A STUDY ON THE CAUSAL RELATIONSHIP BETWEEN RELATIVE EQUITY PERFORMANCE AND THE EXCHANGE RATE

Transcription

1 A STUDY ON THE CAUSAL RELATIONSHIP BETWEEN RELATIVE EQUITY PERFORMANCE AND THE EXCHANGE RATE The Swedsh Case Phlp Barsk* and Magnus Cederlöf Maser s Thess n Inernaonal Economcs Sockholm School of Economcs Absrac The queson wheher here s a causal relaonshp beween exchange raes and eques s unresolved boh n heory and emprcally. The Flow heory posulaes ha exchange raes cause equy reurns whle he Sock heory suggess ha equy reurns cause exchange raes. Prevous emprcal sudes have found mxed resuls alhough he relaonshp beween hese varables end o be sronger n more developed economes and hose sudes ha have found causaly usually conclude ha equy reurns causes exchange raes. Whle mos prevous research has nvesgaed he causaly by lookng a a sngle counres equy marke, we use he reurn dfferenals beween he marke reurns n wo currency areas o es agans he exchange rae. By employng he radonal es for Granger-causaly we fnd ha equy reurn dfferenals Granger causes exchange raes alhough no n he way ha he heorecal background would predc. The resuls are however no ndependen of me-perod snce ess of he fnal sx monhs n our daa-se (he crss perod) generae dfferen resuls. We conclude ha for Sweden, a rse n domesc equy prces encourages nvesors o dversfy away o bonds and foregn asses, more han hey ncrease demand for domesc money. Moreover, he possble falure of ncludng explanaory varables mgh have caused he dfferen oucomes for he wo me perods. Keywords: Granger-causaly, exchange raes, equy reurn dfferenals Tuor: Hans Tson Södersröm Examner: Mas Lundahl Dscussans: Ellen Bernhardson and Lnnéa Graaf Presenaon: June , Sockholm School of Economcs, Room KAW, am. We hank our uor Hans Tson Södersröm, as well as Rckard Sandberg, for valuable npu. * 21419@suden.hhs.se 21424@suden.hhs.se

2 TABL E OF C ON TEN TS 1. Inroducon Theorecal Background An Exogenous Increase n Domesc Oupu The Sock Theory The Moneary Approach The Porfolo-Balance Approach The Flow Theory Prevous Research Our Conrbuon Daa and Graphcal Analyss Mehodology Inroducon o Granger causaly The Granger-causaly es Saonary Lags Causaly and Conegraon Emprcal Resuls Varable Descrpon Tess of Saonary Model Specfcaon The Granger Causaly Tes Fnancal Crss Case Dscusson Techncal Dscusson Inerpreaon of resuls Omed varables Concluson References Appendx

3 1. INTRODUCTION Equy prces and exchange raes are cenral economc varables ha are consanly quoed n meda and whch ons of research has been devoed o. Alhough here s more or less consensus abou how he levels of he exchange rae and equy prces, separaely and n heory, can be explaned, here s nowhere near such consensus on wheher here s a causal relaonshp beween he wo. Theory on he subjec can roughly be dvded no he radonal Flow-heory and he porfolo approach or he Sock heory. The Flow heory s n he leraure hough of as he radonal approach o explan a causal lnk beween exchange raes and equy performance. The heory saes ha exchange raes cause equy reurns hrough s effec on companes fuure cash flows and s ne foregn asses. A deprecaon of a counry s currency would accordng o he Flow heory have a posve effec on ha counry s eques. One reason for he posve effec on companes cash flows from currency deprecaon s he fac ha companes receve more Swedsh kronor for every un hey sell abroad. Anoher reason s he posve balance shee effec, n erms of Swedsh kronor, ha would occur n he even ha a company has ne foregn asses. The Sock heory explans why equy reurns causes exchange raes. Accordng o he Sock heory, equy prces cause exchange raes snce alers he demand for money. If a counry s equy marke rses, people s wealh ncreases. The wealh ncrease s assumed o have a posve effec on money demand, whch s, gven a consan money supply, assumed o lead o a hgher neres rae and a currency apprecaon. In addon o hese hypoheses, here s also heory ha posulaes ha exchange raes and equy prces are no causally relaed. In harmony wh he dsagreemen on he heorecal level, prevous sudes of a possble causal relaonshp beween hese varables has shown vared resuls. Apar from he fac ha possble causal relaons may vary dependng on counry, currency regme, me-perod ec., he fac ha dfferen mehods and models for esng for causaly have been used mgh also explan he dvergen resuls. However, a general concluson ha unes many of he prevous sudes s ha a causal relaon s more lkely o be found n advanced economes and he causaly beween he exchange rae and equy reurns end o be un-dreconal, runnng from equy reurns o exchange raes, n lne wh he Sock heory. Ths sudy apples he sandard es for Granger-causaly, desgned by he Nobel laureae Clve Granger. Granger-causaly s economss favore noon of causaly and wha he bulk of prevous research on causaly beween exchange raes and equy reurns has used. Prevous research has almos exclusvely used a model wh only one counry s equy marke whch has been esed agans he relave prce of 2

4 anoher currency. Alhough he resuls of such ess gve one an undersandng of possble causal lnks beween an exchange rae and an equy marke, such ess overlook he fac ha he heorecal background o a grea exen assumes relave varables. An exchange rae s by defnon he relave prce of wo currences. We argue ha he exchange rae should be esed agans a relave varable for equy reurns n order o enable one o emprcally es he heory. Suppose ha Swedsh eques rse, he Sock heory would hen predc he Swedsh krona o apprecae agans oher currences. Bu f he equy markes n oher currency areas also perform very well he effec on he exchange rae s ambguous. The Sock heory would n fac predc ha he Swedsh krona would deprecae agans a gven counry s currency n he even ha eques perform even beer n ha counry. Ths hghlghs he raonale behnd usng a relave performance measure for eques when esng heory on causaly beween exchange raes and equy reurns. Knowledge abou a possble causal relaonshp would be useful for nvesors, companes and oher marke acors ha are affeced by hese varables. Ths paper examnes wheher here s Granger-causaly beween a blaeral exchange rae for he Swedsh krona and Swedsh equy reurns relave o equy reurns n he oher currency areas. To be able o draw as general conclusons as possble and as a check of he robusness of our resuls ess are made on he SEK/USD exchange rae and SEK/EUR and SEK/GBP equvalens. These exchange raes are esed agans correspondng relave equy performance. The observaons are made up of daly observaons from January 2001 ll February Prevous research ndcaes ha exchange raes and equy performance are casually relaed n advanced economes. Mos sudes, ncludng a sudy on Sweden n he nnees, have found ha he causaly goes from equy performance o exchange raes. Our hypohess s ha we wll fnd a causal relaonshp n all hree cases and ha he causaly wll be un-dreconal, runnng from relave equy reurns o exchange raes n agreemen wh he Sock-heory. Secon 2 goes hrough he heorecal background o famlarze he reader wh he opc and he conflcng heorecal explanaons for he relaonshp beween equy markes and exchange raes. Secon 3 presens a selecon of prevous research and oulnes wha we am o conrbue wh, secon 4 descrbes he daa n hs sudy and secon 5 reas he mehodology. In secon 6 we presen he emprcal resuls, secon 7 dscusses he resuls and secon 8 concludes. 3

5 2. THEORETICAL BACKGROUND The mos common heorecal approaches o hs ssue are he Sock heory (whch explans how equy prces cause changes n exchange raes) and he flow heory (ha suggess an explanaon for why exchange raes cause equy prces), bu here are also explanaons o why exchange raes and equy prces may move accordng o a ceran paern relave o each ohers despe an absence of causaly beween hem. 2.1 AN EXOGENOUS INCREASE IN DOMESTIC OUTPUT One explanaon for he co-varaon of equy prces and exchange raes can be obaned by consderng an exogenous change n domesc oupu. The uncovered neres pary condon posulaes a negave relaon beween domesc oupu and he exchange rae, whle equy prces are posvely relaed o oupu. As descrbed by Krugman and Obsfeld (1997, Chap. 16), he uncovered neres pary condon s based on he assumpon ha nvesors requre he same expeced reurn on domesc and on foregn currency deposs. The auhors presen he followng equlbrum equaon: EQUATION 1 R R * ( E e E ) / E where R s he neres rae on he domesc currency deposs, R* s he neres rae on foregn currency deposs, E s he exchange rae (uns of domesc currency per un of foregn currency) and E e s he expeced fuure exchange rae. We assume E e and R* o be gven. If he neres rae on domesc currency deposs decreases, an offseng mmedae deprecaon of he domesc currency s requred n order o keep he expeced reurn on domesc currency deposs consan. Provded ha E e has no changed, such a deprecaon resuls n an expeced fuure apprecaon of he domesc currency, so ha he expeced reurn on boh currences are equalzed. Krugman and Obsfeld (1997) also sae ha n equlbrum, real money supply (M S /P) mus equal real money demand L(R,Y). When he neres rae falls, or when domesc oupu goes up whle money supply remans consan, real money demand rses. The ncrease n domesc oupu causes an ncrease n real money demand due o he fac ha a larger number of ransacons wll ake place n he economy. Ths drves up he domesc neres rae. Gven ha E e and R* are unchanged, equaon 1 makes clear ha E mus fall,.e. he domesc currency apprecae, as a resul of he hgher oupu. 4

6 Equy prces are n general defned as he presen value of fuure cash flows (Savárek 2005). Based on he defnon n Bode e al. (2008, p ), equy prces can, gven ha k e > g, be represened by equaon 2, where FCFE denoes cash flow avalable o equy holders, k E denoes he cos of equy and g s he long-erm growh rae n FCFE. EQUATION 2 Value FCFE k E g Besdes from havng a posve effec on he value of he domesc currency, a rse n domesc oupu can also be assumed o gve rse o hgher cash flows for companes, whch n urn drves up equy prces. On he oher hand, he ncrease n he neres rae ha comes as a resul of he hgher domesc oupu pushes up k E, whch has a negave effec on equy prces. However, f we assume ha he posve effec on equy prces s domnan, he uncovered neres pary condon n combnaon wh he equy prcng formula (equaon 1) ogeher descrbe how an exogenous change n domesc oupu, workng va he neres rae and FCFE, affecs boh he exchange rae and equy prces whou posulang any drec causaly beween he wo varables. 2.2 THE STOCK THEORY Accordng o he Sock heory, he exchange rae s deermned by ndvduals wllngness o hold domesc vs. foregn asses. Whn he Sock heory we dsngush beween wo dfferen approaches, he moneary approach and he porfolo balance approach. The logc s he same for he wo approaches, bu he frs s lmed o deal wh he role of money, whle he laer akes on a broader vew as akes oher asse ypes no consderaon as well (Krueger 1983, p. 81) THE MONETARY APPROACH Accordng o Rosenberg (2003, pp ), he moneary approach reas he demand for and supply of money as he man deermnans of exchange raes, and says ha expansonary moneary polces, provdng excess money supply, push down he value of he currency as ndvduals ncrease her holdngs of foregn asses. Krueger (1983, pp ) furher pons ou ha when czens of a counry consder hemselves possessng excess amouns of money, he mpors of goods, servces and asses wll ncrease relave o expors. Ths effec can be explaned by he neres pary condon; as he neres 5

7 rae goes down, respondng o ncreased money supply, he currency deprecaes so ha an apprecaon o E e can be expeced n he fuure. The moneary approach s less comprehensve and complee han he porfolo-balance approach, and wdely regarded as nsuffcen o explan exchange rae deermnaon, due o he falure of akng oher explanaory varables no consderaon (Rosenberg 2003, p. 171). Therefore, he porfolo-balance approach beer serves as a bass for our analyss THE PORTFOLIO-BALANCE APPROACH Accordng o Krueger (1983, p. 87), he porfolo-balance approach focuses on movemens n people s wllngness o hold domesc vs. foregn money and secures, and he exchange rae balances ndvduals wllngness o hold foregn and domesc asses, respecvely. An exogenous rse n domesc equy prces resuls n hgher wealh, encouragng nvesors o demand more money, whch rases domesc neres raes so ha he domesc currency apprecaes (e.g., Savárek 2005, and Granger e al. 2000) 1. Savárek (2005) also oulnes a drec effec hrough whch equy reurns lead he exchange rae. As he value of domesc asses ncreases, nvesors ncrease he wegh of domesc asses n her porfolos a he expense of foregn asses. In order o enable hs change n holdngs from foregn o domesc eques, nvesors have o sell foregn and acqure domesc currency. Therefore, an ncrease n equy prces causes an nsananeous apprecaon of he domesc currency. In concluson, he Sock heory provdes an explanaon for a causal relaon runnng from equy prces o exchange raes, where an exogenous rse n domesc equy prces generaes an apprecaon of he domesc currency. 2.3 THE FLOW THEORY The Flow heory s ofen referred o as he radonal framework for explanng he relaon beween exchange raes and equy reurns (Granger 2000). Lke mos oher sudes of Granger-causaly beween exchange raes and equy reurns, we base our descrpon of he Flow heory on Aggarwal (1981). If he domesc currency deprecaes, he counry s nernaonal compeveness s mproved. Ths nfers enhanced prospecs for fuure cash flows for domesc frms ha are relyng on expors, mpor compeng producon or foregn operaons. Two reasons for he enhancemen can be denfed. One s ha he 1 For a deeper dscusson, see Krueger (1983, pp ). 6

8 prces of expors and mpor compeng goods n erms of he domesc currency rse, allowng domesc companes o ncrease revenues eher by ulsng hese hgher prces or by ncreasng volumes by lowerng her prces n erms of foregn currency 2. The oher reason s ha he value of ne foregn asses ncreases n erms of domesc currency when he domesc currency deprecaes. Ths generaes a balance shee gan f ne foregn asses are posve. Companes dependen on mpored goods or npus, on he oher hand, wll face hgher coss and less compeveness compared o foregn acors. Hence, cash flows wll ge smaller and equy prces wll fall. Smlarly, a balance shee loss wll h hose companes ha have ne foregn lables. However, he ncreased foregn rade should resul n ha domesc frms on he whole become beer off wh a deprecaon of he domesc currency. To conclude, an apprecaon of he Swedsh krona shall, due o he effec on revenues, lead o lower equy prces. In wha drecon he balance shee effec would work,.e. wheher Swedsh companes possess posve or negave ne foregn asses, s hard o ell, due o he complex and globalsed ownershp suaons. However, hs fac n self makes he ssue less relevan o consder, as mples sgnfcan dffcules for nvesors o assess how exchange rae movemens affec companes balance shees. 3. PREVIOUS RESEARCH The frs sudy relaed o hs area of research was made by Franck and Young (1972); hey nvesgaed he mpac of more volale exchange raes, followng he fnancal crses a he me, on U.S. companes. They se ou o examne wheher here was any relaonshp ha could have polcy mplcaons for companes. By usng smple regresson and correlaon echnques, hey found no sgnfcan neracon beween hese varables ha companes can make use of. A more relevan sudy, and ofen ced pece of work, was made by Aggarwal (1981). Aggarwal looks a he correlaon beween he USD exchange rae and U.S. Sock ndces, usng monhly observaons, durng He defnes he exchange rae as he USD agans a rade weghed currency baske conanng he currences of he Uned Saes fory sx larges radng parners. Equy prces are represened by hree U.S. equy ndces. He fnds a posve correlaon n lne wh he flow heory, ha exchange raes lead equy prces. 2 Whle exchange rae changes have a drec effec only on companes nvolved n expors and mpors, companes acng solely on he domesc marke are affeced as well. If, for nsance, a deprecaon of he domesc currency resuls n hgher prces of mpored producon npus, hen companes ha formerly have acqured hese npus from abroad wll o a greaer exen urn o domesc producers. Ths makes he prces of domescally produced npus go up as well. 7

9 Before he 90 s, sudes of he relaon beween exchange raes and equy prces were lmed o he sascal mehods avalable a he me. Savárek (2005) pons ou ha Bahman-Oskooee and Sohraban (1992) were among he poneers when comes o make use of conegraon and Granger-causaly ess o nvesgae a possble causal relaon beween exchange raes and equy prces. The auhors used monhly daa o examne he relaon beween he USD effecve exchange rae and he S&P 500 ndex for he me perod and conclude ha here was bdreconal causaly, whch means ha he causaly goes n boh drecons. Overall, mos of he research ha has been made on he relaon beween exchange raes and equy prces has focused on he US and Souheas Asa. Pan e al. uses daly daa o examne he dynamc lnkages for seven Eas Asan counres, ncludng Hong Kong, Japan, Korea, Malaysa, Sngapore, Tawan, and Thaland, for he me perod; January 1988 and Ocober They fnd a sgnfcan causal relaon runnng from exchange raes o equy prces for Hong Kong, Japan, Malaysa, and Thaland before he 1997 Asan fnancal crss. They also fnd a causal relaon runnng from equy prces o exchange raes for Hong Kong, Korea, and Sngapore. A rse n Equy prces causes he currences o apprecae. Durng he fnancal crses, when boh he equy prces and he value of hese counres currences fell freely, no counry showed any sgnfcan causal relaon from equy prces o he exchange rae. However, hey all, wh he excepon of Malaysa, showed a causal relaon from exchange raes o equy prces. The auhors pon ou ha a crss, such as he Asan fnancal crss of 1997, may aler he naure of equy prce-exchange rae relaons. The resuls are obaned n spe of he fac ha none of hese economes, wh he excepon of Japan, have an enrely free floang exchange rae arrangemen, somehng ha one could suspec would dampen any lnkages. Doong e al. (2005) use weekly daa o examne he relaon for Indonesa, Malaysa, he Phlppnes, Souh Korea, Thaland, and Tawan beween 1989 and They fnd bdreconal causaly beween exchange raes and equy prces n Indonesa, Korea, Malaysa, and Thaland. Furher, wh he excepon of Thaland, equy prces n he counres under sudy are negavely relaed o he exchange rae, hence, a deprecaon of he currency s assocaed wh a fall n equy prces. Granger a al. (2000), smlarly o Pan e al. ses ou o nvesgae f here s any causal relaonshp beween exchange raes and equy prces n her free fall durng he Asan fnancal crss. Usng daly daa, hey fnd ha mos counres can be descrbed by he porfolo approach, ha equy prces lead exchange raes, or here s feedback neracon or bdreconal causaly (eher marke can ake he lead). Furher, he auhors underlne ha alhough hey fnd sascal relaonshps, s dffcul o nerpre he resuls snce hey can be generaed from oher srucural relaons such as he neres pary condon or IS-LM relaed polces. As an 8

10 example hey pon ou ha a recessonary shock or oher unfavourable nformaon on a counry can make boh he counry s equy marke and currency fall. In addon o only ncorporang exchange raes and equy prces o he model, he auhors nclude he US equy marke, he FEDs fund rae, he respecve counres neres raes and he dfference beween hese raes. The US equy marke s ncluded n he model snce research ndcaes ha has sgnfcan nfluence over he Asan equy markes and he neres raes are ncluded because hey mrror economc prospecs and are very much relaed o boh exchange raes and equy prces. Savarek (2005) nvesgaes he ssue by esng he shor- and long erm relaon beween exchange raes and equy prces n he US as well as n four old EU counres and four new members of he EU, usng monhly daa. Savarek dvdes hs daa se no wo me perods; ncludes only developed counres and , ncludng all counres. The resuls show ha causaly beween he varables s sronges n counres wh more developed foregn exchange markes. Furher, he shor- and long erm causaly s more powerful n he laer me perod, suggesng ha as capal markes has become more negraed, and capal conrols have been abolshed, he lnk beween exchange raes and equy prces has become sronger. However he drecon of causaly s no unform bu dffers beween counres. The auhor also concludes ha no relaon can be deermned beween he varables n he four new EU counres n he sudy. Savárek s explanaon o hs s ha hese counres equy markes are no algned wh her respecve real economes and ha hey do no arac nernaonal nvesors o any greaer exen. Fazel (2005) s crcal owards hose ha argue for a causal relaonshp beween exchange raes and equy prces. Fazel recognzes ha a causal relaon can be rue durng ceran crcumsances a shorer me perods bu ha here s no sable long erm causal relaonshp beween he varables. Fazel argues ha boh exchange raes and equy prces are endogenous varables and ha her long-erm relaonshp s dependen on he exogenous varable ha causes exchange raes and equy prces. The exogenous varable could be he neres rae. The neres rae has wo componens, he real neres rae and nflaon. Fazel argues ha wheher a change n he neres rae s caused by a change n nflaon or a change n he real neres rae wll have dfferen effecs on he exchange rae and equy prces. Hence, he relaonshp beween exchange raes and equy prces are dependen on he cause of changes n he nomnal neres rae and ha cause s unsable over me. Fazel hypoheszes ha here s no sable relaonshp beween equy prces n he Euro zone and he Euro. By employng smple regresson analyss he founds ha he varables are no correlaed. 9

11 Whle mos prevous research has suded he relaonshp beween equy prces and blaeral exchange raes by lookng only a a counry s equy prce ndex and he exchange rae and how hese me seres nerac, Ajay e al. (1998) sudy he relaonshp beween hese varables by lookng a he dfference n equy reurns beween wo counres and her respecve exchange rae. The auhors employ sandard Granger-causaly ess on seven advanced economes and egh emergng Asan economes. Causaly s found; runnng from equy reurns o exchange raes, for all advances economes bu he resuls for he emergng economes s mxed. The auhors conclude ha her resuls can be explaned by a hgher level of negraon beween equy- and exchange markes n he advanced economes compared o he emergng economes. The sudy s performed wh daly as well as wh weekly daa; boh daa ses generae he same resuls n he advanced economes, alhough daly daa generae sronger resuls. However, he resuls dffer dependng on daa frequency n he case of he emergng economes. To our knowledge, he only sudy of Granger-causaly beween hese varables ha has been made on Sweden was performed by Haem-J and Irandous (2002). They examned he causal relaon beween he OMX PI ndex and he nomnal effecve exchange rae as measured by he TCW ndex. They used monhly observaons over he me perod ,.e. he frs years afer he floang currency regme was nroduced n Sweden. By usng he relavely new Granger non-causaly es, developed by Toda and Yamamoo (1995), hey fnd ha he causaly s undreconal and runs from equy prces o he exchange rae. The SEK ends o apprecae when equy prces go up. 3.1 OUR CONTRIBUTION Ths essay sudes he Granger-causaly beween relave equy reurns and exchange raes n lne wh Ajay e al. (1998). We am o shed lgh on wheher here s a causal relaonshp beween he exchange rae for he Swedsh krona and hree oher currency areas currences and how well he respecve currency areas equy markes perform n relaon o he Swedsh equy marke. Alhough he bulk of prevous research on hs relaonshp has no used relave equy reurns, we argue ha s necessary o use relave reurns. As explaned n he nroducon, a sudy ha uses absolue reurns s no able o draw any reasonable conclusons regardng wheher he fndngs mach he heorecal background. The heorecal background assumes ha boh varables are relave. The Haem-J and Irandous (2002) sudy on Sweden ha nvesgaed he causal relaon beween equy reurns and exchange raes dd no use relave equy reurns. Furher, he daa se ha was used was monhly observaons from 1993 ll We wan o conrbue o he research on hs opc by usng daly observaons from 2001 ll 2009 of relave equy reurns and exchange raes. 10

12 4. DATA AND GRAPHICAL ANALYSIS 3 The daa se employed n hs sudy consss of daly observaons of he exchange rae beween he Swedsh krona and he hree currences ha Sweden s engaged n mos rade wh, he Euro, he USD and he GBP (KIX-ndex). In addon, he daly reurn dfferenals beween comparable equy ndces relaed o each currency s ncluded. The equy ndces are chosen so ha hey represen he broad performance n he respecve markes and hey are denomnaed n her respecve currences. Moreover, he dfferenals beween he respecve cenral bank raes are ncluded n he models as a conrol varable. All daa are colleced from Thomson s Daasream. The Swedsh equy marke s represened by he OMX Sockholm ndex whch ncludes all eques lsed on he Nordc exchange n Sockholm. The Euro Zone equy marke s represened by he S&P Eurozone Broad Marke Index, he Brsh equy marke s represened by he FTSE All-share ndex (excludng mulnaonals) and symbolzng he U.S. equy marke s he S&P1500 Super Compose ndex. We use he equy ndces daly closng prces and he me dfference wh he U.S. marke s dsregarded (we do no lag he S&P1500 Super Compose). The exchange raes ha we use are colleced from banks a 9:30 A.M (Swedsh me) and hese are mached wh he prevous day s equy prces. Prevous research has used vared observaon frequences when sudyng he causal relaonshp beween exchange raes and equy performance. The mos common frequences ha have been esed are daly and monhly. The choce of frequency s smply a queson of ones belef on he lead and lag me. More recen sudes end o use daly observaons and sudes wh daly observaons are also he ones ha o he greaes exen have found Granger-causaly. Granger e al. (2000) pon ou ha daly daa s necessary n order o capure capal movemens. Fgure 1 below llusraes he reurn dfference beween OMXS and S&P1500 and he exchange rae beween he SEK and he USD. In 2001 Swedsh eques were performng worse han U.S. eques and he SEK deprecaed. In 2002 and 2003 Swedsh equy prces connued o perform less well han s US equvalens, however, he SEK apprecaed sgnfcanly. In 2004 s hard o dscern any parcular paern bu n 2005, when Swedsh eques performance was much sronger han he U.S. equvalens, he SEK deprecaed sgnfcanly. The developmen n 2006 was characerzed by an apprecang SEK, whle Swedsh eques performed relavely beer overall hough here was no clear rend. Boh 2007 and 2008 are characerzed by exreme volaly n he relave equy performance varable whle he SEK apprecae seadly unl md 2008, when sared o deprecae sgnfcanly. From he char one canno 3 The chars n hs secon have he exchange rae on he rgh hand axs and he reurn dfferenal on he lef hand axs. The reurns dfferenals are calculaed by ndexng all ndces so ha hey sar a 100 ( =100, hence, he lef hand sde axs represen percenage pon dfferenals beween he ndces. 11

13 make any nference abou wheher here s a causal relaonshp beween hese varables. The way hese me seres move show no clear paern hroughou he perod. Wha one can deec s perods of me wh a clear negave, or posve, correlaon beween he varables. I s no feasble o dsngush movemens on a daly bass why s mpossble o ge an dea abou any day-o-day paern. FIGURE OMXS-S&P1500 SEK/USD Fgure 2 descrbe he reurn dfferenal beween OMXS and FTSE All-share and he SEK/GBP exchange rae. As n he US case above, here was a clear negave relaonshp beween hese varables n he greaer par of 2001; Swedsh eques were performng worse han s Brsh equvalens whle he SEK deprecaed. From 2002 ll 2006 one can no dsngush any parcular paern. In 2007 he exchange rae does no move much whle Swedsh eques connue o ouperform he Brsh equvalens and n 2008 he SEK apprecaed sgnfcanly whle reurns do no dffer much beween he respecve markes. As, n he U.S. case we canno deec any clear correlaon beween he exchange rae and he equy reurn dfferenal hroughou he perod. 12

14 FIGURE OMXS-FTSE All-share SEK/GBP Fgure 3 llusraes he equy reurn dfferenal beween OMXS and he S&P Euro Zone ndex and he SEK/EUR exchange rae. We can see from he char ha he exchange rae dd no move much durng he greaer par of he me perod. Swedsh eques dd however perform consderably beer han European eques durng hs me perod. However, from md-2007, European eques began o cach up and n md-2008 he SEK sared o deprecae radcally. Agan, we canno draw any general concluson abou he relaonshp beween hese varables. FIGURE , , ,5 10 9,5 9 8,5 8 OMXS-S&PEUROZONE SEK/EUR 13

15 5. METHODOLOGY Research on he causal relaonshp beween equy prces and exchange raes has been conduced wh varous mehods. However, prevous research has almos exclusvely reled on Granger causaly n one way or anoher. Economss end o use he radonal approach, desgned by Granger (1969), whereas economercans have begun o use more advanced ess such as he Granger non-causaly es developed by Toda and Yamamoo (1995). Furher, and as menoned above, mos sudes do no use a relave equy prce varable bu look only a one equy prce ndex. Also, some sudes look a he real exchange rae and/or conrol for varables such as he neres rae whle ohers do no. These dfferences n ess and models used mpose dffcules when comparng resuls and make one hnk wce before decdng whch es o use and whch varables o nclude. Ths sudy uses he radonal es for Granger causaly wh, f necessary, precedng ess for conegraon o arrve a he proper model for conducng he es. A specfcaon of he varables wll follow below n secon INTRODUCTION TO GRANGER CAUSALITY If one looks up he word causaly n a dconary one wll read ha s he relaon of cause and effec. The concep can seem rval bu s acually no as crysal clear as mgh appear. One can say ha causaly s a phlosophcal concep whch has no correc defnon. I s an ssue ha has ackled he mnds of hnkers such as Arsole and he Scholacs. Davd Hume was he frs phlosopher o rea causaly n a macroeconomc conex, one of hs more famous works s he quanave heory of money whch saes ha he sock of money n relaon o he sock of avalable goods causes he prce level (Hoover, 2001, p. 2). Snce Hume s days he debae on causaly and wha s has connued bu he ools and echnques o nvesgae he maer has become ever so sophscaed. Today, accordng o Hoover (2001 p. 150), Granger-Causaly s economs s favoure noon of causaly. Granger (1969) suggess a daa-based echnque for enablng one o decde wheher wo varables are casually lnked. Granger (1980) saes ha audes owards causaly are wdespread, here are hose ha ake he sance ha s mpossble o defne causaly whle ohers beleve ha everyone has her own defnon of wha causaly s. The dfferng perspecves make dffcul o come up wh a generally accepable defnon. Granger has proposed a defnon whch has found, more or less, general suppor. The defnon ress on he axom ha he pas and presen may cause he fuure, bu he fuure canno cause he pas. Furher, he defnon assumes ha he causng varable adds explanaory power o an even n addon o all oher knowledge n he unverse. 14

16 From Granger (1980), he general defnon s ha: Y n s sad o cause X n+1 f P(X n+1 Є A Ω n ) P(X n+1 Є A Ω n - Y n ), for some A, where X n and Y n are me-ordered ses of varables and Ω n s he se of non redundan nformaon avalable a me n. Tha Ω n does no nclude any redundan nformaon mples ha f some varable Z n s funconally relaed o one or more oher varables, n a deermnsc fashon, hen Z n should be excluded from Ω n. For causaon o occur, he causng varable (Y n n he defnon above) needs o have some unque nformaon abou wha value he varable s causng wll ake. The defnon above s no operaonally possble. Praccal mplemenaon demands a lmed daa se, a lmed number of lags and only a couple of varables. These consrans do mply some dffcules. Granger (1980) pons ou ha daa nadequacy can cause problems, for nsance, f daa s no gahered frequenly enough. If a causal relaon s evden on a weekly bass bu daa s recorded on a monhly bass hen he causal relaon wll appear o be nsananeous and wll be mpossble o deermne wheher here s a causal relaonshp or f boh seres have a common cause. Sorensen (2005) saes ha nsananeous causaly occurs when he me seres are correlaed, whch economc me seres ofen are. If one hen fnds granger causaly n one drecon, one may feel ha he case for real causaly s sronger. Furher, accordng o Granger (1980), he problem of mssng varables can lead o msnerpreaon of one s resuls, an apparen causaon can be proved o be spurous once addonal varables are added. Relaed o hs s he possbly of unobservable varables, Granger (1980) exemplfes hs wh he hunder lghnng example; ha X causes boh Y and Z bu he causal lag s shown from X o Y, hen from X o Z. If X s no observed, Y wll appear o cause Z. Hence, somemes he mssng varable wll be avalable and, when added o he nformaon se, he leadng ndcaor (Y n he hunder and lghnng example) wll no longer appear o cause. When he mssng varable s unobservable one can no ell f a varable s a cause or only a leadng ndcaor. Furher, f he me ha an even s recorded devaes from when an even occurs, hs needs o be aken no accoun n nerpreaon. Granger (1980) hghlghs he mporance of sophscaon of he analyss used n decdng proper causal relaons o es and ha nerpreaon mus be conduced wh care. Granger (1988) furher saes ha exra knowledge s useful when nerpreng he resuls, such as economc heory. Sorensen (2005) saes ha Granger causaly measures f one hng happens before anoher hng and helps predc nohng else. 15

17 5.2 THE GRANGER-CAUSALITY TEST The es for Granger causaly nvolves esmang he followng par of regressons: m m Y Y X u m m X X Y u A varable X(Y) Granger causes a varable Y(X) f he error varance of a regresson of Y(X) on s own pas hsory and on he pas hsory of X(Y) s sascally sgnfcanly lower han he error varance of a regresson of Y(X) on s own pas hsory alone. Hence, Granger-causaly sresses he paerns of correlaon found n emprcal daa (Hoover 2001 p. 132). In pracce, hs s done by an F es 4. Accordng o Gujara (2003 p. 697) we can dsngush beween four dfferen oucomes of he es: 1. Undreconal causaly from Y o X. 2. Undreconal causaly from X o Y. 3. Feedback or blaeral causaly. 4. Independence. The Granger causaly es assumes ha he varables X and Y are saonary. Moreover, he number of lags s an mporan queson ha affecs he resul of he es. If one fnds ha he varables are negraed of order one, denoed I(1), whch s expeced for many mporan macroeconomc varables, a es for conegraon mus be performed o decde wheher we need o proceed wh a Vecor Error Correcon Model or no (Engle and Granger 1987). Conegraon would mply ha a lnear combnaon of he wo me seres, negraed of order one, s saonary. In addon, hs would mply ha here s a causal relaon beween he varables (Granger 1988). I s descrbed below how hese ssues are handled n hs sudy. 4 An unresrced (UR) regresson and a resrced (R) regresson are formed. The laer does no conan he varable(s) whch we wan o es wheher hey have sgnfcan explanaory power. The F sasc s calculaed from: F ( m, n K ) ( RSS R RSS UR RSS /( n UR ) / K ) m where RSS s he resdual sum of squares, m s he number of varables ha are excluded n he resrced regresson, n s he number of observaons and K s number of parameers n he unresrced regresson. If he compued F value exceeds he crcal F value, he null hypohess, H0: β1 = β2 = = βm = 0, s rejeced. 16

18 5.2.1 STATIONARITY Ths secon s enrely based on Gujara (2003, pp ). A process s consdered saonary f s mean equals zero, has consan varance, and he covarance of wo me perods s consan rrespecve of whch me perods are used and he dsance beween hem. The process s sad o be weakly saonary f he wo frs condons are fulflled bu he covarance beween wo me perods depends on he dsance beween he me perods, bu no on when s calculaed. If he process s saonary around a rend, s sad o be rend-saonary. A common example of non-saonary me seres s he random walk model (RWM). A saonary me seres ha s suaed below s mean wll have a larger probably of ncreasng han decreasng as s nex move. For a RWM, he probably of an ncrease s always equal o he probably of a decrease, rrespecve of wheher s found above or below s hsorcal mean value. Thus, has he same mean as a correspondng saonary seres, bu s movemens along s mean s drawn-ou so ha crosses he mean value less frequenly. RWM may appear wh or whou drf. In some cases, akng frs dfference of a RWM can make saonary. In ha case he seres s negraed of order 1, denoed as I(1). If one has o ake frs dfference wce o oban a saonary seres s negraed of order 2, I(2), and f we have o ake frs dfference d mes he seres s an I(d) process. A seres ha s negraed of order 0 s saonary LAGS I s saed n secon 5 ha he number of lags affecs he resul of he Granger-causaly es. Ths s of course relaed o he problems ha can occur wh he es for Granger-causaly, as descrbed n secon 5.1, n he even ha he pon n me ha a causal relaonshp occurs and he frequency of he daa gahered devaes. From he defnon of Granger-causaly, he cause canno occur afer he effec, whch mples ha he lag s eher posve or zero, zero mplyng nsananeous causaly. Granger (1988) argues ha nsananeous causaly does no occur n macroeconomcs bu ha he possbly of mssng varables canno be ruled ou. Ths mples ha he es for Granger-causaly assumes posve lags CAUSALITY AND COINTEGRATION As saed above, wo varables are sad o be conegraed f hey are boh non-saonary, e.g. I(1) processes, bu a lnear combnaon of he varables s saonary, I(0). Accordng o Gujara (2003, p. 822) ha mples ha he lnear combnaon of he me seres cancels ou he sochasc rends n he 17

19 varables and ha here s a long-erm or equlbrum relaonshp beween he varables. Granger (1988) saes ha hs can be explaned by ha here exss a consan, alpha, such ha z = x - αy, s I(0) EMPIRICAL RESULTS 6.1 VARIABLE DESCRIPTION To oban equy reurns, we ransform he equy ndces no her naural logarhmc form, whch we hen ake n frs-dfference,.e. each observaon less he prevous observaon. Ths approxmaely equals he percenage changes. We hen subrac he percenage reurn of each respecve foregn ndex from he reurn on he OMXS ndex. In ha way we oban he percenage reurn on Swedsh eques relave o he percenage reurn of each foregn eques marke. As exchange rae varables we use he logarhmc form of blaeral exchange raes beween he Swedsh Krona (SEK) and he foregn currences under consderaon, defned as uns of SEK per un of foregn currency. By usng he log form, we crcumven any poenal problems semmng from heeroscedascy (Wooldrdge 2009, p. 191), whch n oher case could nvaldae he usual and F sascs (Wooldrdge 2009, p. 432). The neres rae plays a cenral role n many heores dealng wh he relaon beween equy prces and exchange raes. Therefore, movemens n he neres rae ha appears as exogenous n our sysem,.e. whch are no caused by changes n equy prces, mgh aler he exchange rae whou beng drven by equy prces. Ths can make he causaly beween exchange raes and equy prces appear as weaker han s. Thus, s adequae o conrol for exogenous changes n he neres rae. For ha reason we nclude relave changes n he dfferen markes cenral bank neres raes. These varables, whch we henceforh refer o as he neres varables and denoe by R (wh he superscrp ellng o whch cenral 5 Granger (1983) has shown ha f x and y are conegraed hey wll hen be generaed by an error correcon model lke he one below or oherwse he model wll be mss specfed. m m Y ( Y X ) Y X u m m X ( Y X ) X Y u

20 bank s neres rae he Swedsh neres rae s se n relaon), are calculaed by akng he frs dfference of he dfference beween he Swedsh Repo Rae and he Euro Shor Term Repo, he US Federal Funds Rae and he UK Clearng Banks Base Rae, respecvely. By ncludng he relevan neres varable n each regresson we can dscern he effec of moneary polcy shocks from he causaly beween relave equy reurns and exchange raes. 6.2 TESTS OF STATIONARITY To ensure ha all varables are saonary, we conduc he ADF es 6 on each varable, wh up o fve lags. We use he Akake Informaon Creron 7 (AIC) o decde whch number of lags ha are approprae o 6 To es wheher a me seres conans a un roo or no,.e. f s saonary, a Dckey-Fuller (DF) es can be used. I s based on he followng equaon Y Y u (1) u s a whe nose error erm. If 1 (1) becomes a non-saonary sochasc process, or more narrowly a random walk wh drf. We can rearrange (1) so ha Y Y u 1 (2) where represens he frs-dfference and ( 1). The DF es employs he null hypohess: 0, ha s, he seres s non-saonary. Under he null hypohess, he esmaed value of follows he Dckey-Fuller ype of dsrbuon. (Dckey and Fuller 1979) If u s auocorrelaed an augmened Dckey-Fuller (ADF) es can be used. In hs es (2) s exended o conan one or more lagged values of he dependen varable as explanaory varables. The reason for ha s ha f he error erm s auocorrelaed, he seres wll change beween values above and values below zero eher more or less frequenly han f was uncorrelaed. Includng more lags ends o even ou he rounds of observaons above or below zero, erasng he bas n he error erm. The es s carred ou n he same way as he DF es,.e. by esng f he null hypohess of 0 can be rejeced or no. The regresson s as follows: Y Y m Y (3) where s a pure whe nose error erm. The number of lags of he dependen varable ha shall be ncluded can be esed emprcally, by checkng whch model has he bes f. (Ello e al. 1996) 7 AIC s a measure of model f, and can be used o es whch model s mos approprae. For nsance models wh dfferen lag lenghs can be compared. The lower he AIC value, he beer fed s he model. The equaon we use hroughou hs paper s he followng: AIC = 2k + n(ln(rss / n)) 19

21 nclude n he ADF es. The equy reurn varables are all saonary, whch was expeced snce hey are already dfferenaed once from her levels 8. The case s he same wh he neres varables. All of he exchange raes are, on he oher hand, non-saonary. Therefore we dfferenae hem and ha urns ou o make hem saonary. As a resul we henceforh use he frs-dfference form of he exchange raes, whch mples ha we deal wh percenage changes n exchange raes as well. (See appendx for dealed resuls). Snce he equy reurn varables are all saonary and no negraed of order 1, I(1), as he exchange raes are, hese varables are no conegraed. Hence, he equy reurn dfferenals and he exchange raes do no have a long-erm equlbrum relaonshp. We can herefore go on o es for Granger-causaly whou ncludng an error correcon erm. 6.3 MODEL SPECIFICATION Before we go on o es for Granger-causaly we need o specfy he models. Frsly, we wan o deermne wheher or no o nclude he neres rae varable as a conrol varable. And gven ha he neres varable should be ncluded n he model, we only wan o nclude hose lags ha are sgnfcan. 9 Secondly, we wll apply AIC o sele on he number of lags o nclude of he explanaory exchange rae and equy reurn dfference varables n he models 1-6. The resulng number of lags n each model ndcaes he lead lag me srucure n he relaonshps. The resulng number of lags n each model s repored n able 1. where k s he number of parameers, n s he number of observaons and RSS s he resdual sum of squares of he model. 8 See secon for an explanaon. 9 To decde wheher s approprae o nclude he neres varable n he models, we run he regressons of models 1-6, wh k equal o 1 o 5. We hen urn our aenon o he values of he neres varables and her lags. As a decson rule of humb, we have chosen o proceed wh hose ha have coeffcens sgnfcan a he 5 % level. We fnd ha for model 1 he fourh lag of he neres varable has a sgnfcan mpac, for model 2 he unlagged varable s sgnfcan for all regressons (.e. rrespecve of he k value) and he frs lag of he neres varable when 1 k 5. For model 3 he hrd lag s sgnfcan, for model 4 he second, hrd and fourh lags, and for models 5 and 6 no neres varables are sgnfcan. 20

22 MODEL 1 OMXrelEZ k k OMXrelEZ SEK / EUR R ECB u 1 MODEL 2 OMXrelSP k k OMXrelSP SEK / USD R FED u 2 MODEL 3 OMXrelFTSE k k OMXrelFTSE SEK / GBP R BoE u 3 MODEL 4 SEK / EUR k SEK / EUR k 1 3 romxrelez R ECB u 4 MODEL 5 SEK / USD k SEK / USD k 1 3 OMXrelSP R FED u 5 MODEL 6 SEK / GBP k SEK / GBP k 1 3 OMXrelFTSE R BoE u THE GRANGER CAUSALITY TEST When he models are specfed we can go on o conduc he Granger-causaly es. We hen agan run models 1-6 above wh he approprae number of lags and wh proper ncluson of he neres varable. As descrbed n secon 5.2, he es s conduced by runnng an unresrced and a resrced regresson n order o generae an F-sasc, where he resrced regresson, as explanaores, only ncludes he lagged values of he dependen varable. In he even ha he F-sasc s sgnfcan, he null hypohess can be rejeced. A rejecon of he null hypohess would mply ha we rejec ha lagged values of equy reurn dfferenals, when changes n exchange raes are used as he dependen varable or vce versa, do no Granger cause exchange raes. The resuls are repored n able 1. 21

23 TABLE 1. THE RESULTS FROM THE GRANGER-CAUSALITY TEST (THE BASE CASE) Dependen Varable Lags Crcal F value (1 % sgn.) Observed F-value romxrelez FX-rae does no cause equy reurns romxrelsp FX-rae does no cause equy reurns romxrelftse FX-rae does no cause equy reurns SEK/EUR Equy reurns do no cause FX-rae SEK/USD Equy reurns do no cause FX-rae SEK/GBP Equy reurns do no cause FX-rae H 0 Resul Canno rejec Canno rejec Canno rejec Rejec Rejec Rejec The resuls are n lne wh our hypohess. Relave equy performance un-dreconally Granger causes exchange raes FINANCIAL CRISIS CASE Because of he nense volaly ha has characerzed he exchange and equy markes for he pas sx monhs we hough ha would be neresng o solae ha perod and examne f he resuls would equal he base case n secon 6.4. The graphcal analyses n secon 4 llusrae ha boh he relave equy performance varables and he exchange raes have reaced dramacally o he fnancal urmol. Alhough, how hey have moved n accordance o each oher vares beween he markes. Furher, a large proporon of prevous research has suded he causal relaonshp beween exchange raes and equy durng he Asan fnancal crss and found dfferen resuls when solang he crss perod from when hey have suded an exended daa se. We have defned he crss perod as; pos-he Lehman Brohers collapse (16/9-08) unl he end of our daa se (27/2-09). We use he same varables as n he base case, wh he dfference ha he exchange rae varables are aken n he frs-dfference, whou conducng any ess on her levels forms. We es for saonary n he same way as before. As expeced, all varables are saonary. We also assess whch neres rae dfferenals ha have a sgnfcan effec on he dependen varables, by consderng her values and wheher hese are sgnfcan. Despe he cenral bank s hgh acveness, wh mulple sharp cus n neres raes, hese varables have a low mpac on exchange raes and equy reurns. The resuls from he es for Granger-causaly are repored n able 2. 22

24 TABLE 2. RESULTS FROM THE GRANGER-CAUSALITY TEST (THE CRISIS CASE) Dependen Varable Lags Crcal F value (1 % sgn.) Observed F-value H 0 romxrelez FX-rae does no cause equy reurns romxrelsp FX-rae does no cause equy reurns romxrelftse FX-rae does no cause equy reurns SEK/EUR Equy reurns do no cause FX-rae SEK/USD Equy reurns do no cause FX-rae SEK/GBP Equy reurns do no cause FX-rae Resul Canno rejec Canno rejec Canno rejec Canno rejec Canno rejec Canno rejec For hs perod, our hypohess, ha relave equy reurns Granger cause exchange raes, mus be rejeced. A he 5 % sgnfcance level, Granger causaly does no exs beween any par of varables. A he 10 % sgnfcance level, Swedsh equy reurns relave o he reurn on US eques granger cause he SEK/USD exchange rae. 7. DISCUSSION 7.1 TECHNICAL DISCUSSION The resuls are n lne wh our hypohess, relave equy performance un-dreconally Granger causes exchange raes for all currences n he sample. Ths s he same resul as mos prevous research on advanced economes have found (see for nsance Ajay e al. (1998), Haem-J and Irandous (2002), and Savárek (2005)). The choce of usng daly observaons was movaed by he fac ha prevous research ndcaes ha hs s he approprae frequency o use n order o capure he causal relaon. Alhough, hs sudy confrms our hypohess ha relave equy reurns Granger causes exchange raes on a daly bass, one canno rule ou ha one would fnd Granger-causaly f usng, for nsance, monhly observaons as well, as he prevous Swedsh sudy dd. Tha would ndcae a more long-erm causaly as oppose o our resuls ha ndcae a shor-erm causaly. I could however be he case ha capal mobly has goen faser and equy markes and exchange raes more algned n he more globalsed world economy, as for nsance Savárek (2005) argues. An mplcaon of hs evolvemen can possbly be ha he causal srucural dynamcs have changed from more long-erm o shor-erm, from monhly o daly. I canno be dscarded ha a causal relaon could be found n an even hgher frequency han daly. There could be a cause and effec relaonshp beween hese varables whn an nraday. 23

25 Anoher aspec ha affecs he resuls of hs knd of sudy s of course he daa ha one chooses o represen he respecve equy markes. We have chosen broad marke ndces. One may encouner dfferen resuls f choosng o look a, for nsance, only large companes ha can be assumed o be nvolved n relavely more rade. The causal relaonshp mgh also depend on whch secor a gven company s nvolved n. An neresng queson s wheher here s a seady relaonshp beween hese varables or f vares and makes resuls dependen on whch specfc me-perod one chooses o sudy. The dvergen resuls from prevous sudes ndcae ha hs may be he case. We solaed he fnal sx monhs n our daa se, Sep 08 ll Feb 09, he crss perod and esed for Granger-causaly. The resuls from hese ess were no n lne wh he resuls from he base case. Durng he crses we found no causal relaon beween relave equy reurns and exchange raes n any of he cases. We can herefore conclude ha our resuls o some exen depend on he me-perod ha we have chosen. The fac ha we do no fnd any Granger-causaly durng he crss perod can possbly be explaned by ha, durng he marke urmol, equy reurn dfferenals and exchange raes have been caused by oher omed or unobserved varables. Pan e al. (2005), Ramasamy and Yeung (2005) and Shew (2008) also found devang resuls when hey separaely suded he Asan fnancal crss whch was ncluded n her longer erm daa ses on Asan counres. The es for Granger-causaly provdes nformaon abou wheher pas values of one varable carres nformaon useful o predc anoher varable. The es n self does no generae an answer o how a varable, ha Granger causes anoher varable, s causng he oher varable. For nsance, f Grangercausaly s un-dreconal from X o Y, he es does no reveal wheher X has a posve or negave mpac on Y. However, you can sll look a he coeffcens from he esmaed regressons nvolvng he lags of, say, X and hey do have a sgn whch you can nfer some conclusons from. We have found Granger-causaly runnng from relave equy reurns o exchange raes. The resuls are n accordance wh he Sock heory n ha he equy marke causes exchange raes. The Sock heory suggess ha when domesc eques perform relavely beer han a foregn counry s eques, he domesc currency apprecaes agans he foregn counry s currency. In hs case, ha mples ha he relave equy performance varable should have a negave mpac on he exchange rae varable. To evaluae wheher ha s he case we urn o he sgn of he coeffcens n he models. All coeffcens and her values are repored n he appendx. From here one can see ha when consderng he unresrced regressons, havng exchange rae varables as dependens, all lagged equy reurn varables have posve coeffcens. Of hose, many (a he 5 % sgnfcance level, a leas one for each regresson) are sgnfcan. From hs, we draw he concluson ha here s a posve relaon beween relave Swedsh 24