Are the Gains from Foreign Diversification Diminishing? Assessing the Impact with Cross-listed Stocks. February 2010 ABSTRACT

Transcription

1 Are he Gains from Foreign Diversificaion Diminishing? Assessing he Impac wih Cross-lised Socks Choong Tze Chua *, Sandy Lai * and Karen K. Lewis, February 2010 ABSTRACT Foreign diversificaion has a long hisory in financial economics. In his paper, we re-examine his issue wih foreign companies ha are lised on US exchanges, combining feaures of hree differen lieraures. One lieraure suggess ha domesic porfolios including cross-lised socks can duplicae he behavior of foreign marke reurns wihou he need for US invesors o go abroad. A second lieraure finds ha he reurns from hese foreign socks ofen become more sensiive o he US marke afer cross-lising. Third, he emerging marke on lieraure finds evidence ha he relaionships across sock markes shif afer sock marke liberalizaions. In his paper, we combine aspecs of hese hree lieraures o assess he impac on foreign diversificaion wih cross-lised firms for a US invesor. For his purpose, we use he Bai and Perron (1998) break dae esimaor o es for and esimae breaks in he sensiiviy of individual foreign socks lised on he NYSE and NASDAQ. We find ha reurns on foreign socks have become more sensiive o he US marke boh direcly hrough heir company US beas and indirecly hrough heir home marke beas agains he US marke. As a resul, he minimum variance allocaion ino a porfolio of hese companies declines over ime. During he financial crises of he lae 2000s, invesmen in foreign company socks reduce risk only if hese socks can be shored. JEL Classificaion: G15, F36, C32 Keywords: Capial marke inegraion; inernaional diversificaion; break dae analysis; equiy crosslising * Deparmen of Finance, Singapore Managemen Universiy Deparmen of Finance, Singapore Managemen Universiy Deparmen of Finance, Wharon School, Universiy of Pennsylvania and NBER Acknowledgemens: We hank Geer Bekaer, Bernard Dumas, Vihang Errunza, Bob Hodrick, Andrew Karolyi, Magnus Dahlquis, Gangadhar Darbha, Craig MacKinlay, Paolo Soderlind, Jessica Wacher, Frank Warnock, Amir Yaron, and paricipans a he Darden Inernaional Finance Conference, he Kansas Ciy Federal Reserve Bank, he Inernaional Moneary Fund, Singapore Managemen Universiy, he Sociey for Financial Economerics, he Swedish Insiue for Financial Research, and he Wharon Micro-Lunch Finance seminar for useful commens and suggesions. We acknowledge funding from he Wharon-SMU Research Cener a Singapore Managemen Universiy wih hanks. Any errors are our responsibiliy.

2 Over he pas few decades an increasing number of companies have lised heir equiies across inernaional borders. The availabiliy of hese socks on he exchanges of differen counries has pu hem a he cener of academic and policy discussion abou he degree of inegraion of financial markes. These discussions have generally focused upon hree differen hemes. Firs, he domesic availabiliy of foreign socks may provide inernaional diversificaion for domesic invesors wihou hese invesors having o direcly inves abroad. As such, he availabiliy of hese socks implies a relaively low ransacion cos way o acquire foreign asses. 1 Second, he behavior of cross-lised socks around he lising dae suggess ha inernaional markes are no fully inegraed. An exensive lieraure has shown ha hese socks exhibi abnormal reurns around he dae, a behavior ha is difficul o reconcile wih inegraed markes. 2 Third, for emerging markes, he abiliy o cross-lis in anoher marke is ofen aken as a sign of liberalizaion. Indeed, some papers have used he earlies dae a which a domesic company could lis abroad as a proxy for liberalizaion daes. 3 Oher sudies use changes in he sock price o reflec pricing of he ouside world as a way o mark he liberalizaion even direcly. 4 In general, hen, he pricing behavior of cross-lised socks is cenral o he quesion of financial marke inegraion. On an individual level, inernaional financial inegraion implies ha he invesor has access o he same porfolio performance using domesic exchanges as foreign exchanges. Thus, he diversificaion poenial of socks should be he same wheher he sock is cross-lised or no. Despie he imporance of his quesion, relaively lile research has focused direcly upon he diversificaion poenial of cross-lised socks over ime. Errunza, Hogan and Hung (1999) form porfolios of domesically raded securiies including foreign socks, and show ha hese porfolios span he foreign markes. However, hey do no direcly examine he diversificaion poenial of hese socks or how he porfolios would have performed before cross-lising. By conras, he exensive lieraure on he price impac of cross-lising on foreign socks focuses direcly on he change in sock prices before and afer cross-lising. As surveyed by Karolyi (2006), hese sudies ofen find ha he sensiiviies of hese socks on local and foreign markes change before and afer cross-lising. Bu hese sudies do no sudy he porfolio performance implicaions of hese changes for a ypical domesic invesor. Finally, he lieraure on emerging marke liberalizaion uses he asse pricing implicaions of an inegraed financial model o eiher examine he implicaions of he liberalizaion as in Henry (2000,2003) or dae he economic even as in Bekaer, Harvey, and Lumsdaine (2002). 1 See Errunza, Hogan, and Hung (1999) as well as he discussion below. 2 See for example he survey by Karolyi (2006). 3 Bekaer, Harvey, and Lumsdaine (2002) and Henry (2000) use his proxy, for example. 4 See for example Bakaer and Harvey (1995,1997).

3 In his paper, we begin o fill he gap beween hese lieraures by focusing upon he asse pricing behavior of cross-lised socks over ime. Focusing upon his behavior allows us o address several quesions. Firs, wihou imposing informaion abou cross-lising daes, have he comovemens beween cross-lised socks and he domesic and foreign sock markes changed over ime? Second, if hese relaionships have changed over ime, wha are he implicaions for inernaional diversificaion by a ypical US invesor? Third, how do hese changes correspond o he risk sensiiviies of he foreign socks before and afer cross-lising? Fourh, do he increases in foreign socks in he US provide greaer opporuniies for inernaional diversificaion wihou going o foreign markes direcly? Or do hese foreign socks merely mimic he behavior of oher foreign socks ha have been previously lised? To address hese quesions, we analyze he local marke behavior of foreign socks lised in he wo major sock exchanges in he Unied Saes, he New York Sock Exchange and NASDAQ. We consider a US invesor wih access o hese markes and hence he available socks a a poin in ime. We hen ake he socks for each of hese companies and examine wheher and how he asse pricing sensiiviies of he sock reurns have changed wih respec o he US marke over ime. We hen form porfolios of hese companies and examine he diversificaion poenial o he US invesor. For his purpose, we require an empirical approach ha allows for changes in asse pricing characerisics over ime, bu does no impose hese changes. Moreover, in keeping wih he even sudy approach aken in boh he cross-lising lieraure and he emerging marke liberalizaion lieraure, we consider discree changes in sock price behavior. Since he break-dae esimaor of Bai and Perron (1998) delivers boh of hese feaures, we incorporae his mehodology ino our approach. Our invesigaion akes he following sraegy. For each sock price in local markes, we firs es for he number of breaks. If here is evidence for breaks, we esimae he break daes. We hen examine he facor loadings before and afer hese daes o provide a ime series of asse pricing characerisics. We hen form hese esimaes ino porfolios of foreign socks ha include poenial shifs in co-movemens. Finally, we consider how a US invesor would allocae his wealh porfolio if given he opporuniy o inves in hese foreign socks. Given hese porfolio allocaions, we ask how much risk reducion would be provided by hese invesmens. Our analysis provides four main resuls. Firs, a high proporion of companies exhibi evidence of shifs in heir sensiiviy oward he US marke over ime. Similarly, we canno rejec he hypohesis of srucural breaks beween he US and over 80% of he foreign sock markes in which he foreign cross-lised companies are domiciled. Second, foreign companies and foreign counries alike have generally become more correlaed wih he US marke over ime. As a resul, hese shifs work agains 2

4 diversificaion. Third, foreign sock reurns become more sensiive o he US marke afer lising in he US. For example, he marke-weighed average of beas of foreign companies on he US marke before cross-lising is abou 0.49, bu during and afer lising is abou Fourh, he porfolios of foreign socks generally rack heir local markes before and afer cross-lising. However, since hese foreign markes have become more correlaed wih he US marke over ime, he sensiiviy of he foreign companies o he US marke is furher exacerbaed. As a resul, during he recen financial crisis he foreign markes can reduce risk only if hey can be shored. As described above, we use he Bai- Perron esimaor o es for break daes in he hisory of cross-lised socks in he US. Similarly, Bekaer, Harvey, and Lumsdaine (2002) use he Bai-Perron esimaor o es for breaks in asse pricing relaionships o dae he implici liberalizaion evens for some emerging marke economies. 5 While we share he use of he Bai-Perron mehodology, here are imporan differences in our empirical sraegy. Bekaer, Harvey, and Lumsdaine sudy breaks in emerging marke indices using vecor-auoregressions including macro-economic variables ha migh be correlaed wih liberalizaion. By conras, in keeping wih he even sudy-driven cross-lising lieraure, we es for breaks a he individual firm level and examine he implicaions for parameers in even ime. To our knowledge, our paper represens he firs sudy o analyze he poenial for individual breaks for a large number of socks and hen sudy he resuling porfolio implicaions. Moreover, while companies from emerging markes are represened in our cross-lised porfolios, we are ineresed in he full range of foreign companies including hose from developed markes as well. 6 Finally, our analysis differs in ha we can consider wheher he individual firm reurns reflec breaks a he counry level. Using our approach, we are capable of differeniaing he breaks in he reurns a he counry level from he breaks in reurns only a he firm level. The paper is organized as follows. Secion 1 gives an overview of he daa and mehodology. Secion 2 repors he break dae and parameer esimaes for he foreign companies as well as heir home markes. To gain insigh ino he economic significance of hese parameers, Secion 3 considers a hough experimen in which a US invesor observes hese parameers and hen aemps o opimally diversify risk. Secion 4 provides concluding remarks. Secion 1: The Empirical Framework 5 Anoher approach used o examine liberalizaion is o esimae a regime swiching model. An early example in he lieraure is Bekaer and Harvey (1995) while a more recen example ha allows for regime-specific spillovers is Baele (2005). 6 Neverheless, we discuss how our esimaes compare below. 3

5 To examine he behavior of foreign company reurns over ime, we require a mehodology ha can allow for poenial changes in he sensiiviy of foreign reurns o he US, bu does no impose any change a priori. Below, we begin by describing he asse pricing model. In keeping wih he crosslising and liberalizaion lieraure, reurns depend upon boh local and foreign facors. We hen explain he empirical mehodology and daa before urning o resuls. 1a. Asse Pricing Model have he form: Sandard facor pricing models used in he lieraure on inernaional sock reurns ypically r = + ' f + e (1) i i i i Where r i is he nominal excess reurn on he equiy of company i ha is domiciled in counry l a dae, f is a vecor of facors a ime ha affec he reurns on socks from he equiy marke of counry l, β il is a vecor of facor inensiy parameers for firm i, α il is a consan parameer and e i is a residual. Since all he analysis below is based upon excess reurns, we will simply call hem reurns hroughou. The cross-lising lieraure has ypically aken a one or wo facor version of his model as he benchmark for conducing even sudies. For example, Sarkissian and Schill (2009) examine he effecs of cross-lisings by firms around he world using marke models of he form: 7 r = + r + e (2a) i i i i Where r is he local marke reurn so ha (2a) is he sandard closed economy CAPM, and of he form: r = + r + r + e (2b) i i i iu u i Where (2b) includes u r he reurn of he foreign marke in which he sock is cross-lised. Since we only consider companies ha are cross-lised in he US, u r refers o he US marke reurn below. Furhermore, we will focus upon he marke model in (2b) because we are ineresed in examining he sensiiviy of he foreign company reurns on he US marke. However, we will also examine ess of iu he hypohesis ha is zero. While he cross-lising lieraure has focused upon he parsimonious wo facor model, here may be more facors ha are imporan for explaining inernaional sock reurns. For example, Bekaer, Hodrick, and Zhang (2009) show ha a facor model ha includes addiional global and local Fama- French facors bes explains he reurns of companies ha comprise he MSCI World Index. If hese 7 Sarkissian and Schill (2009) also consider a hird model ha subsiues he wolrd marke reurn for he foreign marke. Preliminary esimaes based upon he world marke insead of he US marke obained similar resuls o hose repored below. 4

6 facors are imporan for explaining he foreign companies lised in he US, hey will appear in he residuals of equaions (2) and may affec he variance of residuals. Ib. Daa To address he quesions posed in he inroducion, we require a daa se of foreign company reurns lised in he Unied Saes wih sufficien hisory afer cross-lising o analyze poenial changes. For his purpose, we choose foreign companies ha are lised in he Unied Saes in July 2004 since i implies a leas five years of daa unil Our analysis herefore provides a clear picure of an invesor s decision in However, we are also ineresed in how he se of socks may have changed over ime, boh before 2004 and aferwards. To examine he effecs before 2004, we consider wo exreme assumpions abou when hese socks became available o US invesors, as described below. On he oher hand, he availabiliy of his se of socks afer 2004 is relaively sable since less han 1% of our sample was delised by Foreign socks rade on a variey of exchanges in he US, including he over he couner marke (OTC) and insiuional invesor-only markes (RADR, 144A). In his paper, we resric he analysis o foreign socks on he public exchanges for wo main reasons. Firs, our goal in his paper is o consider foreign company diversificaion from he viewpoin of a represenaive small US invesor. We herefore exclude foreign socks ha are only available o large insiuional invesors. Second, OTC socks do no require he same level of disclosure requiremens as do domesic and foreign socks on he public exchanges. As such, domesic invesors may consider hese foreign socks o have higher informaion coss. Exchange-raded foreign companies in he US primarily rade on he NYSE and NASDAQ. 9 In his sudy, we use weekly sock reurns in foreign markes for paren non-us companies ha had socks rading on he New York Sock Exchange in The ime period is from January 1970 or he earlies dae of availabiliy o Ocober All reurn series are measured in US dollars o represen he value from he poin of view of a US invesor. For non-canadian companies, he daa were colleced in he following seps. 10 Sep (1) A daa se of all foreign companies wih socks lised on he New York Sock Exchange were obained from he Bank of New York, he primary cusodian bank for ADRs in his counry. This se was cross-checked 8 Similarly, Sarkissian and Schill (2009) choose 1999 because hey focus upon long run reurns afer cross-lising of up o en years. 9 In 2004, he marke value of foreign socks on he NYSE and NASDAQ ogeher comprised 98% of he oal marke value across public exchanges. A he 2000 peak of NASDAQ, he foreign companies hi a max of 27% of his oal. Thus, he companies lised on NYSE comprise mos of he foreign marke cap in he US. In 2004, only 10 foreign companies were raded on he AMEX and we exclude hem for simpliciy. 10 More deails abou he consrucion of he daa are given in Appendix A of he paper. 5

7 wih lisings from he NYSE iself and JP Morgan, anoher ADR cusodian bank. Sep (2) For each of hese companies, sock reurns in he home marke and marke values for he full available hisory were colleced from Daasream. Canadian companies rade direcly on US exchanges wihou ADR regisraion. As such, hese companies are no lised on cusodian bank ADR direcories. Andrew Karolyi kindly provided he names and idenifying mneumonic codes for he Canadian companies lised in he US as colleced from Worldscope. 11 We require reurns from local marke indices as well since foreign company reurns depend upon local markes. For his purpose, we use he Daa Sream Toal Marke indices for he home marke of each foreign company ha liss in he US. 12 Weekly reurns are consruced for each of hese indices reconvered ino US dollars from 1970, or he earlies available, unil Ocober The reurns are ransformed ino excess reurns by subracing he weekly T-bill rae. I is imporan o noe ha we will generally no assume ha US invesors have access o he availabiliy of he reurns on hese indices over ime. We only assume ha hese reurns mimic he facors ha US invesors view as imporan drivers in foreign reurn behavior. Table 1 provides summary informaion abou his daa se. Panel A repors on he break-down of firms across exchanges and indusries. NYSE has 380 companies coming from 39 foreign counries, while 196 foreign companies domiciled in 28 foreign counries are lised on NASDAQ. There are hree foreign counries represened on NASDAQ bu no NYSE, Malaysia, Singapore, and Sweden. Thus, he oal number of foreign counries represened on he wo exchanges is 42. Panel A also gives he number of differen indusries represened using he JP Morgan indusry caegorizaion. NYSE rades foreign companies coming from all 47 indusries, while NASDAQ foreign companies only produce in 40 indusries. Finally, Panel A shows ha he foreign companies lised on NYSE are generally older han hose on NASDAQ. The average number of observaions across firms on he NYSE is 1092, or abou 21 years, while ha same average across firms on NASDAQ is 862, or abou 17 years. Panel B of Table 1 breaks down he informaion by he home counry of he company. The firs column gives he dae a which he marke index daa begin for each counry, ranging from January 5, 1973 for many counries o June 24, 1994 for Porugal. The columns o he righ provide more informaion abou he composiion of he foreign company presence on each exchange. The home counry of he larges number of foreign companies is Canada, followed by he Unied Kingdom. Emerging markes generally have he lowes number of foreign companies on he exchanges. Moreover, 11 These daa were used in Doidge, Karolyi, and Sulz (2004,2005). 12 The index includes reinvesed dividends convered ino US dollars. 6

8 he average number of observaions from hese foreign companies is generally lower. For example, he Phillipines has only wo companies on he NYSE and one company on NASDAQ, and across hese hree companies he average number of weekly observaions is 411 or abou 8 years. Below we will discuss he impac of he differing number of observaions across counries on he resuls. 1c. Economeric Analysis While he facor model has been used hroughou inernaional asse pricing sudies, a number of sudies have shown ha he parameers change over ime. parameers are ofen assumed o shif a he ime of cross-lising. 13 In sudies of cross-lising evens, he Similarly, analysis of marke liberalizaions such as Henry (2000, 2003) ypically consider regime changes in which he local marke reurn becomes inegraed wih he world a he liberalizaion dae. Furhermore, a large lieraure has found ha he variance and covariances of inernaional sock reurns are ime-varying. 14 To sudy he diversificaion poenial of cross-lised firms over ime, we herefore require an empirical sraegy ha allows he facor loading parameers o shif. In keeping wih he cross-lising and liberalizaion lieraure, we permi hese parameers o shif discreely. Bu since we are ineresed in examining he sensiiviy o US reurns over ime, we need a framework ha does no force he shif o occur a a poin in ime or a all. For his purpose, we use he break dae esimaor developed by Bai and Perron (1998). This esimaor finds he dae or daes in he ime series when he facor sensiiives are mos likely o have shifed. Bekaer, Harvey and Lumsdaine (2002) use his esimaor in a vecor auoregression of marke index reurns and macroeconomic variables o ry o dae liberalizaion. By conras, we use he esimaor o recover a ime series of shifing beas for each foreign company in our sample. Given his ime series for each firm, we build a marke-weighed porfolio of hese companies. To undersand he esimaion procedure, we firs describe he basic BP framework in a single equaion case before explaining how we exend his analysis o build up a cross-secion of hese ime-series esimaes for many equaions. Single-Equaion Esimaion: The Bai-Perron esimaor requires specifying a maximum number of breaks in he parameers. Therefore, our analysis begins by esimaing his number of breaks. For now, we assume ha his number of breaks is simply given as m. To economize on noaion for developing he esimaor o be used below, we subsume he firm superscrips and rewrie he general facor model in (1) as: 13 For example, Foerser and Karolyi (1999) assume ha he alphas and beas on local and foreign markes shif a he even dae. Recenly, Sarkissian and Shill (2009) assume ha only he beas shif, bu again hey shif a he even dae. See he survey in Karolyi (2006) for oher examples. 14 For early works examining he relaionship beween shifing variances and marke liberalizaions see Bekaer and Harvey (1995, 1997). Bekaer, Hodrick and Zhang (2009) use ime-varying beas o find he bes fiing facor model for he se of companies in he MSCI World Index. 7

9 = Bai and Perron (1998) show ha unknown breakpoins can be esimaed consisenly by r = f + e (3) where r is he asse reurn series, e is he residual, and δ is he parameer vecor δ = {α, β } and where f is rewrien o include a consan as he firs facor. Clearly, he specificaions in equaions (2) can be subsumed ino his framework. We hen consider m poenial shifs in he parameer vecor δ. Thus, he model in (3) can be rewrien as: r = f + e (4) where δ τ is a fixed parameer vecor for each period τ, τ = 1,, m+1 on he inervals implied by = {1,, T 1, T 1+1,, T 2, T 2+1,, T 3,, T m,, T} (5) for T 0 = 0 and T m+1 = T. Noe ha he consan parameer model in (3) is a special case of (4) where m minimizing over he sum of squared residuals for all possible pariions of he daa ino m+1 differen inervals. In oher words, T 1, T 2,., T m can be consisenly esimaed by solving he following minimizaion: m1 2 T ˆ 1,T ˆ 2,..., T ˆ m} arg min [ r f ] T1, T2,..., Tm 1 { T( 1) 1,..., T} (6) Bai and Perron (1998) also derive he limiing disribuion of hese break poin esimaes providing confidence inervals on he breakpoin esimaes. While he esimaion of he break daes requires minimizing he sum of squared residuals for all possible m pariions of he daa, Bai and Perron (2003b) show ha he esimaor can have poor properies when he minimal lengh of he pariion becomes oo small. The reason is inuiively clear --- finer pariions of he inervals will imply fewer observaions and, herefore, less precise esimaes. Bai and Perron (2003b) propose consraining he minimal lengh of a pariion segmen for calculaing he sum of squares in he argmin calculaion in (6). This minimal lengh is defined as a proporion of he oal sample size so ha he percenage rimming consrain is used o consruc a minimal lengh of a segmen: h = T. Bai and Perron (2003b) show ha he size of his rimming facor depends upon 15 Sock (1994) describes he difficulies beween esing for srucural breaks versus parameric changes ha would sugges non-saionariy. As Bai and Perron (2003a) show, he algorihm for he model o be esimaed below can be exended o hreshold swiching models. 8

10 he number of maximum breaks, m, and derive criical values based upon his saisic. Bai and Perron (2003a) repor Mone Carlo simulaions of he finie sample properies of various ess in erms of his rimming parameer h/ T. They find ha he accuracy of he ess depends upon his parameer, a poin we reurn o below. Muli-Equaion Esimaion: The Bai-Perron esimaor described above was developed for an individual ime series. Since our goal is o develop a cross-secional as well as ime-series picure of he covariaion paern in foreign relaive o domesic reurns, we apply his framework o muliple equaions. Tha is, we examine each company reurn separaely o build up a se of: (a) he number of breaks; (b) he break dae esimaes and heir associaed confidence inervals; and (c) he parameers per sub-period inerval. Specifically, we firs es for he number of breaks, m i, for each company i. We hen esimae he se of break daes: ˆ i ˆ i ˆ i (T 1, T 2,..., T i ) and δ m τ τ = 1,, m i +1. Defining L as he oal number of counries and N as he oal number of companies, we can rewrie he wo facor model for company i allowing for breaks as in equaion (2b) over all companies i as: r = + r + r + e i i i iu u i i 1,..., N, 1,, L, 1,, m i (7) Noe ha he number of parameer shifs, m, differ by company and include as a possibiliy ha m i =0; i.e., no breaks. Moreover, no resricions are placed on he variance of he residual, u,, over subperiods. Indeed, he variance will generally change over subperiods, T τ, and across counries, l. In he empirical esimaes below, he sandard errors are also correced for a general condiional heeroskedasiciy as in Whie (1980) and Andrews (1991). 1d. Measuring Diversificaion Gains Given he esimaed panel of parameers and variances of cross-lised companies, we can evaluae he impac of hese changes on foreign diversificaion. To assess he impac of hese changes, we consider a represenaive US invesor who seeks o opimize his equiy porfolio using foreign equiy. To focus upon he relaionship beween he US and foreign markes, we form marke-weighed N porfolio of he foreign companies, r z i 1 r F i i where z i is he marke weigh of foreign company i a ime as a proporion of oal foreign company marke weighs, and use he US reurn as he oher porfolio. For comparison wih companies no lised in he US, we also consider porfolios of he foreign marke indices as well given by r L L i x 1 r where x is he marke weigh of marke index l a ime as a proporion of foreign counries ha have companies lised on he US exchange. 9

11 We hen ask how he US invesor would opimally choose his porfolio allocaion among hese asses. If means differ significanly among he porfolios and he invesor is no compleely riskaverse, hen he will choose a angency porfolio ha provides he highes risk-adjused reurns. By conras, if he wishes o minimize porfolio variance or he does no believe ha excess reurns are significanly differen from zero, he would choose a minimum variance porfolio allocaion. Below we focus upon he minimum variance allocaion for hree main reasons. Firs, variance reducion has been he focus of much of he inernaional diversificaion lieraure, including sudies in which he mean of reurns may be equal. As such, he gains from reducing variance should provide a lower bound on any gains based upon improvemens in mean reurns. 16 Second, sudies examining opimal porfolio choice based upon mean esimaes have found ha porfolio allocaions will respond o he marke ha has been doing well, bu will no necessarily reflec expeced fuure reurns. 17 Third, an exensive lieraure has found ha he excess reurns are ypically insignificanly differen from zero implying imprecisely measured porfolio shares. 18 In general, he minimum variance opimizaion gives a porfolio allocaion based upon he disribuion of reurns from he porfolio as r p : p K k k k 1 r r (8) where K is he number of asses and where k is he porfolio weigh from asse k. Under he assumpion ha reurns are exogenous and iid, weighs on he minimum variance porfolio are given by: 19 MinVar 1 V 1 ' V where ω is he K x 1 vecor of opimal porfolio shares, ι is a K dimensional vecor of ones, and V is he variance-covariance marix of reurns. We use his framework below o evaluae wo ses of porfolio menus available o he US invesor. Firs, we assume he porfolio of he US marke and he porfolio of cross-lised socks: r r, r P F U. Second, consider he possibiliy ha he invesor can also hold he foreign marke indices so ha: r P F, L, U r r r. We use he panel of parameer esimaes o compue he variance- (9) 16 For a survey, see Lewis (1999). 17 This poin is made in Black and Lierman (1992), among ohers. 18 See for example Brien-Jones (1999). Using a Bayesian approach, Pasor (2000) evaluaes he perceived esimaion risk by he invesor needed o generae home bias. 19 For example, he soluion o he minimum variance are given in Campbell, Lo, and MacKinlay (1997), Chaper 5. 10

12 covariance marix of reurns V for each year. To evaluae he economic significance of our esimaes, we hen compare his minimum variance using foreign socks wih he variance using he US marke only. As we show below, he diversificaion gains from long foreign invesmens are paricularly large during he early par of he sample in he 1970s, bu decline over ime. Secion II: Break Dae and Parameer Esimaes In order o examine he poenial gains from inernaional diversificaion using cross-lised companies, we require he esimaed parameers and residual variances over ime. This secion repors he resuls of esing for poenial breaks and he summarizes he disribuion of parameer esimaes. Secion III will use hese resuls o consider he impac on he minimum variance of he porfolio described above. IIa. Foreign Markes and he US Esimaing equaion (7) requires examining breaks in he relaionship beween he reurns of companies from each counry and boh he local sock marke, r and he US marke, u r. Noe ha he relaionship beween hese wo variables mus be sable, or else he esimaed facor model will be desabilized for reasons unrelaed o he company reurns. However, here are a leas hree reasons o suspec insabiliy beween he US and foreign markes. Firs, he emerging marke lieraure has demonsraed ha liberalizaions may induce he marke reurn relaionships o endogenously shif. 20 Second, a number of papers have suggesed ha he developed markes have become more correlaed over ime. Third, during crisis imes, Longin and Solnik (2001) have argued ha markes can become more correlaed. As such, higher correlaions during crises can undermine he abiliy o gain from diversificaion. Before sudying he company reurns, we firs es for sabiliy beween he reurns in foreign markes and he US using a sandard world CAPM and allowing for possible parameer shifs given by: r = + r + u, for τ = 1,, m+1; (10) w, To avoid confusion, we will use he previous noaion for indexing consan parameer inervals over ime as τ. However, below we will no require hese inervals o be he same for company reurns. 20 On emerging marke liberalizaions and he effecs on sock prices, see for example Bonser-Neal, e al (1990), Bekaer and Harvey (1997,2000), Henry(2000), and Bekaer, Harvey, and Lumsdaine (2002). Henry (2006) provides a survey of he lieraure on capial marke liberalizaions. 11

13 Bai and Perron (2003a) describe he properies of various break ess agains differen alernaives. In paricular, he limiing disribuion of hese ess depends upon he proporion of he minimal subinerval, measured by ε. We conduced he analysis here and hroughou he paper assuming ε is as small as 5%. However, as he Mone Carlo sudies of Bai and Perron (2003a,b) sugges, assuming pariions ha are oo small can over-esimae he number of breaks. Therefore, o be conservaive, we repor he esimaes based upon assuming ε is 15% of he sample bu we will reurn o he possibiliy ha breaks occur more ofen in Secion III below. 21 Table 2 repors he resuls of hese ess for each of he counry regressions in equaion (10). The resuls in Panel A indeed sugges ha breaks in he relaionship beween he US and foreign markes are imporan. The firs hree columns repor he proporions of he 42 counry index reurns ha rejec he hypohesis of no breaks versus he hypohesis of m breaks using he so-called sup F es. This es finds he highes F es for m breaks by aking all he differen pariions of subsamples as given in equaion (6). The firs column of Table 2A shows ha he hypohesis of no break agains he alernaive of a leas one break is rejeced for 85.7% of he counry indices a a 10% marginal significance level and even for 81% of he counries a a 1% marginal significance level. As he second and hird columns show, hese proporions increase higher when allowing for even more breaks While Bai and Perron advocae using he supf es wih given numbers of breaks, hey acknowledge ha here are circumsances in which he resuls migh be decepive. For example, for a regime swiching model in which he parameers swich back o an iniial regime, he es will underesimae he number of breaks. For his reason, hey also sugges esing he hypohesis of no breaks agains an unknown number of breaks. The las wo columns of Panels A repor he proporion of counries ha rejeced his hypohesis using wo versions of he double maximum es. The WD Max es weighs he ess of individual breaks such ha he marginal p-values are equal across values of m. By conras, he UD Max es weighs all values of m equally. Again, he able shows he proporion of counries ha rejec he hypohesis of no break is significanly higher han he MSL. Panel B of Table 2 provides summary evidence for he sequenial supf es given by marginal significance levels (MSL) of 10%, 5%, and 2.5%. In his es, a sequenial procedure esimaes each break one a a ime, and esimaion sops when he supf(τ+1 τ) es is no longer significan a he given marginal significance level. To idenify m l, we conduc sequenial SupF ess 21 In Mone Carlo simulaions, Bai and Perron find ha he maximal value of m for 0.15 is 5. Since m is 4 or less in all he analysis in his paper, his appears relaively conservaive. 12

14 for each counry, allowing up o four subperiods. 22 The firs column of Panel B repors he proporion of he counries ha rejeced he hypohesis of zero breaks. The las hree columns of Panel V repor he proporion of counries ha show evidence of one break, wo breaks and hree breaks, respecively. Counries wih one break make up he majoriy of he cases ranging from 61% a 10% MSL o 85% a 1% MSL. The number of counries wih evidence of 3 breaks is smaller a only 3 o 14%. We nex esimae he break dae equaions for each counry reurn series. Defining ˆm as he esimaed number of parameer breaks for counry l, he resul of our esimaion is a se of ˆm break dae esimaes for l = 1,, L given by (T ˆ, T ˆ,..., T ˆ ) (11a) 1 2 mˆ and parameer esimaes for each inerval τ = 1,, ˆm +1 for counry l given by { ˆ, ˆ, u ˆ } (11b) Where he residual is normally disribued wih possibly differing variance across inervals, u 2, ~ N(0, ) (11c) We hus obain a se of parameers by subperiod along wih break poins and confidence inervals around each esimae of he breakpoin and parameers. Figure1a plos he break-poin esimaes for each year by counry along wih is confidence inervals for he 5% marginal significance case. The confidence inerval for each counry excludes he upper and lower 5% of he esimaed break dae disribuion. The figure shows several relaionships. Firs, excep for a few noable excepions, he confidence inervals around he breaks are conained o wihin wo o hree years. Excepions are he breaks in he lae 1970s o early 1980s of Denmark and Ireland and he single break for Taiwan in he 2000s. Second break daes are generally more ighly esimaed. Second, mos of he breaks occur in he early 2000s. Figure 1b provides anoher look a his relaionship by showing he frequency of breaks over ime. Wheher looking a only single break counries or over all breaks, he peak of he disribuion occurs around One possibiliy is ha he financial crisis of lae 2000s induces a break a he laer par of he sample ha is capured around his ime. We reurn o his possibiliy below. Bekaer, Harvey, and Lumsdaine (2002) use he Bai-Perron esimaor in andem wih a vecorauoregression of macroeconomic variables o es for liberalizaions. Our focus here is on he risksensiiviies of cross-lised socks and as such inclusion daes of our counry marke indices are driven 22 As will be shown below, he counry reurns show lile evidence of more han hree breaks anyway, so his seems like a fairly conservaive assumpion for he maximum number of breaks, m. 13

15 by he inclusion daes of local-lised companies. Neverheless, he appendix shows ha for counries and daa periods in common wih Bekaer, Harvey and Lumsdaine (2002), our resuls are qualiaively similar. While hese figures repor he break dae esimaes in (11a), Table 3 provides summary saisics abou he parameer esimaes of (11b) for he MSL of 5% 23. These saisics are repored for differen groupings of porfolios and across pseudo-periods beween breaks. Counries wih no breaks have parameers 1 for he whole period, counries wih one break creae a new subperiod wih esimaes 2 a he same ime, ec. 24 This hypoheical period decomposiion allows us o examine he properies of he parameer disribuion wihin breaks. In our minimum variance porfolio esimaes below, we will also repor he effecs of parameers aligned over ime by year. For each porfolio in Table 3, he able repors he cross secional mean of he bea esimaes, heir sandard errors and heir correlaions wih he US marke, labeled β l Mean, Sd Err Mean, and Corr( r l,r u ), respecively. I also gives he cross-secional sandard deviaion of he bea esimaes given in he row referenced by β l Sd Dev, and he number of counries in he pseudo-sample indicaed by No. of Obs. Panel A shows he Marke Weighed Porfolios and Equally Weighed Porfolios for all counries. Three main feaures can be seen across hese columns. Firs, he mean beas generally increase over he periods oward one. The marke weighed porfolio bea mean is only abou 0.35 in Period 1, bu is abou 0.80 for Period 2. While here are fewer counries wih wo and hree breaks, he means over hese laer periods increase as well. A similar paern holds for he Equally Weighed Porfolio. Second, he correlaions of hese counry reurns wih he US also increase over he periods beginning a abou 0.20 for period 1 o 0.36 in period 2 and 0.44 in period 3. Third, he sandard error means have sayed relaively low, generally no exceeding 0.06 so ha he hypohesis of bea equal o zero can ypically be rejeced. Taken ogeher, hese parameers are consisen wih he general view ha markes have become more correlaed a inegraed over ime. Panel B shows similar resuls for a marke-weighed breakdown of developed counries versus emerging markes. While he mean of he sandard errors is higher for emerging markes, he general endency for mean bea and correlaions wih he US o rise over ime can be seen in boh porfolios. 23 For he MSLs of 2.5% and 10% he esimaes are virually idenical. 24 More precisely, he pseudo-periods are formed by allocaing he esimaes for each counry ino he maximum number of 1 periods. In oher words, defining his maximum as mˆ Max{ m,..., m L }, he parameer esimaes by pseudo-periods are given by: { 1, 2,..., m 1} for l = 1,, L where if m 1, or if m m 1 1,.., L 14

16 Panel C deails he breakdown of porfolios by regions. In every case, he bea means and correlaions increase beween periods 1 and 2. In some cases, here is a reversion o a lower bea in he hird period bu hese are based upon sample sizes of wo or even one counry. Overall, hese resuls sugges ha he relaionship beween foreign marke indices and he US marke has shifed over ime. The bea of foreign markes on he US has increased owards one and he correlaions have also rended upward. We nex esimae our relaionships beween he cross-lised firms and he US markes correcing for he shifs in he home markes over ime. 1Ib. Foreign Companies and he US Marke Recall ha he framework for foreign company reurns was given by (2b), repeaed here for convenience: r = + r + r + e (2b) i i i iu u i However, as we have noed above, he join disribuion of r u,r has been unsable over he sample period. If local socks have a sable relaionship wih heir local marke over ime bu he local markes become more correlaed wih he US markes, his shif will make local socks appear o have an unsable relaionship wih he US marke. These counry level breaks will hen conaminae esimaes abou he relaionship beween foreign socks rading in he US and heir relaionship wih he US marke. This relaionship can be seen by subsiuing he shifing counry reurn process r l from (3 ) ino he company reurn in (12 ). This implies: r = + [ + r + u ]+ r + e i i i u iu u i, r i i i u i = a + b r + Where i i a + b i i i iu + u + e i i i, (12) And where, as above, τ indexes he subinerval in which foreign marke indices are sable agains he US marke reurn. Equaion (13) shows ha even if he facor loadings of he foreign socks on he local and iu US marke, and i, are no ime-varying, an esimae of he parameers in a regression of foreign socks on he US marke would be. This resuls from he shifing facor loadings of he local marke on he US, and. 15

17 A he same ime, he relaionship beween foreign socks cross-lised in he US and he US marke iself may change for differen reasons. Using even sudies, a vas lieraure on inernaional cross-lisings has found ha a company s cos of capial ends o fall afer cross-lising. Moreover, he beas of he foreign sock ofen changes agains he US. 25 Ohers such as Baruch and Saar (2009) have argued ha he decision o lis on an exchange arises from he percepion ha he company is more similar o oher socks on a given exchange. If here are shifs in individual foreign sock reurns as a resul of lising in he US marke, i is herefore unclear wheher hese shifs would occur before or afer he cross-lising. Moreover, hese changes in individual sock behavior need no correspond o general feaures abou he relaionship beween he US marke and he company s home marke. Therefore, we firs ask he quesion of wheher here are shifs in he relaionship beween crosslised socks and he US marke afer conrolling for shifs beween he home sock marke and he US marke. To es his hypohesis, we use he esimaes for he parameers of he home counry in (11b) { ˆ, ˆ, u ˆ } and hen es wheher here are any addiional breaks in equaion (12) using he sequenial sup(f) ess. 26 If rejeced, we consider wheher he rejecion arises from insabiliy in local beas or US beas. Table 4 repors summary saisics of hese ess. Panel A gives a summary of he number and proporion of firms ha come from counries wih No Breaks (m=0), One Break (m=1), Two Breaks (m=2), and so forh. Only abou 5% of he firms come from counries ha did no show evidence of a change in asse pricing relaionships wih he US. Anoher 62% come from counries wih one break, while only 9% of he firms come from counries ha show evidence of wo breaks. On he oher hand, 24% of he firms come from counries wih hree breaks. This laer resul is largely due o Canada which has he larges number of foreign companies in he US, bu also has hree breaks poenially arising from is longer hisory of inegraion wih he US. Panel B shows he resuls of he sequenial sup(f) es for he firm reurns condiioning on he sock index parameers. The column labeled No Breaks indicaes ha 277 firms or abou 49% of he firms did no show evidence of breaks beyond he counry level. The remaining hree columns show ha he reurns from hose firms ha did rejec he hypohesis of no addiional breaks appeared o have only one break. In paricular, 231 firms had evidence of only one break while 55 firms appeared o have wo 25 See for example, Foerser and Karolyi (1999). 26 By condiioning he esimaion on he firs sage counry regression parameer esimaes, his second sage may suffer from a generaed regressions problem ha will undersae he rue sandard errors hereby poenially biasing he Wald ess oward rejecion. To ry o miigae his possibiliy, we allow for general condiional heeroskedasiciy in he Wald ess. 16

18 breaks. The reurns from only 6 or abou 1% of he firms indicaed hree breaks beyond he counry level. For he firms rejecing no parameer insabiliy beyond he counry level, Panel C examines he source of insabiliy. Using he definiion for he esimaed parameers in equaion (12), we idenify he i iu firm level parameers over he counry subinervals as:,, =1,...,m 1 and hen es a series of Wald ess for each firm. The firs wo columns repor he number of rejecions of he hypoheses ha each of he wo beas are zero for each sock. If he bea on he local marke is zero, hen here is no local i effec on he sock reurn during he period as can be seen by subsiuing 0 ino equaion (12) which gives r r e (13) i i iw w i In his case, he sock reurn depends only on he world CAPM. Alernaively, when he bea on he US iu marke is zero, he sock depends only on he local effecs. Subsiuing 0 ino equaion (12) implies: r = + + r + u + e (14) i i i i u i i, Thus, he reurn from company i depends upon he US marke reurn only indirecly hrough is bea wih i he home marke,, since is home sock marke in urn depends upon he US sock marke. As he firs wo columns of Panel C show, he zero bea resricion is rejeced for boh he local and US beas for mos of he firms. However, abou 85% of he firms rejec he zero local bea effec while only 58% of he firms rejec he zero US bea effec. The same paern carries over o he nex wo column ha repor ess ha he local and US effecs are consan over he subperiods. Sixy-hree percen of he firms rejec he hypohesis ha he local effecs are consan over ime while 44% of he firms rejec he es ha US effecs are sable. Given he evidence for addiional parameer insabiliy for abou half of he foreign socks, we nex examine he behavior of reurns for hese individual socks more closely. For each of he foreign companies, we esimae he following model: r = + r + r + e, for i = 1,..., N; =1,..., n 1 (15) i i i iu u i i, where r is as given by equaion (10), r = + r + u, for 1,, L, 1,, (10) u, Equaion (15) now allows explicily for he possibiliy of shifs in he company level reurns. Noe ha he number of breaks and heir implied subperiods may differ for he counry and firm reurns. In oher 17

19 words, for he reurns of firm i in counry l, he esimaes allow for τ ζ, n i m l. As a resul, he breakdaes of he firm may differ from he counry reurns. The ime inerval mapping analogous o equaion (4) is hen: 27 { (-1) +1,, } for { 1, 2,., n } where he esimaes of are: i n 1 i i 2 ˆ1, ˆ2,..., ˆ i } arg min [ 'f ] n r 1, 2,..., (16) n i 1 { ( 1) 1,..., } And o 0, j T. n While he regressions in (16) conain boh local home counry reurns and US 1 marke reurns, hese variables are joinly unsable as documened above. Therefore, we condiion he firm level esimaion on hese macro breaks. As for he counry-level esimaion, we firs esimae he break daes for he roughly 50% of firms ha show evidence of parameer insabiliy. These break daes esimaes and heir confidence inervals are ploed in Figure 2. In general, he daes are ighly esimaed wihin one o hree years as wih he counry esimaes. However, here are some ouliers when hese inervals exceed eigh years. Tables 5 and 6 provide summary saisics on he firm reurn local marke bea and US marke bea, respecively. These saisics are based upon he same porfolio breakdowns as repored for he counry regressions. I should be noed, however, ha hese porfolio saisics are now based upon marke weighs across firm capializaions, no counry index capializaions. The local marke beas in Table 5 show lile change over ime. In paricular, Panel A shows ha he marke weighed beas increase from subperiod one o wo from 0.66 o 0.75 while he equally weighed porfolio beas are essenially fla a around 0.7. Panel B demonsraes ha his paern is robus across companies coming from emerging and developed markes. Moreover, he correlaion beween he reurns and he home marke appears o be relaively sable over he subperiods. Panel C furher breaks he informaion down ino geographic regions, conveying some ineresing disincions across hese areas. Generally, he companies from Asia and he Middle Eas & Africa end o have lower beas 27 While he ime inervals depend upon each firm i, we subsume he firm superscrips for ease of exposiion. 18

20 wih heir home markes a around 0.3, while he companies from oher areas have beas on heir home markes closer o one. Table 6 repors he same summary saisics for he company US marke beas. For hese porfolio parameers, he means increase more sharply. For he marke-weighed porfolio, he US marke beas in Period 1 is only bu increases o in Period 2. These mean beas increase even more over he following wo periods, peaking a by Period 4, hough he means for hese laer periods are based upon a much smaller number of observaions. A similar bu more aenuaed paern hold for he Equally Weighed porfolio. This paern is also robus o decomposiion beween he developed and emerging marke companies as repored in Panel B. Ineresingly, he correlaion beween cross-lised company reurns and he US marke increases over subperiods. Across all counries, he mean correlaion increases from 0.16 in period 1 o 0.32 in period 4. Moreover his paern holds for he breakdown beween developed and emerging marke companies as well. Panel C of Table 6 repors he US marke bea saisics for porfolios decomposed ino geographic area. For all of he geographic areas, he marke-weighed beas of company reurns agains he US increase beween he firs and las period. Furhermore, he mean correlaion of hese sock reurns wih he US marke increases as well, even for companies from developed counries. For example, he correlaion beween European cross-lised socks and he US is on-average jus 0.16 in period 1, bu increases o 0.24 in period 2, 0.27 in period 3 and finally 0.34 in period 4. Taken ogeher, he parameer resuls in Tables 5 and 6 sugges ha even afer conrolling for he apparen shif oward inegraion of marke indices, he se of cross-lised companies have become more correlaed wih he US. Firs, he indirec relaionship wih he US marke has increased. Tha is, Table 5 shows ha local marke beas have increased oward one and since he local marke indices agains he i US has also increased, he produc of hese beas has increased. Second, he direc relaionship wih he US marke has increased as well. Table 6 demonsraes ha US marke beas have increased oward one and he mean correlaions wih he US have also increased. 1Ic. Shifs in US Marke Sensiiviy and Cross-Lising The resuls above show ha he co-movemen wih he US of boh he foreign companies ha are cross-lised in he US and heir home marke indices have increased over ime. However, he summary saisics do no necessarily say anyhing abou how hese relaionships have changed before or afer cross-lising. As noed above, a number of papers have conduced even sudy analysis a he ime of cross-lising o examine he impac on reurns. For his purpose, he bea coefficiens are ypically 19