD: acual fuure ER changes (blue circles and forecas ER changes (red lines 3-monh 0 1-year year year 4-year.5 5-year ER Forecasing -.5 wih Long Mauriy Forward Raes - 48

49 0 6 2 CAD/USD: acual fuure ER changes (blue circles and forecas ER changes (red lines 3-monh year 2-year year 4-year 5-year ER Forecasing wih -.6 Long Mauriy Forward Raes

50 AUD/USD: acual fuure ER changes (blue circles and forecas ER changes (red lines.5 3-monh 1-year 2-year year year year ER Forecasing -.6 wih -.6 Long Mauriy Forward Raes

51 3-monh NZD/USD: acual fuure ER changes (blue circles and forecas ER changes (red lines - 1-year year year year year ER Forecasing -.6 wih -.6 Long Mauriy Forward Raes

52 NOK/USD: acual fuure ER changes (blue circles and forecas ER changes (red lines 3-monh 1-year 2-year year 4-year.6 5-year ER Forecasing -.5 wih -.6 Long Mauriy Forward Raes

53 SEK/USD: acual fuure ER changes (blue circles and forecas ER changes (red lines 3-monh.5 1-year year year year year ER Forecasing -.6 wih -.6 Long Mauriy Forward Raes

54 Figures: Exchange rae levels and forecass The nex slides show: The acual spo exchange rae (blue and ou of sample forecass up o 5 years ahead (red he laer only for December and June 54

55 2 USD_GBP Model = saceq_3y

56 160 JPY_USD Model = vecm_s_i5y

57 2 1.8 CHF_USD Model = vecm_s_i5y

58 CAD_USD Model = sacmod_3y

59 1 USD_AUD Model = saceq_3y

60 .9.8 USD_NZD Model = sacmod_2y

61 10 NOK_USD 10 9 Model = saceq_3y

62 11 10 SEK_USD Model = sacmod_5y

63 A. Boosrap es We compare nesed models (he random walk is nesed in all models!, and calculae forecass as dynamic ieraion of one-sep ahead forecass, sandard asympoic ess do no apply for esing he null hypohesis of equal forecas accuracy. Clark and Wes (2006, 2007 sugges an adjusmen of he MSPE saisics is valid only for models esimaed in direc form (i.e. Long-horizon regression, as our EQ-model. Bu C&W find also, ha a boosrap es has favorable properies (size and power. We adop a boosrap es similarly o relaed papers as Mark (1995, Kilian (1999 McCracken/Sepp (

64 A. Boosrap-es: sep by sep 1. Impose he null hypohesis of no predicabiliy in he model, esimae, and sore he esimaed residuals. 2. Sample wih replacemen he residuals for a sample of 500 plus he acual lengh of he ime series sudied. 3. Creae a boosrap ime series of he changes in he log exchange rae and all oher ime series in he model recursively using he boosrapped residuals, based on saring values se equal o he values of he firs observaion of he rue series. Discarding he firs 500 observaions leads o a boosrapped sample for he same lengh as he rue series. 4. Esimae and forecas using he boosrapped sample he same way as for he rue daa se and calculae forecas saisics. 5. Repea seps imes o ge an empirical boosrapped disribuion of he es saisics and calculae he p-values as he lower ail of his disribuion from he es saisics received for he rue daa. 64

65 A. Boosrap DGP The boosrap daa generaing process (DGP is he resriced version of 2nd specificaion (MOD s =ε 1, ( h ( h f = φ 0 + φ1 f 1 + ε2, Under he null exchange rae changes are no predicable (=random walk. 65