Exchange Raes, Equiy Prices, and Capial Flows Harald Hau Deparmen of Finance, INSEAD Hélène Rey Deparmen of Economics and Woodrow Wilson School, Princeon Universiy We develop an equilibrium model in which exchange raes, sock prices, and capial flows are joinly deermined under incomplee foreign exchange (forex) risk rading. Incomplee hedging of forex risk, documened for U.S. global muual funds, induces he following price and capial flow dynamics: Higher reurns in he home equiy marke relaive o he foreign equiy marke are associaed wih a home currency depreciaion. Ne equiy flows ino he foreign marke are posiively correlaed wih a foreign currency appreciaion. The model predicions are srongly suppored a daily, monhly, and quarerly frequencies for 17 OECD counries vis-à-vis he Unied Saes. Correlaions are sronges afer 1990 and for counries wih higher equiy marke capializaion relaive o GDP, suggesing ha he observed exchange rae dynamics is indeed relaed o equiy marke developmen. The las 25 years have been characerized by a remarkable increase in inernaional capial mobiliy. While gross cross-border ransacions in bond and equiy for he Unied Saes were equivalen o only 4% of GDP in 1975, his share increased o 100% in he early 1990s and has grown o 245% by 2000. Furhermore, a growing proporion of hese capial flows consiss of equiy as opposed o bank loans or governmen bonds 1 The Deniz Igan provided ousanding research assisance. We hank Mike Woodford for his commens. Thanks also o paricipans in he 2004 American Economeric Associaion Winer Meeings, he 2003 European summer symposium in financial markes, he FX microsrucure conference a he Sockholm Insiue for Finance and a he London School of Economics (Financial Marke Group), he 2002 NBER IFM summer insiue, and in seminars a Columbia Universiy, INSEAD, London Business School, ESCP-EAP (Paris), Georgeown Universiy, George Washingon Universiy, and he IMF. We are boh very graeful o he IMF Research Deparmen for is warm hospialiy and is simulaing environmen while wriing pars of his paper. Sergio Schmukler and Sijn Claessens provided he sock marke capializaion daa. This paper is par of a research nework on The Analysis of Inernaional Capial Markes: Undersanding Europe s Role in he Global Economy, funded by he European Commission under he Research Training Nework Program (Conrac No. HPRNŒCTŒ 1999Œ00067). Address correspondence o Harald Hau, Deparmen of Finance, Boulevard de Consance, 77305 Fonainebleau Cedex, France, or e-mail: harald.hau@insead.edu. 1 The London-based research firm Cross Border Capial repors ha during he period 1975 1984, bank loans accouned on average for 39.5% of oal ouflows from major indusrialized counries (60.3% of inflows), while equiies accouned for only 9.5% of ouflows (6.1% of inflows). During he 1985 1994 period, hese proporions were reversed. Bank loans accouned only for 8.3% of ouflows (16.3% of inflows), while equiies jumped o 35.9% of ouflows (31.6% of inflows). Similarly Lane and Milesi- Ferrei (2003) repor ha he raio of foreign asses and liabiliies o GDP has increased by 250% over he period 1984 2001. The same raio compued only for equiy and FDI has more han ripled over he same period. See also Frankel (1994) and Obsfeld and Taylor (2002). ª The Auhor 2005. Published by Oxford Universiy Press on behalf of The Sociey for Financial Sudies. All righs reserved. For permissions, please email: journals.permissions@oxfordjournals.org. doi:10.1093/rfs/hhj008 Advance Access publicaion Ocober 28, 2005
The Review of Financial Sudies / v 19 n 1 2006 increasing size and equiy conen of curren capial flows has no ye inspired a new financial marke paradigm for exchange rae heory, in which exchange raes, equiy marke reurns, and capial flows are joinly deermined. Recenly, posiive exchange rae heory has advanced mosly ouside he scope of radiional macroeconomic heory, plagued wih is nooriously poor empirical performance [Meese and Rogoff (1982, 1983)] and wih widespread pessimism abou he explanaory power of macro variables in general o explain shor- o medium-run exchange rae movemens. 2 The empirical microsrucure lieraure has examined he role of foreign exchange (forex) order flow defined as he difference beween buy and sell orders. Evans and Lyons (2002a, 2002b, 2002c, 2003), Hau, Killeen, and Moore (2002), Killeen, Lyons, and Moore (2006), Lyons (2001), and Rime (2001) show ha order flow from elecronic rading sysems has remarkably high correlaion wih conemporaneous exchange rae changes. Since order flow in he forex marke is a leas parly deermined by invesors desires for porfolio shifs, hese resuls sugges an imporan linkage beween exchange rae dynamics and invesor behavior. The mos comprehensive order flow daa are owned by global cusodians like Sae Sree, which underake a large proporion of global equiy clearing. Such (proprieary) daa have been analyzed by Froo and Ramadorai (2005) and Froo, O Connell, and Seasholes (2001). The resuls show ha he impac of invesor order flow on he exchange rae is very persisen and peaks a horizons of abou a monh for major currencies. Overall, he linkage beween order flow and exchange rae movemens appears very srong, nowihsanding he possibiliy ha exchange raes may also move because of public informaion only and wihou any ransacion. Bu he capial flow exchange rae linkage has no ye been imbedded in a heoreical framework in which order flow is derived from opimizing inernaional invesmen behavior. There is sill no model ha bridges he gap beween forex microsrucure and macroeconomic fundamenals. To develop such a framework and explore is empirical implicaions are he main objecives of his aricle. Our model depars from he exising lieraure on inernaional porfolio choice in several imporan ways. Firs, we focus exclusively on modeling shor- o medium-run exchange rae flucuaions and emphasize accordingly invesmen flows as he main deerminan of he exchange rae. The flow deerminaion can be undersood as a consequence of limied forex arbirage of risk averse speculaors. Tradiional porfolio balance models have ypically imposed a purchasing power 2 Frankel and Rose (1995) summarize he siuaion by saying ha [n]o model based on such sandard fundamenals like money supplies, real income, ineres raes, inflaion raes, and curren accoun balances will ever succeed in explaining or predicing a high percenage of he variaion in he exchange rae, a leas a shor- or medium-erm frequencies. 274
Exchange Raes, Equiy Prices, and Capial Flows pariy condiion for he exchange rae deerminaion. We absrac enirely from curren accoun consideraions, since he empirical lieraure has unambiguously shown ha goods marke variables do no explain exchange rae movemens a he shor- o medium-run frequencies. 3 Second, he exising sochasic porfolio balance models ypically assume exogenous asse price processes. This precludes any feedback effecs of opimal asse demands on he equilibrium price processes. Our framework fully endogenizes he equiy marke prices as well as he exchange rae and hereby allows a meaningful analysis of correlaion srucure of equiy reurns relaive o exchange rae reurns and equiy flows. Third, unlike his lieraure, we make he assumpion ha bond supplies are infiniely elasic, which allows us o significanly simplify he dynamics of bond holdings in our model. Fourh, our mos imporan srucural assumpion concerns incomplee forex risk rading. In complee markes and in a compleely symmeric wo-counry model wih equal marke capializaions, exchange rae risk hedging is a free lunch [Karolyi and Sulz (2002) and Perold and Schulman (1988)]. Invesors in he home counry can simply swap and eliminae forex risk by rading i wih foreign invesors holding he reciprocal risk. Under full forex risk hedging, he domesic and inernaional invesmen problems are alike, unless we separae home and foreign invesors by asymmeric informaion, differen consumpion opporuniies, or preferences. Bu he evidence on forex hedging srongly suggess ha marke compleeness represens a highly counerfacual benchmark. We have survey evidence on muual funds and oher insiuional invesors, which manage a large proporion of U.S. foreign equiy invesmens. Their lower ransacion coss and higher financial sophisicaion make hem beer candidaes for forex risk rading compared o individual invesors. Do hey swap forex risk wih heir foreign counerpars? Levich, Hay, and Ripson (1999) surveyed 298 U.S. insiuional invesors and found ha more han 20% were no even permied o hold derivaive conracs in heir invesmen porfolio. A furher 25% of insiuional invesors were formally unconsrained, bu did no rade in derivaives. The remaining 55% of insiuional invesors hedged only a minor proporion of heir forex exposure. For he full sample, Levich, Hay, and Ripson (1999) calculaed ha forex risk hedging concerned only 8% of he oal foreign equiy invesmen. 4 Porfolio managers cied 3 Hence, we make he polar assumpion of he one chosen by he New Open Economy Macroeconomics lieraure, which ends o focus exclusively on he goods marke and o shu down he capial accoun by assuming specific uiliy funcions [see for example Obsfeld and Rogoff (2000)]. Noe ha alhough his lieraure is unsuccessful a explaining exchange rae movemens, i is well suied o address a hos of oher imporan issues ha our simple model canno ackle. We herefore see our approach and he exising lieraure as complemenary. 4 We also consuled marke expers in wo large U.S. cusodians. Independen sources a boh Sae Sree Bank and Ciibank esimaed he noional forex hedge a <10%. This confirms he survey evidence. 275
The Review of Financial Sudies / v 19 n 1 2006 monioring problems, lack of knowledge, and public and regulaory percepions as mos imporan reasons for he resriced forex derivaive use. The developmen of he derivaive marke nowihsanding, only a minor proporion of he oal macroeconomic forex reurn risk seems o be separaely raded and eliminaed. The ypical foreign equiy invesor holds currency reurn and foreign equiy reurn risk as a bundle. Exposure o exchange rae risk implies ha he inernaional invesor generally cares abou boh he volailiy of he exchange rae and he correlaion srucure of exchange raes and foreign equiy reurns. For example, higher exchange rae volailiy ends o induce a home equiy bias. On he oher hand, a negaive correlaion beween forex rae reurns and foreign sock marke reurns reduces he reurn volailiy in home currency erms and makes foreign invesmen more aracive. Porfolio choice herefore depends on exchange rae dynamics. Bu dynamic porfolio choice should simulaneously affec he exchange rae. Differences in he performance or value of he home and foreign sock marke change he exchange rae risk exposure of boh invesors and give rise o porfolio rebalancing. Such dynamic rebalancing of equiy porfolios hen iniiaes forex order flow, which in urn induces exchange rae movemens. We capure his ineracion beween opimal porfolio choice under marke incompleeness and exchange rae dynamics in a simple model. In paricular, exchange raes, porfolio equiy flows, and equiy reurns are joinly and endogenously deermined. Bu o preserve racabiliy and gain some inuiion on how he ineracion beween exchange rae and equiy markes operae, we had o make some srong assumpions. We assume ha in each of he wo counries of our world economy, here is a consan risk-free ineres rae and an exogenous sochasic dividend process for he equiy marke. Domesic and foreign invesors are risk averse and maximize a simple rade-off beween insananeous rading profis and heir variance. Any porfolio shif or dividend repariaion riggers an increase in demand for forex as invesors do no hold foreign currency balances and all asse ransacions are underaken in he currency of denominaion of he asse. Hence, a ne ouflow ou of he domesic economy (which, for example, sems from purchases of foreign equiies by domesic residens) ranslaes ino purchases of he foreign currency. Conversely, a ne capial inflow leads o purchases of he domesic currency. 5 One imporan building block of our model is he forex marke. The exchange rae is deermined under marke clearing in he forex marke where privae invesor order flows ha sems from porfolio rebalancing 5 Since equiy flows accoun for above 30% of gross capial flows for developed counries in he early 1990s, he cusomer order flow hey generae is quaniaively imporan. We also noe ha he gross crossborder equiy volumes are roughly of a similar magniude as he cusomer dealer segmen of he FX spo marke. 276
Exchange Raes, Equiy Prices, and Capial Flows and dividend repariaion mee a less han fully elasic forex supply of liquidiy-providing financial insiuions. This implies ha order flow drives he exchange rae in accordance wih he empirical findings in he recen finance microsrucure lieraure. The model we develop has esable implicaions regarding he relaive volailiies of equiy and exchange rae reurns; correlaions beween sock index (excess) reurns and exchange rae reurns; and correlaions beween porfolio flows and exchange rae reurns. We highligh here he hree main empirical implicaions of our model:. Marke incompleeness in combinaion wih a low price elasiciy of forex liquidiy supply generaes exchange raes which are almos as volaile as equiy prices.. Higher reurns in he home equiy marke (in local currency) relaive o he foreign equiy marke are associaed wih a home currency depreciaion: he model predics wha amouns o an uncovered equiy pariy condiion.. Ne equiy flows ino he foreign marke are posiively correlaed wih a foreign currency appreciaion. We confron hese model predicions wih he daa. Raios of exchange rae volailiy o equiy reurn volailiy are generally smaller han one and in he range replicaed by he model. Reurn correlaions are examined wih daily, monhly, and quarerly sock index and exchange rae reurn daa for 17 OECD counries. Srong saisical evidence is produced for a negaive correlaion beween excess reurns on foreign over U.S. equiy and reurns on he foreign currency as prediced by he model. Hence, boh heory and evidence conradic he convenional wisdom ha a srong equiy marke comes wih a srong currency. We also highligh ha hese findings are produced a high saisical significance in conras o he well-known failure of uncovered ineres pariy for he same se of counries. The evidence for he negaive correlaion beween excess equiy reurns and exchange rae is sronges for he pos-1990 period, when equiy markes became more open. Cross-secionally, we find ha he negaive correlaion is more pronounced for counries wih he mos developed equiy markes. Finally, we also use monhly equiy flow daa on he same OECD counries o verify he porfolio flow implicaions. In accordance wih he model, he pooled regressions reveal a posiive correlaion beween equiy flows ino he foreign marke and he appreciaion of he foreign currency. The main inuiion behind he uncovered equiy pariy condiion is one of porfolio rebalancing. Whenever foreign equiy holdings ouperform domesic holdings, domesic invesors are exposed o higher relaive exchange rae exposure. They repariae some of he foreign equiy wealh o decrease he exchange rae risk. By doing so, hey sell he foreign 277
The Review of Financial Sudies / v 19 n 1 2006 currency, and his leads o a foreign currency depreciaion. Therefore, porfolio rebalancing creaes a negaive correlaion beween equiy marke reurn differenials and exchange rae reurn. Secion 1 discusses he lieraure before we describe he model in secion 3. In secion 4, we solve he model for wo special cases, namely he case of financial auarky and full inegraion in a complee marke seing. These wo polar cases provide wo benchmarks for he general case of financial inegraion under marke incompleeness explored in secion 5. We summarize he mos imporan esable implicaions in secion 6 before confroning hem wih he daa in secion 7. Conclusions follow in secion 8. 1. The Seing I is useful o siuae our analysis in he exising exchange rae lieraure. Our approach differs from previous sudies in he following respecs: (i) he emphasis on equiy flows relaive o he new open macroeconomics lieraure, (ii) he microfoundaions for he asse demands and he endogeneiy of he asse price processes relaive o radiional porfolio balance models, (iii) he financial marke incompleeness assumpion relaive o he real business cycle lieraure, (iv) he endogeneiy of he order flows relaive o he forex microsrucure lieraure, and (v) he explici modeling of he exchange rae relaive o he finance lieraure. Macroeconomic heory has recenly emphasized beer microfoundaions ogeher wih a more rigorous modeling of he dynamic curren accoun. This approach is exemplified by Obsfeld and Rogoff (1995) and surveyed in Lane (2001). Bu inernaional equiy markes do no play an imporan role in his framework. While monopolisic profis occur in hese models, hey ypically accrue enirely o domesic residens and herefore do no give rise o any equiy flows. In he spiri of he radiional asse marke approach o exchange raes [surveyed by Branson and Henderson (1985)], we view shor-run exchange rae movemens deermined by financial marke. We exend exising porfolio balance models by allowing microfoundaions of he asse demands and an endogenous deerminaion of he equiy price and exchange rae processes under marke clearing. We obain sharper esable implicaions for he correlaion srucure of forex reurns, equiy reurns, and equiy flows. Our analysis feaures incomplee forex risk rading as an imporan srucural assumpion. To he exen ha real business cycle models allow for inernaional asse rade, hey ypically examine he resuling exchange rae dynamics in a complee marke seing. 6 In his idealized 6 Capial marke incompleeness se our model apar from he Lucas (1982) model and much of he sochasic dynamic general equilibrium lieraure. 278
Exchange Raes, Equiy Prices, and Capial Flows seing,allbenefisfrominernaional exchange rae risk rading are realized. We argue ha his assumpion is a odds wih curren evidence on very low hedge raios for foreign equiy invesmen as discussed above. In our view, he marke rades equiy fairly fricionlessly across borders, bu fails o realize he full benefi of rading he associaed forex risk. This marke incompleeness is no relaed o he absence of he markes (forex derivaives exis), bu raher o ransacion and agency coss of using hem. This aricle is inspired by he new empirical lieraure on he microsrucure of he forex marke. Order flow is idenified as an imporan deerminan of exchange rae dynamics. We inerpre his lieraure as evidence for a less han infiniely-elasic forex supply and explore is consequences for opimal inernaional porfolio invesmen. 7 In our model, forex order flow is derived endogenously from he opimal dynamic porfolio policy. Also, he ime horizon for our analysis exends o several monhs unlike he high frequency focus in many microsrucure models. These models also ypically involve informaional asymmeries, which play no role in our analysis. Finally, our analysis relaes o a recen lieraure on inernaional equiy flows. Some of his work is mainly empirical [Bekaer and Harvey (2000), Bekaer, Harvey, and Lumsdaine (2002), and Pores and Rey (2005); Richards (2005)]. Brennan and Cao (1997) and Griffin, Nardari, and Sulz (2002) also provide a heoreical analysis of foreign invesmen behavior. Bu boh reaed foreign invesmen like domesic invesmen by modeling only dollar reurns. Insead of an exchange rae, home and foreign invesors are separaed by informaion asymmeries [Brennan and Cao (1997)] or by exogenous differences in reurn expecaions [Griffin, Nardari, and Sulz (2002)]. Unlike hese models, our framework assumes ha foreign and home invesors are separaed by an exchange rae and pursue invesmen objecives in he currency of heir respecive residence. 2. The Model A world wih wo counries has a home and a foreign invesor. Boh invesors are risk averse and can inves in risky home and foreign equiies and in riskless bonds. Equiies pay a coninuous sochasic dividend flow. Purchase of a foreign equiy by a domesic agen is seled in foreign currency and herefore requires a parallel purchase of foreign currency in he forex marke. Increases in foreign equiy holdings herefore generae 7 In a similar spiri, Osler (1998) and Carlson and Osler (2000) model he exchange rae as he price equaing supply and demand on a foreign exchange marke where curren accoun raders mee raional currency speculaors. 279
The Review of Financial Sudies / v 19 n 1 2006 an order flow in he forex marke. 8 Invesors do no hold money balances in equilibrium, since hey are dominaed by invesmens in he riskless bonds, which generae a nominal reurn of r and r in he respecive local currencies. Cenral banks in boh counries peg he ineres rae so ha he bond supplies are assumed o be infiniely price elasic. The wo ineres raes r and r are exogenous; for symmery we impose r ¼ r. Foreign dividend income is eiher reinvesed in foreign equiy or repariaed for home counry invesmen. The supply of home and foreign equiy is fixed and is price deermined by marke clearing. The supply of forex is less han perfecly elasic o reflec he empirical findings of he forex microsrucure lieraure. The evidence presened in he inroducion srongly suggess ha incomplee hedging of foreign invesmen is he more realisic benchmark compared o a world of full inernaional exchange rae risk sharing. We herefore do no allow for shor-selling of foreign bonds, as a shor posiion in foreign bonds works as a forex hedge on he foreign equiy invesmen. I is imporan o highligh ha he shorsale consrain is binding in he seady-sae equilibrium. 9 Inuiively, he home bond invesmen always sricly dominaes he foreign bond invesmen under idenical foreign and home bond reurns and addiional exchange rae risk on he foreign bond. Since home invesors would like o hold a shor posiion in foreign bonds o hedge he currency risk of heir foreign equiy posiion, 10 bu are prohibied from doing so, hey can a bes choose a zero posiion of foreign bonds. To simplify he exposiion and reduce noaions, we herefore presen he model as if invesors were prevened from invesing in foreign bonds alogeher. 11 The marke srucure is summarized as follows: 8 We assume ha when an agen purchases an equiy from a foreign agen, she iniiaes he purchase of foreign exchange, so ha our ne currency flow coincides wih he convenional definiion of he order flow (ne of buyer over seller iniiaed rades). Conversely if a domesic agen sells a foreign equiy ha she owns o a foreign invesor, he sale is seled in foreign currency and he domesic agen hen eiher convers he money in her own currency and buys a domesic bond or reinves i in foreign asses. In he aggregae, his implies ha here is a sraighforward correspondence beween ne capial ouflows ou of he domesic economy and ne domesic currency sale on one hand, and capial inflows ino he domesic economy and ne domesic currency purchases on he oher hand. 9 For a formal proof, see Appendix F of he working paper version [Hau and Rey (2003), NBER WP 9398]. 10 We sudy only equilibria in which invesors have posiive ne foreign equiy holdings in he seady sae, since hese are he only empirically relevan cases. 11 Holding zero foreign bonds sricly dominaes any posiive foreign bond posiion only for seady-sae values of he equilibrium price process and in some neighborhood around hese values. Large deviaions of he exchange rae from he long-run equilibrium may generae expecaions of exchange rae changes which make posiive foreign bond holdings opimal for one of he invesors. In he case of large expeced exchange rae changes, he equivalence of shor-sale consrains and zero foreign bond holdings breaks down and we have o assume zero foreign bond holdings direcly. 280
Exchange Raes, Equiy Prices, and Capial Flows Assumpion 1: Asse Marke Srucure A home (h) and a foreign (f) sock marke provide exogenous sochasic dividend flows D h and D f in local currency. Home and foreign invesors can inves in boh sock markes. In addiion, each invesor can inves in a domesic bond providing a riskless consan reurn r in he respecive local currency. Invesors in our model are risk averse and heir objecive is o find an opimal rade-off beween expeced profi flow of heir asse posiion and he insananeous profi risk. Each invesor measures profis in home currency. This invesor objecive implies paricularly racable asse demand funcions which are linear in he raio of expeced reurn and insananeous reurn risk. 12 Formally, we assume: Assumpion 2: Invesor Behavior Home and foreign invesors are risk averse and maximize (in local currency erms) a mean variance objecive for he profi flow. 13 Home invesors choose a porfolio of home and foreign equiy, K ¼ðK h ; Kf Þ, and foreign ¼ðK f ; K h Þ. Le invesors choose a porfolio of foreign and home equiy, K dr ¼ðdR h ; drf Þ T and dr ¼ðdRf ; dr h Þ T denoe he corresponding excess payoffs (in local currency erms over he local riskless bond) for domesic and foreign invesors, respecively. 14 The corresponding sochasic excess profi flows follow as and he wo invesors opimize max f max f K h,kf K f,k h d ¼ K dr d ¼ K dr, g E g E Z 1 s¼ Z 1 s¼ e rðs Þ e rðs Þ d s 1 2 d2 s d s 1 2 d2 s, 12 The common dynamic CARA uiliy framework produces similar asse demands which differ only by an addiional ineremporal hedging demand componen proporional o he covariance beween asse excess reurn and he sae variables. For reasons of racabiliy and simpliciy, we chose no o model hedging demands o focus on he dynamic ineracions beween he equiy and forex markes. The mean variance objecive here follows iner alia Hau (1998). 13 For he ime horizons relevan for our exercise (1 day o several monhs), prices can be considered o be sicky in local currency. 14 The ransposed vecor is marked by T. 281
The Review of Financial Sudies / v 19 n 1 2006 where E denoes he raional expecaion operaor and he invesor risk aversion. Invesor wealh evolves as dw ¼ d þ W rd dw ¼ d þ W rd: Boh sock markes have o clear under he opimal asse demand. For simpliciy, we normalize he quaniy of ousanding equiy o one. This implies K h þ K h ¼ 1 ð1þ K f þ K f ¼ 1: as he wo asse marke-clearing condiions. An addiional marke-clearing condiion applies o he forex marke wih an exchange rae E expressed in unis of foreign currency per unis of domesic currency. Denoing home and foreign equiy prices in local currencies by P h and P f, respecively, we can measure he equiy-relaed capial flows dq ou of he home counry (in foreign currency erms) as dq ¼ E K h D h d Kf D f d þ dk f P f E dk h h P The firs wo erms capure he ouflow if all dividends are repariaed. Bu invesors can also increase heir holdings of foreign equiy asses. The ne purchases of foreign equiy, dk f and dk h are capured by he hird and fourh erms. Le us for example denoe he euro area as he foreign and he Unied Saes as he home counry. Then dq represens he oal ne capial flow induced by equiy rade (boh dividend repariaion and ne purchases) by U.S. invesors ino he euro area, in euro erms. An increase in E (denominaed in euro per dollar) corresponds o a dollar appreciaion agains he euro. Any ne capial flow ou of a counry is, in our model, idenical o a ne demand for foreign currency as all invesmen is assumed o occur in local currency. We can herefore also idenify dq wih he equiy rade-induced order flow for foreign currency in he forex marke. 15 Furhermore, he above ne capial flow ou of he home counry (or forex order flow) can be linearly approximaed by dq D ¼ E E K Dd þ EK h K f Dd þ ED h Df þ dk f EdK h Kd ð2þ P: ð3þ 15 Remember ha here is no rade in he foreign riskless bond in he seady-sae equilibrium, so he forex order flow resuls only from equiy rade and dividend repariaion. 282
Exchange Raes, Equiy Prices, and Capial Flows where he upper bar variables denoe he uncondiional means of he sochasic variables. The linearizaion renders he analysis racable. The ne forex order flow of invesors is absorbed by liquidiy-supplying banks which can buffer forex imbalances. 16 The following assumpion characerizes he liquidiy supply Assumpion 3: Price-Elasic Excess Supply of Foreign Exchange The foreign exchange marke clears for a less han fully price-elasic excess supply curve wih elasiciy parameer. For an equilibrium exchange rae E, he excess supply of foreign exchange is given by Q S ¼ ðe EÞ where E denoes he seady-sae exchange rae level. An increase in E (euro depreciaion) decreases he excess supply of euro balances. Such an upward-sloping currency supply schedule can be inerpreed lierally as he se of limi orders in an elecronic order book like Reuers Dealing 2000-2 or EBS. 17 Lineariy of he supply curve simplifies he analysis. Bu we can also provide a more srucural inerpreaion of he supply curve and he parameer. Such a microfoundaion can eiher be based on imperfec ineremporal speculaion of risk averse currency raders or alernaively be moivaed by more long-run real rade effecs. Imperfec ineremporal speculaion by risk averse currency raders may presen he mos plausible inerpreaion for less han fully elasic shor-run excess supply curve. Currency speculaors end o sell dollars for euros when he dollar is high and buy dollars when he dollar is low. Differen ypes of speculaors provide liquidiy a differen horizons. Forex marke makers ake posiions wih half-lives measured in hours, while he half-lives of posiions of proprieary rading desks, hedge funds, and non-financial corporaions are measured in days, weeks, or monhs. Ineremporal risky arbirage is imperfec since in pracice raders do no have infiniely deep pockes. They face capial consrains [Shleifer and Vishny (1997)]. Generally, ineremporal speculaion involves considerable risk and needs o be compensaed by expeced rading profi. Risk averse forex raders maximize a quadraic objecive funcion sricly parallel o he equiy invesors (see assumpion 2), 16 A generalizaion of he model consiss in allowing for addiional curren accoun imbalances given by CA d ¼ E E d. Mos microfounded rade or macroeconomic models generae a defici for he curren accoun of U.S. when he dollar is srong and vice versa ( is he exchange rae elasiciy of he curren accoun). This generalizaion is sraighforward and allows o reinroduce he goods marke in he analysis. 17 For a recen descripion of he microsrucure of he foreign exchange marke, see Hau, Killeen, and Moore (2002). 283
The Review of Financial Sudies / v 19 n 1 2006 max fq S g E ð 1 e rðs Þ s¼ d s 1 2 d2 s where currency rading profis are given by d ¼ Q S de and denoes he risk aversion of he currency speculaors. The opimal liquidiy supply Q S is herefore given by Q S ¼E ðde Þ 2 ed. Assuming, as will be he case in our model, ha he exchange rae follows an Ornsein Uhlenbeck process revering o a (consan) equilibrium value E a speed e, hen he expeced exchange rae change E ðde Þis equal o e E E 2 e. Therefore, he opimal currency supply can be rewrien as Q S 2 ¼ e E E e which is of he form E E. This highlighs he role of raional exchange rae expecaions for he currency raders despie he apparen absence of such expecaions in he formulaion of he above supply curve. 18 The parameer is deermined by he degree of risk aversion of currency speculaors and he saisical characerisics of he exchange rae process. In paricular, if currency speculaors are almos risk neural, and herefore arbirage aggressively deviaions of he exchange rae from is long run level E, hen he supply of currency is very price elasic. 19 Marke clearing in he forex marke requires Q S ¼ Q D, and he forex rae is subjec o he consrain de ¼ E E K Dd þ EK h K f Dd þ ED h Df Kd þ dk f EdK h P: ð4þ The exchange rae dynamics is herefore ied o he relaive dividend flows, ED h Df, he relaive level of foreign asse holdings EK h K f, and heir relaive changes EdK h dk f. The relaive dividend flows are exogenous, bu he opimal relaive foreign equiy holdings are endogenously deermined and depend in urn on he exchange rae dynamics. We normalize E o 1, because he wo counries are symmerical. I is sraighforward o express he excess payoffs (over he riskless asse) on a uni of home equiy over he inerval d as dr h.tocharacerizehe foreign excess payoff dr f in home currency, we use a linear approximaion 18 For a recen empirical analysis of ineremporal liquidiy supply in he forex marke, see Bjønnes, Rime, and Solheim (2005). 19 An alernaive microfoundaion for he less han fully price-elasic currency supply resides simply in he dynamics of impor and expor markes for goods and services [see also Osler (1998)]. Mos macroeconomic models incorporae shor-run nominal price rigidiies, and here are herefore compeiiveness effecs on inernaional goods markes when a currency flucuaes. A counry ends o run a rade surplus when he domesic currency is undervalued (relaive o he long-run level E ) and a rade defici in he case of overvaluaion. For example, a euro undervaluaion E > E generaes a euro area rade surplus and herefore an excess demand for euro balances. In his case, he parameer depends on he elasiciy of subsiuion beween domesic and foreign goods and he degree of nominal rigidiy in he good markes. 284
Exchange Raes, Equiy Prices, and Capial Flows around he seady-sae exchange rae E ¼ 1 and he seady-sae price P. Formally, excess payoffs are given as dr h ¼ dph rph d þ Dh d dr f de P þ dp f de dp f rp f PE ð 1Þ d þ D f DE ð 1Þ d for he home and foreign asses, respecively. Excess reurns follow as dr h =P and drf =P, respecively. The exchange rae componen of he foreign payoff is given by PdE and he exchange rae reurn by de. 20 Finally, we specify he sochasic srucure of he sae variables: Assumpion 4: Sochasic Srucure The home and foreign dividends expressed in local currencies follow independen Ornsein Uhlenbeck processes wih idenical variance and mean reversion D > 0 given by dd h ¼ DðD D h Þd þ Ddw h dd f ¼ D ðd D f Þd þ D dw f : The innovaions dw h and dw f are independen. The mean reversion of all sochasic processes simplify he analysis considerably. We can now inroduce variables F h and F f which denoe he expeced presen value of he fuure discouned dividend flow, F h ¼E ð 1 s¼ F f ¼E ð 1 s¼ D h s e rðs Þ ds ¼ f 0 þ f D D h D f s e rðs Þ ds ¼ f 0 þ f D D f, wih consan erms defined as f D ¼ 1=ð D þ rþ and f 0 ¼ðr 1 f D ÞD. The risk aversion of he invesors and he marke incompleeness wih respec o forex risk rading imply ha he asse price will generally differ from his fundamenal value. 20 The model is closed and here is no sock-flow inconsisency. A foreign equiy purchase of he home invesor is seled in foreign currency. Bu he foreign equiy seller immediaely reinvess his liquidiy and holds zero money balances since money is a dominaed sore of value. He can eiher exchange i in he forex marke if he reinvess in equiy abroad, or bring i o his cenral bank a a fixed riskless rae. Cenral banks hus absorb he addiional liquidiy a he fixed rae r. 285
The Review of Financial Sudies / v 19 n 1 2006 3. Two Special Cases I is insrucive o explore wo special variaions of our model. Firs, we cover he exreme case in which no foreign asse holdings are allowed. We refer o his case as financial auarky. I provides a useful closed economy benchmark for he sock marke equilibrium, in which invesors do no inernaionally share heir domesic equiy risk. The opposie exreme assumpion is o allow boh he equiy risk and he exchange rae risk o be fully and separaely raded. This second benchmark characerizes he inernaional financial marke equilibrium wih complee risk sharing. Formally, i is idenical o an economy wih wo freely radeable asses. The exchange rae is a redundan price. As empirically mos relevan, we consider a hird case in which equiy is freely raded bu he exchange rae risk is no. We analyze his case in secion 5. Solving he model always requires hree seps. Firs, we posulae a linear soluion for he asse prices and he exchange rae. Second, we derive he opimal asse demand under he conjecured soluion. Third, we impose he marke-clearing condiions, show ha he resuling price funcions are indeed of he conjecured form, and finally solve for he coefficiens. To provide for a more coheren exposiion, we summarize our resuls in various proposiions. All derivaions are relegaed o appendices. 3.1 Financial auarky Under financial auarky, he home invesor s foreign equiy posiion ðk f Þ and he foreign invesor s home equiy posiion ðk h Þ are assumed o be zero. All domesic asses are owned by domesic invesors, hence! K f ¼ 1 0 : 1 0 K h K f K h The financial marke equilibrium for he home and foreign equiy marke can be deermined separaely. Proposiion 1 saes he resul: Proposiion 1: Equilibrium under Financial Auarchy Assume a wo-counry world in which home invesors hold he domesic asse and foreign invesors he foreign asse. The home and foreign sock marke prices are given by P h ¼ p 0 þ p F F h P f ¼ p 0 þ p F F f wih p 0 ¼ R 2 r. and pf ¼ 1. The (insananeous) reurn volailiy follows as 2 R ¼ 2 D ð D þ rþ 2. Proof : See Appendix A. 286
Exchange Raes, Equiy Prices, and Capial Flows A price parameer p F ¼ 1 implies ha he asse prices are proporional o heir fundamenal values F h and F f, respecively. The fundamenal values represen he expeced discouned fuure cash flows. The risk aversion of he invesors is refleced in he coefficien p 0 50, which capures he equiy risk premium as a price discoun. I is proporional o he invesor risk aversion and he insananeous variance 2 R of he excess reurn processes. These equilibrium resuls are sandard for a closed economy wih a fixed asse supply and mean variance preferences for he invesor. 3.2 Equilibrium wih complee risk sharing A second model variaion consiss in he full risk-sharing benchmark. Forex risk can hen be fully raded eiher hrough derivaive conracs or hrough shor sales of he foreign riskless bond. Perfec and complee risk rading resuls in he eliminaion of all exchange rae risk. Inuiively, home and foreign invesors hold exacly opposie and off-seing exchange rae risk in heir global equiy porfolio. They jus need o swap he forex risk and hereby eliminae i. 21 The resuling financial marke equilibrium is saed in proposiion 2: Proposiion 2: Equilibrium wih Complee Risk Sharing The home and foreign sock marke prices and he exchange rae are given by P h ¼ p 0 þ p F F h P f ¼ p 0 þ p F F f E ¼ 1 where we define p 0 ¼ 2 R =2r, and p ¼ 1. The (insananeous) reurn F volailiy follows as 2 R ¼ 2 D = ð D þ rþ 2. The domesic and foreign porfolio posiions of he wo invesors are equal and consan wih!! K h K f 1 1 2 2 ¼ K f K h Proof: An idenical riskless rae in he home and foreign counry under complee markes implies a consan exchange rae, E ¼ 1. The complee soluion is derived in Appendix B. Firs, we noe ha he exchange rae is consan. In a world of perfec risk sharing, he wo-counry model is no differen from one domesic 1 2 1 2 21 The exchange rae risk can be fully eliminaed because of he symmery of he wo-counry seup. In a more general model, forex risk can only be parially eliminaed hrough swapping. 287
The Review of Financial Sudies / v 19 n 1 2006 economy wih wo socks. Home and foreign invesors each hold equal and consan shares of he world marke porfolio. The asse prices move one o one wih heir fundamenal values, F h and F f, respecively. The risk sharing across he wo invesor groups implies ha he asse price risk discoun p 0 50 is only half as large as in he auarky case for he same reurn volailiy 2 R. This implies lower average asse reurns under marke inegraion. Evidence ha financial inegraion indeed reduces marke sock reurns is provided by Bekaer and Harvey (2000), Henry (2000), and Sulz (1999) among ohers. These auhors show reduced capial coss or excess reurns on equiy for emerging counries following heir capial marke liberalizaion. We furher highligh ha complee forex risk rading implies no paricular correlaion srucure beween exchange rae and equiy reurns. The exchange rae is a redundan price and consan. This implicaion is of course a odds wih he high exchange rae volailiy observed in pracice. Bu i provides a useful benchmark for he following secion which explores he case of equiy marke inegraion under incomplee exchange rae risk rading. 4. Foreign Invesmen under Incomplee Risk Sharing We now rea he case in which a forex marke allows invesmen in he foreign equiy, bu exchange rae risk rading is incomplee. If he exchange rae moves sochasically, home invesors wih foreign equiy holdings incur an addiional exchange rae risk in addiion o he risk of he sochasic dividend flow. Foreign invesors hold he opposie risk due o ownership sakes in foreign equiy. If his reciprocal exchange rae risk were radeable, i could be perfecly eliminaed as assumed in he perfec marke case discussed in secion 4.2. Bu now we assume ha such forex risk rading does no occur. The non-radeabiliy of he forex risk no only excludes derivaive conracs, bu also requires ha invesors canno shor-sell he foreign riskless asse. Shor-selling of foreign riskless asses effecively amouns o a separae rading of he exchange rae risk. As discussed before, assuming a no shor-sale consrain on he riskless foreign asse implies zero foreign bond holdings in he seady sae. If unconsrained, invesors should seek a shor posiion in he foreign riskless asse equivalen o heir foreign equiy sake. Bu hey would no seek a long posiion which adds exchange rae risk o he porfolio. The shor-selling consrain is binding. Seing he foreign bond posiion o zero does no represen an addiional resricion. 4.1 Exchange rae dynamics Before we conjecure he exchange rae dynamics under incomplee markes, i is useful o highligh wo principal equilibrium forces which shape 288
Exchange Raes, Equiy Prices, and Capial Flows his dynamics. The firs equilibrium endency is governed by he less han fully elasic supply for forex order flow. Forex order flow dq D in Equaion (3) is accommodaed by financial insiuions which finance hese home ouflows according o an upward-sloping supply curve. The elasiciy of forex liquidiy supply cerainly influences he impac of ne order flow on he exchange rae and indirecly he adjusmen speed owards he seady-sae exchange rae, E. We associae he supply-induced mean reversion wih a firs characerisic roo (labeled z). A second imporan parameer for exchange rae dynamics is he mean reversion of he dividend processes. This mean reversion D is exogenous, and any feedback effec from he exchange rae dynamics o he dividend process is ruled ou by assumpion. An imporan simplifying feaure of our model is is symmery beween he home and foreign counry. Symmery implies ha he exchange rae can depend only on differences beween home and foreign counry variables, bu no on a counry-specific variable iself. Oherwise he symmery would be broken. The symmery requiremen also implies ha exchange rae surprises can depend only on curren and pas relaive dividend innovaions, dw s ¼ dw h s dwf s. These relaive innovaions are he only exogenous source of exchange rae dynamics. Finally, we highligh he lineariy of he model srucure. The forex order flow consrain is linearized and he exogenous dividend dynamics is linear by assumpion. Moreover, we have assumed a mean variance uiliy funcion which ranslaes linear dividend, price, and reurn processes ino linear asse demands. I is herefore jusified o resric our aenion o he class of linear exchange rae and price processes. The argumen for wo fundamenal equilibrium forces explains why we focus on wo sae variables D and, boh of which depend for reasons of model symmery on curren and pas relaive dividend innovaions dw s only. The following proposiion 3 saes he conjecured exchange rae process and derives is implicaions for he order flow consrain (4). Proposiion 3: Exchange Rae Dynamics Assume ha (i) equiy prices P ¼ðP h ; P f Þ depend linearly on he exchange rae E and he dividend processes D ¼ðD h ; D f Þ and (ii) he exchange rae has he following linear represenaion wih E ¼ 1 þ e D D þ e, 289
The Review of Financial Sudies / v 19 n 1 2006 D ¼ D h Df ¼ ¼ ð 1 ð 1 e zð sþ dw s, e Dð s Þ D dw s where z50 and dw s ¼ dw h s dwf s. Then i follows ha he order flow consrain (4) is of he simple form de ¼ k 1 D d þ k 2 ðe 1Þd þ k 3 dw, where k 1, k 2, and k 3 represen undeermined coefficiens. Proof: The derivaion is provided in Appendix C1. We have o show ha for a linear price and a linear exchange rae, invesor uiliy maximizaion implies opimal foreign equiy demands K h ; K f such ha he expression ðk h and dw. K f ÞDd þðdk f dk h ÞP in Equaion (4) is linear in E 1; D Under lineariy of he price and exchange rae processes, he order flow consrain simplifies o a differenial equaion in only wo sae variables D and E 1. This allows us o characerize he exchange rae dynamics as a sysem of wo firs-order differenial equaions, dd de ¼ D 0 k 1 k 2 D E 1 d þ D k 3 dw : The associaed characerisic roos are D and k 2. A sable soluion requires k 2 50. The exchange rae soluion can hen be wrien as a linear combinaion e D D þ e of he wo eigenvecors and ð D ¼ e Dð sþ D dw s 1 ¼ ð 1 e k 2ð sþ dw s, as conjecured in proposiion 3. To find he soluion parameers, we have o impose he marke-clearing condiions (1) and deermine he seady-sae levels for he equiy price, P, and he foreign equiy holding, K. Non-negaive (seady sae) prices P>0 and posiive (seady sae) home and foreign equiy holdings 290
Exchange Raes, Equiy Prices, and Capial Flows 05K51 imply furher resricions on he parameer domain of our model. In paricular we have o impose an upper bound on he risk aversion and a lower bound on he elasiciy of he forex liquidiy supply o obain plausible seady-sae values. Proposiion 4 characerizes he equilibrium properies: Proposiion 4: Exisence and Uniqueness of he Incomplee Risk-Sharing Equilibrium Le he economy be characerized by assumpions 1 o 4. For a sufficienly low risk aversion of he invesors 5 and a sufficienly price-elasic forex supply >, here exiss a unique sable linear equilibrium P h ¼ p 0 þ p F F h þ p D D þ p P f ¼ p 0 þ p F F f p D D p E ¼ 1 þ e D D þ e, where we define F h and F f as he expeced presen values of he fuure home and foreign dividend flows, respecively (as in secion 3). The variable D ¼ D h Df represens he relaive dividend flows for he wo counries and a weighed average of pas relaive dividend innovaions decaying a an endogenous rae z50 as defined in proposiion 3. The price parameers can be signed as K h K f K f K h p 0 50, p F ¼ 1, p D > 0, e D 50, e D D þ e 50 Opimal porfolio holdings are given by! ¼ 1 K K þ 1 K K 1 1 1 1 1 2 ðm DD þ m Þ for he parameers m D 50, and m >0 defined in Appendix C1. Proof: For a derivaion see Appendix C. As in he previous full risk-sharing case, we find ha invesor risk aversion requires an equiy risk premium in he form of a price discoun p 0 50. As before, a coefficien p F ¼ 1 implies ha he equiy price reflecs he fundamenal value of expeced fuure dividends, F h and F f, respecively. Moreover, wo new sochasic erms D and influence asse prices and he exchange rae. These addiional erms reflec changes in he asse prices and exchange rae dynamics induced by he incompleeness of forex risk rading. The exchange rae is no longer consan and exchange rae volailiy imply asymmeric holdings of home and foreign equiy. In addiion, he opimal porfolio posiions change proporionally o m D D þ m. The dynamic equilibrium is characerized by consan 291
The Review of Financial Sudies / v 19 n 1 2006 rebalancing of he opimal porfolios. We herefore have endogenous equiy purchases and sales as a resul of opimal equiy risk rading under consrained forex risk rading. The ne equiy flows and he corresponding forex order flow in urn generae he equilibrium exchange rae dynamics under he price elasic forex liquidiy supply. 4.2 Economic inerpreaion Invesors in he wo counries care abou nominal rading profis in heir domesic currency. This does no imply, however, ha hey only inves in home asses. Given ha foreign asse invesmen provides an equiy risk diversificaion benefi, foreign equiy ownership is desirable for he home invesor. Bu his diversificaion benefi comes a he cos of exchange rae risk on foreign equiy posiions and foreign dividend income. Incomplee inernaional exchange rae risk rading implies ha his exchange rae risk is no eliminaed. Moreover, he respecive exposure of he home and foreign invesor o forex risk varies wih he relaive performance of he home and foreign equiy marke. Any ouperformance of he foreign equiy marke over he home equiy marke will end o increase he relaive exposure of he home invesor o exchange rae risk and herefore alers his rade-off beween diversificaion benefis and he coss of bearing currency risk. The foreign invesor on he oher hand does no face any currency risk on he higher marke capializaion of he foreign marke which provides payoffs in his own currency. The foreign invesor herefore has a comparaive advanage for holding a larger share of he foreign marke capializaion given is relaive value increase. The home invesor can be expeced o decrease his foreign posiion and his forex exposure. We refer o his as he risk rebalancing channel for capial flows. The risk rebalancing channel implies an opimal invesmen behavior for he home invesor which is counercyclical o he foreign marke excess performance. Inspecion of proposiion 4 shows ha for high foreign marke fundamenals ðf h F f 50;, D ¼ D h Df 50Þ, he foreign holdings of he home invesors ðk f Þ decreases by he erm 2 1 m DD 50, where m D 50. This porfolio rebalancing consiues an opimal adjusmen of his equiy posiions in he face of exchange rae risk and incomplee forex risk rading. 22 Bu a second effec creaes addiional capial flows. A higher relaive foreign marke capializaion coincides wih relaively higher foreign dividend flows ðd d ¼ðD h Df Þd50Þ. In he symmeric seady sae, in which home and foreign invesors hold equal shares of equiy abroad, he home invesor s foreign dividend income will exceed foreign invesor s 22 For developed equiy markes, rading coss like fees and selemen coss are sufficienly small o be unlikely o impede porfolio adjusmen. As for he price impac of rades, i is fully incorporaed ino he model since invesors raionally foresee he equilibrium price impac of heir reallocaions. 292