Combining Mean Reversion and Momentum Trading Strategies in. Foreign Exchange Markets


 Ralf Carroll
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1 Combnng Mean Reverson and Momenum Tradng Sraeges n Foregn Exchange Markes Alna F. Serban * Deparmen of Economcs, Wes Vrgna Unversy Morganown WV, November 2009 Absrac The leraure on equy markes documens he exsence of mean reverson and momenum phenomena. Researchers n foregn exchange markes fnd ha foregn exchange raes also dsplay behavors akn o momenum and mean reverson. Ths paper mplemens a radng sraegy combnng mean reverson and momenum n foregn exchange markes. The sraegy was orgnally desgned for equy markes, bu also generaes abnormal reurns when appled o uncovered neres pary devaons for en counres. I fnd ha he paern for he posons hus creaed n he foregn exchange markes s qualavely smlar o ha found n he equy markes. Quanavely, hs sraegy performs beer n foregn exchange markes han n equy markes. Also, ouperforms radonal foregn exchange radng sraeges, such as carry rades and movng average rules. JEL classfcaons: F31, G11, G15 Keywords: Uncovered Ineres Pary; Mean Reverson; Momenum; Foregn Exchange; Tradng Sraeges. * Tel: ; fax: ; emal:
2 1. Inroducon Foregn exchange marke radng sraeges have araced much aenon, especally snce Fama (1984) nroduced he forward puzzle, whch argues ha forward exchange raes are based predcors of spo exchange raes. Ths paper ses forh a new sraegy n he foregn exchange (FX) markes ha combnes mean reverson and momenum. Even hough he sraegy was orgnally desgned for equy markes, I fnd ha produces hgher Sharpe raos han radonal FX sraeges. The sarng pon of hs paper, he forward puzzle, resuls from he reecon of he Uncovered Ineres Pary (UIP) heory. UIP saes ha he change n he exchange rae should ncorporae any neres rae dfferenals beween he wo currences. A large leraure exss examnng f and when UIP holds. 1 Ths paper res o fnd a paern n he devaons from UIP and o explore he smlary beween hs paern and ha of sock reurns. The leraure reveals wha looks lke mean reverson and momenum n boh markes. A long run mean reverng paern n currency values has been uncovered by Engel and Hamlon (1990); a shor erm momenum effec generaes profably n FX marke radng (Okunev and Whe, 2003). 2 Chang and Jang (1995) noce ha foregn exchange reurns show srong posve correlaons n he shorrun (momenum behavor) and negave correlaons n he longrun (mean reverng behavor). Ths paper generaes abnormal reurns by employng a sraegy ha combnes he long run and shor run paerns of he devaons from UIP. 1 For more deals on UIP, see for nsance Blson (1981); Froo and Frankel (1989); Chabou and Wrgh (2005). 2 Okunev and Whe acually use a movng average rule o creae profs for he speculaors on he FX marke, bu hey name hs a smple momenum sraegy. The sraegy n my paper s dfferen from hers. 1
3 The success of he combned momenummean reverson sraegy brngs abou anoher neresng ssue: he puzzlng relaonshp beween sock and FX markes. The smlares beween he sock and FX markes are perplexng because macroeconomc fundamenals explan sock reurns, bu no exchange raes (Meese and Rogoff, 1983 a, b). Tradonal heory dcaes ha wo markes no relyng on he same fundamenal varables canno behave smlarly. Ye, I fnd he wo markes comparable. Ths resul s n lne wh early sudes ha depc smlar emprcal regulares n FX and sock markes (Mussa, 1979). One possble explanaon sprngs from Engel and Wes (2005), who fnd ha exchange raes explan macroeconomc fundamenals, no he reverse. Ths fndng, corroboraed wh he fndng ha fundamenals explan sock reurns, provdes one possble channel for he relaon beween he wo analyzed markes. Anoher fascnang explanaon s ha he rsk facors affecng boh sock and FX reurns reman unknown bu are somehow conneced. An addonal explanaon s ha smlar behavoral bases operae n boh markes, leadng o smlar neffcences. To explore he smlares beween he sock and FX markes, I frs consder he nonparamerc approach ha Jegadeesh (1990) and Jegadeesh and Tman (1993, 2001) explo. These papers consruc porfolo decles based on prevous monhs reurns and choose a wnner and a loser decle. By buyng he wnner and sellng he loser a zeronvesmen porfolo s consruced and hs porfolo s held for less han a year. The auhors fnd ha he reurn on her zeronvesmen porfolo s always posve. If hs porfolo s held for more han a year, however, he reurn becomes zero or negave. In Jegadeesh and Tman (2001), he auhors explo he raonale behnd hese resuls. They reec daa mnng explanaons and rsk compensaon, fndng ha behavoral models 2
4 parally explan he abnormal reurns. The aforemenoned nonparamerc sraegy s used n he FX marke by denfyng a wnner and a loser currency based on prevous devaons from UIP. I fnd ha he wnner connues o have hgh reurns and he loser low reurns for he subsequen 9 12 monhs, bu, n he subsequen 4 5 years, he wnner and loser porfolos swch posons. However, one canno combne mean reverson and momenum sraeges wh hs approach. Balvers and Wu (2006) use an alernave approach o generae radng profs n he sock marke: a paramerc sraegy. They consder he effec of momenum and mean reverson only and conclude ha he resulng sraegy can lead o sgnfcan profs when appled o he sock markes of 18 developed counres. A conraran sraegy or a momenum sraegy by self leads o lower abnormal reurns han he combnaon sraegy. I fnd ha he parameers obaned for he FX marke are quanavely smlar o hose for he sock marke; hence we expec smlar radng sraegy reurns for he zero nvesmen porfolos. The FX marke reurns have lower volaly han equy marke reurns. Consequenly, I consder he Sharpe raos, whch allow me o compare rskoreward profles of he same sraegy, bu n he wo dfferen markes. The Sharpe raos obaned n he FX marke are sgnfcanly larger han hose obaned n he sock marke. The paper s organzed as follows. The second secon descrbes he daa and presens prelmnary resuls showng ha devaons from UIP exhb momenum nally and subsequen mean reverng behavor. The hrd secon descrbes he model and he fourh examnes he model emprcally and compares he resuls o he exsng leraure. The fnal secon concludes. 3
5 2. Daa Descrpon and Prelmnary Sascs 2.1. Daa Descrpon The daa se consss of he 1 monh forward and spo exchange raes from he Bank of Inernaonal Selemens and Daasream. Due o avalably, he daa come from wo sources: for he perod December 1978 December 2001 from he BIS daase, and for January 2002 February 2008 from Daasream. I oban monhly daa for he Belgan Franc, Canadan Dollar, Swss Franc, German Mark/Euro, French Franc, UK Pound, Ialan Lra, Japanese Yen and Duch Gulder. I focus on well developed currences wh lqud markes, n whch currency speculaon can be easly mplemened. Due o daa avalably, he leraure on he FX marke usually only covers hese currences. I work wh December 1978 hrough February 2008 as he me perod for he noneuro zone counres and December 1978 hrough December 1998 for he Eurozone counres. 3 The German Mark s he only Eurozone currency wh daa from December 1978 hrough February 2008 (afer December 1998, he Euro akes s place n he daa). The US Dollar serves as he home currency. The monhly equy marke reurns are obaned from he Morgan Sanley Capal Inernaonal (MSCI) Barra equy marke prce ndexes for he same se of nne developed counres plus he US. The sample perod s December 1978 hrough February The rsk free rae s he onemonh Treasury bll rae (from Ibboson Assocaes), obaned from Kenneh French s webse. 3 I ook a few years afer he collapse of he Breon Woods Sysem o esablsh a floang exchange sysem and for speculaon o be possble. Tha s why mos of he leraure only consders daa on he FX marke sarng around
6 2.2. Ineres Pary Condons UIP saes ha he currences a a forward premum should apprecae. The forward puzzle suggess ha he exac oppose happens: hese currences acually end o deprecae. An nvesor who borrows money n her home counry (wh an neres rae of r ) and lends n anoher counry wh a hgher neres rae ( r ) should expec a zero reurn due o he changes n exchange rae (denoed a me by S, n uns of home counry currency per foregn counry currency). In oher words: E( S ) + (1) r = (1+ r ) S Wh hs sraegy, nvesors leave her poson uncovered from o +1 and only make arrangemens o change he foregn currency no domesc currency a me +1. The UIP saes ha he markes equlbrae he reurn on he domesc currency asse wh he expeced yeld of he uncovered poson n he foregn currency. If he nvesors leave nohng o chance and make arrangemens o conver foregn o domesc a +1 by usng a forward exchange rae F, absence of rskless arbrage profs mples ha: F 1 + r = (1+ r ) (2) S Equaon (2) s known as Covered Ineres Pary (CIP). Takng logs of (1) and (2) and gnorng expecaons, we oban: r r = s +1 s, wh s ln S (3) r r = f s, wh f ln F (4) If boh condons hold, follows ha: s +1 s = f s (5) 5
7 Equaon (5) accouns for he neres rae dfferenal mpled by he CIP condon. 4 as follows: y Ths paper s concerned wh he devaons from UIP, denoed by y and defned + 1 = s+ 1 s ) ( f s ) = s+ 1 ( f (6) Table 1 presens summary descrpve sascs of he reurns for UIP posons n he nne currences and for varous smlar posons n he sock marke: annualzed mean reurns, sandard devaons and Sharpe raos. Gven he low mean reurns n he FX marke (relave o he sock marke), leverage s wdely used n pracce o provde he desred mean reurns. The Sharpe raos provde he proper comparson beween he FX and equy markes snce hey reman nvaran o he degree of leverage. [Inser Table 1 here] Panel A dsplays summary sascs for UIP posons n he FX marke, Panel B descrbes sock marke excess reurns compued from he MSCI Barra prce ndexes, and Panel C shows descrpve sascs for a sraegy of buyng US ndex and shor sellng a foregn ndex, he sock marke counerpar of he UIP posons n he FX marke. The mean reurns for he UIP posons n panel A range from o 1.81 percen and he sandard devaons from 4.68 o percen. In Panel B, he mean reurns for he sock marke ndexes range from 7.08 o percen and sandard devaons from o percen. Evdenly, more dsperson exss n he daa for he sock marke reurns han for he FX marke, as expeced from he leraure (Burnsde, 2008; Burnsde e al., 2008). By akng he US sock marke as he benchmark counry (by analogy o he FX posons), he sraegy ha Panel C proposes gves very low mean reurns (rangng from 4 The CIP s he condon used by large banks for deermnng he exchange raes and neres raes a whch radng s acually conduced. See Taylor (1987, 1989, 1995), Byan (1995), Isard (2006). 6
8 2.31 o 4.29 percen), and very hgh sandard devaons (from o percen); hs agan shows a much hgher dsperson n he equy marke han n he FX marke. The Sharpe raos are relavely low n Panels A and C and relavely hgh n Panel B Confrmng Mean Reverson and Momenum To check for mean reverson and momenum, one can use he Jegadeesh and Tman (1993, 2001) sraegy easly and effecvely by applyng hs sraegy o he devaons from UIP. The sraegy consders he cumulave devaons from UIP for every currency over he prevous J monhs (where J akes he values of 6, 9, or 12). Each monh I rank he currences on he bass of pas devaons from UIP and he currency wh he hghes cumulave reurn classfes as he wnner, whle he currency wh he lowes reurn becomes he loser. For hese currences I compue he cumulave devaons from UIP over he subsequen K monhs (where K s 6, 9, 12, 24, 36, 48, and 60). I assgn he wnner and loser for every monh; consequenly, he holdng perods overlap. Fgure 1 summarzes he resuls for all permuaons of hs sraegy. [Inser Fgure 1 here] From he graph, one can asceran efforlessly ha he wnner s mean reurn sars ou posve and connues o be posve unl he momenum effec dsappears (afer abou one year). The loser s reurn appears o be a mrror mage of he wnner s reurn. Sarng around year four, he resuls are reversed and he losers ouperform he wnners. These resuls do no dffer from he resuls on he sock marke (De Bond and Thaler, 1985, 1987; Jegadeesh and Tman, 1993, 2001; Lee and Swamnahan, 2000; Balvers e al., 2000; Koen e al., 2006). I am he frs o mplemen a sraegy of combnng mean 7
9 reverson and momenum n he FX marke. Ths sraegy generaes sgnfcan abnormal reurns n hs marke, as shown n he followng secons. 3. Model and Parameer Esmaon 3.1. Model Fama and French (1988) and Summers (1986) consder a smple model for sock prces (her naural log s represened by x) ha s he sum of a random walk and a saonary componen. The saonary componen classfes as a frsorder auoregressve process ha represens he long emporary swngs n sock prces (characerzed by coeffcen δ). The parameer µ capures he random walk drf componen. Smlarly, bu addng a coeffcen for he momenum effec ρ, Balvers and Wu (2006) consruc he log of sock prces (wh dvdends added and renvesed) as: x J δ ) µ + δ x 1 + ρ ( x x 1 ) + = 1 = ( 1 ε (7) They noe ha he log of he prce wh dvdends renvesed mples ha he reurn s y x x 1 = and ha he log of he prce equals he cumulave reurn afer correcon for marke rsk: x = y s= 1 s (8) I use equaon (7) o fnd abnormal reurns n he FX marke. Theδ represen he speed of mean reverson and can dffer by counry, whle heρ represen he momenum srengh and can vary by counry and by lag. The parameer µ also vares by counry. From equaon (7), he reurn of my sraegy s: y J δ )( x 1 µ ) + ρ ( x x 1 ) + = 1 = ( 1 ε (9) 8
10 The models proposed by Fama and French (1988) and Summers (1986) consder only mean reverson, hence all he ρ n her models equal zero. In equaon (9) s heorecally possble for ρ and δ o be ousde he nerval [0, 1], bu emprcally I expec hem o fall nsde he nerval. The frs par of equaon (9) represens he mean reverson componen, whle he second par represens he momenum effec. Therefore, one can wre my model as: y = MRV + MOM + ε (10) If heρ and 1 δ dverge from zero, hen he mean reverson and momenum effecs should be correlaed. In order o check for ha correlaon, I consder he smple model n whch ρ only vares by counry (as does δ ): y = ( 1 δ )( x 1 µ ) + ρ ( x 1 x J 1) + ε (11) Takng no consderaon he defnons of MOM and MRV, equaon (9) and saonary mply: cov( MRV, MOM ) (1 δ ) ρ [1 corr( x, x )] var( x ) < 0 = J Snce δ and ρ boh le beween 0 and 1, he covarance beween he wo effecs has a negave sgn. Inuvely, a posve momenum effec pushes he reurn upward, whle he mean reverson effec ends o brng he cumulave reurn back o s mean, so downward. Therefore, one can ancpae a negave correlaon beween he wo effecs. Omng one of he wo effecs leads o based esmaon of he parameers. Omng mean reverson requres δ = 1 n equaon (11): y = α MOM + β MOM ( x 1 x J 1) + ε, MOM 5 5 For a complee dervaon, check Balvers and Wu,
11 1 Corr( X, X X ) Var( X ) plmβ MOM = ρ (1 δ ) < ρ. Var( X X ) [ 1 1 J 1 ] 1 Consequenly, 1 J 1 Hence, he measured mpac of momenum s smaller f mean reverson s omed. By he same logc, f one runs he followng equaon assumng no momenum, ρ = 0 n equaon (11): y = α MRV + β MRV x 1+ ε, MRV plmβ 1 Corr( X, X ρ Var( X ) Var( X ) [ 1 1 J 1 ] 1 Then: = (1 ) + > (1 ) MRV δ 1 X X J 1 So he mean reverson coeffcen esmaon s nconssen and mples a based upward halflfe, leadng o a possble spurous reecon of mean reverson Parameer Esmaon The model n equaon (9) consders a oal number of parameers equal o 9(J+2) (9δ, 9µ and 9J ρ ). Tha s a very large number of parameers o esmae. Consequenly, n order o avod mulcollneary problems and o mprove effcency, I only allow ) δ. µ o dffer by counry (whch accouns for possble msprcng a he begnnng of he perod), whle: δ = δ ρ = ρ, for all and I use he full range of my sample and oban he parameer esmaes usng a pooled model and J=12. Table 2 presens he resuls. [Inser Table 2 here] 6 Halflfe s he expeced me for he analyzed sochasc varable o reurn half of he way oward he equlbrum level, µ. I s compued as ln(0.5)/ln(1δ ). 10
12 The frs column repors he parameer esmaes when allowng boh mean reverson and momenum. Boh coeffcens are sascally sgnfcan. The mean reverson coeffcen δ pooled across counres equals , mplyng a halflfe of 44 monhs. The speed of mean reverson 1 δ s sgnfcanly posve and equals The momenum parameer ρ pooled across counres s a sascally sgnfcan and posve These resuls le very close o hose obaned for he sock marke by Balvers and Wu (2006): he halflfe for he combnaon sraegy remans he same for he wo markes, and he momenum effec s sronger n he FX marke (ρ = compared o n he sock marke). The second and hrd columns show he parameer esmaes for each of he wo pure sraeges. The mean reverson coeffcen ncreases n he pure mean reverson sraegy (0.9921) leadng o a very long halflfe of 88 monhs. The heorecal asympoc bas n he mean reverson coeffcen when omng momenum s cov( x, x ρ var( x x ) 1 1 J 1 = 1 ) Emprcally, he dfference says posve and very close o he heorecal value (0.0077). In he pure momenum sraegy, he srengh of momenum s ndeed smaller (sll posve and sascally sgnfcan) and equal o (he momenum effec s sronger n he FX marke han n he sock marke even n hs case). The heorecal asympoc bas of he momenum coeffcen ρ s cov( x 1, x 1 x J 1) (1 δ ) = and agan les very close o he emprcal bas var( x x ) 1 J 1 ( ). If we compare columns 1 and 2 of Table 2, he halflfe for he combnaon sraegy dmnshes. Inuvely, hs s expeced due o wo effecs of momenum: he frs 11
13 nal effec of momenum s posve and causes he downurn o come laer and he second momenum effec sars afer he downurn and shorens he halflfe. The remander of Table 2 repors he varance decomposon. From equaon (10) we observe ha: var( y ) = var( MRV ) + var( MOM ) + 2 cov( MRV, MOM ) +σ (12) 2 ε The varance of he reurns s deermned n large par by he errors (hence he small R 2 of 4.06 percen) and he res by he varance of mean reverson, momenum and her covarance. The small coeffcen of deermnaon s acually hgher han ha obaned for he sock marke. 7 The varance of momenum explans 4.03 percen of he varaon n he reurns from UIP, whle he varance of mean reverson explans only abou onehrd as much of he varaon n reurns (1.55 percen). For he sock marke, he wo effecs hold smlar mporance n explanng he reurns. Mean reverson remans a very mporan componen and should no be dsregarded as follows for nsance from he bas n he momenum coeffcen when mean reverson s omed. The correlaon beween he wo effecs s heorecally and emprcally negave and abou he same sze as ha obaned for he sock marke ( 0.30 n he FX marke; 0.35 n he sock marke). 4. Tradng Sraeges I employ a mean reverson momenum combnaon sraegy, currenly developed only for he sock marke, for he FX marke. I use he followng varaon of equaon (9) by only allowng µ o change by counry, whle ρ and δ say fxed by counry and lags: 7 Balvers and Wu (2006) oban 2.12%. 12
14 y J 1 µ ) + ρ( x x 1) = 1 = (1 δ )( x + ε Based on he frs 1/3 of he sample, usng OLS, I esmae he reurn (13) y for each currency. Max denoes he currency wh he hghes expeced reurn and Mn denoes he currency wh he lowes expeced reurn. I form a porfolo by akng a long poson on Max and a shor poson on Mn (denoed by Max Mn) and I hold hese posons for he nex K monhs (where K can be 1, 3, 6, 9, and 12). In each subsequen perod, I apply he same procedure, updang he sample perod by one monh each me. 8 For December 1979 hrough December 1998, one can choose from nne currences; afer December 1998, Max and Mn are seleced from he remanng four noneuro counres plus he Euro. Agan, due o a very large number of parameers o esmae, I only allow µ o change by counry. For he resuls of he pure momenum and pure mean reverson sraeges, one akes he decsons n he exac same way and usng he same equaon (13), bu ρ s assumed o equal zero for he pure mean reverson sraegy and δ s assumed o equal one for he pure momenum sraegy The Pure Mean Reverson Sraegy Table 3 repors averages and sandard errors for he annualzed reurns of Max and Max Mn porfolos for dfferen holdng perods K. The shaded areas repor he means of he zeronvesmen porfolos. Panel A presens he resuls for he pure mean reverson sraegy. The mean reurn for he zeronvesmen porfolo ranges from around 0.4 percen for K=1 o 4.1 percen for K=12. [Inser Table 3 here] 8 So I use as a frs sorng perod monhs 1 o 1/3 of he sample, hen monhs 2 o 1/3 of he sample +1 monh and so on, rollng he sample forward. 13
15 A smlar mean reverson sraegy has no been mplemened n he FX markes. However, Neely (1998) noes ha here s a longrun endency of exchange raes o rever o purchasng power pary (PPP) values and hs mgh be why cenral banks make excess profs when nervenng n he FX marke. Rogoff (1996) fnds ha he PPP does rever o a longrun mean and ypcally he leraure repors a halflfe of hree o fve years. A sudy prepared by Deusche Bank (2007) noces ha PPP s one of he bes fundamenals ha can forecas he exchange raes and consrucs a conraran sraegy. Dependng on he me perod consdered, hey oban mean excess reurns rangng from 3.8 o 4.3 percen. The pure mean reverson sraegy hs paper consrucs leads usually o lower average reurns. However, he wo sraeges are dfferen n ha he former presens a conraran sraegy based on reverson o he PPP The Pure Momenum Sraegy Panel B presens he annualzed mean reurns and sandard errors for Max and Max Mn porfolos for dfferen combnaons of K and J when δ=1. The rend of he mean reurns s very smlar o ha obaned for he sock marke, bu he annualzed average Max Mn porfolo s usually smaller for he FX marke (as expeced). Some of he average reurns for he zeronvesmen porfolo are negave. The averages are larger when J s 3, 6 or 9 monhs. Ths resul confrms he heorecal fndng ha avodng he mean reverson componen mgh gve a shorer momenum lag. Snce he rend s smlar for dfferen J, I only presen he case of J=12. The Max Mn mean porfolo reurn sars from a sascally sgnfcan 3 percen for K=1, hen ncreases o a maxmum of 6 percen for K=12. These reurns are smlar o he 5 7 percen per year obaned by Okunev and Whe (2003) for her smple momenumlke 14
16 sraegy. However, n some cases, he mean reurns here ouperform he Okunev and Whe (2003) sraegy. Ths resul s fascnang consderng he fac ha hey employ a sraegy desgned for he FX marke, whle I use a sraegy orgnally desgned for he sock marke The Combnaon Sraegy Table 4 presens he annualzed mean reurns, sandard errors and Sharpe raos for he combnaon sraegy. For comparson, he able also repors he resuls usng he same sraegy n he sock marke for each combnaon (J, K). The able also shows he oucomes of he sraegy afer ransacon coss. Includng he noransacon coss rows of he able allows a more drec comparson beween he sock and FX markes. Also, he ransacon coss hs paper employs are only esmaed, no acual. FX marke ransacon coss are no very large. Accordng o Szakmary and Mahur,1997, LeBaron, 1999, and Goodman, 1979 hey range from 0.05 o 0.2 percen for developed counres. I consder he maxmum of a 0.2 percen ransacon cos, whch s subraced from he reurn each me a purchase or shor sell of a new currency occurs. [Inser Table 4 here] The noransacon coss sraegy for J=12 generaes a mean reurn for he zeronvesmen porfolo of around percen and smlar mean reurns for J<12. For J=15, he mean reurns are much lower, rangng from 2.9 o 6.2 percen. 9 Transacon coss do no sgnfcanly aler he resuls. 9 Followng Cochrane (2005, p. 447), I check how he mean reurns compare o he heorecal reurns. For he combnaon sraegy, usng dfferen µ and he same δ and ρ (across counres and momenum lags), I oban he heorecal reurn. I use he resuls from Table 2. The procedure proposed by Cochrane mulples he sandard devaon of he reurn, , by he sandardzed expeced reurn of he currency n he op 9 h of he sandard normal dsrbuon (0.1894, obaned from he expeced reurn of he sandard normal varable over he nerval o nfny), and hen by he square roo of R 2 ( ). I oban an 15
17 The comparson beween hese resuls and he resuls obaned hrough he pure mean reverson sraegy s no sraghforward, snce he laer sraegy assumes J=0. One can sudy hs comparson by compung an overall average for he combnaon sraegy for each K and fndng he dfference beween ha average and he mean zeronvesmen porfolos n Table 4. For all K s, he mean reurns ncrease wh he use of he combnaon sraegy. Comparng he average reurns beween he combnaon sraegy and he momenum sraegy s much easer. There are 25 pars (J, K) for each of he wo sraeges and for 23 of hese he combnaon sraegy generaes hgher mean reurns. The comparson beween he FX marke and he sock marke s one of he man obecves of hs paper. As dscussed prevously, he Sharpe rao s he bes merc for comparng he wo dfferen markes. In only one case, he Sharpe rao for he sock marke s larger han ha for he FX marke. On average, sandard errors for he FX combnaon sraegy are 33 percen of he sandard errors for he sock combnaon sraegy, whle he mean reurns for FX are around 81 percen of he mean reurn for socks. Ths gves Sharpe raos around 2.5 mes hgher for he FX han for he sock marke. 10 Dfferen sraeges have been employed n he equy marke leraure. For a buyandhold sraegy, he Sharpe rao for he world marke s and ha for he US s 0.644, accordng o Balvers e al. (2000). So he resuls ha derve from usng hs combnaon sraegy for he sock marke are no unusual. Balvers e al. (2000) also expeced annualzed reurn for he op currency of 11.29%. Afer followng he same procedure for he boom currency, I oban he annualzed heorecal reurn of he Max Mn porfolo o be 22.58%. Ths heorecal reurn s larger han he 12.7% annualzed reurn obaned n Table 4, for he combnaon J = 12 and K = 1. In hs lgh he reurns obaned n hs paper are no oo hgh. 10 These dfferences beween he wo markes are ypcal. For nsance, Okunev and Whe (2003) repor annualzed mean reurns of 5 6 percen and sandard errors of for a momenum sraegy n he FX marke. Lee and Swamnahan (2000) oban for a momenum sraegy (holdng perod of one year) n he sock marke an annual mean reurn of percen and sandard errors of
18 apply wo mean reverson sraeges n he sock marke: her own sraegy, and DeBond and Thaler s (1985) conraran sraegy. The Sharpe raos obaned are and respecvely. In Table 4, for 18 ou of 25 (J, K) combnaons he sock marke has hgher Sharpe raos han he Balvers e al. (2000) sraegy and, for 24 ou of 25, hgher Sharpe raos han he DeBond and Thaler (1985) sraegy. Hence he combnaon sraegy produces much hgher Sharpe raos han oher sraeges employed n he sock marke. Moreover, usually produces Sharpe raos 2 or 3 mes larger han he DeBond and Thaler (1985) sraegy. I nex compare he Sharpe raos for he combnaon sraegy n he FX marke o Sharpe raos for oher sraeges n he FX marke. In he FX marke, perhaps he mos common sraegy s carry rade. Burnsde e al. (2008) oban an average annual reurn of 4.80 percen and a Sharpe rao of When consderng ransacon coss, he mean reurns n Burnsde e al. (2008) only decrease o 4.44 percen, whle he Sharpe rao falls o These resuls confrm ha akng ransacon coss no consderaon n he FX marke does no subsanally modfy he abnormal reurns obaned, or he Sharpe raos. Oher sraeges mplemened n he FX marke are echncal radng rules. LeBaron (1999) fnds annualzed Sharpe raos rangng from 0.67 o 0.96 for a dynamc radng rule sraegy. 11 The resuls obaned by mplemenng he combnaon sraegy usually ouperform oher sraeges n he FX marke. When creang he sraegy ha combnes mean reverson and momenum, he average of annualzed mean reurns obaned for J<15 s 11.9 percen for no ransacon coss and 8.6 percen when ransacon coss are ncluded. The average Sharpe rao s 1.5 and 1.08 respecvely. When J=15, he momenum effec has already passed, so he mean 11 Neely (1998, 2002), Sapp (2004) and Saacke (2002) oban smlar reurns when furher nvesgang he radng rules profably. 17
19 reurns and Sharpe raos of he sraegy are noceably lower (and n some cases negave when ransacon coss are ncluded). The sock marke Sharpe raos are no unusual, bu sgnfcanly hgher when one uses he combnaon sraegy nsead of oher sraeges. Smlarly, he FX marke resuls for he combnaon sraegy ouperform oher sraeges employed n he FX marke, and also provde sgnfcanly hgher Sharpe raos han hose found for he sock marke Concluson Ths paper employs a radng sraegy, prevously appled only o he sock marke ha creaes abnormal reurns n he FX marke. By runnng a smple paramerc es, I fnd ha UIP devaons follow mean reverson and momenum. In he FX marke he halflfe of mean reverson s very close o ha obaned for he sock marke, whle he momenum effec s sronger han n he sock marke. The combnaon sraegy creaes sgnfcan abnormal mean reurns (slghly underperformng hose of he sock marke) and Sharpe raos usually much hgher han n he sock marke. The resuls are also srong n comparson o sraeges developed specfcally for FX markes. Transacon coss do no aler he resuls sgnfcanly. I consder developed counres only, and he sample pos January 1999 consss of us fve currences afer he brh of he Euro. The porfolo I consruc should be even more profable f he currency choces are more numerous. Ths paper conrbues o he leraure no only by applyng a new sraegy n he FX marke, bu by applyng one orgnally desgned for he sock marke. The FX leraure consders mean reverng behavor oward PPP values and momenum radng 12 Resuls of robusness checks (dfferen me perods, parameers allowed o vary by counry and/or lag) do no sgnfcanly change he resuls and are avalable upon reques. 18
20 sraeges based on movng average rules. I brng a fresh perspecve o undersandng FX marke dynamcs by consderng rsky asse reurns, nsead of macroeconomc fundamenals. Ths allows for he creaon of a sraegy based on reurns (compued n hs case from devaons from UIP) and a drec comparson of he exploably of he reurn paerns beween he FX and he sock marke. Up o now sraeges employed n one marke have no been successfully mplemened n he oher marke, lkely due o fundamenal dfferences beween he wo markes. For nsance, echncal radng rules were found o be compleely useless n he sock marke snce he publcaon of Fama and Blume (1966), bu profable n he FX marke (Sweeney, 1986; Szakmary and Mahur, 1997; and LeBaron, 1999), suggesng maor dfferences beween he markes. The srkng resuls here, on he oher hand, rase he queson of why he wo markes behave so smlarly. Many papers challenge he effcency of he wo markes. Neely (2002) examnes he possbly ha he FX marke s neffcen due o Cenral Bank nervenon. He argues ha he abnormal reurns obaned n he FX marke hrough echncal rules, bu no exsng n he sock marke, are due o hese nervenons ha have no relevance for he sock marke. Ths paper challenges ha fndng. I fnd evdence ha he FX and sock marke neffcences have smlar paerns. One s lef o wonder wheher he wo markes are ndeed neffcen, or wheher, n fac, here exss an unobserved rsk facor ha explans hese reurns. A possble heory s he overreacon hypohess proposed from a behavoral perspecve (e.g. DeBond and Thaler, 1985, 1987) for he sock marke: ndvduals end o overreac o recen nformaon, creang momenum. Afer some me, exreme movemens n prces 19