BIS Working Papers No 366 Currency Momentum Strategies by Lukas Menkhoff, Lucio Sarno, Maik Schmeling and Andreas Schrimpf Monetary and Economic Department December 2011 JEL classification: F31, G12, G15. Keywords:MomentumReturns,LimitstoArbitrage,Idiosyncratic Volatility, Carry Trades.

BIS Working Papers are written by members of the Monetary and Economic Department of the Bank for International Settlements, and from time to time by other economists, and are published by the Bank. The papers are on subjects of topical interest and are technical in character. The views expressed in them are those of their authors and not necessarily the views of the BIS. This publication is available on the BIS website (www.bis.org). BankforInternationalSettlements2011.Allrightsreserved.Briefexcerptsmaybe reproduced or translated provided the source is stated. ISSN 1020-0959 (print) ISBN 1682-7678 (online) CurrencyMomentumStrategiesLukasMenkhoLucioSarnoMaikSchmelingAndreasSchrimpfAbstractWeprovideabroadempiricalinvestigationofmomentumstrategiesintheforeignex-changemarket. Wendasignicantcross-sectional spreadinexcessreturnsofupto10%p.a. betweenpastwinnerandlosercurrencies. Thisspreadinexcessreturnsisnotexplainedbytraditional riskfactors, itispartiallyexplainedbytransactioncostsand shows behavior consistent with investor under- and over-reaction. Moreover, cross-sectional currencymomentumhas verydierent properties fromthe widelystudiedcarrytradeandisnothighlycorrelatedwithreturnsof benchmarktechnical tradingrules. However, thereseemtobeveryeectivelimitstoarbitragewhichpreventmo-mentumreturnsfrombeingeasilyexploitableincurrencymarkets.JELClassication: F31,G12,G15.Keywords: MomentumReturns,LimitstoArbitrage,IdiosyncraticVolatility,CarryTrades.WewouldliketothankananonymousReferee,KlausAdam,AlessandroBeber,CraigBurnside,DarrellDue, JacobGyntelberg, Marcel Fratzscher, Jens Jackwerth, GerganaJostova, Aneel Keswani, MichaelMelvin,ChristopherNeely,JesperRangvid,StephanSiegel,SheridanTitman,ChristianUpperandseminarparticipants at several institutions for helpful comments. Wearealsothankful for their input toseveralforeignexchangepractitioners: Thomas Stolper (GoldmanSachs), Bilal Hafeez(DeutscheBank), GarethBerry(UBS),andGeoKendrick(Nomura). SarnoacknowledgesnancialsupportfromtheEconomicandSocial Research Council (No. RES-062-23-2340),Schmeling gratefully acknowledges nancial support by theGermanResearchFoundation(DFG), andSchrimpf isgrateful forsupportfromCREATESfundedbytheDanishNational ResearchFoundation. Theviewsexpressedinthispaperarethoseof theauthorsanddonotnecessarilyreectthoseoftheBankforInternationalSettlements.DepartmentofEconomics,LeibnizUniversitatHannover,KonigswortherPlatz1,30167Hannover,Ger-many,Tel: +495117624552,Emails: menkho@gif.uni-hannover.de,schmeling@gif.uni-hannover.de.Cass Business School, Singapore Management University, andCentre for Economic PolicyResearch(CEPR). Correspondingauthor: Facultyof Finance, Cass Business School, CityUniversityLondon, 106Bunhill Row, London EC1Y8TZ, UK, Tel: +44 20 7040 8772, Fax: +44 20 7040 8881, Email: lu-cio.sarno@city.ac.uk.Centralbahnplatz2,BankforInternationalSettlements,4002Basel,Switzerland. Tel: +41612808942.Email: andreas.schrimpf@bis.org.1. IntroductionMomentumreturnsinstockmarketsprovideastrongchallengetostandardnancetheory.Simplybuyingassets withhighrecent returns andsellingassets withlowrecent returnsresults inaveryprotableinvestment strategywhosereturns aredicult tounderstandbymeansof standardriskfactors(JegadeeshandTitman, 1993, 2001). Consequently, re-searchers have proposed various explanations which focus not only on conventional risk-basedmodels (e.g. Harvey and Siddique, 2000; Chordia and Shivakumar, 2002; Johnson, 2002; Pas-torandStambaugh, 2003; LiuandZhang, 2011), butalsooncharacteristicssuchascreditrisk(Avramov, Chordia, Jostova, andPhilipov,2007)orbankruptcyrisk(Eisdorfer,2008),limitstoarbitrage(e.g. Chabot, Ghysels, andJagannathan, 2009), behavioral explanationssuch as investor under-reaction (e.g. Chui, Titman, and Wei, 2010), or high transaction costs(KorajczykandSadka, 2004). Despitethisprogress, theliteraturedoesnotseemtohavesettledonagenerallyacceptedexplanationformomentumreturnsyet.In this paper, we study foreign exchange (FX) markets as a natural laboratory for the analysisofmomentum returns. Compared to stock markets,FXmarkets aremore liquid andfeaturehugetransactionvolumesandlowtransactioncosts,theyarepopulatedlargelybysophisti-catedprofessional investors, andtherearenonatural short-sellingconstraintsthatpreventtheshortingofpastloserassetstofullyimplementmomentumstrategies. Hence, consider-ingFXmarketsraisesthehurdleforgeneratingsignicantexcessreturnsfrommomentumstrategiesconsiderably.Surprisingly, thereislittleevidenceonmomentuminthecross-sectionofcurrencies. Largecross-country data sets were rare in the past so that the earlier literature has generally focusedonmomentumstrategiesinthetime-seriesof currencies, i.e. momentumstrategieswhereindividual currencies arebought andsoldover timedependingonvarioussortsof signalssuchasmovingaveragecross-overs, lterrules, channel breakouts, etc. Thisliteraturehasshownthatcertaintechnicaltradingrulesweretemporarilyprotablebutthattheirprotsoftentendtodeteriorateovertimeasmoretraderslearnaboutthesestrategiesandstartto1exploitthem(e.g., LevichandThomasIII, 1993; Pukthuanthong-Le, Levich, andThomasIII, 2007; Neely, Weller, andUlrich, 2009, amongothers). Asurveyof this literatureisprovidedbyMenkhoandTaylor(2007). However,someevidenceontheexistenceofcross-sectional momentumprots intheFXmarket is providedbyOkunevandWhite(2003),Asness, Moskowitz, andPedersen(2009)andBurnside, Eichenbaum, andRebelo(2011)inthecontextofsmallcrosssectionsofmajorcurrencies. Relativetoourpaper,thesestudieshaveadierentfocus, however, anddonotprovideaunifyinganalysisforunderstandingreturnstocross-sectionalcurrencymomentumreturns.The main contribution of this paper is to study the economic anatomy of momentum protsin FX markets. We start by forming currency portfolios where an investor is long in currencieswith high past excess returns (so-calledwinners) and short in currencies with low past excessreturns(so-called losers). WetaketheviewpointofaU.S.investorandconsiderexchangerates against the U.S. dollar (USD). Our data cover the period from January 1976 to January2010, andwestudyacross-sectionof upto48currencies. Wegobeyondearlierresearchoncurrencymomentumby(a) providinganin-depthanalysis of therelativeimportanceof systematicversusunsystematicriskforunderstandingmomentumreturns, (b)carefullycomparingmomentumstrategiestocarrytradesandtechnicaltradingrules,(c)quantifyingtheimportanceof transactioncosts, andinvestigatingnon-standardsourcesof momentumreturns,suchas(d)under-andover-reactionor(e)limitstoarbitrage.Wendlargeandsignicantexcessreturnstocurrencymomentumstrategiesofupto10%per annum(p.a). As inJegadeeshandTitman(2001), we ndsome evidence of returncontinuationandsubsequent reversals over longer horizons of upto36months, whichisconsistentwithbehavioral biases, suchasinvestorunder- andover-reaction, andsuggeststhatmomentumeectsindierentassetclassesmayshareacommonsource. Importantly,currency momentum is very dierent from the popular carry trade in FX markets, providing2high returns which are largely unrelated to carry trade returns.1Currency momentum returnsare also dierent from returns generated by technical trading rules,which have been studiedin a large empirical literature (e.g. (e.g. Dooley and Shafer, 1976; Sweeney, 1986; Levich andThomasIII,1993;Neely,Weller,andUlrich,2009).Inordertorationalizethesehighexcessreturnsof currencymomentumstrategies, wein-vestigatewhethercurrencymomentumissignicantlyaectedby(i)transactioncosts, (ii)business cycleriskandother traditional riskfactors, and(iii) dierent forms of limits toarbitrage. Wendthatmomentumreturnsareindeedfairlysensitivetotransactioncosts.Adjustingreturnsforbid-askspreadslowerstheprotabilityof momentumstrategiessig-nicantlysincemomentumportfoliosareskewedtowardscurrencieswithhightransactioncosts. However,transactioncostsareunabletocompletelyaccountforcurrencymomentumreturns.Also, momentum returns in FX markets are not systematically related to standard proxies forbusiness cycle risk, liquidity risk (Brunnermeier, Nagel, and Pedersen, 2009), the carry traderiskfactorproposedbyLustig,Roussanov,andVerdelhan(2011),volatilityrisk(Menkho,Sarno, Schmeling, andSchrimpf, 2011), thethreeFama-Frenchfactors(FamaandFrench,1992) or a four-factor model including a U.S. stock return momentum factor (Carhart, 1997).Inshort, theredoesnotseemtobeasystematicriskfactorwhichwouldexplain(net)mo-mentumreturns, aresultwhichisakintothecorrespondingndingsbasedonU.S. equitymomentum.However, theprotabilityof currencymomentumstrategiesvariessignicantlyover time,whichmayinducelimitstoarbitrageforthemajormarketparticipantsinFXmarkets(e.g.proprietarytraders andhedgefunds), whousuallyhaverather short investment horizons1Thecarrytradeis apopular tradingstrategythat borrows incurrencies withlowinterest rates andinvestsincurrencieswithhighinterestrates. Accordingtouncoveredinterestparity, if investorsareriskneutral andformexpectations rationally, exchangeratechanges will eliminateanygainarisingfromthedierentialin interest rates across countries. However,a number of empiricalstudies show that high interestratecurrenciestendtoappreciate, whilelowinterestratecurrenciestendtodepreciate. Asaconsequence,carry trades form a protable investment strategy, giving rise to the forward premium puzzle (Fama, 1984).SeeBurnside,Eichenbaum,Kleshchelski,andRebelo(2011),Lustig,Roussanov,andVerdelhan(2011),andMenkho,Sarno,Schmeling,andSchrimpf(2011).3andmaythusact myopically(e.g. Shleifer andVishny, 1997).2Furthermore, momentumreturns are clearly related to currency characteristics. Returns are much higher in currencieswithhigh(lagged)idiosyncraticvolatility(about8%p.a.) comparedtocurrencieswithlowidiosyncraticvolatility(about 4%p.a.). Returns arealsorelatedtomeasures of countryrisk,i.e. momentumstrategiesincountrieswithahighriskratingtendtoyieldsignicantlypositiveexcessreturns, whereasmomentumstrategiesincountrieswithlowriskratingsdonot. Finally, asimilareectisfoundforameasureofexchangeratestabilityrisk(i.e. theexpectedriskofobservinglargecurrencymovementsinthefuture).In summary, we provide evidence that, despite FX markets dierences relative to stock mar-kets, the properties of momentum strategies are fairly similar, which suggests that momentumprots in dierent asset classes may share a common root. Similar to stock markets, the highexcessreturnsof currencymomentumstrategiescanbe(only)partiallyexplainedbytheirsensitivity to high transaction costs. Another piece of explanation of why momentum in cur-rency markets persists is that there might be eective obstacles constraining the deploymentof arbitrage capital to exploit the phenomenon. We nd that currency momentum strategiesareriskyinthat their returns arerather unstableover short timeperiods andthat theirexposure is subject to fundamental investment risk, captured by idiosyncratic characteristicsofthecurrenciesinvolved.Theremainderofthispaperproceedsasfollows. WeselectivelydiscussearlierliteratureinSection2. Section3detailsourdataandportfolioformationprocedure. Section4describesmomentum returns in FX markets and compares momentum strategies with benchmark tech-nicaltradingrulesandthepopularcarrytrade, whileSection5discussestheresultsofourtests seeking to explain the high returns to currency momentum strategies. Section 6 providesrobustnesschecksandSection7concludes. AdditionalresultscanbefoundinanAppendixtothispaper.2We usethe termlimits toarbitrageheretomeanthat tradingmomentumstrategies exposes theinvestortorisksnotcapturedbytraditional covarianceriskmeasuressothatananomalylikemomentumreturnsisnoteasilyexploitable. Thisdenitionisinlinewithmuchoftherecentliteraturebutitshouldbenotedthattheterm(originallyduetoKeynes)initiallyreferredtothemarketsinabilitytoexploitrisk-freearbitrageopportunities. Relativetothismoreprecisedenition,ourtestsaremorecloselyrelatedto limitstospeculation.42. RelatedLiteratureAcademicstudiesaboutmomentumstrategiesaremostlyfocusedonstockmarketsbutmo-mentumeectshavebeenalsodetectedinbondandcommoditymarkets. Tosetthestage,we briey survey this literature before we turn to FX markets and highlight the contributionsofthispaper.Stockmarket momentum. Momentumeectsarewell documentedinequitymarketsfor almost twodecades. Theempirical literatureis highlyinuencedbytheworkof Je-gadeeshandTitman(1993),whoshowinathoroughanalysisoftheU.S.stockmarketthatsimplemomentumstrategiesgeneratehighreturns,intheorderofabout12%p.a.,andaredicult to rationalize by standard asset pricing models. Subsequent studies extend the orig-inal researchintonewdomains, includingmanycountriesworldwidebeyondtheU.S. (e.g.Rouwenhorst, 1998, 1999; Chan, Hameed, andTong, 2000; Chui, Titman, andWei, 2010)andhigherfrequencies(GutierrezJr. andKelley,2008).Whileequitymomentumis anestablishedempirical fact, explanations havebeenheavilydisputed. The major approaches to explain momentum can be classied as (i) risk-based andcharacteristics-based explanations, (ii) explanations invoking cognitive biases or informationalissues, and (iii) explanations based on transaction costs or other forms of limits to arbitrage.Startingwithrisk-basedandcharacteristics-basedexplanations(i), earlystudiesshowthatmomentumreturnsarediculttorationalizebycovarianceriskwithstandardfactors(e.g.FamaandFrench, 1996; JegadeeshandTitman, 2001). Inthesamevein, linkingmomen-tumtomacroeconomicriskhasprovenratherchallenging.3Bycontrast, rm-specicchar-acteristics have beenshowntobe linkedtomomentum, e.g. momentumappears tobestrongeramongsmallerrms(Hong, Lim, andStein, 2000), amongrmswithlowercreditrating (Avramov, Chordia, Jostova, and Philipov, 2007), and among rms with high revenue3Forinstance, ChordiaandShivakumar(2002)ndsupportfortime-varyingriskfactorsexplainingmo-mentumreturns,whereasGrinandMartin(2003)andCooper,Gutierrez,andHameed(2004)donot.5growthvolatility(Sagi andSeascholes, 2007). Also, momentumreturnsappeartoalargeextentconcentratedinrmswithahighlikelihoodtogobankrupt(Eisdorfer, 2008). Em-piricalworkinvokingbehavioralbiases(ii)inexplainingmomentumfocusingforexampleoninvestorsunder-reactiontonewsalsofeaturedprominentlysincethebeginningofthedebate(JegadeeshandTitman,1993)andinsubsequentwork(e.g.JegadeeshandTitman,2001; Grinblatt and Han, 2005; Hvidkjaer, 2006).4Stressing how information is incorporatedintoprices, Chan, Jegadeesh, andLakonishok(1996)provideearlyevidencethatanalystsearningsforecastsrespondgraduallytonewswhichmightgenerateunder-reaction. Hong,Lim, and Stein (2000) demonstrate in detail the relation between weak analyst coverage andstrongermomentum.5Analstrandexplorestheroleoftransactioncostsorlimitstoarbi-trage (iii) in explaining momentum. Lesmond, Schill, and Zhou (2004) state that reasonablyhigh transaction costs may wipe out momentum prots. Korajczyk and Sadka (2004) qualifythis nding as they argue that momentum strategies may be designed in a way to limit trans-actioncosts;thiswillleadtoamoremoderatecostlevelsothatevenverylargemomentumportfolios(withassetsworthmorethanonebillionU.S.dollars)arestillhighlyprotable.Momentuminbonds andcommodities. Momentumhas alsobeenshowntoexistinother asset classes. Regarding bondmarkets, momentumstrategies do not workforinvestment-grade bonds (Gebhardt, Hvidkjaer, andSwaminathan, 2005) or bonds at thecountrylevel (Asness, Moskowitz, andPedersen, 2009), butyieldpositivereturnsfornon-investmentgradecorporatebonds(Jostova, Nikolova, Philipov, andStahel, 2010). Furtheranalysis shows that momentum returns are not related to liquidity but seem to reect defaultriskinthewinnerandloserportfolios. Regardingcommoditymarkets, thehighreturnstomomentumstrategiesareshowntoberelatedtomarketstateswithlowlevelofinventoriesthat indicatehigher risk(Gorton, Hayashi, andRouwenhorst, 2008). Thesendings ten-tativelysuggestcommonsourcesof momentumprotswhichseemtobebasedontherisk4Behavioral models e.g. by Daniel, Hirshleifer, and Subrahmanyam (1998), Barberis, Shleifer, and Vishny(1998), HongandStein(1999)accountformomentumeectsbyallowingfordeviationsfromfullyrationalbehaviorsuchasover-condence,slowupdatingofinvestorbeliefsandinformationimperfections.5Inaddition, analystbehaviorwill lead, duringtheperiodof informationincorporation, toinformationheterogeneityamonginvestors,whichisshownbyVerardo(2009)toberelatedtomomentum.6characteristicsoftheunderlyingassets.Currencymomentum. Incontrasttotheextensiveliteratureonmomentumstrategiesinstockmarkets, theliteratureoncurrencymomentumhasmostlydevelopedasomewhatdierentlineofresearch. Themoststrikingdierenceisthefactthatcurrencymomentumstudiesgenerallydonotanalyzemomentuminacross-sectionofcurrenciesbutinthetime-seriesofsingleexchangerates, oftenframedas technical tradingrules.6ThisliteratureissurveyedinMenkhoandTaylor(2007)andwewill discussitinmoredepthbelow. Thistime-seriesliteraturehasextensivelyexaminedwhichkindsoftradingrulesworkbest.One exception from the time-series focus is Okunev and White (2003) who analyze a universeof eight currencies over 20 years, from January 1980 to June 2000. At the end of each month,theinvestorgoeslonginthecurrencywiththebestlast-monthperformanceandgoesshortinthecurrencywiththeworstlast-monthperformance. Thisyieldsareturnof about6%p.a., whichislargelyindependentof thebasecurrencychosenandof thespecictradingrulechosen, i.e. howexactlythebest andworst currenciesareidentied. Thus, thereisclearindicationthatcurrencymomentumstrategiesmaybeprotableandthusworthyofathoroughexamination.7Burnside,Eichenbaum,andRebelo(2011)investigatereturnstoanequally-weighted momentum portfolio that aggregates over momentum positions in individualcurrencies. Theynd(aswedointhispaper)thatstandardriskfactorscannotaccountforcurrencymomentumreturns.TechnicaltradinginFXmarkets. Technical trading in FX is in most cases the same astrend following, that is exploiting the momentum of a market. These time-series momentumstrategies include lter rules and moving average rules. A lter rule gives the signal to invest(to take a short position) in a currency if a dened upwards (downwards) exchange rate changehasoccurred,suchasa1or2percentchange. Amovingaveragerulegivessignalsifshort-6See,e.g.,HarrisandYilmaz(2009),Neely,Weller,andUlrich(2009),andSerban(2010)inthisrespect.7Morerecently, Asness, Moskowitz, andPedersen(2009) havealsoinvestigatedreturns toacurrencymomentumstrategybasedontencurrencies. Thefocusoftheirpaperisverydierentfromours, however,withitsprimaryobjectivebeingtoexplorethecommonalityofmomentumacrossassetclasses.7termexchangerateaveragesbecomelargerorsmallerthanlonger-termaverages.8Simpletrendfollowingtradingstrategiesof thiskindprovideattractivereturns, evenconsideringinterestratedierentialsandtransactioncosts, asforexampletheearlystudiesof DooleyandShafer(1976)orSweeney(1986)havedemonstrated.9Theseearlystudieshavebeenchallengedbysubsequentworkexaminingwhethertrendfol-lowingtradingstrategiesarealsoprotableinlater periods. WhereasDooleyandShafer(1983)andLevichandThomasIII (1993)conrmprotabilityout-of-sample, studiesalsocoveringthe1990sand2000sndthattheabovementionedsimpletrendfollowingstrate-giesappliedtothesamesetof exchangeratesnolongeryieldattractivereturns(see, e.g.,Olson, 2004; Pukthuanthong-Le, Levich, andThomasIII, 2007; Neely, Weller, andUlrich,2009). However, prots are still found if either new forms of trend following strategies or newexchangeratesareconsidered.10Contributionsofthispaper. Incontrasttotheabundanceoftime-seriesstudies,thereislittleevidenceoncross-sectional aspectsof currencymomentum, whoseimportancehasclearlyriseninfaceof therealitiesof todaysFXmarkets. Whereastherewereabouttenconvertibleandliquidcurrenciesinthe1970s, therearemorethan30currenciesavailabletoinvestors today. Andwhile transactionvolumes usedtobe dominatedbybanks FXtraders, assetmanagersof variouskinds(includinghedgefunds)haveemergedassomeofthekeyplayersintodaysFXmarkets. Overall, volumes, tradableassetsandparticipantshave changed,which culminates in the perception of FX as a separate asset class,in paralleltoe.g. equitiesandbonds(King, Osler, andRime, 2011). Evenretail investorsnowadays8For example, a1,5(or 5,20) rule suggests tobuyEuroagainst US-dollar, if the 1(5) dayUS-dollar/Eurorateishigherthanits5-day(20-day)average.9These strategies are also implemented in practice and the widespread use has led, e.g., Lequeux and Acar(1998)tobuildanindexbasedonmovingaveragerulestoserveasabenchmarkforCommodityTradingAdvisors.10Lesswell-knownandlessstudiedformsincludechannelrules,geneticprogramming-basedrules,Markovmodel-basedrulesandothers(e.g. Neely, Weller, andDittmar, 1997). NeelyandWeller(2011)providearecentoverviewof dierenttradingrulesincurrencytrading. Neely, Weller, andUlrich(2009)showthattheserulesarestillprotableuntiltheendoftheirsampleperiodin2005. Pukthuanthong-LeandThomasIII (2008) conrm that standard trading rules in the main exchange rates do not generate prots when recentdataareconsidered,whereasthesamerulesyieldhighreturnsinemergingmarketsexchangerates.8have access to various FX investment strategies via structured products. This naturally leadstostudyingcross-sectionalcurrencymomentumtakingintoaccountthesenewfeaturesandindustrypractices.11Inthispaper, wegobeyondearlierresearchinanumberofdirections. First, weanalyzeamuch longer time span and, more importantly, a much larger cross-section of currencies whichincludescurrenciesofdevelopedandemergingcountries. Thisextendedsampleacrosstimeandcurrenciesiscrucial forouranalysisofreturnstocurrencymomentumstrategiessinceitallowsustobetteridentifyreturnvariationovertime(and, hence, statesofthebusinesscycle)aswell asacrosscurrenciesthatarestructurallydierentandshouldhavedierentexposurestoglobal riskfactors. Second, wecantakeexplicitaccountof transactioncosts,whichiscrucial sincemomentumreturnsareonlyrelevantaslongastheysurviverealistictransaction costs. Third, we take a close look at possible limits to arbitrage (which are a keytheme in the recent literature on equity momentum) and investigate the role of idiosyncraticreturnvolatility,countryrisk,andtheriskofexchangeratestability. Insum,weprovideadetailed account of the economic anatomy and drivers of currency momentum strategies thathasbeenmissingintheliteratureuntilnow.3. DataandCurrencyPortfoliosThissectiondescribesourdata, thecomputationof currencyexcessreturns, andthecon-structionofmomentumportfolios.Datasourceandsamplecurrencies. Thedataforspotexchangeratesand1-monthforward exchange rates cover the sample period from January 1976 to January 2010, and areobtainedfromBBIandReuters(viaDatastream). Wedenotethespotandforwardratesinlogs as sand f, respectively. Spot and forward rates are end-of-month data (last trading day11Wethankananonymous refereefor pointingthis out. Aninvestment product suchas theCurrencyMomentumETFofDeutscheBank,whichisaccessibleevenforretailinvestors,mayserveasanexampleofthesenewtrends.9inagivenmonth)andarethereforenotaveragedoveramonth.Ourtotalsampleconsistsofthefollowing48countries: Australia,Austria,Belgium,Brazil,Bulgaria, Canada, Croatia, Cyprus, CzechRepublic, Denmark, Egypt, Euroarea, Finland,France,Germany,Greece,HongKong,Hungary,India,Indonesia,Ireland,Israel,Italy,Ice-land, Japan, Kuwait, Malaysia, Mexico, Netherlands, NewZealand, Norway, Philippines,Poland, Portugal, Russia, SaudiArabia, Singapore, Slovakia, Slovenia, SouthAfrica, SouthKorea,Spain,Sweden,Switzerland,Taiwan,Thailand,Ukraine,UnitedKingdom.It is worthnoting that, comparedto e.g. Lustig, Roussanov, andVerdelhan(2011) orMenkho, Sarno, Schmeling, andSchrimpf (2011), whosesamples start in1983andhavesevencurrencypairs inthebeginningof thesample(mainly) basedonBBI dataquotedagainsttheU.S.dollar,weemployalongertimeseriesthatextendsbackto1976. Wedosoby complementing BBI data (which only start in 1983) with Reuters data quoted against theBritish Pound as in Burnside, Eichenbaum, Kleshchelski, and Rebelo (2011). We have a totalof16currenciesforthislongertimespanandconvertthesedatatoquotationsagainsttheU.S.dollar. These16countriesare: Austria,Belgium,Canada,Denmark,France,Germany,Ireland, Italy, Japan, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, andtheUnited Kingdom. In addition to the larger cross-section and longer time series,we also havebid and ask quotes for spot and forward rates available so that we can adjust for transactioncostsforthewholeperiodfrom1976to2010.Finally, we note that our eective sample size varies over time as data for emerging countriesbecomeavailableorwhencurrenciesceasetoexist, e.g., duetotheadoptionof theEuro.ToillustratethispointweplotthenumberofcurrencieswithavailabledataforeachmonthofoursampleinFigure1(solidline). Ascanbeinferredfromthisgraph, oursampledoesnotcoverall 48currenciesatthesametimesincedataavailabilityvariesnaturallyduetoinclusionandexclusionofcurrencies. Thetotalsumofactualobservations(currency-monthcombinations)is9,403asopposedtothetheoreticalmaximumof19, 584(408months 48currencies). IndividualstartandenddatesforeachcurrencyareshowninTableA.1intheAppendix.10Figure1abouthereThedashedlineinFigure1alsoshows thenumber of availablecurrencies whicharenottightlypeggedtoothercurrencies. Asmaybeexpected, therearefewercurrenciesof thissort, especiallyintheveryearlypartof thesample. Whileitisnotproblematicpersetoperformmomentumtradingstrategies intightlylinkedcurrencies, onewouldexpect thatmomentumprotsshouldberelativelylowerintheveryearlyyearsofoursample. Thisiswhatwendinourempiricalanalysisbelow.12Currencyexcessreturns. ExcessmonthlyreturnstoaU.S.investorforholdingforeigncurrencykaregivenbyrxkt+1 ikt itskt+1 fkt skt+1(1)wheresandf denotethe(log)spotand1-monthforwardrate(foreigncurrencyunitperUSD),respectively. sdenotesthelogspotratechangeorreturn. Descriptivestatisticsforexcessreturns,forwarddiscounts,andbid-askspreadsarereportedintheAppendix(TableA.1).Forfuturereference,wealsodenenetcurrencyexcessreturns,i.e. currencyexcessreturnsafter bid-askspreads. These returns onlyapplywheninvestigatingdynamic investmentstrategies(momentumstrategiesinourcase), whereinvestorsformportfoliosofcurrencies.We detail the construction of portfolios below and simply dene how we adjust for transactioncostshere.Thenetreturnforacurrencythatentersaportfolioattimetandexitstheportfolioattheend of the month is computed as rxlt+1= fbt sat+1for a long position and rxst+1= fat+sbt+1forashortposition. Ana(b)superscriptindicatestheask(bid)quote. Acurrencythatentersaportfoliobutstaysintheportfolioattheendofthemonthhasanetexcessreturn12Wethankananonymousrefereeforpointingthisout.11rxlt+1= fbt st+1foralongpositionandrxst+1= fat+ st+1forashortposition,whereasacurrency that exits a portfolio at the end of month t but already was in the current portfoliothemonthbefore(t 1)hasanexcessreturnofrxlt+1=fbt sat+1foralongpositionandrxst+1= fat+ sbt+1forashortposition. Hence,sinceforwardcontractsinoursamplehaveamaturityofonemonth, theinvestoralwaysincurstransactioncostsintheforwardlegofhispositionbutdoesnotalwayshavetotradethespotmarketlegofhispositionifhestaysinvestedinaforeigncurrency. Inaddition, weassumethattheinvestorhastoestablishanewpositionineachsinglecurrencyintherstmonth(January1976)andthathehastosell all positions in the last month (at the end of January 2010). Note that bid and ask ratesare daily (not averaged over the month) so that they correspond exactly to the end-of-monthdataforspotandforwardrates.However, one has tobear inmindthat bid-askspreads fromBBI/Reuters are basedonindicative quotes which aretoo high(see e.g. Lyons, 2001) relative to actual eective spreadsin FX markets so that our results with net returns (after deducting the bid-ask spread) shouldbeunderstoodasundercuttingthelowerboundontheprotabilityofmomentumstrategiesand not as the exactreturn. For this reason, we frequently provide results with and withouttransactioncostsbelowinourempirical analysis. Wedenotereturnsorspotratechangesafterdeductingbid-askspreadsas netreturns and netspotratechanges,respectively.Portfolio construction. At the end of each month, we form six portfolios based on laggedreturns over the previous f= 1, 3, 6, 9, 12 months (fdenotes the formation period) and theseportfolios areheldfor h=1, 3, 6, 9, 12months (hdenotes theholdingperiod). Theonesixthof all availablecurrenciesinagivenmonthwhichhavethelowestlaggedreturnsareallocated to the rst portfolio (denoted Low), the next sixth is allocated to portfolio 2, andso on, and the one sixth of all currencies with the highest lagged returns are allocated to thesixthportfolio(denoted High). Hence, thisprocedureyieldsatime-seriesof sixcurrencymomentumportfolios excess returns andis analogous tothe constructionof momentum12portfoliosintheequitymarketliterature.13However, sinceinterestratedierentials(forwarddiscounts)contributeasignicantshareof theexcess returnof currencyinvestments, wealsotrackthepurespot ratechanges ofmomentumportfolios themselves andreport themseparatelyinmanytables. This way,wecancheckwhethercurrencymomentumismainlydrivenbyinterestratedierentialsorwhetheritoccursinspotrates,too.Finally, inmostanalysesweworkwiththeportfoliowhichislonginthewinnercurrencies(portfolio High )andshortinthelosercurrencies(portfolio Low ). Theseportfoliosaredenoted MOMf,hwhere fand h represent the formation and holding period, respectively, asdenedabove. Wealsorefertotheseportfoliossimplyas long-short momentumportfoliosor highminuslow portfolios. Animportantfeatureof theselong-shortportfoliosisthattheyaredollar-neutral, sincethedollarcomponentcancelsoutwhentakingthedierencebetween(any)twoportfolios.4. CharacterizingCurrencyMomentumReturnsInthissection,wepresentourmainempiricalresultsregardingtheprotabilityandcharac-teristics of currency momentum strategies (Section 4.1), the stability of the strategies out-of-sample (Section 4.2), the dierence between currency momentum and technical trading rules(Section 4.3), the dierence between currency momentum and carry trades (Section 4.4), andthelong-runreturnbehaviorofmomentumstrategies(Section4.5).13LustigandVerdelhan(2007)werethersttoformportfoliosof currencyexcessreturnstobeabletoexplainreturnstothecarrytrade. Thisapproachof formingcurrencyportfolioshasprovedveryuseful inuncoveringtheeconomicdriversof carrytraderiskpremiaandhasbeenfollowedbyseveral otherpapersafterwards. This way of constructing momentum returns diers from much of the earlier literature on technicaltradingincurrencymarketswhichmostlyworksinthetime-seriesof individual currencypairs(andthenpotentiallyaggregate across all currencies inthe sample). Our approachis closer tohowmomentumisstudiedintheequitymarketliteratureanditisalsocloselyrelatedtohowthenancial industrysetsuptradablemomentumportfolios. Forexample, DeutscheBankoersacurrencymomentumETFbasedonG10currenciesandtheunderlyingindexislong(short)inthethreebest(worst)performingcurrenciesoverthelasttwelvemonths(DeutscheBank,2010).134.1. ReturnstoMomentumStrategiesinCurrencyMarketsTable 1, Panel A, shows average annualized excess returns (left panel) and spot rate changes(right panel) for a number of high minus low momentum portfolios with formation and holdingperiodseachvaryingbetweenoneandtwelvemonths: f, h=1, 3, 6, 9, 12. Averageexcessreturns in the left panel are based on sorting on lagged excess returns, and average spot ratechangesintherightpanel arebasedonsortingonlaggedspotratechanges. Toprovideaperspectiveonprotabilityof FXmomentumrelativetorisk, Panel Bof Table1reportsSharperatiosforthesamestrategies.Turningtoexcess returns intheleft panel rst, wendthat momentumstrategies yieldsubstantial (andstatisticallyhighlysignicant)excessreturnsof about6 10%forshortholdingperiodsofonemonthandtheirprotsslowlyfadeoutwhenincreasingtheholdingperiod. Thelatterndingisquitepronouncedsincethereisamonotonedeclineinaverageexcess returns whenmovingfromshort holdingperiods tolonger holdingperiods hfor agiven formation period f. However, we nd many instances of signicant momentum returnsforstrategieswithlongerholdingperiodsaswell,sothatmomentumisnotconnedtoveryshortholdingperiods.In the right panel of Table 1, Panel A, we also report the average dierence between spot ratechanges for the high and low portfolio. For ease of exposition, we actually report the negativeof thelogspotratechange(inthenotationof Section3)sothathighervaluesindicateapositivecontributionofspotratemovementstoamomentumstrategystotalexcessreturn.Interestingly, the protability of currency momentum strategies is also clearly visible in spotratechangesthemselvesandisthusnotmostlydrivenbytheinterestratedierential asisthecaseforcarrytrades(see, e.g., Lustig, Roussanov, andVerdelhan, 2011). Infact, thestrategywithatwelvemonthsformationperiodiscompletelydrivenbyfavorablespotratechangesandtheinterestratedierentialreducestheexcessreturnsomewhat.Table1abouthere14As notedabove, results tendtobestrongest for aholdingperiodof h=1month. Wethereforefocusonthesestrategiesinmostofthefollowinganalysisastheyseemtopresentthehardestchallengewhentryingtounderstandmomentumreturnsincurrencymarkets.Sincethelevel of averageexcessreturnsisalsoclearlydependentontheformationperiodf, weprovideresultsforthethreestrategieswithf=1, 6,and12monthsinourempiricalanalysesbelow. Insum, mostofouranalysisintheremainderofthepaperfocusesonthethreebenchmarkstrategiesMOM1,1, MOM6,1,andMOM12,1.14Asarstandsimplemeansofinvestigatingapossiblelinkbetweenmomentumreturnsandthestateofthebusinesscycle,andtoprovideagraphicalexpositionofmomentumreturnsaccruingtoinvestors, Figure2shows cumulativeexcess returns for thethreebenchmarkmomentum strategies MOM1,1, MOM6,1, and MOM12,1over the full sample period. Shadedareas correspondtoNBERrecessions. As illustratedbythe gure, there is noobviouscorrelationofmomentumreturnswiththestateofthebusinesscycle(asexaminedlaterinSection5.2). However,thethreebenchmarkmomentumstrategiesshowsomeco-movementbutarenotperfectlycorrelated.Figure2abouthereSharpeRatios. Inordertogetarstmeasureofrisk-adjustedreturns,PanelBofTable1presentsSharpeRatiosforthemomentumstrategiesshowninTable1aboveinPanelA,andnormalizedspot ratechanges(averagespot ratechanges dividedbytheir standarddeviation) inPanel B. Corroboratingthe evidence above, currencymomentumstrategiesseem highly protable, at least for a subset of strategies. For example, the annualized SharpeRatio of the MOM(1,1) strategy is 0.95,which seems very high,even in comparison to carrytrades(see,e.g.,Menkho,Sarno,Schmeling,andSchrimpf,2011,whoreportanannualizedSharpeRatioof0.82foracarrytradestrategy). Hence,evenwhentakingriskintoaccountonthebasisofSharpeRatios,momentumstrategiesseemhighlyattractive. Inaddition,we14Onemightworrythatsomecurrencieswerenotalwaystradableduringoursampleperioddueto, e.g.,capitalaccountrestrictions. WeproviderobustnesschecksonthisissueinSection6.1.15see from Panel B of Table 1 that this performance is largely driven by spot rate changes andthatitisnotdominatedbytheinterestratecomponentofexcessreturns.Momentumreturns andsizeof thecross-section. Asnotedaboveintheprevioussection, our eective sample size never exceeds 40 currencies and is therefore relatively smallcomparedtosample sizes usedin, e.g., the equitymomentumliterature. However, it iswell knownfromearlierworkthatevensmall portfoliosof currenciescanyieldlargegainsfromdiversicationsincecurrenciestendtobelesscorrelatedthanstocks(e.g., Burnside,Eichenbaum, andRebelo,2008). Inordertoexplorethelinkbetweenthesizeofthecross-section and the magnitude of momentum returns, we conduct a stylized simulation experimentas follows. In each run i, we randomly draw (without replacement) a set of Ncurrencies fromthesetofall48currencieswhileimposingtherestrictionthatwehavedataforatleastsixcurrencies in each month of the sample period from January 1976 to January 2010. We thencalculateaverageannualizedmomentumexcessreturnsforaMOM(1,1)strategyandsavethis result. We do this 5,000 times for each cross-section size Nand average over momentumprotstoobtainanestimateof the typical momentumprotconditional onobservingacross-sectionofsizeN. ForN= 48wesimplyreportthemomentumprotfromTable1.Figure3showsresultsfromthisexerciseanditcanbeseenthatexpandingthesizeofthecross-sectionisveryusefulforsmallcross-sectionsbutmuchlessimportantforlargercross-sections. Inotherwords,therearedecreasinggainsfromexpandingthesizeofthetradablecurrencyuniverse. Themaximumlevel ofreturnsisroughlyobtainedforacross-sectionofsize N= 36. Hence, although our cross-section is far from what is used in the equity marketliterature, one canbe condent that the results are quite representative of the currencymarketasawhole.Figure3abouthere164.2. Out-of-samplePerspectiveOursetuptoillustrateFXmomentumprots, whichisakintotheequityliterature, hasaclearout-of-samplecomponent, sinceweformportfoliosbasedonlaggedinformationonly.Hence,themomentumstrategiesdiscussedaboveareimplementableinrealtime. However,averagereturnscanvarymarkedlyacrossdierentstrategies(thatis,dierentcombinationsof formationandholdingperiod), andcanalsobefairlylow. For example, thestrategywithatwelvemonths formationandholdingperiodonlyyields 1.89%p.a. over thefullsample whereas the strategy with a one month formation and holding periods experienced anannualized average return close to 10%. This particular information is only available ex postand an investor could not have conditioned on this information in 1976. Hence, it is interestingtoexaminewhetherinvestorscouldhaveactuallyexploitedthesemomentumprotstakingintoaccountthatthereisexanteuncertaintyaboutwhichspecicmomentumstrategytofollow.15Put dierently, do specic momentum strategies identied to be attractive in-samplecontinuetodowell?Wetacklethisquestionbyinvestigatingreturnstowhatweterm Momentum2 strategies.To do so,we imagine an investor who can invest in 144 dierent strategies (all combinationsoff= 1, 2, ..., 12andh = 1, 2, ..., 12)andhastorelyonsomemechanismtoselectbetweenthesedierentstrategies. Anaturalmechanisminourcontextistolettheinvestorrelyonmomentuminlaggedmomentumreturns (as measuredover anevaluationperiod). Morespecically, weform9portfoliosoutof theuniverseof 144possiblemomentumstrategies.These nine portfolios are based on a ranking of the momentum strategiesthemselves by theirlaggedreturnsduringanevaluationperiod, hencethetermMomentum2. ResultsforthisexerciseareshowninTable2whichreportsreturnsforall 9Momentum2portfolios(fromworstlaggedreturns tobestlaggedreturns) andabest minus worstportfolio. Forrobustnessweshowresultsforlagsof1, 3, 6, 9, 12, 60,and120monthsoverwhichindividualmomentumstrategies areevaluated. As canbeseen, usinglaggedmomentumreturns toidentifyfuturemomentumreturns seems feasible. For example, conditioningjust onlast15Silber (1994) also investigates whether trading strategies identied as protable over an in-sample periodcontinuetoperformwellinanout-of-sampleperiod.17months returnacross all possiblestrategies leads toanannualizedaverageexcess returnof 7.67%p.a. Asforthesimplemomentumstrategiesabove, weseeadecliningpatterninreturns when moving to longer selection windows. For example, using a window of 120 monthsleads to much lower returns of only 2.70% p.a., which, however, are still signicantly dierentfromzero. Mostimportantly, theseresultsindicate, however, thatspecicFXmomentumstrategiesthat performedwell inthepast tendtocontinuetodowell andarethusquitestable.Table2abouthereWhile the above analysis conrms that momentumreturns are exploitable inanout-of-samplesetting, wefurtherexaminethisissuefromasomewhatdierentanglebyasimpleinvestigationof thesub-samplestabilityof momentumprots. Todoso, TableA.2intheAppendixshowsaverageannualizedexcessreturnsandSharpeRatiosforfoursubperiodsofequal length. We report results for formation periods of f= 1, 3, 6, 9, 12 and a holding periodof one month. As can be seen, the ranking of these ve dierent strategies is fairly stable overthe four subperiods. In other words, it is never the case that one strategy does extremely wellinonesubperiodbutthenproduceslargelossesinthenextsubperiod. Overall,weconcludethat it should have been possible for an investor to exploit momentum strategies in real time.4.3. ComparingMomentumandTechnicalTradingRulesThe results presented above suggest that momentum eects in the cross-section of currenciesarequitestrongandthatmomentumstrategiesconsequentlyyieldhighexcessreturnsandSharpeRatios. However,animportantquestioniswhetherthecurrencymomentumreturnsdocumented above can be regarded as a novel phenomenon per se or whether they may merelyreectreturnstotechnicaltradingstrategiesthathavebeendocumentedextensivelyintheearlierliterature.Toinvestigatethisissue,wecomputereturnstothreebenchmarkmovingaveragecross-over18rules that have been employed frequently in earlier work on technical trading in FX markets.These strategies are based on moving averages of 1 and 20 days (1, 20), 1 and 50 days (1, 50),and 1 and 200 days (1, 200) (see, among others, Dooley and Shafer, 1983; Levich and ThomasIII, 1993; Neely, Weller, and Ulrich, 2009).16While it is clearly not the case that these threestrategies are perfect proxies for all possible technical trading strategies, their prominence inthe earlier literature makes them interesting for comparison with our cross-sectional currencymomentumstrategies.Tosetthestage,werstcomputereturnstothesemovingaveragerulesforallcurrenciesinour sample individually and then aggregate these strategies into an equally-weighted portfolio.Panel Aof Table3reportsdescriptivestatisticsforthethreerules, whichshowthatthesestrategies are protable, with annual mean excess returns around 5% and high annual SharpeRatios between 0.77 and 0.88. Hence, these strategies form an interesting benchmark for ourmomentumreturns.To assess whether returns to the moving average rules described above capture returns to thecurrency momentum strategies, we run regressions of momentum returns for the MOM(1,1),MOM(6,1), and MOM(12,1) strategies on returns of the three moving average rules. ResultsareshowninPanelBofTable3.Table3abouthereIt canbe seenthat, eventhoughmovingaverage rule returns andcurrencymomentumaretosomeextentcorrelated, thelargestR2onlyamountsto26%. Moreimportantly, allinterceptestimates(s)arelargeineconomictermsandstronglysignicantinstatisticalterms. Hence, itseemsfairtoconcludethatcurrencymomentumisnotcloselyrelatedtobenchmark technical trading strategies as studied in the earlier literature, and that controllingforreturnsof thesetradingrulesdoesnotwipeoutreturnstoourcross-sectional currencymomentum.16These trading strategies generate a buy (sell) signal,when the shorter moving average crosses the longermovingaveragefrombelow(above).19Inaddition, we alsoexamine returns toindividual currencies momentumstrategies, i.e.whereaninvestorislongorshortineachcurrencydependingonlaggedreturnsinthesamecurrency(thisstrategyisalsostudiedinMoskowitz, Ooi, andPedersen, 2011). WereportdescriptivestatisticsforreturnsofeachcurrencyinPanelAofTableA.3intheAppendix,alongwiththeaverageacrosscountries, anequallyweightedportfolioofall individual cur-renciesstrategies,and,forcomparison,thecross-sectionalmomentumstrategyemployedinthispaperinPanel B. Itcanbeseenthatmostof thesetime-seriesmomentumstrategiesare protable on average (Panel A of Table A.3) but that an aggregate strategy (the equallyweighted portfolio, EW, in Panel B) is less protable than a cross-sectional momentum strat-egy (MOM(1,1) in Panel B), which has a much higher average excess return (almost twice ashigh)andSharpeRatio.4.4. ComparingCurrencyMomentumandtheCarryTradeAnimportant questionis towhat extent momentumstrategies simplycapture the sameinformationasthepopularcarrytradestrategyinFXmarkets, whereinvestorsgolonginhighinterest ratecurrencies andshort inlowinterest ratecurrencies. After all, interestratedierentialsarestronglyautocorrelatedandspotratechangesdonotseemtoadjusttocompensate for this interest rate dierential, whichis well-knowninthe literature asthe forwardpremiumpuzzle (Fama, 1984). Hence, itmaybethecasethatlaggedhighreturnssimplyproxyforlaggedhighinterestratedierentialsandthat,therefore,currencymomentumreturnsareverysimilartocarrytradereturns. Inordertoaddressthisconcern,we perform a comprehensive comparison between momentum returns and carry trade returnsinthissection. Theresultsclearlyshowthatcarrytradeandmomentumstrategies,aswellastheirassociatedreturns,areinfactverydierent.Comparingportfolioproperties. We rst investigate characteristics of momentumandcarry trade portfolios, which are reported in Table 4. The table shows descriptive statistics forthe six momentum portfolios with a formation and holding period of one month and six carry20trade portfolios where currencies are sorted into portfolios depending on their lagged interestrate, as in e.g. Lustig, Roussanov, and Verdelhan (2011) or Menkho, Sarno, Schmeling, andSchrimpf(2011).17Table4abouthereAscanbeinferredfromthistable, thereisamonotonicallyincreasingpatterninaveragereturnsforbothcross-sectionsbutnoclearpatterninhighermomentsofthereturndistri-bution. Whilethelevel of averagereturnsandstandarddeviationsof thehighminuslowmomentumandcarrytradeportfolios is roughlysimilar, wendthat thetwolong-shortportfoliosareclearlydierentintermsof theirskewness. Whilethecarrytradeproducesnegatively skewed excess returns (also see Brunnermeier, Nagel, and Pedersen, 2009), we ndaslightlypositiveskewnessforthemomentumstrategy.Moreinterestingly, thelasttworowsofeachpanel showlaggedaveragereturnsandlaggedaverageforwarddiscountsforeachportfolioatthetimeofportfolioformation. Momentumportfoliosdohaveapositivespreadinforwarddiscountsandcarrytradeportfolioshaveapositivespreadinlaggedreturns, butthesespreadsaremuchlowerinabsolutevaluethanthespreadinthecharacteristicusedforsortingcurrenciesintoportfolios. Morespecically,theaveragecross-sectionalspreadinforwarddiscounts(inannualizedterms)atthetimeofportfolio formation is about 4.6% (5.13% versus 0.44%) for the momentum cross section butaveragesmorethan15%forthecarrytradecrosssection. Similarly, theaveragespreadinlaggedreturnsisalmost6%forthemomentumportfolios(2.94%versus 2.93%)butonly0.84%forthecarrytradecross-section. Hence, momentumandcarrytradestrategiesmaybesomewhatrelatedbutarefarfrombeingidentical.Returncorrelations. Table5, Panel A, shows correlationcoecients betweenreturnstomomentumportfolios andcarrytrade portfolios. We showresults for the long-short17Toconservespaceinthistable,wefocusonthemomentumstrategywithf= 1andh = 1. Resultsaresimilarfortheotherstrategies.21momentumstrategiesMOM1,1, MOM6,1, andMOM12,1andalwaysreportthecorrelationbetweencorrespondingportfolios; e.g. thecorrelationof momentumportfolio2andcarrytrade portfolio2, or the correlationbetweenthe highminus low(H-L) carrytrade andmomentumportfolios. It canbe seenthat the correlations of excess returns for the sixportfoliosareratherhighbutthatthereisbasicallynocorrelationbetweenthehighminuslowportfolios, andthelatterrepresentthewaycarrytradeandmomentumstrategiesaretypicallyimplementedbymarket participants. Thus, the returntofollowingacurrencymomentum strategy is basically uncorrelated with carry trade returns and this nding holdstrueregardlessoftherespectiveformationperiodunderlyingamomentumstrategy.Table5abouthereIncontrast,weshowinPanelBthatthehighminuslowportfoliosofthethreemomentumstrategies are muchmore highlycorrelatedandreachcorrelations of more than70%forMOM6,1and MOM12,1. Hence, it seems fair to conclude that returns to dierent momentumstrategiesarelikelytoshareastrongcommoncomponent.That excess returns tocarrytrades andmomentumstrategies are basicallyuncorrelatedinFXmarkets appears inlinewithreal-worldstrategies of manycurrencyinvestors whocombinemomentumandcarrytradepositions intheir portfolios totakeadvantageof analleged diversication benet from following the two strategies simultaneously.18For example,duringtherecentnancial crisisfromJuly2007toJune2009, thebenchmarkmomentumstrategywithh = f= 1experiencedanaveragemonthlyreturnof0.80%whereasthecarrytradeyieldedanegativeaveragemonthlyreturnof 0.05%. Thereturncorrelationofthesetwostrategieswasaslowas 31%overthesetwoyears. Hence,thetwostrategiesshowedaclearlydierentbehaviorduringthisperiod.18PattonandRamadorai (2011)forexampleshowinageneral universeof hedgefunds(notnecessarilycurrencyfunds) that there is signicant exposure to carrytrade andmomentum-type returns andthatthis exposureis time-varying. PojarlievandLevich(2010) showviastyleregressions that currencyfundmanagersengageinbothcarrytradeandmomentum-typestrategies. MelvinandShand(2011)showthatcurrency managers follow momentum strategies but that their exposure to momentum and the way momentumstrategiesareimplementedchangeovertime.22Double sorts. Next, we provide results based on double sorts. To this end, we rst double-sortcurrenciesintotwoportfoliosdependingonwhetheracurrencyhasalaggedforwarddiscount above or below the median (of all available currencies), and then into three portfoliosdependingontheirlaggedexcessreturn. Portfoliosarere-balancedeachmonth(i.e. h = 1).Table6showsresultsforthesedoublesortsforformationperiodsof f =1, 3, 12months.Thereisnomaterial dierencebetweenmomentumreturnsamonghighversuslowinterestratecurrencies. Forexample, thehighminuslowmomentumreturnforastrategywithaonemonthformationperiodbasedonlowinterestratecurrenciesis5.06%p.a. onaverage,whereas it is 5.36%p.a. for highinterest ratecurrencies. Hence, thedierencebetweenthesetwohighminuslowmomentumportfoliosislessthan0.30%p.a. andnotstatisticallysignicant(withat-statisticofonly0.17). Findingsfortheothertwoformationperiodsareverysimilar.Table6abouthereAsabove, wedonotndastrongrelationbetweenmomentumandcarrytradestrategiesandthedoublesortssuggestthatthetwostrategiesarelargelyindependent. Infact,goinglong in currencies with high lagged returns and high interest rates whilst shorting currencieswithlowreturnsandlowinterestratesgeneratesanexcessreturnof10.52%p.a., whichisevenlargerthanthespreadinbothmomentumorcarrytradeportfoliostakenindividually.Cross-sectionalregressions. Finally, we want to separate the eects of lagged excess re-turns and lagged interest rate dierentials on future excess returns. To this end, we run Fama-MacBethtypecross-sectional regressionsof currencyexcessreturns(orspotratechanges)on (i) lagged excess returns over the last lmonths, (ii) lagged forward discounts, and/or (iii)laggedspotratechangesforeachmonthofoursample,i.e.rxkt= t + rx,trxkt;t1 + FD,t(ft1st1) + s,tskt;t1 + t(2)23wherethesubscript t ; t 1refers toavariabledenedover thelastmonths usinginformation available at time t1. This procedure yields a time-series of coecient estimates(t, t) and we report the mean of these time series and t-statistics based on Newey and West(1987) standard errors in Table 7 in the spirit of the approach by Fama and MacBeth (1973).19Thesecross-sectional regressions servetodisentangletheinformationcontainedinlaggedreturns(orspotratechanges)andforwarddiscountsforfutureexcessreturns(orspotratechanges)inaregressionframeworkandonthelevel of individual currencies. Momentumstrategies require individual currencies excess returns to vary cross-sectionally in a way thatispredictablebylaggedreturns. Cross-sectional regressionsallowustotestforthiseectwhilesimultaneouslycontrollingfor interestratedierentialsand, hence, complementthedoublesortsabovewhichworkonaportfoliolevel anddonotnecessarilycontrol forbothfactorsatthesametimeduetosequentialsorting.PanelAshowsresultsforregressionswhereweuselaggedexcessreturns,forwarddiscounts,and/or spot rate changes over the last month as explanatory variables, whereas Panels B andCshowresultsforvaluesoflequaltosixandtwelve,respectively.20Turningtoresultsforexcessreturnsrst(leftpartofTable7),wendthatlaggedreturns,laggedforwarddiscounts,aswellaslaggedspotratechangesarecross-sectionallypositivelyrelatedtosubsequent currencyreturns evenwhenincludingtheminjoint specications.Hence, momentumeectsarerobusttocontrollingforforwarddiscounts(interestratedif-ferentials). Furthermore,itisnoteworthythatlaggedspotratechangesdoaboutaswellaslagged excess returns in the cross-sectional regressions so that momentum seems to originatefrom spot rate changes and not from lagged interest rate dierentials, which corroborates ourndingthatcarrytradesandmomentumaredierent.Table7abouthere19SeeforexampleGutierrezJr. andKelley(2008),whoemployasimilarmethodology.20Foreaseofinterpretation,wemultiplyspotratechangesbyminusone,sothathighervaluesmeanthattheforeigncurrencyisappreciatingagainsttheUSD.24The right part of Table 7 shows the same calculations but with spot rate changes as dependentvariables. While the eect of lagged returns or spot rate changes is very similar to our resultsdescribedabove, wendthat theforwarddiscount has anegative impact onfuturespotratechanges. However, thecoecientsbasedonunivariateregressionsarealwayssmallerthanoneinabsolutevalue. Hence,aonepercenthigherinterestrateinaforeigncountryisonlyfollowedbyadepreciationsmallerthanonepercentrelativetoothercurrenciesexcessreturns against the USD, consistent with the existence of a forward bias (Fama, 1984). Notethatthesearecross-sectional regressionssothatresultsdonotnecessarilytranslateintoatime-seriessettinginwhichtheforwardpremiumpuzzlehastypicallybeenstudied.4.5. Post-formationMomentumReturnsJegadeesh and Titman (2001) suggest that momentum returns are driven by slow informationdiusion that leads to under-reaction and persistence in returns (also see Chui, Titman, andWei, 2010). This initial under-reactionmayfurthermore be accompaniedbysubsequentover-reactionwhichmagniesthedriftinreturnsbuthastobecorrectedoverthelongrun.Toinvestigatetheseissues, JegadeeshandTitman(2001)studythepost-formationholdingperiodreturnsof momentumstrategiesoverlongertimespans(i.e. thereturnsoverlonghorizonsafterportfolioformationwheretheportfoliocompositionisheldconstant). Theynd a (roughly) inverted U-shaped pattern, i.e. returns tend to increase for several monthsuptooneyearafterportfolioformationbutthenpeakandstarttodecreasesignicantly.Jegadeesh and Titman interpret this pattern as evidence of initial under-reaction which drivespricesandsubsequentover-reactiontotheseriesof highreturns, pushingpricesupabovethefundamentalvalueoftheasset. Thisover-reactionisthencorrectedoverlongerperiods,leading to the observed predictable pattern of increasing and decreasing returns after portfolio25formation.21Asarstcheckofthishypothesisforcurrencymarkets, weplotcumulativepost-formationexcess returns over periods of 1, 2, . . . , 60months for thezero-cost long-short momentumportfolioswithaone, six, andtwelvemonthsformationperiod(i.e. MOM1, MOM6, andMOM12)inFigure4. Returnsinthepost-formationperiodareoverlappingsinceweformnewportfolioseachmonthbut track theseportfoliosfor 60months. Thereisa clearpatternof increasingreturnswhichpeaksafter 8 12monthsacrossstrategiesandasubsequentperiod of declining excess returns. The decline is more pronounced for momentum strategieswithlongerformationperiods. Thus, onthefaceof it, thisevidencelooksverysimilartothepatternidentiedinequitymarketsasinJegadeeshandTitman(2001). Thisresultisinterestingsinceitsuggeststhatcurrencyandequitymarketmomentummayhavesimilarorigins.22Figure4abouthereInsum, these results oncurrencymomentumare consistent withthose onstockmarketmomentum, wheremomentumreturnsmaybe(atleastpartly)drivenbyslowinformationprocessingandinvestorover-reaction. However,giventhehighlyliquidFXmarketwhichisdominated by professional traders and investors it is hard to believe that investor irrational-ities of this kind are not quickly arbitraged away. Thus, it is worthwhile to examine possiblelimitstoarbitrageactivitywhichcouldexplainthepersistenceofmomentumprotsinFXmarkets. Thisisaddressedinthenextsection.21Thereisrelativelylittleworkonbehavioral eectsincurrencymarkets(comparedtoequitymarkets).Burnside,Han,Hirshleifer,andWang(2010)recentlyshow,however,thatconceptsfrombehavioralnancemaybeusefultounderstandFXphenomenaaswell. Inaddition,BacchettaandvanWincoop(2010)arguethat many FX portfolios are still not actively managed but that portfolio decisions are often taken infrequently,whichcanbefullyrationalduetothecostsofportfolioadjustments. ThismechanismcouldalsoaccountforslowdiusionofinformationintopricesinFXmarkets. Investorsinfrequentportfolioadjustmentdecisions,slow-movingcapitaldeployedtoexploitarbitrageopportunitiesandtheimplicationsoftheseaspectsforthedynamicsofassetpricemovementsarealsodemonstratedrecentlyinDue(2010).22Wealsoprovidethesameresultsforpost-formationdriftincumulativespotratechangesinFigureA.1intheAppendixandndaverysimilarpattern(althoughwithasomewhatlowermagnitudewithrespecttotheinitialpriceincreases)sothattheresultdiscussedabovedoesnotseemtobedrivenbyinterestratedierentialsbutalsostemsfrompricechanges.265. UnderstandingtheResults5.1. TransactionCostsWhatroledotransactioncostsplayformomentumreturns? Toaddressthisquestion, werst report momentum returns after transaction costs in Table 8, which is otherwise identicaltoTable1butprovidesanadjustmentfortransactioncosts. Forthistable, weimposethefullquotedbid-askspreads. Thisspreadisknowntobetoolargerelativetoactualeectivespreads(Lyons, 2001). Hence, theseresultsarelikelytounderestimatemomentumreturns(or equivalently to provide a lower bound on protability), whereas neglecting spreads clearlyoverstatesmomentumreturns.Table8abouthereThe results showthat transactioncosts couldbe animportant factor for understandingmomentumreturnsincurrencymarkets(Burnside, Eichenbaum, Kleshchelski, andRebelo,2006;Burnside,Eichenbaum,andRebelo,2007). Whenapplyingthefullspread,returnsforthebeststrategy(withf, h = 1)dropfromnearly10%toabout4%p.a. andtheywipeoutmostoftheprotofmanyotherstrategies. Interestingly,theeectsoftransactioncostsontheaveragespotratechangesofportfolios(whichareadjustedforbid-askinananalogousfashiontoexcessreturns)arerelativelylessaected. Tomakethefull eectoftransactioncostsmoretransparent, wealsoplotcumulativenetexcessreturns(aftertransactioncosts)for the three baseline strategies MOM1,1, MOM6,1, and MOM12,1 in Figure 5. Again, shadedareas correspond to NBER recessions. It can be seen that FX momentum strategies are muchmore protable (after transactioncosts) inthe later part of the sample, but momentumstrategies do not always deliver high returns to investors. Instead, there is much variation inprotability.Figure5abouthere27Next, giventhat thequotedspreadis knowntobetoohighrelativetoeectivespreads,wefollowGoyal andSaretto(2009)andreportresultsformomentumexcessreturnsaftertransactioncostsof75%(PanelA)and50%(PanelB)ofquotedspreadsinTable9.Table9abouthereResultsforthesemorerealisticbid-askspreadadjustmentsindicatethattransactioncostsclearly matter but that they are not the sole driver of FX momentum returns as we nd thatmanystrategiesstillyieldeconomicallyhighandstatisticallysignicantreturnsonaverage.Further scrutinizingthis issue, wecanbreakuptheimportanceof transactioncosts intoturnoveracrossportfoliosandbid-askspreadsacrossportfolios. WeprovideresultsonbothissuesintheAppendix(TableA.4). Twomainconclusionsemergefromthisexercise. First,turnover can be extremely high, reaching values of more than 70% per month for the strategywithaonemonthformationandholdingperiod. Second,thewinnerandlosercurrenciesdohavehighertransactioncoststhantheaverageexchangerateandthemarkuprangesfromabout 2.5 to 7 basis points per month. Accordingly, trading in the winner and loser currencies(asisnecessarytosetupamomentumstrategy)ismorecostlythantradingintheaveragecurrencypair. Hence,transactioncostsclearlymattertoaconsiderableextent.However, giventhattransactioncostsshouldbeexpectedtodeclineovertimeduetomoreecienttradingtechnologies(suchaselectronictradingnetworksoperatedbye.g. EBSandReuters), it seems unclear whether transactioncosts areabletofullyexplainmomentumreturns. Figure6shows averagebid-askspreads across currencies for eachmonthinoursampleandseparatelyforall countriesandforthesubsampleof 15developedcountriesasdenedabove. Whilethereisalotoftime-seriesvariationinaveragespreads,itisthecasethat spreads have trended downwards over our sample period. This downward trend is mostclearlyseenforthesampleofdevelopedcountriesforwhichwehavealmostcompletedatahistoriesandforwhichaveragespreadsarenotdrivenbythefrequentinclusionofemergingmarket currencies that induce some large spikes inaverage spreads whenlookingat thesampleof all countries. Overall, thedownwardtrendinbid-askspreadsseemstosuggest28thatnewtechnologyhasswampedthepositiveeectofvolatilityonbid-askspreads. Thus,it is interesting to also investigate momentum strategies over a later part of our sample wherebid-askspreadstendtobeloweronaveragesincelowertransactioncostscouldeitherimply(i) higher momentum returns due to lower trading costs or (ii) lower momentum returns sincelowertradingcostsfacilitatemorecapitalbeingdeployedforarbitrageactivity.Figure6abouthereAppendixTableA.11showsresultsforthesamecalculationsunderlyingTable1abovebutweonlyincludetheperiodJanuary1992toJanuary2010inordertolearnaboutwhethertheprotabilityofmomentumstrategiesincreasesordeclinesoverthisrecentperiodoflowtransactioncosts. Wendthatunadjustedmomentumreturnsreachlevelssimilartothosefor the full sample (Panel A) but that transaction cost-adjusted net excess returns (Panel B)areclearlyhigherand, forexample, reachaverageannualizedvaluesof morethan7%forthe1-monthstrategyMOM1,1. Thus,lowerbid-askspreadsdonotnecessarilyleadtolower(unadjusted)excessreturns, whichfurtherindicatesthattransactioncostsarenotthesoledriving force behind momentum eects. This evidence also indicates that momentum returnsareaphenomenonwhichisstillexploitablenowadays.5.2. MomentumReturnsandBusinessCycleRiskTable 10, Panel A, shows results from univariate time-series regressions of momentum returnsonvarious riskfactors or business cyclestatevariables (see, e.g., Burnside, Eichenbaum,Kleshchelski,andRebelo,2011;Sarno,Schneider,andWagner,2011,forsimilarregressionsinthe context of currencyreturns). These factors include macrovariables or other riskfactors from the earlier literature: Consumption stands for real growth in non-durables andservicesconsumptionexpenditures, Employment denotesU.S. total nonfarmemploymentgrowth, ISM denotestheISMmanufacturingindex, IP denotesgrowthinrealindustrialproduction,CPIdenotes theinationrate,M2is thegrowthinreal moneybalances,Disp Inc is growth in real disposable personal income, TED denotes the TED spread (the29dierencebetween3-monthinterbankrate,Liborand3-monthT-Billrate), Term denotesthetermspread(20-year maturityminus 3-monthT-Bill rate), HMLFXis thereturntothecarrytradelong-shortportfolio(Lustig,Roussanov,andVerdelhan,2011),andV OLFXisaproxyforglobal FXvolatility(Menkho, Sarno, Schmeling, andSchrimpf, 2011). Wenote that the alphas in these regressions cannot be interpreted as a measure of risk-adjustedreturnsformostspecicationssincewearemainlyemployingmacrovariablesorothernon-return based factors here. Statistical signicance at the 5% level or below is indicated by boldnumbers. However, looking across momentum strategies and macro-nance risk factors, thereis little evidence that exposure to these factors is able to account for momentum returns. TheadjustedR2saregenerallytinyandmostslopecoecientsareinsignicantlydierentfromzero.23Table10aboutherePanel Bof Table 10shows amultivariate regressionof momentumreturns onthe threeFama-Frenchfactors augmentedbythe U.S. stockmomentumfactor (UMD), andit canagainbeseenthatthereisbasicallynoexplanatorypower. Moreover, thealphasintheseregressions (which are annualized and in percentages) can be interpreted as the risk-adjustedperformanceofmomentumreturnssincethefactorsareexcessreturnsinthiscase. Acrossstrategies, the alphas are fairly high, as judged by this particular model for returns. Based onearlierresearchfortheU.S.stockmarket,thisresultdoesnotcomeasasurpriseregardingthethreeFama-Frenchfactors but it seems noteworthythat currencymomentumis alsounrelatedtotheUMDfactor.2423Asmentionedearlier,oneexceptionisthemomentumstrategywitha12monthsformationperiodandglobalFXvolatility. WendahighlysignicantslopecoecienthereandapositiveR2. Menkho,Sarno,Schmeling, and Schrimpf (2011) show for this momentum strategy that innovations to global FX volatility doindeedcapturealargeamountofthecross-sectionalspreadinreturnsandthatvolatilityriskissignicantlypriced. However,wedonotndthatFXvolatilityriskhelpsmuchforunderstandingmomentumreturnsofthestrategieswithshortformationperiodsofonemonthorsixmonths.24We have also experimented with more elaborate cross-sectional asset pricing tests for both macro factorsand return-based factors but, as may be expected on the basis of the time-series results reported in Table 10,didnotndanyimprovementinresults.30Insum, there is little evidence that standardbusiness cycle variables or portfolio-basedriskfactorshelptounderstandmomentumreturns, i.e. itseemsthatthelatterarelargelydisconnectedfromU.S.businesscyclerisk. ThisndingsquareswellwithearlierresultsforU.S. equity momentum, which is hard to explain by relying on its covariance with macro riskfactors(e.g.GrinandMartin,2003;Cooper,Gutierrez,andHameed,2004).5.3. LimitstoArbitrage: Time-variationinMomentumProtabilityNext, weareinterestedinthestabilityof momentumreturnsovertime. SinceFXmarketparticipants (e.g. proprietarytradingdesks, asset managers andhedge funds) generallyhaveshortinvestmenthorizons,time-variationinmomentumprotscouldalsorepresentanimportantobstaclefortakingarbitragepositionsinFXmarkets.Figure 7 plots average excess returns to the three long-short momentum portfolios MOM1,1,MOM6,1,andMOM12,1overrollingwindowsof36months. Theleftpartshowsunadjustedreturnswhiletherightpartof thegureshowsnetexcessreturnsaftertransactioncosts.Itcanbeseenthattheprotabilityofmomentumstrategiesistime-varyingandthatbothadjustedandunadjustedreturnsappeartobehigheroverthesecondpartofthesample. Infact, momentum returns for all three strategies have been rather high between 2000 and 2005reachinglevelsofmonthlynetexcessreturnsofabout2%permonth.Figure7abouthereMost importantly, this gure alsoillustrates that momentumreturns are far frombeingconstantevenoverintermediatetimeintervalsof several years. Hence, aninvestorseekingto prot from momentum returns has to have a long enough investment horizon. This resultseems important, since the bulkof currencyspeculationis accountedfor byprofessionalmarket participants and proprietary traders who have a rather short horizon over which theirperformanceisevaluated(Lyons, 2001). Hence, momentumstrategiesarepotentiallyriskyfor myopic market participants, so that large time-variation in the performance of momentum31returnsmayimpedearbitrageactivitybysomeofthekeyFXmarketplayers.255.4. LimitstoArbitrage: IdiosyncraticvolatilityUnlikeinstockmarkets,therearenonaturalshort-sellingconstraintsinFXmarkets. How-ever,inordertoconductarbitrageincurrencymarkets,aninvestorobviouslyhastosetuppositionswhichhemaywishtohedgesuchthatthepositionbecomesapurebetonreturncontinuationbutnotonanysortofsystematicrisk. Hence,weinvestigatewhethermomen-tum returns are dierent between currencies with high or low idiosyncratic volatility (relativetoanFXassetpricingmodel). Findingthatcurrencymomentumisstrongeramonghighidiosyncraticvolatilitycurrencieswouldimplythatattemptstoarbitragethesemomentumreturnsawaymayberiskysinceitwillbehardtondasecondpairofcurrenciesthatcanbeusedasahedgefactorunrelatedtosimplereturncontinuation.Tothisend,PanelAofTable11showsresultsfromdouble-sortingcurrenciesrstintotwoportfolios dependingonwhether acurrencyhas alaggedidiosyncraticvolatilityaboveorbelowthemedian(of all availablecurrencies), andthenintothreeportfoliosdependingontheirlaggedexcessreturn.26Forall threeformationperiodswestudy(i.e. fiseither1, 6,or12),wendthatmomentumreturnsarehigheramongcurrencieswithhighidiosyncraticvolatilitythanamongcurrencieswithlowidiosyncraticvolatility(IV OL). Thereturnsdif-ferences arequitelargeineconomicterms. For example, sortingonlaggedidiosyncraticvolatilityandlaggedonemonthreturnsleadstoanannualizedmomentumexcessreturnof3.97%amongcurrencieswithlowIV OL, whereasamomentumstrategyamongcurrencieswithhighIV OLyieldsanaverageexcessreturnof8.09%p.a. Thus, momentumstrategies25Theroleoffrictions(e.g. marginandcapitalconstraints)onthedeploymentofarbitragecapitaltoin-vestment opportunities by institutional investors is stressed for instance in recent work by Mitchell, Pedersen,andPulvino(2007). Excellentrecentsurveysonlimitstoarbitrageandslow-movingcapital whichprovideanobstacletothecorrectiveactionsofrational arbitrageursareprovidedbyDue(2010)andGrombandVayanos(2010).26Idiosyncraticvolatilityforeachcurrencyjinmonthtiscomputedfromaregressionofcurrencyreturnsonaconstant, theDollarriskfactor, andtheHMLFXfactorofLustig, Roussanov, andVerdelhan(2011).Idiosyncraticvolatilityisthencomputedastheabsolutevalueof theregressionresidual inmontht. WendsimilarresultstothosereportedbelowwhenweemploythevolatilityriskfactorproposedbyMenkho,Sarno,Schmeling,andSchrimpf(2011).32aremuchmoreprotableamongcurrencieswithhighidiosyncraticrisk.Table11abouthere5.5. LimitstoArbitrage: CountryRiskAnatural limittoarbitrageinforeignexchangemarketsiscountryrisk. Institutional con-straints such as country limits, for instance, may prevent position-taking in currencies of highriskcountries. Arbitrageactivityinvolvingthesecountriescurrenciesalsoexposesinvestorstotheriskofpotential suddencapital accountrestrictionsandsharpexchangeratemoves.Thisimpliesthat arbitragestrategiesinvolvingthesecountries currenciesaremuchmoreriskycomparedtothoseinvolvingcurrenciesof well developedandhighlystablecountrieswithlowriskratings.Wenowperformthesameanalysisasabovebutsortinsteadonameasureof countryrisk(CRISK)andameasureof exchangeratestabilityrisk(XSTAB). ThesedataarebasedontheInternationalCountryRiskGuide(ICRG)databasefromthePoliticalRiskServices(PRS)group.27Weemploythecompositecountryriskrating(whichcompriseseconomic,political, and nancial risk of a country) as a general proxy for the riskiness of a given countryand exchange rate stability risk as a specic proxy for the risk of sharp currency movements.28Data for these risk proxies start in January 1985 and we employ the log deviation of the riskratingofacountryfromtheratingoftheU.S.asaproxyofrelativeriskforaU.S.investor.ThesetuphereissomewhatakintoAvramov,Chordia,Jostova,andPhilipov(2007,2010),whoshowthatU.S.stockmomentumismainlyconcentratedinhighcreditriskrmswhichare illiquidandhardtosell short.29Hence, credit riskproxies for hurdles toarbitrageactivity. In our context, we focus on country risk as a natural proxy for limits to arbitrage in27These data are quite common as proxies for country risk;see e.g. Bekaert,Harvey,Lundblad,and Siegel(2007),whoalsouseriskindicatorsfromthisdatabase.28Theexchangeratestabilityriskproxymeasurestheperceivedriskoflargeexchangeratemovementsinthenearfuture.29Inasimilarvein, Jostova, Nikolova, Philipov, andStahel (2010)showthatmomentumprotsinU.S.corporatebondreturnsderivesolelyfromlongandshortpositionsinnon-investmentgradebonds.33FXmarkets. Highriskcountriesaremorepoliticallyunstable, economicallylessdevelopedand more volatile so that establishing positions in the associated currencies poses non-trivialthreatsof suddencapital accountrestrictionsandnon-convertibilityof currency. Inshort,arbitrage activity involving these countries currencies should be clearly more risky comparedtowelldevelopedandhighlystablecountrieswithlowriskratingssimilartotheU.S.Panels B and C of Table 11 shows results for double sorts on either country risk or exchangerate stability risk and momentum. Corroborating our earlier ndings for idiosyncratic volatil-ity,wendthatmomentumreturnsaresignicantlypositiveandalwayslargerinhigh-riskcountries thaninlow-riskcountries, where momentumstrategies donot yieldsignicantexcessreturns. Hence, foraninvestortoprotfromcurrencymomentumstrategies, itisnecessary to operate in markets for currencies of risky countries. This is especially importantsince, unlikemomentumstrategiesindomesticU.S.stocks, investmentsinforeigncurrencyare always subject to risks of capital controls and non-convertibility. Therefore,country riskshouldbeanimportantlimittoarbitrageactivityinFXmarkets.Finally, weexaminewhether our ndings abovearedrivenbycountryriskbeingrelatedlinearly to the cross-sectional spread in momentum returns and whether momentum is dier-entlyaectedthancarrytrades. TableA.15(which,asanexample,isbasedonthestrategywithaonemonthformationandholdingperiod) intheAppendixshows aclear pattern.Countryriskandexchangeratestabilityriskarehighforbothwinnerandlosercurrencies(Panel A)inthemomentumstrategy. Hence, itisnotthecasethattheseriskratingsaresimple proxies for interest rate dierentials which drive our results. Instead, currency momen-tumstrategiesrequirethataninvestorhastogolongandshortinthemostriskycountries.Thisisespeciallytruesincemomentumprotsstemfromboththelongandshortsideofthe position (see Table 4, Panel A) so that it is necessary to set up both positions. Contrarytothis, thecross-sectionof forwarddiscountsortedportfolioswhichformthebasisof thecarry trade (Table A.15, Panel B) shows a very dierent pattern. Country risk is highest forcarry trade target currencies (high interest rate currencies) and lowest for carry trade fundingcurrencies(lowinterestratecurrencies). Thissquareswellwiththendingthatmostofthecarrytradereturncomesfromthelongpositionof thestrategy(4, Panel B). Inanycase,34these results indicate that country risk has a non-linear impact on the cross-sectional spreadinmomentumportfolios returnsand, again, thattheanatomyof carrytradestrategiesisverydierentfromcurrencymomentum.Developedcountries. Finally, a shortcut to looking at country risk may also be to denea sample of clearly developed countries that have stable exchange rate regimes and are mostliquid. Table A.12 in the Appendix shows results before and after transaction costs similar tothose in Table 1 but we limit the cross-section to 15 developed countries.30It is clear from thistablethatmomentumreturnsaremuchsmallerandbasicallynon-existentaftertransactioncosts whenlookingat currencies of developedcountries. This ndingis interestingsinceitsuggeststhattheprotabilityof momentumstrategiesdependsonwhethersmallerandpresumablyless liquidcurrencies areincludedintheinvestment universeor not. Again,thisshowsthatlimitstoarbitrageareanimportantfactorinexplainingthepersistenceofmomentumreturnsinFXmarkets.6. Robustnessandadditionaltests6.1. CapitalaccountrestrictionsandtradabilityWehavedocumentedabovethatmomentumreturnsarelargeinFXmarketswhenexam-iningabroadcross-sectionthatalsoincludessmallercurrenciesfromemergingmarkets. Apotential concern regarding these results is whether all currencies have actually been tradablethroughoutthesampleperiodastheremaybecapital controlsforsomecountriesorotherissuesrenderingtradinginthesecurrenciesinfeasible. Manyofthesesmallercurrenciesdoindeed show up in the loser and winner portfolios quite frequently which is shown in Table A.5intheAppendix. Thistablereportsthefrequencywithwhicheachcurrencyisincludedinthe winner and loser portfolio of the MOM(1,1) strategy. The table shows, quite expectedly,30ThesecountriesareAustralia, Belgium, Canada, Denmark, Euroarea, France, Germany, Italy, Japan,Netherlands,NewZealand,Norway,Sweden,Switzerland,andtheUnitedKingdom.35that several larger currencies (e.g., Australia, Canada, Japan, NewZealand, Switzerland,UnitedKingdom) areoftenincludedinthemomentumstrategybut thisdominancerestsat least partlyonthelonger sampleperiods availablefor thesecurrencies. However, thetablealsoshowslargeinclusionfrequenciesforemergingmarketssuchasBrazil, Indonesia,Poland, or Singapore. Hence, it seems worthwhile to investigate whether issues of tradability(orconvertibility)aectourresults.As arst exercise, welimit thesampletocurrencies whichhaveapositivescoreonthecapitalaccountopennessindexofChinnandIto(2006),bothintheformationandholdingperiod, tocontrol forthepossibilitythatsomecurrenciesarenottradableorthattheyareonlytradedinmoreopaqueoshoremarkets whichwouldnot beadequatelyreectedinthedata. WereportresultsforthisrestrictedsubsetinTable12,PanelA.Ascanbeseen,theresultsarenotaectedbyexcludingthesecurrencies. Moreover,countrieswithnegativecapital account openness index values do not account for a large share of the relevant cornerportfolios(lessthan20%onaverage). WhileapositivescoreintheChinn-Itoindexalreadyexcludes a number of countries (even developed countries, e.g., the U.K. from 1976 to 1978),weadditionallyrunthesameexerciseundertheconstraintthatacountryhastohaveanindex score of at least one. This requirement eliminates several currencies almost completelyfrom the sample (e.g., Brazil, Philippines, Poland, and South Korea) and signicantly reducestheinvestablesampleperiodforothercountries(e.g., Belgiumonlybecomesinvestableinthe1990s). ResultsforthislterareshowninPanelBofTable12butalsodonotindicatethatmomentumisprimarilydrivenbycurrencieswhichexhibitlimitationstoinvestability.Table12abouthereWhiletheaboveanalysissuggeststhattradabilityissuesdonotwipeoutmomentumprotsinFXmarkets,weadditionallyranasmallsurveyamongfourlargebrokersinFXmarkets(GoldmanSachs, DeutscheBank, UBS, Nomura) andaskedwhichcurrencies wouldhavebeen impossible (or nearly impossible) to trade in a dynamic portfolio strategy that requiresfrequentrebalancing. Basedontheiranswers, werestrictedoursetof tradablecurrencies36andcomputedmomentumreturnsontheresultingsample. Thefollowingrestrictionswereimposed: CzechRepublic (not tradable before 1999), Hungary(2000), Indonesia(1999),Malaysia(1999), Philipines(1999), Singapore(1999), SouthAfrica(2001), Taiwan(1999),HongKong(1986), andThailand(1999).31Results for this limitedsampleareshowninTable13,PanelA.CorroboratingtheevidencebasedontheChinn/Itoindexabove,wendthat momentumprots arestill signicant after takingintoaccount likelyrestrictions ontradabilityofcountries.Table13abouthereAs a nal check, we augmented the market practitioners list by eliminating all currencies withlargetradinginnon-deliverableforwardsinoshoremarketswhichmaynotbeadequatelycoveredbyourpriceandinterestratedata. Thesecurrenciesinclude: Brazil,Egypt,India,Indonesia, SouthKorea, Malaysia, thePhilippines, andTaiwan. Resultsforthisevenmorerestricted set of currencies are shown in Panel B of Table 13 but only strengthen our ndingsabove.In sum, we nd that accounting for capital account restrictions (or other trading restrictions)does not signicantlyweakenaveragemomentumreturns despiteexcludingmanysmalleremergingmarketsfromoursample. Thisndingseemstobedrivenbythefactthatmostminor currencies (whicharemorelikelytobesubject tocapital controls) onlyenter oursampleveryrecentlyand,thus,donotdrivethelionsshareofourresult.6.2. AdditionaltestsDierent base currencies. So far, we have investigated momentum prots from the view-pointofaU.S. investor. Forrobustness, wealsopresentresultsforaBritish(GBP), Swiss(CHF), Canadian(CAD), andSwedish(SEK)investor, i.e., weconvertall datasuchthat31Mostofthesurveyrespondentsotherrestrictions,forexample,regardingEgyptorSaudiArabia,wereactuallyalreadyreectedinourdatawheredatahistoriesofseveralcurrenciesstartverylateattheendofthe1990sorearly2000s(seeTableA.1intheAppendix).37theyarequotedagainstoneof thesefouralternativenumeraires. Theeectivesizeof thecross-section is, of course, unchanged since we lose one currency (the numeraire) but includetheUSDasa new currency.ResultsareshowninTablesA.6andA.7intheAppendixforexcessreturnsandspotratechanges, respectively. It canbeseenthat results arebasicallyunchangedrelativetothebenchmarkcasesothatmomentumisnotaU.S.dollarphenomenon. Thisresultisreason-able since our momentum portfolios are dollar-neutral by construction (the USD componentcancelsoutinthelongminusshortportfolio). Hence, changingthenumerairehaslittletonoeectontheprotabilityofmomentumstrategies.Furthermore,wealso runregressionsofmomentumexcessreturnsforthefourdierentbasecurrencies on a set of risk factors to rule out the possibility that momentum returns are morecloselylinkedtotraditional riskfactorsfornon-U.S. investors. Duetodatalimitations, wecannot obtain data for all risk factors considered in Table 10 so that we focus on the followingsetof riskfactorswhichshouldsucetocapturebroadeconomicconditionsinthesefourcountries: growthinreal industrial production(IP), CPI ination, growthinreal moneybalances, changes in the term spread, and (local) stock market returns. Results are reportedinTableA.8intheAppendixandwend(similartotheU.S.caseinTable10above)thatmomentum returns are not closely linked to any of these standard macro-nance risk factors.Currencyregimes. Anotherquestionof relevanceiswhethermomentumstrategiescanbeenhancedbyconsideringinformationaboutcurrencyregimes. Intuitively,currenciesthatarepeggedorareonlyallowedtomoveinverysmallbands(ortargetzones)shouldbelessuseful insettingupamomentumstrategythanfreelyoatingcurrenciesorcurrenciesthatare allowed to move in larger bands. To address this issue we limit our sample of currencies to(i) free oats, managed oats, pre-announced crawling bands (wider than or equal to +/-2%),de facto crawling bands (narrower than or equal to +/-5%), moving bands (narrower than orequal to +/-2%) or (ii) free oats only. Sample (i) corresponds to category 3 whereas sample(ii)correspondstocategory4of theIMFs(coarse)classicationof exchangerateregimes38availableonCarmenReinhartswebpage.32Results for these two samples of less heavily managed currencies are shown in Table A.9. Thesample period starts in 1986 here to have a large enough cross-section for free oats (also seeFigure1). Panel Areportsdescriptivestatisticsforsixmomentumportfoliosandthelongminusshortportfolioforsample(i). Thereisamonotonicallyincreasingspreadinaverageexcessreturnsandasignicantlypositiveaverageexcessreturnforthemomentumstrategylong in winners and short in losers regardless of the formation period. Panel B shows resultsfor sample (ii) which only comprises free oats. Average excess returns tend to be somewhatlowerforformationperiodsofoneandsixmonthsbutsomewhathigherforthe12-monthsformationperiod.Insum,theredoesnotseemtobeaclearbenetfromconcentratingononlyfreelyoatingcurrencies. While freely oating currencies have more roomfor large price swings,excludingless exible exchange rates results in a smaller cross-section and excludes a number of slowlytrendingrateswhicharemanagedincrawlingbands.Central bankinterventions. Central bankinterventions havebeenconsideredas onepotential sourceof momentumprots earlyintheliterature. For example, Silber (1994)showsthattechnicaltradingrulesaremorevaluablewhengovernmentagenciesinterveneinthemarket. However, laterpapersreachdierentconclusionssothattherelationbetweenocialinterventionandmomentumtradingislessclear-cut. Inthisvein,Neely(2002)ndsthatinterventionsdonotinuencetechnicaltradingprotsandthatmomentumprotsaremorelikelytoprecedeinterventionratherthanbeingcausedbythem.3332http://www.carmenreinhart.com/data/browse-by-topic/topics/12. IMFcategories1and2corre-spond to more restrictive regimes. It is important to note that for the last several years, the IMF classicationofeachcountry(publishedintheAnnualReportonExchangeArrangementsandExchangeRestrictions)isbased on the countrys actual (de facto) policy, as determined by the IMF. For some countries this classica-tioncoulddierfromthecountrysocial(dejure)statedpolicy. Formostofoursample,onlytheocialstatedpolicyisreportedbytheIMF.33Also, seeNeely(1998)foranoverviewofseveral ndingsintheliteratureoninterventionsandreturnstotechnical trading. See SarnoandTaylor (2001) for acomprehensive surveyonthe impact of ocialinterventiononexchangerates.39Giventheprominenceofthistopicintheearlierliteraturewebrieyexaminetherelation-ship between intervention and momentum returns in Table A.10 in the Appendix. We reportresults for regressions of momentum excess returns for our three benchmark strategies on con-temporaneousandlaggedcentralbankinterventionactivity. Interventionactivityisproxiedfor by the sum of absolute intervention amounts of all central banks in the USD (against anyforeigncurrency). DataforthisexerciseareobtainedfromtheFederalReserveBankofSt.Louis. Ourresultsshowthatinterventionsarenotverypowerful incapturingmomentumreturns, broadlyconsistentwiththendingsinNeely(2002). However, itshouldbenotedthatouranalysisisintentionallysimpleandthatthereareseriousdataissueswithcentralbankinterventionswhichareusuallynotmadepublic.EuropeanMonetarySystem(EMS). Asanadditionalrobustnesscheck,wecalculatemomentumprotswhereweexcludeall countriesparticipatingintheEMS(exceptfortheDeutschmark) andfocus onthe1990s wherecurrencies of thesecountries movedinlock-step.34Sincemomentuminanyofthesecountriesshouldbeveryshort-liveditseemslikelythat excludingthese currencies will yieldlarger momentumprots. We plot cumulativemomentumexcessreturns(fortheMOM(1,1)strategy)from1990to1998inFigureA.2inthe Appendix and do indeed nd that excluding EMS member countries leads to a somewhatbetterperformance. Hence, theresultsreportedinthemaintextseemconservativeanditshould be possible to increase the protability of momentum strategies by carefully accountingforthecorrelationstructureofcurrencies.7. ConclusionWehaveempiricallyinvestigatedmomentumstrategiesinFXmarkets,whichrelyonreturncontinuationamongwinnerandlosercurrencies. Wendthatthesestrategiesyieldsurpris-ingly high unconditional average excess returns of up to 10% per year and that these returns34NeelyandWeller(1999)investigatereturnstotechnicaltradingrulesinEMScurrenciesovertheperiodfrom1986to1996andndthattheygeneratesignicantexcessreturns.40arehardtounderstandinaframeworkthatreliesoncovarianceriskwithstandardriskfac-tors. Incontrasttoanexplanationbasedonsystematicrisk, wendevidenceforunder-and subsequent over-reaction in long-horizon momentum returns. In this sense, the evidenceforcurrencymomentumseemssimilartowhathasbeenfoundforequitymarketsinearlierliterature.Wealsondthatmomentumreturnsaredierentfrommoreconventional technical trad-ingrules. Astechnical tradingmostlyaimsatexploitingtrendsormomentumincurrencymovements,itmaybeexpectedthatreturnstothesestrategiesarepositivelyrelatedtoourcross-sectional momentumreturns. Wend, however, thatreturnstobenchmarktechnicaltradingrulesaresomewhatlowerandthatthecorrelationwithourmomentumstrategiesisrathersmall. Moreover, currencymomentumstrategiesareverydierentfromthepopularcarrytradeinFXmarkets. Hence,itcomesasnosurprisethatmomentumisnotwellcap-turedbytheglobalfactorsthathavebeenshowntoberelatedtocarrytradereturnsintheearlierliterature. Rather, momentumandthecarrytradearedierentphenomenawhichrequireadierentexplanation.However, currency momentum returns do not come as a free lunch for investors trying to ex-ploitthesestrategies. WendthatmomentumportfoliosintheFXmarketaresignicantlyskewed towards minor currencies which have relatively high transaction costs, accounting forroughly 50% of momentum returns. Also, the concentration of minor currencies in momentumportfoliosraisestheneedtosetuptradingpositionsincurrencieswithhigheridiosyncraticvolatility,highercountryrisk,andhigherexpectedriskofexchangerateinstabilities,whichclearlyimposesriskstoinvestorsthatarenotcapturedbystandardriskfactorsinacovari-anceriskframework. Hence, thereseemtobeeectivelimits toarbitragewhichpreventastraightforwardexploitationof momentumreturns. Furthermore, momentumprotsarehighlytime-varying, whichmayalsoposeanobstacletoarbitrageactivityforsomeof thekeyFXmarketparticipants(e.g. proprietarytradersandhedgefunds)whotypicallyhavefairlyshort-terminvestmenthorizons.Seenfromabroaderperspective, thereismountingevidencethatmomentumcanbeseen41asanubiquitousphenomenoninnancial markets(e.g. Asness, Moskowitz, andPedersen,2009). Akeycontributionof thispaperistoshowthatmomentumstrategiesdeliverhighexcessreturnsinFXmarkets, comparableinmagnitudetotheexcessreturnsdocumentedinstockmarkets. Thisoccursdespitethespecial characteristicsof currencymarkets, suchashugetradingvolume(KingandRime,2010),mostlyprofessionaltraders,noshort-sellingconstraints and a considerable degree of central bank interference. However, we show that FXmomentumreturnsarenotdrivenbypolicymeasuresincludingmonetaryregimes,currencyinterventionor theimplementationof capital account controls. Momentumreturns stemprimarily from currencies that are hard to hedge and have high country risk, which is similartorecent ndings that equitymomentumis concentratedinstocks withhighcredit risk(Avramov, Chordia, Jostova, andPhilipov, 2007), andmomentumincorporate bonds isconcentrated in non-investment grade bonds (Jostova, Nikolova, Philipov, and Stahel, 2010).Insum, thesendings suggest that theremaybeacommonsourceof momentumprotsacrossassetclasses.42ReferencesAsness, C. S., T. J. Moskowitz, L. H. Pedersen, 2009. ValueandMomentumEverywhere.WorkingPaper,UniversityofChicago,BoothSchoolofBusiness.Avramov, D., T. 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