Improve the yen carry trade with economic fundamentals

Transcription

1 Invesmen Managemen and Financial Innovaions, Volume 7, Issue 4, Ming Li (USA) Improve he yen carry rade wih economic fundamenals Absrac In his paper, economic fundamenal variables are used o predic he exchange raes of major currencies agains he Japanese yen in a facor augmened regression, where he facor is consruced from he risk premium of each currency. he yen carry rade is hen simulaed based on hese forecass. Carry rades based on hese forecass ou-perform he naive carry rade based on he random walk forecas in erms of risk-adjused reurns and reurn skewness. he beer performance is robus for differen ime periods and afer conrolling for he ransacion cos. he resul suggess ha fundamenals are useful in pracice alhough he academia generally consider hem ineffecive in predicing exchange raes. Keywords: yen carry rade, exchange rae models, economic fundamenals, facor augmened regression, Kalman filering, currency risk premium. JEL Classificaion: F3, F37, G5. Inroducion his sudy invesigaes wheher he economic fundamenals of exchange rae models can improve he performance of currency rading. Paricularly, we focus on he economic fundamenals used in he aylor rule. Unlike he classic macroeconomics, where ineres rae is he equilibrium resul of moneary variables, he aylor rule specifies how he ineres rae responds o economic fundamenals. For example, when he inflaion rae rises, he ineres rae will increase in he aylor rule while i will decrease in he moneary model. According o Engel and Wes (5), he aylor rule models are gaining momenum recenly because hey appear o be he poenial candidae o bea he random walk model. Many sudies have found improvemen in he forecasing abiliy of he exchange rae models when hey include he economic fundamenals relaed o he aylor rule (see Chinn and Pascual, 5; Choi, Mark and Sul, 6; Engel and Wes 5; 6; Engel, Mark and Wes, 7; Molodsova and Papell, 8; Murray and Papell, ; aylor, Peel, and Sarno, ). Given his encouraging developmen in he exchange rae modeling, one would wonder how useful he economic fundamenals are in he decision-making of currency invesmens. We focus on a paricular ype of currency rading he yen carry rade. Carry rade is a simple currency rading sraegy of borrowing low-ineres-rae currency and invesing in high-ineres-rae currency. he Japanese yen has become he major funding currency of he carry rade since he mid-99s because of is unusually low ineres raes. Profi from he yen carry rade is he sum of he ineres rae differenial beween he yen and a arge currency, and he change in he exchange rae of he arge Ming Li,. Galai, Heah, and McGuire (7) claim ha he yen accouned for abou 8% of funding currency for carry rades in 7. currency. According o uncovered ineres rae pariy (UIRP), carry rade is unprofiable on average because he ineres rae differenial would be offse by he relaive depreciaion of he arge currency. However, almos all empirical sudies poin o he opposie conclusion (for insance, see Cheung, Chinn, and Pascual, ; Engel, 996; Lewis, 995; Mark and Sul, ; Meese and Rogoff, 983a; 983b). his implies ha he carry rader can pocke boh he ineres rae differenial and he appreciaion of he arge currency, wih zero capial. I is precisely for his reason ha he cohor of hedge funds engaging in carry rade is growing. he use of economic fundamenals in currency rading presens a mixed picure. According o Cheung and Chinn (), 9% of shor-erm foreign exchange (FX) raders in he UK rade currencies wih echnical analysis. For example, PowerShares DB G Currency Harves (icker: DBV), an exchange raded fund (EF), rades simply by borrowing lowineres-rae currency and invesing in high-ineresrae currency. On he oher hand, Moore Capial s Global Fund, a hedge fund, uses solid macro fundamenals o guide is carry rade. Bu one quesion remains unanswered. Are he economic fundamenals useful in improving he profiabiliy of he carry rade a all? his sudy is moivaed by Engel and Wes (5), who show ha economic fundamenals and exchange raes are closely linked, even hough he consensus in academia is ha for predicion, exchange rae models canno bea he random walk. Furhermore, Engel, Mark, and Wes (7) indicae ha he unobservable facor in he exchange raes hemselves may conain useful informaion for predicion. Naurally we would guess ha he economic fundamenals should be useful for he carry rade. o fully uncover he usefulness of he economic fundamenals, a dynamic facor model is employed o exrac informaion from he risk premium in exchange raes. his mehod is appealing in ha he 93

2 Invesmen Managemen and Financial Innovaions, Volume 7, Issue 4, facor is derived from he ineres rae pariy and has economic meaning. he facor is hen combined wih oher economic fundamenal variables in he aylor rule o forecas exchange raes in a facor augmened regression (FAR) model. Specifically, he facor is esimaed in a dynamic facor model wih he Kalman filering echnique. o accommodae possible nonlineariy in he exchange rae models, we also experimen wih adding nonlinear forms of ineres rae differenials as explanaory variables in he FAR. We recognize ha some success has been repored in nonlinear modeling of foreign exchange raes, bu do no find suppor for his success. he yen carry rade is simulaed in each of he following major arge currencies: Ausralian dollar, New Zealand dollar, Briish pound, Canadian dollar, euro, and U.S. dollar. For each currency, he carry rade follows a go or no-go binary process a a monhly frequency. When he expeced reurn is posiive, he carry rade is execued; oherwise, he rade is skipped or a shor posiion in he arge currency is aken o enhance profi. he expeced reurn is calculaed based on he forecas exchange raes agains he yen. Several specificaions of FARbased forecasing models are esed agains he random walk model. Under he random walk heory, a naive carry rade will always occur as long as he ineres rae is higher for he arge currency han for he yen. Average reurn, Sharpe raio, and skewness of reurns are he main performance saisics repored. he performance of yen carry rade wih fundamenals are compared o models wihou fundamenals random walk or AR(). he resuls show a beer performance of carry rades when he fundamenals are added. In paricular, if he aylor rule fundamenals are included under he FAR framework, carry rade generaes beer risk-adjused reurns across he six arge currencies as well as he equally-weighed porfolio. o compare he ail risk, we compue he skewness of reurns oo. he skewness is sharply improved in he FAR framework. he conclusion remains he same, even afer accouning for ransacion coss and simulaion in differen periods. his paper sands ou wih he use of a dynamic facor framework 3. I is well known ha ime- One criicism of he facor analysis is is lack of economic or financial meaning. Leland (997) poined ou ha he sandard Sharpe raio is no applicable in non-normal or dynamic seings. 3 For applicaion of FAR model, see Ludvisgson and Ng (9) on analysis of bond risk premia, Bernanke and Boivin (3) and Giannone e al. (5) on moneary policy analysis, and Sock and Wason (5) on business cycle forecasing. Bai and Ng (8) provide a comprehensive survey on his opic. 94 varying risk premiums in equiy may be able o explain and predic reurns (see, for example, Ferson and Harvey, 99). he mos recen effor by Engel, Mark, and Wes (7) has generaed a lo ineres in his aspec in predicing exchange raes, followed by Chrisiansen, Ranaldo, and Soderllind (). We find a similar paern, ha a macro-fundamenal derived facor plays a decisive role in boosing he reurns o carry rade. We aribue his success o he facor s high persisence and srong correlaion wih he exchange rae. he Diebold-Mariano es and a simple coun of direcional forecass also confirm he superior forecasing abiliy of he FAR model. he paper is organized as follows. Secion presens he exchange rae models. hen we presen he empirical resulsan analysis of facors and forecas evaluaion and realiy cheak. he las Secion concludes.. Foreign exchange rae model and esimaion mehod he predicive regression model of exchange rae is: s F F z, () where ~, NID, where s is he log exchange rae expressed as unis of yen per uni of arge currency and s + = s + s. An increase in s indicaes appreciaion of he arge currency and depreciaion of he yen, and vice versa. he regression model is parsimonious. When we se F =, z =, he regression is he random walk (RW) model. his is he sandard benchmark in he exchange rae predicion lieraure and pracice. Anoher specificaion wihou fundamenals is obained by seing F =, and z = s s. his is an AR() model ha has been used exensively. he regression equaion has a generaed regressor F, which is called he facor. he facor is esimaed from he UIRP: i i s F, () where i is he ineres rae of he yen and i is he ineres rae of he arge (foreign) currency. An aserisk denoes variables in he non-japan (arge) counry. he unobservable F is regarded as he risk premium of exchange raes. he ineres rae pariy simply saes ha he curren spo rae is expeced o depreciae/appreciae by he amoun of he ineres rae differenial ex ane. If he ineres pariy holds, a linear regression of he change in exchange rae ono he ineres rae differenial should yield a coefficien of one. Unforunaely, mos empirical sudies

3 have found he coefficien o be near zero or negaive. Engel and Wes (5) argued ha he failure of he UIRP has o do wih he unobservable componen F and his componen conains useful informaion for predicing exchange raes. For his reason, we will apply he ineres rae pariy o esimaing he facor. Engel and Wes (5) argue ha he exchange rae iself conains informaion ha is hard o exrac from observable fundamenals. his informaion migh include risk premium or daa abou fundamenals, which is usually persisen and ime-varying. By his noion, he facor follows he dynamic process: s i i F v, (3) F af w, where w and v are idenically independenly disribued (i.i.d.) whie noises. he parameer a measures he persisence of he facor and is beween and. he procedure o esimae he unobservable facor F involves he Kalman filering echnique and maximum likelihood mehod. he esimaion procedure is presened in he Appendix. Readers are referred o Hamilon (994) and Green (3) for sandard reamen of equaion (3) on esimaing he dynamic facor. See Bai (3), Bai and Ng (8), and Sock and Wason (5) for more discussion on saisical inference of he dynamic facor model. he specificaion of z is inspired by ineres rae pariy and he recen success of he aylor rule, Model (Random walk):, F, z s. Model (AR()):, z s. Invesmen Managemen and Financial Innovaions, Volume 7, Issue 4, z i i Oi i, (4) where Oi i of he ineres rae differenials. When Oi i is he polynomial of higher orders is zero, he regression equaion () is he UIRP. Furhermore, given he recen empirical evidence on he possibiliy of beaing he random walk by using he aylor rule model, he choice of fundamenal variables is narrowed according o he aylor rule. Specifically, ineres raes are deermined by key macroeconomic variables: economic growh rae, inflaion raes and pas ineres raes 3. he ineres rae differenial is consruced simply as 4 : i i i i i. y y y (5) Since many sudies have shown ha he exchange rae is possibly a nonlinear funcion of fundamenals (see Chinn, 99; 8; aylor, Peel, and Sarno, ; Kilian and aylor, 3; Rossi, 5), a ype of nonlineariy for Oi i in our FAR framework is considered as follows: 3 i i i i i. O i (6) i i3 In summary, he following is a lis of various specificaions of equaion () ha are esed in his paper. F F, z y y y i i i s F y i Model 3 (AR() + aylor rule):. Model 4 (aylor rule):, z y y i i. Model 5 (aylor rule + Nonlinear): 3 F, z y y y i i i ii i i3i i. Model 6 (Facor + aylor rule): z yy y ii i. Model 7 (Facor + aylor rule + Nonlinear): 3 y i i i3 z y y i i i i i i. 34 he Kalman filering and maximum likelihood esimaion (MLE) mehod is more convenien han he principal componen analysis for wo reasons: () principal componen analysis (PCA) is more fi for saic facors; and () non-saionary daa can be used o esimae he facor consisenly under he Kalman filering and MLE mehod. Models incorporaing aylor rule fundamenals, as propounded by Engel and Wes (6), Mark (7), Molodsova and Papell (8), and Molodsova, Nikolsko-Rzhevskyy, and Papell (8) have recenly gained prominence as a means of explaining movemens in he exchange rae. 3 Much of he aylor rule lieraure uses expeced inflaion in he moneary policy rule. Since we don have daa on expeced inflaion in all counries we sudy, we leave ou his variable in our aylor rule model. 4 See Engel, Mark, and Wes (7) for deailed discussion on equaion (5). 95

4 Invesmen Managemen and Financial Innovaions, Volume 7, Issue 4,. Carry rade In his paper, a carry rade is a binary rading sraegy in spo markes ha is based on projeced reurn. he rading rule is ha if i i> and he expeced reurn is posiive as prediced by he model, here is carry rade beween a arge foreign currency and he yen. We use c = o denoe a decision of carry rade: c i E s i i and i oherwise., Noe ha under he random walk heory, he change of expeced exchange rae is zero, i.e. Es, so he carry rade decision depends solely on he ineres rae differenial. Because he yen has been on he lowes ineres rae among he major currencies since he mid-99s, he yen carry rade will almos always occur, under he random walk forecas. he size of he carry rade is he borrowed amoun of yen. he profi in carry rade can be scaled by is size. For he size of, he reurn o carry rade is calculaed as: i i s, r, if if c, c. In periods wihou carry rade, he facor model predics relaively large depreciaion of he arge currency. his implies ha shoring he arge currency would generae addiional profi. We enhance he carry rade by reversing he currency rade in he spo marke during hese periods. We erm his sraegy he enhanced carry rade (EC). he reurn o EC is calculaed as i i s r s, 3. Empirical resuls, if if c, c. 3.. Daa. he daa consis of monhly series of all variables, (wih excepions noed below). he sample size is 444, due o he loss of one observaion o differencing. We sudy bilaeral Japanese yen exchange raes versus hose of he six oher counries: Ausralia, Canada, he Eurozone, New Zealand, he Unied Kingdom, and he U.S. he Federal Reserve s (FRED) is he source for he end-of-monh exchange raes. We sampled end-of- monh exchange raes from daily exchange raes. he inernaional financial saisics (IFS) CD-ROM is he source for all he fundamenal economic variables: money supply, indusrial producion, consumer prices, and ineres raes. Since consumer price index (CPI) and indusrial producion daa for Canada and New Zealand are missing for earlier years 3, daa for and are used, respecively. German exchange raes and fundamenals are subsiued for hose of Eurozone before he ou-of-sample performance esing sars from January 999, when he euro became official. A each monh, we use daa only up o he prior monh for forecasing. Any missing daa will be impued wih he cubic spline mehod in Malab. We hen esimae he unobservable facor. Afer obaining he sequence of facors, we esimae coefficiens of equaion () using he OLS mehod and forecas exchange raes for ha monh. he ou-of-sample forecas is hen used o consruc carry rade sraegy. Performance is compued using he realized exchange raes. he process is performed for each of he six naions. he Figure illusraes how daa are used a January 999. he same process is repeaed as we move on o he nex period, unil January. herefore, 45 monhs of rade decision ake place in oal. Since volailiy is no esimaed, we can consruc a mean-variance opimal porfolio. herefore, we presen performance of an equally-weighed porfolio of he six carry rades. Daa used for esimaing facor and FAR Fig.. Daa used in Jenuary 999 able presens some basic saisics of he whole sample. Variables are all very volaile because heir relaively large sample deviaions are compared o heir sample means. All counries have higher ineres raes on average han Japan. Excep for he UK, all counries experienced lower indusrial growh raes han Japan. Panel B in able repors he augmened Dickey- Fuller ess of uni-roo for hree ime series: change in exchange raes (s), ineres rae differenials (i i), and he risk premium (s (i i)). Boh s and s (i i) seem o be non-saionary ime series because we are unable o rejec he null of uni roos in hem. his makes our choice of mehod o esimae he dynamic facor o be he Kalman filering because generally he Bayesian mehod is relaively robus o non-saionariy. Noe ha buying arge currency in forward markes is an equivalen carry rade sraegy. An EC is where a shor sale of arge currency is execued when carry rade is prediced o lose Impued daa would be very unreliable because of a large block of missing daa. 4 he exchange rae of he euro is convered from he German mark a he rae of mark.95588/euro.

5 Panel A. Average and sandard deviaions of six arge currencies s i i (y y) Invesmen Managemen and Financial Innovaions, Volume 7, Issue 4, able. Basic saisics Ausralia Canada Eurozone New Zealand Unied Kingdom U.S. -.3 (.34).44 (.35). (.8) -.3 (.3).36 (.6). (.8). (.6) -. (.7). (.6). (.) -. (.8) -.3 (.34).73 (.4) -.4 (.9).35 (.38) -. (.).3 (.7) Panel B. Augmened Dickey-Fuller es, H = Uni roo, = Accep, = Rejec s i i 3. s (i i) -.3 (.33).5 (.3). (.6). (.6) Noe: he number in parenheses under each variable is he sandard deviaion of he indicaed variable. An aserisk indicaes a non- Japan value, and he absence of an aserisk indicaes a Japan value; s is he percenage change in he yen exchange rae (a higher value indicaes appreciaion agains he yen); i is he money marke rae or governmen bond yield; y is he growh rae of he indusrial producion index; is he rae of inflaion. Daa are monhly, mosly Excepions include a beginning dae of 975. for Canada and for New Zealand. Monhly daa of CPI for Ausralia and New Zealand are no available. 3.. Performance of carry rades. able repors he annualized reurn, Sharpe raio, and skewness of reurns for he period of Le s firs examine he risk-adjused reurns. We noice ha models wih fundamenals (models 3-7) generally ouperform he RW model or AR() model, which do no include fundamenals. More imporan, models wih facors generae beer reurns han hose wihou. We find ha aylor rule fundamenals have a large improvemen only afer he facor is included (models 6 or 7). For example, for all of he six arge currencies, carry rades generae higher Sharpe raios han models wihou fundamenals. he naive carry (RW) rade generaes posiive reurns for all six currencies agains he yen, wih he reurns ranging from o 9%. he AR() model also has posiive reurns, bu performs somewha worse han even he naive sraegy. Bu eiher of he carry rades in he non-fundamenal models has poor Sharpe raios compared o he average Sharpe raio of.3 in he S&P 5. In conras, carry rade based on FAR (models 6 or 7) improves he Sharpe raio for each one of he six currencies. For insance, he Sharpe raio rises o.65 (model 6) or.7 (model 7) from.5 (RW) or.8 (AR()) for he porfolio. Skewness is an equally imporan performance saisic. Large negaive skewness implies he high probabiliy of large losses such as marke crashes. his is a big concern for invesors because i may mean shor-erm insolvency, even bankrupcy. he wo bigges currency correcions during he esing period, November and Ocober 8, occurred when he yen appreciaed suddenly agains mos of he arge currencies. For insance, he yen appreciaed agains he dollar by 8% in Ocober 8. he huge negaive skewness, for insance -. in he Ausralian dollar naive carry rade, indicaes grea ail risk in he yen carry rade. he FAR model improves he skewness. Carry rades in six currencies have beer skewness han naive carry rades, excep for he U.S. dollar. he Ausralian dollar has a -.48 skewness, which is a grea improvemen over he skewness of is counerpars (-. (RW)) or -.77 (AR()). he improvemen in skewness also clearly shows up on he porfolio. Fundamenals are helpful in deecing he direcion of currency flucuaions. his can be seen from he change of performance in he AR() model. Afer including he aylor fundamenals, AR() performs slighly beer. Bu he fundamenals alone are no enough. Only afer hey are pu ino a FAR framework do hey drasically increase he Sharpe raios and skewness. he Sharpe raio of he equallyweighed porfolio rises from.38 o.65 from.38 (RW) or.8 (AR()) and he skewness increases o -.3 from -.6 (RW) or -.9 (AR()). ECs have even beer skewness from reurns, wih lile sacrifice in reurn. he resuls are shown in able 3. he resuls ell a similar sory as in able, excep wih much beer performance for he FAR models in erms of skewness. he FAR models generae a Sharpe raio of.54 (model 6) or.6 (model 7), bu a grealy improved skewness of.7 for he porfolio. We examined several episodes of large correcion in yen exchange raes. We found ha FAR models have avoided hese periods for carry rades wih 7-8 percen chances (no shown). his conribues o he grea performance of he FAR-based carry rades. he nonlinear erms in models 5 or 7 do no ouperform heir counerpars. A couple of reasons may cause his. Firs, he facor has already absorbed all 97

6 Invesmen Managemen and Financial Innovaions, Volume 7, Issue 4, relevan informaion ha oherwise is conained in he nonlinear erms. We did ry adding nonlinear erms in a sandard regression wihou he facor, and found relaively beer performance. Second, he able. Performance saisics of carry rade specificaion of nonlineariy may no hold up well simply because of lack of knowledge. We did no ry oher forms of nonlineariy, since we fear he arbirary naure of such aemps. Ausralia Canada Eurozone New Zealand Unied Kingdom U.S. Porfolio Model : Random walk Mean reurn Sharpe raio Skewness Model : AR() Mean reurn Sharpe raio Skewness Model 3: AR() + aylor Mean reurn Sharpe raio Skewness Model 4: aylor rule Mean reurn Sharpe raio Skewness Model 5: aylor Rule + nonlinear model Mean reurn Sharpe raio Skewness Model 6: Facor + aylor Rule Mean reurn Sharpe raio Skewness Model 7: Facor + aylor rule + nonlinear model Mean reurn Sharpe raio Skewness Noe: he mean reurn is annualized. he Sharpe raio is defined as he raio of mean reurn o he sandard deviaion. able 3. Performance saisics of enhanced carry rade Ausralia Canada Eurozone New Zealand Unied Kingdom U.S. Porfolio Model : Random walk Mean reurn Sharpe raio Skewness Model : AR() Mean reurn Sharpe raio Skewness Model 3: AR() + aylor Mean reurn Sharpe raio Skewness Model 4: aylor rule Mean reurn Sharpe raio Skewness Regime swich may be anoher way o model nonlineariy. 98

7 Invesmen Managemen and Financial Innovaions, Volume 7, Issue 4, able 3 (con.). Performance saisics of enhanced carry rade Ausralia Canada Eurozone New Zealand Unied Kingdom U.S. Porfolio Model 5: aylor rule + nonlinear model Mean reurn Sharpe raio Skewness Model 6: Facor + aylor rule Mean reurn Sharpe raio Skewness Model 7: Facor + aylor rule + nonlinear model Mean reurn Sharpe raio Skewness See noes in previous ables ransacion cos. he ransacion cos may change he decision making of carry rades ha rely on fundamenals, so i will be helpful o see wha is is effec. A ypical ransacion cos per foreign exchange rade is beween -4 base poins (see Burnside, 7). So we simulae our carry rades for a ransacion cos ranging from bps o 4bps per carry rade. We show he reurn o he porfolio of six carry rades. he resul in able 4 indicaes ha ransacion cos does no change he noion ha FAR-based carry rade ouperforms ha based on RW or AR() models. able 4. Reurns o carry rade wih ransacion cos ransacion cos (bps) Model : Random walk Mean reurn Sharpe raio able 5. Reurns o carry rade in differen periods Skewness Model 6: Carry rade porfolio Mean reurn Sharpe raio Skewness Model 6: Enhanced carry rade porfolio Mean reurn Sharpe raio Skewness Alernaive periods of carry rade. FARbased carry rades are also esed in wo oher periods, and 6.-. able 5 repors he resul for boh periods. Panel A repors he performance saisics for and Panel B repors hose for 6.-. Again, performance saisics in able 6 ell a similar sory o hose in ables and 3: FAR model-based carry rade wih fundamenals ouperforms naive or AR() carry rade. Ausralia Canada Eurozone New Zealand Unied Kingdom U.S. Porfolio Panel A Model : Random walk, naive carry rade Mean reurn Sharpe raio Skewness Model 3: aylor rule Mean reurn Sharpe raio Skewness Model 6: Facor + aylor rule Mean reurn Sharpe raio Skewness Model 6: Facor + aylor rule, enhanced carry rade Mean reurn Sharpe raio Skewness

8 Invesmen Managemen and Financial Innovaions, Volume 7, Issue 4, Panel B able 5 (con.). Reurns o carry rade in differen periods Ausralia Canada Eurozone New Zealand Unied Kingdom U.S. Porfolio Model : Random walk, naive carry rade Mean reurn Sharpe raio Skewness Model 3: aylor rule Mean reurn Sharpe raio Skewness Model 6: Facor + aylor rule Mean reurn Sharpe raio Skewness Model 6: Facor + aylor rule, enhanced carry rade Mean reurn Sharpe raio Skewness An analysis of facors and forecas evaluaion Why does facor maer even hough i is unobservable? We may find a lile clue in he saisics abou he facor. able 6 liss some of he saisics relaed o he esimaed dynamic facor for each arge currency. Panel A repors he conemporaneous correlaion beween he facor and relevan variables. Panel B repors he correlaion beween ime facor and ime variables. One hing sands ou: he facor ha is corre- able 6. Saisics abou facors laed o he exchange rae changes in boh ways wih a high degree of saisical significance. his is probably he reason ha he facor has srong predicive power in carry rades. Anoher fac is ha he facor is very persisen, since is auocorrelaion does no die o zero, even a a ime lag of. Barholomew and Kno (999), Diebold and Nerlove (989), and Rossi (5) show ha a persisen facor has a srong predicive power if i is highly correlaed wih oher variables. Panel A. Correlaion wih facor Ausralia Canada Eurozone New Zealand Unied Kingdom U.S. s i i (y y).39. (.) Panel B. Correlaion wih one-lag facor () s ii (y y).. (.4) (.59) (.94) Panel C. Auocorrelaion of facor (.54) (.58) Lags (.). (.) (.) (.43). (.3) (.).7 (.)

9 Lags Panel C. Auocorrelaion of facor Invesmen Managemen and Financial Innovaions, Volume 7, Issue 4, able 6 (con.). Saisics abou facors Ausralia Canada Eurozone New Zealand Unied Kingdom U.S Noe: Numbers in parenheses are he saisical p-value. A lower p-value indicaes he correlaion coefficien is more significanly differen from zero. able 7. Forecasing performance for monh ahead Underlying he beer profis of carry rades from he FAR models, here is also beer forecasing performance. We believe ha he facors conribue o his. Panel A in able 7 shows he Diebold- Mariano es of he one-monh forecasing performance of fundamenal models agains he random walk model. he ess overwhelmingly indicae ha FAR models could ouperform he random walk. In Panel B, a simple non-parameric analysis of he direcional forecass also poins o he same conclusion: models wih he facors perform beer. Panel A. Diebold-Mariano es Model Model Ausralia Canada Eurozone New Zealand Unied Kingdom U.S. AR() 3 AR() + R 5 R + NL 6 FAR + R 7 FAR + R + NL Panel A. Percenage of correc direcional forecass, oal = 3 Model Model Ausralia Canada Euro Zone New Zealand Unied Kingdom U.S. AR() 4.% 48.9% 44.3% 38.9% 43.5% 5.9% 3 AR() + R 5.% 5.4% 5.9% 4.7% 45.% 55.7% 5 R + NL 46.6% 45.% 5.7% 53.4% 45.8% 5.7% 6 FAR + R 55.% 4.% 54.% 59.5% 5.7% 59.6% 7 FAR + R + NL 54.% 4.% 59.6% 6.8% 6.% 5.% Noe. he forecas sars a February 999 unil January. here are oally 3 monhly forecass for his period. On panel A, he performance of forecasing from each model is esed agains he random walk model using he Diebold-Mariano es. he null hypohesis is ha he specific model performs equally as he random walk model. he es saisics is hen calculaed under he absolue error and uniform kernel for he long-run variance. indicaes he accepance of he null hypohesis while indicaes he rejec of he null. R = aylor rule, NL = Nonlinear, and FAR = Facor augmened regression. 5. Realiy check PowerShares DB G Currency Harves (icker: DBV) is an EF ha has a naive carry rade sraegy of longing currencies wih high ineres raes and shoring he hree counries wih he lowes ineres raes. Since is incepion in Ocober 6, Power- Shares average reurn is -.% and is Sharpe raio is -5.6%, wih an unpleasan skewness of -7%. he performance is similar o ha of yen carry rade based on he RW model (see able 3 or able 5). he FAR-based (model 6) carry rade would have a beer average reurn of.% and a posiive Sharpe raio of.36%. Skewness in reurn is significanly reduced o -.5%. he enhanced carry rade based on he FAR Model 6 generaes an impressive 4.84% reurn and a 33.8% Sharpe raio. Considering he negaive % Sharpe raio of he S&P 5 during he same period, his is a sunning resul. he skewness of 57.7% suggess he EC has avoided many major losses in foreign exchange raes. he cumulaive reurn from he comparison group is also ploed in Figure. Noe ha he S&P 5 (no shown) has a worse reurn han any of he rading sraegies for he same period. able 8 Performance compared o G EF since Ocober 6 G RW C (Model 6) Enhanced C (Model 6) Mean reurn -.% -3.5%.% 4.94% Sharpe raio -5.6% -.63%.36% 33.8% Skewness -7.% -5.8% -5.4% 57.7% Noe: Monhly reurns are annualized. G s reurn daa is obained from finance.yahoo.com.

10 Invesmen Managemen and Financial Innovaions, Volume 7, Issue 4, Conclusion Fig.. Cumulaive reurns o carry rades in recen financial crisis In his paper, exchange rae models wih aylor rule fundamenals improve he profiabiliy of yen carry rades. I is so especially when he fundamenals are used under he facor-augmened regression framework. he virue of he fundamenals is mainly in he form of he derived facors. A brief examinaion of facors shows ha he unobservable facor conains very useful informaion for forecasing fuure exchange raes. I is highly persisen and correlaed wih fuure exchange raes. Given ha we don have a fully working model of exchange rae for predicion, hese aribues make he FAR model he aracive alernaive for exchange rae predicabiliy. We hope his sudy will conribue in his direcion. his paper conribues o he lieraure by invesigaing he usefulness of economic fundamenals in he yen carry rade. Unil recenly, here has been relaively lile aenion o carry rade in he lieraure (see, for example, Burnside, 6; Jordà and aylor, 9). he exising lieraure ends o sudy he implicaion of carry rade for he exchange rae models (see for example, Core, Sarno, and siakas, 8). his paper provides a pracical view of exchange rae modeling for he currency rading communiy. References Anoher conribuion of his sudy is is novel mehod o evaluae he exchange rae models. I presens anoher angle o beaing he random walk model. In recen years here have been several sudies in he aylor rule models in he lieraure of beaing he random walk model (noably Engel and Wes, 6, and Molodsova, anya, and David Papell, 8). Many of hem have found improvemen in he forecasing abiliy of he exchange rae models when hey incorporae he aylor rule (see Choi, Mark, and Sul, 6; Clarida, Gali, and Gerler, 998; Engel and Wes, 6; Engel, Mark and Wes, 7; Gali and Monacelli, 5; MacDonald and aylor, 994; Mark, 995; Murray and Papell, ; aylor, Peel, and Sarno, ). Bu he improvemen mosly shows up in he long-erm forecasing in he mean roo squared prediion errers (MRSPE). In his paper, fundamenals in he aylor rule appear o boos he profis of carry rade in a monhly frequency over he naive carry rade based on non-fundamenals forecass. I suggess ha fundamenals do improve he forecasing abiliy of exchange rae models in erms of carry rades. his is an imporan resul because i implies ha we canno simply dismiss fundamenal models. I is so especially for he invesmen communiy. For praciioners, wha maers ulimaely is he invesmen performance afer all.. Alquis, Ron and Menzie Chinn (7). Convenional and Unconvenional Approaches o Exchange Rae Modeling and Assessmen, SSRN Working Paper.. Bai, Jushan and Serena Ng (8). Large Dimensional Facor Analysis, in Foundaions and rends in Economerics, Wiley, 3 (), pp Core, Sarno, and siakas (8) evaluaed he imporance of fundamenals in he currency porfolio and he relaive performance of differen exchange rae models. More recen sudies, such as Burnside (6) showed profi from carry rades being relaively high even afer conrolling he ransacion cos and hedging he downside risk, which adds anoher challenge o he UIPR.

11 Invesmen Managemen and Financial Innovaions, Volume 7, Issue 4, 3. Barholomew, D.J. and Kno, M. (999). Laen Variable Models and Facor Analysis (nd ediion), Kendall s Library of Saisics 7, London: Arnold. 4. Bernanke, B. and J. Boivin (3). Moneary Policy in a Daa Rich Environmen, Journal of Moneary Economics, 5 (3), pp Brunnermeier, Markus, Sefan Nagel and Lasse H. Pedersen (8). Carry rades and Currency Crashes, NBER Working Paper, Burnside, Craig, Marin Eichenbaum, Isaac Kleshchinski, and Sergio Rebelo (6). he Reurns o Currency Speculaion, Naional Bureau of Economic Research, Working Paper No. 489, Augus. 7. Cheung, Y.W. and M. Chinn (). Currency raders and Exchange Rae Dynamics: a Survey of he U.S. Marke, Journal of Inernaional Money and Finance, Vol. (4), Augus, pp Cheung, Yin-Wong, Menzie D. Chinn, and Anonio Garcia Pascual (). Empirical Exchange Rae Models of he Nineies: are Any Fi o Survive? Naional Bureau of Economic Research, Working Paper No. 9393, December. 9. Chrisiansen, Charloe, Angelo Ranaldo and Paul Soderllind (). he ime-varying Sysemaic Risk of Carry rade Sraegies, SSRN Working Paper.. Chinn, Menzie D. (99). Some Linear and Nonlinear houghs on Exchange Raes, Journal of Inernaional Money and Finance,, June, pp Chinn, Menzie D. (8). Nonlineariies, Business Cycles and Exchange Raes Mimeo, Augus.. Chinn, Menzie D., and Richard A. Meese (995). Banking on Currency Forecass: how Predicable is Change in Money?, Journal of Inernaional Economy, 38, (February), pp Clark, odd E. and Michael W. McCracken (). ess of Equal Forecas Accuracy and Encompassing for Nesed Models, Journal of Economerics, 5, pp Clark, odd E. and Michael W. McCracken (5). Evaluaing Direc Muli-Sep Forecass, Economeric Reviews, 4, pp Clarida, Richard, Jordi Gali and Mark Gerler (998). Moneary Policy Rules and Macroeconomic Sabiliy: Evidence and Some heory, NBER Working Papers 644, NBER. 6. Corcoran, Aidan (9). he deerminans of carry rade risk premia, SSRN Working paper. 7. Corradi, Valenina and Norman R. Swanson (7). Nonparameric Boosrap Procedures for Predicive Inference Based on Recursive Esimaion Schemes, Inernaional Economic Review, 48, pp Core, Pasquale Della, Lucio Sarno and Ilias siakas (9). An Economic Evaluaion of Empirical Exchange Rae Models, he Review of Financial Sudies, Vol. (9), pp Diebold, Francis and Rober Mariano (995). Comparing Predicive Accuracy, Journal of Business and Economic Saisics, 3, pp Diebold, F.X. and Nerlove, M. (989). he dynamics of exchange rae volailiy: a mulivariae laen ARCH model, Journal of Applied Economerics, 4, pp. -.. Engel, Charles (996). he Forward Discoun Anomaly and he Risk Premium: a Survey of Recen Evidence, Journal of Empirical Finance, 3 (June), pp Engel, Charles, Nelson C. Mark and Kenneh D. (7). Wes, Exchange Rae Models Are No as Bad as You hink, NBER Macroeconomics, Annual, pp Engel, Charles, Nelson C. Mark and Kenneh D. Wes (9). Facor Model Forecass of Exchange raes, Working Paper, Deparmen of Economics, Universiy of Wisconsin. 4. Engel, Charles and Kenneh D. Wes (5). Exchange Raes and Fundamenals, Journal of Poliical Economy, 3, June, pp Engel, Charles and Kenneh D. Wes (6). aylor Rules and he Deuschemark-Dollar Real Exchange Rae, Journal of Money, Credi and Banking, 38, Augus, pp Ferson, Wayne and Campbell Harvey (99). Sources of Predicabiliy in Porfolio Reurns, Journal of Financial Analys, May-June, pp Gagnon, Joseph E. and Alain P. Chaboud (9). Wha Can he Daa ell Us abou Carry rades in Japanese Yen? Working Paper, Board of Governors of he Federal Reserve Sysem. 8. Galai, G., A. Heah, and P. McGuire (7). Evidence of Carry rade Aciviy, BIS Quarerly Review, pp Giannone, D., L. Reichlin, and L. Sala (5). VARs, common facors and he empirical validaion of equilibrium business cycle models, Journal of Economerics, 7 (), pp Green, W (), Economeric Analysis, 5ed, Prenice Hall. 3. Gourinchas, Pierre-Olivier and Helene Rey (7), Inernaional Financial Adjusmen, Journal of Poliical Economy, 5 (4), Augus. 3. Hamilon, J (994). ime Series Analysis, Princeon Universiy Press. 33. Lewis, Karen (995). Puzzles in Inernaional Financial Markes, in Gene Grossman and Kenneh Rogoff (eds.) Handbook of Inernaional Economics, Amserdam: Norh-Holland. 34. Kilian, Luz, and Mark P. aylor (3). Why is i So Difficul o Bea he Random Walk Forecas of Exchange Raes? Journal of Inernaional Economy, 6 (May), pp Mark, Nelson C., and Donggyu Sul (). Nominal Exchange Raes and Moneary Fundamenals: Evidence from a Small Pos-Breon Woods Sample, Journal of Inernaional Economy, 53 (February), pp

12 Invesmen Managemen and Financial Innovaions, Volume 7, Issue 4, 36. McCracken, Michael W (7). Asympoics for Ou-Of-Sample ess of Granger Causaliy, Journal of Economerics, 4, pp Meese, Richard A., and Kenneh S. Rogoff (983a). Empirical Exchange Rae Models of he Sevenies: Do hey Fi Ou of Sample?, Journal of Inernaional Economy, 4 (February), pp Meese, Richard A., and Kenneh S. Rogoff (983b). he Ou of Sample Failure of Empirical Exchange Models. In Exchange Raes and Inernaional Macroeconomics, edied by Jacob A. Frenkel, Chicago: Univ. Chicago Press (for NBER). 39. Molodsova, anya, and David Papell (8). Ou-of-Sample Exchange Rae Predicabiliy wih aylor Rule Fundamenals, Universiy of Houson Working Paper. 4. Rossi, Barbara (5). esing Long-Horizon Predicive Abiliy wih High Persisence, and he Meese-Rogoff Puzzle, Inernaional Economic Review, February, 46, pp Sock, J.H. and M.W. Wason (5). Implicaions of dynamic facor models for VAR analysis, NBER Working Paper aylor, Mark P., David A. Peel, and Lucio Sarn (). Nonlinear Mean-Reversion in Real Exchange Raes: oward a Soluion o he Purchasing Power Pariy Puzzles, Inernaional Economic Review, 4 (November), pp Visesen, Claus (). Carry rade Fundamenals and he Financial Crisis 7-, SSRN Working Paper. 44. Wes, Kenneh D. (996). Asympoic Inference abou Predicive Abiliy, Economerica, 64, pp Appendix. Algorihm for esimaing he dynamic facor Kalman filering and maximum likelihood mehod can esimae he ime-varying facor hrough wo seps: () consruc an approximae esimae of he facor using he Kalman filering; () he approximae facor is plugged ino he likelihood funcion o esimae he unknown parameers using he ML. hese wo seps are repeaed unil he esimaes of parameers converge. his algorihm is also called he expecaion-maximizaion (EM) algorihm. Because he algorihm uilizes he Kalman filering, we briefly inroduce he Kalman filering firs.. Kalman filering. he Kalman filering is a se of mahemaical equaions ha provides an efficien compuaional (recursive) soluion of he leas-squares mehod. Deailed derivaion of he filer is provided here. Readers are referred o Hamilon (994). Hamilon (994) for exensive discussion on he Kalman filering for ime series. he Kalman filering addresses he general problem of esimaing he hidden sae F R of a discree-ime process ha is governed by he linear sochasic difference equaion F af w, where a belongs o he inerval of (,). he observaion y s( i i) is y F v. he random variables w and v represen he process and observaion noise respecively. hey are assumed o be independen of each oher, Gaussian and wih probabiliy disribuion: w~ N, Q, ~, v N R. he facor F is assumed o sar wih he iniial value F ~ N, V. Suppose we have already observed a sequence of y a ime, denoed by y,...,y facor is is condiional expecaion on y, i.e. Fˆ EF y. Because noises are Gaussian, he condiional expecaion is he same as he generalized leas-squares esimae. Calculaing y. he bes esimae of he Fˆ for every ime period is edious if we use Fˆ by a se of recur- apply he condiional expecaion. he Kalman filering provides a very efficien way o calculae sive equaions. he recursive formula is shown below. Fˆ afˆ K y Fˆ, K a P Q a P Q R, P I K a P Q. Wih he iniial values P V and Fˆ. 4

13 Invesmen Managemen and Financial Innovaions, Volume 7, Issue 4,. Maximum likelihood esimaion. Here we explain how he parameers are esimaed. Assume we have observed a sample y. Le f y, F F denoe he join densiy of he observable y and unobservable facors F F F,..., f, F so ha: y,f F f F f y F f F F, where f y F exp y F R R f F F F af Q Q lnl log / and / exp. hen he log-likelihood funcion is given by: f y, F F y F R log R F af F V log V log. he parameers needs o be esimaed are aqr,,,, V Q logq. Since F is no observable, he maximum likelihood mehod is pracically impossible. A way o ge around his problem is o replace he facor wih he Kalman filering esimae Fˆ. l he maximum likelihood esimaion of is carried recursively. A ieraion l, an esimae of is obained from l he previous esimae. he ieraive process will sop if he new esimae canno improve he log-likelihood. he following seps illusrae he ieraion process. Sep : Se l and choose wih a good guess. Sep : Se. Calculae he condiional expecaion of he log-likelihood ln L on, calculaing E F y, EF y and F F y E convenienly compued by he Kalman filering. Sep 3: Maximize he log-likelihood funcion L y y E ln L y. I involves. hey are compued using he facor esimae Fˆ, which is E ln o obain a new esimae order necessary condiion or he generalized leas squared o esimae he parameer. Sep 4: Repea seps and 3 unil a sopping crierion is saisfied. l. In his sep, use he firs 5