Information Immobility and the Home Bias Puzzle

Transcription

1 THE JOURNAL OF FINANCE VOL. LXIV, NO. 3 JUNE 2009 Informaton Immoblty and the Home Bas Puzzle STIJN VAN NIEUWERBURGH and LAURA VELDKAMP ABSTRACT Many argue that home bas arses because home nvestors can predct home asset payoffs more accurately than foregners can. But why does global nformaton access not elmnate ths asymmetry? We model nvestors, endowed wth a small home nformaton advantage, who choose what nformaton to learn before they nvest. Surprsngly, even when home nvestors can learn what foregners know, they choose not to: Investors proft more from knowng nformaton others do not know. Learnng amplfes nformaton asymmetry. The model matches patterns of local and ndustry bas, foregn nvestments, portfolo outperformance, and asset prces. Fnally, we propose new avenues for emprcal research. OBSERVED RETURNS ON NATIONAL equty portfolos suggest substantal benefts from nternatonal dversfcaton, yet ndvduals and nsttutons n most countres hold modest amounts of foregn equty. Many studes document such home bas (see French and Poterba (1991), Tesar and Werner (1998), and Ahearne, Grever, and Warnock (2004)). Whle restrctons on nternatonal captal flows may have been a vable explanaton for the home bas 30 years ago, they no longer are today. An alternatve hypothess contends that home nvestors have superor access to nformaton about domestc frms or economc condtons. Ths nformaton-based theory of the home bas mplctly assumes that home nvestors cannot learn about foregn frms, replacng the old assumpton of captal mmoblty by the smlar assumpton of nformaton mmoblty. Our crtque of ths nformaton-based theory of home bas s that domestc Stjn Van Neuwerburgh s wth NYU Stern s Fnance Department and NBER and Laura Veldkamp s wth NYU Stern s Economcs Department and NBER. Thanks to Campbell Harvey and an anonymous assocate edtor and referee for ther comments, whch substantally mproved the paper. Thanks also to Pol Antras; Dave Backus; Perre-Olver Gournchas; Urban Jermann; Davd Lesmond; Karen Lews; Anthony Lynch; Arzu Ozoguz; Hyun Shn; Chrs Sms; Erc Van Wncoop; and Mark Wrght; partcpants at the followng conferences: AEA, AFA, Banque de France conference on Economc Fluctuatons Rsk and Polcy, Budapest SED, CEPR Asset Prcng meetngs n Gerzensee, CEPR-Natonal Bank of Belgum conference on nternatonal adjustment, Cleveland Fed Internatonal Macroeconomcs and Fnance conference, Econometrc Socety, EEA, Fnancal Economcs and Accountng, Fnancal Management Assocaton, Prague workshop n macro theory, NBER EF&G meetngs, and NBER summer nsttute n Internatonal Fnance and Macro; and semnar partcpants at Columba GSB, Emory, Illnos, Iowa, GWU, LBS, LSE, Mnneapols Fed, MIT, New York Fed, NYU, Oho State, Prnceton, Rutgers, UCLA, UCSD, and Vrgna for helpful comments and dscussons. Laura Veldkamp thanks Prnceton Unversty for ts hosptalty and fnancal support through the Peter B. Kenen fellowshp. 1187

2 1188 The Journal of Fnance R nvestors are free to learn about foregn frms. Such cross-border nformaton flows could potentally undermne the home bas. In short, when nvestors can choose whch nformaton to collect, ntal nformaton advantages could dsappear. Most exstng models of asymmetrc nformaton n fnancal markets are slent on nformaton choce. 1 A small but growng lterature on nformaton choce studes how much nformaton nvestors acqure about one rsky asset or models a representatve agent who, by defnton, cannot have asymmetrc nformaton. 2 In ths paper, nstead of askng how much nvestors learn, we ask whch assets they learn about. To answer ths queston requres a model wth three features: nformaton choce, multple rsky assets to learn about, and heterogeneous agents so that nformaton asymmetry s possble. We develop a two-country, ratonal expectatons general equlbrum model where nvestors frst choose what home or foregn nformaton to acqure, and then choose what assets to hold. The pror nformaton home nvestors have about each home asset s payoff s slghtly more precse than the pror nformaton foregners have. The reverse s true for foregn assets. Ths pror nformaton advantage may reflect what s ncdentally observed from one s local envronment. Home nvestors choose whether to acqure addtonal nformaton about ether home or foregn asset payoffs. The nteracton of the nformaton decson and the portfolo decson causes home nvestors to acqure nformaton that magnfes ther comparatve advantage n home assets. If home nvestors undo ther nformaton asymmetry by learnng about foregn assets, they sacrfce excess returns. Ths s because when nformaton ndcates that the foregn assets payoffs wll be hgh, both home and foregn nvestors know ths; as a result, both demand more of the foregn assets, bddng up the foregn assets prce. If nstead home nvestors learn more about home assets than the average nvestor does, then when they observe nformaton ndcatng hgh home asset payoffs, home asset prces wll not fully reflect ths nformaton; rather, prces wll reflect only as much as the average nvestor knows. The dfference between prces and expected payoffs generates home nvestors expected excess return. When choosng what to learn, nvestors seek to make ther nformaton set as dfferent as possble from the average nvestor s. To acheve the maxmum dfference, home nvestors take home assets, whch they start out knowng relatvely more about, and specalze n learnng even more about them. The man 1 Recent work on asymmetrc nformaton n fnancal markets ncludes Banerjee (2007), Ozdenoren and Yuan (2007) and Yuan (2005). The canoncal reference on asymmetrc nformaton wth multple assets s Admat (1985). Work on asymmetrc nformaton and the home bas, n partcular, ncludes Pástor (2000), Brennan and Cao (1997), and Portes, Rey, and Oh (2001). 2 Recent work on nformaton choce n fnance ncludes Peress (2006) and Dow, Goldsten, and Guembel (2007). The canoncal references n ths lterature, Grossman and Stgltz (1980) and Admat and Pflederer (1990), are also about one rsky asset. Our paper also dffers from Calvo and Mendoza (2000), who argue that more scope for nternatonal dversfcaton decreases the value of nformaton. In partcular, we fnd the converse: When nvestors can choose what to learn about, the value of dversfcaton declnes.

3 Informaton Immoblty and the Home Bas Puzzle 1189 result n the frst half of the paper s that nformaton mmoblty perssts not because nvestors cannot learn what locals know, nor because such nformaton s expensve, but because nvestors do not choose to learn what others know: Specalzng n what they already know s a more proftable strategy. Based upon ths fndng that sustaned nformaton asymmetry s possble, the second half of the paper compares the testable predctons of the model to the data. The model s key mechansm s the nteracton between the nformaton choce and the nvestment choce. To llustrate ts mportance, Secton II shuts down ths nteracton by forcng nvestors to take ther portfolos as gven when they choose what to learn. These nvestors mnmze nvestment rsk by learnng about the assets that they are most uncertan about. Wth suffcent capacty, learnng undoes all ntal nformaton advantage and therefore all home bas. Thus, ths model embodes the logc that the asymmetrc nformaton crtcsms are founded on. Secton III shows that when nvestors have ratonal expectatons about ther future optmal portfolo choces, ths logc s reversed. Whle acqurng nformaton that others do not know ncreases expected portfolo returns, that alone does not mply that home nvestors take a long poston n home assets but only that they take a large poston. Home bas, a long poston n the home asset that exceeds what s prescrbed by the standard world market portfolo, arses because home assets offer rsk-adjusted expected excess returns to nformed home nvestors. Informaton about the home asset reduces the rsk or uncertanty that the asset poses wthout reducng ts return, hence the hgh rsk-adjusted returns. How does nformaton reduce uncertanty? An asset s payoff may be very volatle, hgh one perod and low the next. But f an nvestor has nformaton that tells hm when the payoff wll be hgh and when t wll be low, the asset payoff s not very uncertan to that nvestor. Informaton drves a wedge between the condtonal standard devaton (uncertanty or rsk) and the uncondtonal standard devaton (volatlty) of asset payoffs. Whle foregn assets offer lower rsk-adjusted returns to home nvestors, they are stll held for dversfcaton purposes. The optmal portfolo tlts the world market portfolo towards home assets. Consderng how learnng affects portfolo rsk offers an alternatve way of understandng why nvestors wth an ntal nformaton advantage n home assets choose to learn more about home assets. Because of the excess rskadjusted returns, a home nvestor wth a small nformaton advantage ntally expects to hold slghtly more home assets than a foregn nvestor would. Ths small ntal dfference s amplfed because nformaton has ncreasng returns n the value of the asset t pertans to: As the nvestor decdes to hold more of an asset, t becomes more valuable to learn about. So, the nvestor chooses to learn more and hold more of the asset, untl all hs capacty to learn s exhausted on hs home asset. A varety of evdence supports the model s predctons. Secton IV connects the theory to facts about analyst forecasts, portfolo patterns, excess portfolo returns, cross-sectonal asset prces, as well as evdence thought to be

4 1190 The Journal of Fnance R ncompatble wth an nformaton-based home bas explanaton. In partcular, the theory offers a unfed explanaton of home bas and local bas. Whle we cannot clam that no other theory could possbly explan any one of these relatonshps, taken together, they consttute a large body of evdence that s consstent wth one parsmonous theory. A numercal example shows that learnng can magnfy the home bas consderably. When all home nvestors have a small ntal advantage n all home assets, the home bas s between 5% and 46%, dependng on the magntude of nvestors learnng capacty. When each home nvestor has an ntal nformaton advantage that s concentrated n one local asset, the home bas s amplfed, rsng as hgh as the 76% home bas n U.S. portfolo data for a level of capacty that s consstent wth observed excess returns on local assets. Fnally, we derve new testable hypotheses from the model to gude future emprcal work. Informaton advantages have been used to explan exchange rate fluctuatons (Evans and Lyons (2005), Bacchetta and van Wncoop (2006)), the nternatonal consumpton correlaton puzzle (Coval (2003)), nternatonal equty flows (Brennan and Cao (1997)), a bas towards nvestng n local stocks (Coval and Moskowtz (2001)), and the own-company stock puzzle (Boyle, Uppal, and Wang (2003)). Informaton asymmetry s also the bass for other home bas explanatons, such as ambguty averson (Uppal and Wang (2003)). All of these explanatons are bolstered by our fndng that nformaton advantages are not only sustanable when nformaton s moble, but that asymmetry can be amplfed when nvestors can choose what to learn. I. A Model of Learnng and Investng Usng tools from nformaton theory, we construct an equlbrum framework to consder learnng and nvestment choces jontly. Ths model uses the one-nvestor partal equlbrum problem of Van Neuwerburgh and Veldkamp (2008) to buld a heterogeneous agent, two-country general equlbrum model wth a contnuum of nvestors n each country. Ths s a statc model that we break up nto three perods. In perod 1, each nvestor chooses the dstrbuton from whch to draw sgnals about the payoff of the assets, subject to a constrant on the total nformatveness of ther sgnals. In perod 2, each nvestor observes sgnals from the chosen dstrbuton and makes hs nvestment. Prces are set such that the market clears. In perod 3, each nvestor receves the asset payoffs and consumes. A. Preferences Investors, wth absolute rsk averson parameter ρ and facng an N 1 vector of unknown asset payoffs f, a rsk-free rate r, and asset prces p, maxmze ther mean-varance utlty ] U = E [ ρq ( f rp) + ρ2 2 q ˆ q, (1)

5 Informaton Immoblty and the Home Bas Puzzle 1191 where q s the N 1 vector of the quanttes of each asset the nvestor decdes to hold and ˆ s the uncertanty about the payoffs that nvestors face after they learn. 3 When portfolos are chosen n perod 2, the expectaton E s condtonal on the realzaton of the sgnals the nvestor has chosen to see. When sgnals are chosen at tme 1, the nvestor does not know what the realzatons of these sgnals wll be. Therefore, n perod 1, the nvestor has the same objectve, except that expectaton E condtons only on nformaton n pror belefs. Ths utlty functon comes from an exponental form of utlty over termnal wealth. Termnal wealth equals ntal wealth W 0 plus the proft earned from portfolo nvestments: W = rw 0 + q ( f pr). (2) B. Intal Informaton Two countres, home and foregn, have an equal-szed contnuum of nvestors whose preferences are dentcal. Investors are endowed wth pror belefs about a vector of asset payoffs f. Each nvestor s pror belef s an unbased ndependent draw from a normal dstrbuton, whose varance depends on where the nvestor resdes. Home pror belefs are µ N(f, ). Foregn pror belefs are dstrbuted µ N(f, ). Home nvestors have lower varance pror belefs for home assets and foregn nvestors have lower varance belefs for foregn assets. One nterpretaton s that each nvestor gets a free sgnal about each asset n hs home country. We call ths dfference n pror varances a group s ntal nformaton advantage. C. Informaton Acquston Each nvestor knows the true mean and varance of asset payoffs. The only unknown s the realzaton of those payoffs, f, whch s what the nvestor can learn about. Just lke an econometrcan, he can acqure addtonal data to form a more accurate payoff estmate ˆµ. The nvestor chooses what assets to collect data on, subject to a constrant on the total amount of data. Collectng more data on one asset reduces the standard error of hs estmate for that asset s payoff. The posteror varance s that standard error, squared. At tme 2, each nvestor wll observe an N 1 vector of sgnal realzatons η about the vector of asset payoffs f. At tme 1, nvestors choose a varance η such that η N(f, η ). Investors cannot choose whether sgnals wll contan good or bad news. Rather, they choose sgnals that wll contan more precse nformaton 3 A separate Internet Appendx, avalable at dscusses the foundatons for ths utlty formulaton n detal. Note that the results do not depend on the exstence of a rsk-free asset. Suppose nvestors can consume c 1 at the nvestment date and c 2 when asset payoffs are realzed. If preferences are defned over rc 1 + c 2,wherer s the rate of tme preference, the soluton wll be dentcal. The earler consumpton choce takes the place of the rskless nvestment choce.

6 1192 The Journal of Fnance R about some assets than others. Each nvestor s sgnal s ndependent of the sgnals drawn by other nvestors. When payoffs covary, obtanng a sgnal about one asset s payoff s nformatve about other payoffs. To descrbe what a sgnal s about, t s useful to decompose asset payoff rsk nto orthogonal rsk factors and the rsk of each factor. Ths decomposton breaks the pror varance covarance matrx up nto a dagonal egenvalue matrx and an egenvector matrx Ɣ: = Ɣ Ɣ. The s are the pror varances of each rsk factor. The th column of Ɣ (denoted Ɣ ) contans the loadngs of each asset on the th rsk factor. To make aggregaton tractable, we assume that home and foregn pror varances and have the same egenvectors, but dfferent egenvalues. In other words, home and foregn nvestors use ther capacty to reduce dfferent ntal levels of uncertanty about the same set of rsks. Ths assumpton mples that nvestors observe sgnals (Ɣ η) about rsk factor payoffs (Ɣ f ). Learnng about rsk factors (prncpal components analyss) has long been used n fnancal research and among practtoners. It approxmates the rsk categores nvestors mght study: country, busness cycle, ndustry, regonal, and frm-specfc rsk. Nothng prevents nvestors from learnng about many rsk factors. The only thng ths rules out s sgnals wth correlated nformaton about ndependent rsks. Choosng how much to learn about each rsk factor s equvalent to choosng the varance of each entry of the N 1 sgnal vector Ɣ η. Snce the sgnal s unbased, ts mean s Ɣ f. The varance of a prncpal component s ts egenvalue. So, reducng uncertanty about the th rsk factor means choosng a smaller th egenvalue of the sgnal varance covarance matrx η. Sgnals about the payoffs of all assets that load on rsk factor become more accurate. Wth Bayesan updatng, each η results n a unque posteror varance matrx that measures the nvestor s uncertanty about asset payoffs, after ncorporatng what he learned. Snce the mappng between sgnal choces and posterors s unque, nformaton choce s the same as choosng posteror varance, wthout loss of generalty. Snce sums, products, and nverses of pror and sgnal varance matrces have egenvectors Ɣ, posteror belefs wll as well. Denotng posteror belefs wth a hat, ˆ = Ɣ ˆ Ɣ, where Ɣ s gven and the dagonal egenvalue matrx ˆ s the choce varable. The decrease n rsk factor s posteror varance ( ˆ ) measures the decrease n uncertanty acheved through learnng. There are two constrants governng how the nvestor can choose hs sgnals about rsk factors. The frst s the capacty constrant, whch lmts the quantty of nformaton nvestors can observe. Grossman and Stgltz (1980) use the rato of varances of pror and posteror belefs to measure the qualty of nformaton about one rsky asset. We generalze ths metrc to a mult-sgnal settng by boundng the rato of the generalzed pror varance to the generalzed posteror varance, ˆ 1, where generalzed varance s defned as K the determnant of the varance covarance matrx. Capacty K 1 measures how much an nvestor can decrease the uncertanty he faces. For now, K s the same for all nvestors. Snce determnants are a product of egenvalues, the capacty constrant s

7 Informaton Immoblty and the Home Bas Puzzle 1193 ˆ 1 K. (3) The second constrant s the no-negatve-learnng constrant: The nvestor cannot choose to ncrease uncertanty (forget nformaton) about some rsks to free up more capacty to decrease uncertanty about other rsks. We rule ths out by requrng the varance covarance matrx of the sgnal vector η = Ɣ η Ɣ to be postve semdefnte. Snce a matrx s postve semdefnte when all ts egenvalues are postve, the constrant s gven by Ths constrant mples that ˆ 1 η 0. (4) p,. D. Comments on the Learnng Technology The structure we put on the learnng problem keeps t as smple as possble. But many of these assumptons can be relaxed. Frst, our results do not hnge on the assumpton that nvestors learn about prncpal components of asset payoffs. Investors specalze n what they know well, for any arbtrary rsk factor structure. Second, our framework can ncorporate capacty that dffers across nvestors (see Secton IV.C). Thrd, allowng agents to choose how much capacty to acqure does not change the results. Any cost functon ncreasng n K has an equvalent capacty endowment that produces dentcal portfolo outcomes. Fnally, a learnng technology wth dmnshng returns and unlearnable rsk wll moderate, but not overturn, our results. Instead of specalzng n one rsk, nvestors may learn about a lmted set of rsks. But t does not change the concluson that nvestors prefer to learn about what they already have an advantage n. 4 It s not the case that every capacty constrant preserves specalzaton. We use ths constrant because: It s a common dstance measure n econometrcs (a log-lkelhood rato) and statstcs (a Kullback Lebler dstance); t s a bound on entropy reducton, an nformaton measure wth a long hstory n nformaton theory (Shannon (1948)); t can be nterpreted as a technology for reducng measurement error (Hansen and Sargent (2001)); t s a measure of nformaton complexty (Cover and Thomas (1991)); t has been used to forecast foregn exchange returns (Glodjo and Harvey (1994)), and t has been used to descrbe lmted nformaton processng ablty n economc settngs (Sms (2003)). 5 Although we do not prove that ths s the correct learnng technology, 4 The proof of the frst and thrd clams can be found n the Internet Appendx; the proof of the last clam s n Van Neuwerburgh and Veldkamp (2008). 5 Ths learnng technology s also used n models of ratonal nattenton. However, that work focuses on tme-seres phenomena n representatve nvestor models such as delayed response to shocks, nerta, tme to dgest, and consumpton smoothng. See Sms (2003) and Moscarn (2004). Instead, we focus on the nteractons of heterogeneous nvestors learnng choces.

8 1194 The Journal of Fnance R our strategy s to work out ts predctons for nternatonal nvestment choces and ask whether they are consstent wth the data. E. Updatng Belefs When nvestors portfolos are fxed (Secton II), what nvestors learn does not affect the market prce. But when asset demand responds to observed nformaton (Secton III), the market prce s an addtonal nosy sgnal of ths aggregated nformaton. Usng ther pror belefs, ther chosen sgnals, and the nformaton contaned n prces, nvestors form posteror belefs about asset payoffs usng Bayes s law. The nformaton n prces depends on portfolo choces. Appendx B shows that prces p are lnear functons of the true asset payoffs such that (rp A) N(f, p ), for some constant A. An nvestor j s posteror belef about the asset payoff f, condtonal on a pror belef µ j, sgnal η j N(f, η), j and prces, s formed usng Bayesan updatng. The posteror mean s a weghted average of the pror, the sgnal, and prce nformaton, whle the posteror varance s a harmonc mean of the varance of prors, sgnals, and prces: ˆµ j E[ f µ j, η j, p] = ( ( j ) 1 + ( η j ) 1 ) ( p ( j ) 1 µ j + ( η j ) 1η j + 1 p (rp A)) (5) ˆ j V [ f µ j, η j, p] = ( ( j ) 1 + ( η j ) 1 ) p (6) We emphasze that acqurng nformaton (( j η) 1 > 0) always reduces posteror varance. Ths mght appear puzzlng because n an econometrc settng, new data can make us revse varance estmates upward. The dfference s that there s no estmaton of varance n our problem. The true varance of f s known to all nvestors. Rather, ˆ s the varance of the estmate of f. It s a measure of uncertanty, a posteror varance that condtons on the nvestor s nformaton, not a measure of volatlty (pror varance). Under Bayes s law wth normal random varables, more nformaton always reduces uncertanty. 6 F. Market Clearng Asset prces p are determned by market clearng. The per capta supply of the rsky asset s x + x, a postve constant ( x > 0) plus a random (n 1) vector wth known mean and varance and zero covarance across assets: x N(0, σx 2 I). The reason for havng a rsky asset supply s to create some nose n the prce level that prevents nvestors from beng able to perfectly nfer the 6 Our model does not dstngush between rsk and uncertanty because the probablty of each of the states of nature s known.

9 Informaton Immoblty and the Home Bas Puzzle 1195 prvate nformaton of others. Wthout ths nose, no nformaton would be prvate, and no ncentve to learn would exst. We nterpret ths extra source of randomness n prces as due to lqudty or lfe cycle needs of traders. The market clears f nvestors portfolos q j sum to the asset supply: 1 0 q j dj = x + x. G. Defnton of Equlbrum An equlbrum s a set of asset demands, asset prces, and nformaton choces, such that three condtons are satsfed. Frst, gven pror nformaton about asset payoffs f N(µ, ), each nvestor s nformaton choce ˆ and portfolo choce q maxmze (1), subject to capacty (3), no-negatve-learnng (4), and budget (2) constrants. Second, asset prces are set such that the asset market clears. Thrd, belefs are updated, usng Bayes s law (equatons (5) and (6)) and expectatons are ratonal: Perod 1 belefs about the portfolo q are consstent wth the true dstrbuton of the optmal q. II. Why Mght Asymmetrc Informaton Dsappear? Returns to specalzaton come from the nteracton of the nvestment choce and the learnng choce. To hghlght the mportance of ths nteracton, we frst explore a model n whch t s shut down. The only dfference wth the man model n Secton III s that nvestors do not account for the fact that what they learn wll nfluence the portfolo they hold. They take ther portfolo as gven and choose what to learn n order to mnmze portfolo rsk. In ths settng, nvestors learn exclusvely about the most uncertan assets untl ether they run out of capacty, or are equally uncertan about all assets. Learnng undoes ntal nformaton advantages and reduces or elmnates home bas. As Lews (1999, p. 588) put t, Greater uncertanty about foregn returns may nduce the nvestor to pay more attenton to the data and allocate more of hs wealth to foregn equtes. Ths secton explans the bass for ths crtcsm of nformaton-based models of the home bas. In order to shut down the nvestment-learnng nteracton, we assume that the nvestor takes the vector of asset holdngs q as gven and expects to hold the same amount of each rsk factor: Ɣ q = Ɣ kq,, k. The objectve (1) collapses to choosng ˆ s to mnmze (Ɣ q)2 ˆ, subject to the capacty constrant (3) and the no-forgettng constrant (4). The followng result shows that learnng undoes ntal nformaton asymmetry. The proofs of ths and all subsequent propostons are n Appendx A. PROPOSITION 1 (Informaton Acquston n a Model wthout Increasng Returns to Informaton): There exsts a threshold K such that, f capacty s K K, then the optmal nformaton allocaton choce for an nvestor who takes asset holdngs q as gven s to set ˆ = M for all rsk factors {1,..., N} and for some constant M > 0, rrespectve of hs ntal nformaton advantage. If K < K, then ˆ = mn{, M}.

10 1196 The Journal of Fnance R The proposton states that an nvestor who beleves that he wll hold equal amounts of each home and foregn rsk factor optmally chooses to equate the posteror varance across all rsk factors (to some target varance M), gven enough capacty K. Wth hgh enough learnng capacty, havng an ntal advantage n home or foregn rsk wll result n the same posteror varances for both home and foregn assets. Learnng choces compensate for ntal nformaton advantage n such a way as to render the nature of the ntal advantage rrelevant. Any home bas that mght result from the nformaton advantage dsappears when nvestors can learn. On the other hand, f capacty s suffcently low, then equatng posteror precsons on all assets s not feasble. The no-forgettng constrant prevents the nvestor from reducng her nformaton about the home assets to free up capacty to learn about the foregn assets. The constraned optmum s to set posteror varances equal as much as possble. Ths allocaton mples devotng capacty to the most uncertan rsk factor frst. For a home nvestor wth an ntal advantage n home rsk factors and small capacty, ths means usng all capacty to learn about foregn rsk factors. Therefore, ntal nformaton advantages could persst f capacty were low relatve to the ntal advantage. However, f ths explanaton were true, ndvduals would never choose to learn about home assets; they would devote what lttle nformaton capacty they had entrely to learnng about foregn assets. Ths mplcaton seems nconsstent wth the mult-bllon-dollar ndustry that analyzes U.S. stocks, reports on the U.S. economy, manages portfolos of U.S. assets, and then sells ther products to Amercan nvestors. A second mechansm that mght preserve a home nformaton advantage s a hgher cost of processng foregn nformaton. Whle foregn nformaton s lkely harder to learn, ths cost dfference must be large to account for the magntude of the home bas. 7 Snce there s no theory to predct nformaton costs and they are not observable, t s desrable for a theory not to rely on the magntude of the cost dfference. Instead, the model n the next secton requres an arbtrarly small ntal nformaton advantage, possbly generated by a small cost dfference, to endogenously create a large home bas. III. Man Results The prevous secton llustrates how nformaton asymmetry could dsappear. Ths secton analyzes a model where small dfferences n nvestors nformaton not only persst, but are magnfed. The only change n the setup s that nvestors do not take ther asset demand, or the asset demand of other nvestors, to be fxed. Instead, we apply ratonal expectatons: Every nvestor takes nto account that every portfolo n the market depends on what each nvestor learns. We conclude that home nvestors can learn foregn nformaton, but choose not to. They acheve hgher expected utlty from specalzng n what they already know. 7 The Internet Appendx computes ths requred cost.

11 Informaton Immoblty and the Home Bas Puzzle 1197 A. The Perod-2 Portfolo Problem We solve the model usng backward nducton, startng wth the optmal portfolo decson, takng nformaton choces as gven. Gven posteror mean ˆµ j and varance ˆ j of asset payoffs, the portfolo for nvestor j from ether country s q j = 1 ρ ( ˆ j ) 1 ( ˆµ j pr). (7) Aggregatng these asset demands across nvestors and mposng market clearng delvers a soluton for the equlbrum asset prce level that s lnear n the asset payoff f and the unexpected component of asset supply x: p = 1 r (A + f + Cx). Appendx B derves formulas for A and C. B. The Optmal Learnng Problem In perod 1, the nvestor chooses nformaton to maxmze expected utlty. In order to mpose ratonal expectatons, we substtute the equlbrum asset demand (7), nto expected utlty (1). Combnng terms yelds [ ] 1 U = E 2 ( ˆµ j pr) ( ˆ j ) 1 ( ˆµ j pr) µ,. (8) At tme 1, ( ˆµ j pr) s a normal varable, so that U s the mean of a ch-square dstrbuted random varable. The Internet Appendx shows that we can rewrte the perod 1 objectve as max ˆ j ( p + ( ρɣ x ˆ a ) 2 )( ˆ j ) 1, s.t. (3) and (4), (9) where p s the th egenvalue of p and ˆ a ( j ( ˆ j ) 1 ) 1 s the posteror varance of rsk factor for a hypothetcal average nvestor. The key feature of the learnng problem (9) s ts convexty n the posteror varance ( ˆ j ). To llustrate, consder a settng wth one rsk factor n each country, where the objectve s U = L 1 / ˆ 1 + L 2 / ˆ 2 for postve scalars L 1 and L 2. Thus, an ndfference curve s ˆ 2 = L 2 ˆ 1 /(U ˆ 1 L 1 ), whch asymptotes to at ˆ 1 = L 1 /U > 0. The capacty constrant s ˆ 2 = K / ˆ 1, whch asymptotes to at ˆ 1 = 0. Because the ndfference curve s always crossng the capacty constrant from below, the soluton s always a corner soluton. Fgure 1 plots the ndfference curve (for L 1 = L 2 ), the capacty constrant, and the no-negatve learnng bounds for our model (left panel) and the exogenous-portfolo model n Secton II (rght panel). Utlty ncreases as the ndfference curve (dark lne) moves toward the orgn (varance falls). All feasble learnng choces must le on or above the capacty constrant (lghter lne). The no-negatve learnng constrant prohbts posteror varances from exceedng pror varances (dashed lnes). The set of learnng choces that satsfy both constrants s the shaded area. Whenever foregn pror varance s hgher than home pror varance, as n the fgure, the soluton n our model s to devote all

12 1198 The Journal of Fnance R Foregn Asset Posteror Varance Optmal Informaton Choce ndfference curve capacty constrant pror varance Hgher Utlty Home Asset Posteror Varance Foregn Asset Posteror Varance Informaton Choce n Secton II 2 ndfference curve capacty constrant 1.5 pror varance Hgher Utlty Home Asset Posteror Varance Fgure 1. factors. Objectve and constrants n the optmal learnng problem wth two rsk capacty to reducng home asset rsk (the large dot n the left panel). In the model of Secton II (rght panel), the objectve s lnear and the optmum s to reduce varance on home and foregn assets untl ther posteror varances are equal. The rght panel shows why shuttng down the nformaton-portfolo nteracton reverses our man concluson. The followng proposton states that each nvestor j uses hs entre capacty K to learn about one rsk factor s payoff,f Ɣ. The rsk factor the nvestor chooses to devote hs capacty to has the hghest value of the learnng ndex. DEFINITION 1: Investor j s learnng ndex for rsk factor s L j (ρ ˆ aɣ x)2 (( j ) p ) + p. j PROPOSITION 2 (Optmal Informaton Acquston): The optmal nformaton allocaton decson for each nvestor j takes the followng form: ˆ j k = j k for all k and ˆ j < j for rsk factor, where = arg max l=1,...,n {L j l }. Three features make a partcular rsk factor desrable to learn about. Frst, the larger the rsk factor, measured by the supply (Ɣ x)2, the hgher ts learnng ndex. Snce one pece of nformaton can be used more proftably to evaluate 100 shares of an asset than 1 share, nformaton has ncreasng returns, and the nvestor gans more from learnng about a rsk that s abundant. Second, the nvestor should learn about a rsk factor that the average nvestor s uncertan about (hgh ˆ a ). These rsk factors have prces that reveal less nformaton (hgh p ) and have hgher expected returns: Ɣ E[ f pr] = ρ ˆ aɣ x. (See Appendx B for a dervaton.) Thrd, and most mportantly for the pont of the paper, the nvestor should learn about rsk factors that he has less ntal uncertanty about relatve to the average nvestor (hgh ˆ a/ ). Snce these are the assets he wll expect to hold more of, these are more valuable to learn about. The feedback effects of learnng and nvestng can be seen n the learnng ndex. The amount of a rsk factor that an nvestor j expects to hold, based on hs

13 Informaton Immoblty and the Home Bas Puzzle 1199 pror and prce nformaton, s the factor s expected return, dvded by varance: ρ ˆ aɣ x(( j ) p ). Ths expected portfolo holdng shows up n the learnng ndex formula, ndcatng that a hgher expected portfolo share ncreases the value of learnng about the rsk factor. Expectng to learn more about the rsk factor lowers the posteror varance ˆ j. Recomputng the expected portfolo holdng wth varance ˆ j, nstead of (( j ) p ) 1, further ncreases factor s portfolo share and feeds back to ncrease s learnng ndex. Ths nteracton between the learnng and portfolo choces, an endogenous feature of the model, generates ncreasng returns to specalzaton. C. Strategc Substtutablty Because other nvestors learnng lowers the posteror uncertanty ˆ a and the nformatveness of prces p for the rsk factors they learn about, each nvestor prefers to learn about rsk factors that other nvestors do not learn about: L j > 0. Ths s strategc substtutablty. Let I ˆ h be the set of rsk factors a that home nvestors learn about. Snce all home nvestors are ex ante dentcal, each home nvestor j s ndfferent between learnng about any of these rsk factors: L j = L j k for any, k Ih. There s another such set of rsk factors I f for foregn nvestors. The number of rsk factors n each set depends on countrywde nformaton capacty. Despte ther ndfference, the ncentve to specalze ensures that each nvestor wll learn about only one rsk factor. Whle a gven nvestor can learn about any sngle asset n hs ndfference set n equlbrum, strategc substtutablty ensures that the aggregate allocaton of capacty s unque. 8 D. Learnng and Informaton Asymmetry The effect of an ntal nformaton advantage on learnng s smlar to the effect of a comparatve advantage on trade. Home nvestors always have a hgher learnng ndex than foregners do for home rsks, and vce versa for foregn rsks. If home rsks are partcularly valuable to learn about, for example, because those rsks are large (hgh Ɣ x), some foregners may choose to learn about them. But, f home rsks are valuable to learn about, all home nvestors wll specalze n them. Lkewse, f some home nvestors learn about foregn rsks, then all foregners must be specalzng n foregn rsks as well. The one pattern the model rules out s that home nvestors learn about foregn rsk and foregners learn about home rsk. Ths s analogous to the prncple of comparatve advantage: If country A has an advantage n producng apples and country B 8 For proofs of strategc substtutablty and equlbrum unqueness, see part A of the Internet Appendx. In what follows, we consder a symmetrc mxed strategy equlbrum where, for each rsk factor and any two nvestors j, j,fl j L j then the probablty that nvestor j learns about s at least as hgh as the probablty that j learns about.

14 1200 The Journal of Fnance R an advantage n bananas, the one producton pattern that s not possble s that country A produces bananas and B apples. Investors never make up for ther ntal nformaton asymmetry by each learnng about the others advantage. Instead, posteror belefs dverge relatve to prors: Informaton asymmetry s amplfed. Let h ( h ) denote home (foregn) nvestors pror varance for an arbtrary home rsk factor h, and let ˆ h ( ˆ h ) denote the average home (foregn) nvestor s posteror varance for h. PROPOSITION 3 (Learnng Amplfes Informaton Asymmetry): For every home rsk factor h, ˆ 1 h ( ˆ h ) 1 1 h ( h ) 1. A specal case of ths result arses when home and foregn countres are perfectly symmetrc: They have an equal number of rsk factors of equal sze wth equal payoff varances. In ths case, home nvestors learn exclusvely about home rsks and foregn nvestors learn exclusvely about foregn rsks. Ths result follows drectly from the learnng ndex n Proposton 2. An nvestor wth no nformaton advantage would have dentcal learnng ndces for home and foregn rsks. Thus, he would be ndfferent between learnng about home and foregn rsks. Snce nvestors wth no nformaton advantage are ndfferent, any ntal advantage n home rsk (lower j n the learnng ndex) breaks that ndfference, tlts preferences toward learnng more about home rsk, and amplfes the ntal advantage. At the other extreme, wth very asymmetrc markets, amplfcaton dsappears. If the home market s much smaller than the foregn market, the learnng ndex for the foregn rsk factors would be much hgher for both the home and the foregn nvestor, and all nvestors optmally learn about foregn rsk factors. The rato of home and foregn nvestors posteror precsons wll then be the same as the rato of ther pror precsons. The ntal advantage s just preserved. For all ntermedate cases, posteror belef dfferences between foregn and home nvestors about home assets are greater than pror belef dfferences. Ths leads us to conclude that learnng amplfes the ntal nformaton advantage. E. Home Bas n Investors Portfolos To understand the effect of learnng on home bas, we compare our model s predctons to two benchmark portfolos. The frst portfolo would arse as the optmal portfolo n an economy wth no nformaton advantage and no capacty to learn. Home nvestors and foregn nvestors have dentcal belefs and hold dentcal portfolos, whch depend on the random asset supply. The expected portfolo s the per capta expected supply: E[q dv ] = x. It s the world market portfolo, the perfectly dversfed portfolo of home and foregn assets. A second natural benchmark portfolo s one where nvestors have ntal nformaton advantages and can process the nformaton n prces, but cannot

15 Informaton Immoblty and the Home Bas Puzzle 1201 acqure sgnals: E[q no learn ] = Ɣ(( j ) p )( ( ) p ) 1 Ɣ x, for an nvestor j. 9 For comparson, note that the no-advantage portfolo can be wrtten as E[q dv ] = ƔIƔ x. What makes the no-learnng portfolo dfferent from the no-advantage portfolo s the ntal nformaton advantage: ( j ) ( ) 1. The no-learnng portfolo tlts away from the world market portfolo toward the rsk factors n whch the nvestor has an ntal advantage. For example, ths s the knd of nformaton advantage that Ahearne, Grever, and Warnock (2004) capture when they estmate the home bas that uncertanty about foregn accountng standards could generate. The optmal expected portfolo wth nformaton acquston takes the form E[q] = Ɣ ˆ 1 ˆ a Ɣ x. (10) Specalzaton n learnng does not mply specalzaton n portfolo holdngs. Even f an nvestor only learns about one home rsk factor, he stll holds all other assets for dversfcaton purposes. Each nvestor j s optmal portfolo takes the world market portfolo ( x) and tlts t toward the assets that he knows more about than the average nvestor (hgh ( ˆ j ) 1 ˆ a). Let Ɣ h be a sum of the egenvectors n Ɣ that correspond to the home rsk factors. Then Ɣ h q quantfes how much total home rsk an nvestor s holdng n hs portfolo. DEFINITION 2: The home bas n a portfolo q s the dfference between the home rsk exposure n q and n the dversfed portfolo, H j (q) E[ Ɣ j q] E[ Ɣ j qdv ], for an nvestor j {h, f }. The fnal proposton shows that the home bas n the optmal portfolo (10) exceeds the home bas n the no-learnng portfolo. PROPOSITION 4 (Learnng Increases Home Bas): The home bas s larger when nvestors can learn than when they cannot: H j (q) H j (q no learn ), for an nvestor j {h, f }. Learnng has two effects on an nvestor s portfolo. Frst, t magnfes the asset poston, and second, t tlts the portfolo toward the assets learned about. The frst effect can be seen n (10): Learnng ncreases the precson of belefs ˆ 1 > p. Lower rsk n factor makes nvestors want to take larger postons n, postve or negatve. But why should the poston n home assets be a large long poston, rather than a large short one? The second effect s an equlbrum effect. The return on an asset compensates the average nvestor for the amount of rsk he bears, ˆ a. The fact that foregn nvestors are nvestng n home assets wthout knowng much about them (typcally as part of a dversfed portfolo) rases ˆ a and thus the asset s return. Home nvestors j are beng compensated for more rsk than they bear ( ˆ a > ˆ j ). In other words, the home assets delver hgh rsk-adjusted returns. Hgh returns make a long 9 Part A of the Internet Appendx derves all portfolo expressons.

16 1202 The Journal of Fnance R poston optmal, on average. Both the magntude and the general equlbrum effect ncrease home bas. 10 IV. Brngng the Theory to Data A number of recent papers present alternatve explanatons for home bas. Some of these explanatons are behavoral: Huberman (2001) explores famlarty, Cohen (2009) explores loyalty, Morse and Shve (2008) propose patrotsm, whle Graham, Harvey, and Huang (2006) nvestgate overconfdence. Others argue, lke ths paper does, that home bas s the outcome of ratonal nvestor choce: Cole, Malath and Postlewate (2001) and DeMarzo, Kanel, and Kremer (2004) clam that nvestors have preference-based or market prce based ncentves to hold portfolos smlar to those of ther neghbors. At the same tme, an actve lterature attempts to dstngush between the varous theores by documentng facts related to the home bas. Whle each fact taken alone may be explaned by alternatve theores, t s dffcult to fnd one parsmonous theory that can explan a large set of facts. Rather than addng new facts, ths secton taps nto the exstng emprcal lterature and connects the theory to the evdence, qualtatvely and quanttatvely (Sectons A and B). It also reconcles exstng facts that appear to be at odds wth an nformaton explanaton (Secton C) and offers new predctons to gude future emprcal work (Secton D). A. Facts That Support Model Predctons A.1. Drect Evdence of Informaton Asymmetry Bae, Stulz, and Tan (2008) measure nformaton asymmetry and lnk t to home bas. They show that home analysts n 32 countres make more precse earnngs forecasts for home stocks than foregn analysts do. On average, the ncrease n precson s 8%. Furthermore, the sze of the home analyst advantage s related to home bas. When local analysts forecasts are more precse relatve to foregners forecasts (more nformaton asymmetry), foregn nvestors hold less of that country s assets. Guso and Jappell (2006) examne survey data on the tme that customers of a leadng Italan bank spend acqurng fnancal nformaton. Those who spend more tme on nformaton collecton hold portfolos that are less dversfed and earn sgnfcantly hgher returns. 10 It s possble that a hghly negatve sgnal realzaton on a home asset would make home nvestors who are nformed want to short that asset. Short sellng s unlkely to occur on a large scale n general equlbrum, however. The dramatc fall n prces from wdespread shortng would sgnal the bad news to foregn nvestors, makng them unwllng to take the opposte large long postons. Low prces would also make home nvestors more wllng to hold home assets, despte ther low payoffs.

17 Informaton Immoblty and the Home Bas Puzzle 1203 A.2. Local Bas Home bas s not just a country-level effect. Investors also favor local assets, headquartered near ther home, over frms n the same country located further away (Coval and Moskowtz (2001)). A unfed explanaton for home and local bas s somethng that many theores cannot provde. Ther coexstence makes an nformaton-based explanaton appealng. Malloy (2005) offers drect evdence that local analysts do n fact have nformaton advantages. He shows that local analysts forecasts better predct stock returns and that they earn abnormal returns on ther local assets. By gvng nvestors slghtly more precse ntal nformaton about local assets, ths model can explan the local bas. Suppose that home nvestors each had an advantage n only one home rsk factor, the one most concentrated n ther regon s asset. An nvestor j from regon m draws an ndependent pror belef µ j N(f, m ), where m = Ɣ m Ɣ and m has an mth dagonal entry that s lower than t s for nvestors from other regons. In ths model, local nvestors have an ncentve to learn more about ther local assets because of ther ntal nformaton advantage (Proposton 2). Local advantages also amplfy the effects of home advantages: When fewer nvestors share an advantage n the same local rsk, locals have a larger advantage relatve to the average nvestor (hgher ˆ a m / m j n the learnng ndex). A more specalzed advantage magnfes the optmal portfolo bas (E[Ɣ m q] = ˆ a m / m(ɣ j m x)). Because returns to specalzaton ncrease when nformaton advantages are more concentrated, nvestors dversfy less. We llustrate ths amplfcaton effect n Secton B. A.3. Industry Bas One source of pror nformaton advantage could be one s ndustry. If so, nvestors should renforce that nformaton asymmetry by learnng more about that ndustry and nvestng more n t. Massa and Smonov (2006) confrm ths predcton. They show that Swedsh nvestors buy assets closely related to ther nonfnancal ncome. Two facts make the authors conclude that the portfolo bas could be nformaton-drven. When an nvestor changes ndustres, hs holdngs of assets n that ndustry declne. More mportantly, famlartybased portfolos yeld hgher returns than dversfed ones. Another source of pror nformaton s one s classmates. Cohen, Frazzn, and Malloy (2007) fnd that fund managers overnvest n frms run by ther former classmates and make excess returns on those nvestments. Ths s consstent wth an ntal nformaton advantage acqured n school. A.4. Underdversfed Foregn Investment One feature of portfolo data that s dffcult to explan s the concentraton wthn the foregn component of home nvestors portfolos. The part of a portfolo nvested n any gven foregn country should therefore be dversfed. Kang and Stulz (1997) show that ths s not the case. Usng data on foregn nvestors

18 1204 The Journal of Fnance R n Japan, they show that foregners portfolos of Japanese assets overweght large frms and assets whose returns correlate hghly wth aggregate rsk. Ths pattern s consstent wth our model. Suppose than an Amercan nvestor chooses to learn about and nvest n Japanese assets. Holdng equal the average uncertanty ( ˆ a ), nose n prces ( p ), and Amercan pror uncertanty ( ) about each Japanese rsk, the most valuable rsk to reduce s the one wth the largest quantty (hghest Ɣ x n Proposton 2). In other words, the Amercan should learn about the largest rsk factors, aggregate macroeconomc rsk, and the rsks assocated wth the largest frms. Snce nvestors, on average, hold more of the assets they ve learned about, the model predcts that Amercans who hold Japanese assets wll not dversfy ther Japanese holdngs. Instead, they wll overweght large, hgh-beta frms. A.5. Portfolo Outperformance If transacton costs or behavoral bases are responsble for underdversfcaton, then concentrated portfolos should delver no addtonal proft. In contrast, f nvestors n our model concentrate ther portfolos, t s because they have nformatonal advantages. Ther concentrated portfolos should outperform dversfed ones. 11 There s emprcal evdence for such outperformance. Ivkovc, Salm, and Wesbenner (2008) fnd that concentrated nvestors outperform dversfed ones by as much as 3% per year. Out-performance s even hgher for nvestments n local stocks, where natural nformatonal asymmetres are most lkely to be present (see also Coval and Moskowtz (2001), Massa and Smonov (2006), and Ivkovc and Wesbenner (2005)). If fund managers have superor nformaton about stocks n partcular ndustres, they should outperform n these ndustres. Kacperczyk, Salm, and Zheng (2005) show that funds wth above-medan ndustry concentraton yeld an average return that s 1.1% per year hgher than those wth below-medan concentraton. The model also predcts that home nvestors should outperform foregn nvestors on home assets. Choe, Kho, and Stulz (2005) document home asset outperformance by Korean nvestors. Whle one mght thnk that ths s only true for ndvdual nvestors, Hau (2001) documents excess German asset returns for professonal traders n Germany. Smlarly, Shukla and van Inwegen (1995) document that U.S. mutual funds earn hgher returns on U.S. assets than U.K. funds do. Dvorak (2007) argues that Indonesan nvestors outperform foregners on Indonesan assets, even when that nvestment s ntermedated by a professonal. A.6. Cross-sectonal Asset Returns Investors want to learn nformaton others do not know because assets that many other nvestors learn about have hgh prces and low expected returns. 11 Part C of the Internet Appendx proves that concentrated portfolos acheve hgher expected returns. It also uses the theory to nterpret measures of portfolo rsk.

19 Informaton Immoblty and the Home Bas Puzzle 1205 Thus, a falsfable predcton of the model s ts negatve relatonshp between nformaton and expected returns. Three studes confrm ths predcton. Frst, Botosan (1997) and Easley, Hvdkjaer, and O Hara (2002) fnd that more publc nformaton lowers an asset s return. Second, Pástor, and Verones (2003) fnd that frms wth more abundant hstorcal data offer lower returns. Fnally, Greenstone, Oyer, and Vssng-Jorgenson (2006) analyze a mandatory dsclosure law that changed a group of frms from beng low-nformaton to hghnformaton. They fnd that between proposal and passage of the law, prces of the most affected frms rose, producng abnormal excess returns of 11% to 22%. After passage, excess returns dsappeared. Our model only speaks to the last example by way of a comparatve statc: Frms wth more publc nformaton have a lower ˆ a and hgher prces. It seems concevable that a dynamc extenson of the model could generate a slow nformaton dffuson process durng whch stock prces gradually ncrease. B. Quanttatve Evaluaton: Is Capacty Large Enough? A key unobserved varable n the model s the nvestor s capacty, whch regulates how much he can learn. Ths exercse nfers capacty from estmates of portfolo outperformance. The test s: Does ths nferred level of capacty delver observed home bas? Ths s a useful test because t tells us f home bas s ratonalzed by proft maxmzaton. Before proceedng, we frst explore how asset correlaton and local nformaton affect the optmal degree of home bas. Two countres have 1,000 dentcal nvestors each. The fve home and fve foregn assets are all uncorrelated. Foregners start out α tmes more uncertan about home rsks (1 + α) h = h, and home nvestors are α tmes more uncertan about foregn rsks f = (1 + α) f. We consder a 10% nformaton advantage (α = 0.1). Rsk averson s ρ = 2. The supply of each asset has mean x = 100 and standard devaton 10. Expected payoffs for home and foregn assets are equal and are equally spaced between one and two. The mean of the average nvestor s pror belef s the asset s true payoff. The standard devaton of pror belefs s between 15% to 30%, such that all assets have the same pror expected payoff to standard devaton rato. To explore varous levels of capacty, we transform K nto a more ntutve measure: K = 1 K 1/2 s how much an nvestor can reduce the standard devaton of one asset through learnng. Followng conventon, home bas s home bas = 1 1 share of home asset n home portfolo share of foregn assets n world portfolo. (11) In ths example, as n the data, the share of foregn assets n the world portfolo s 0.5. In a world where there s no ntal nformaton advantage and no learnng capacty, home bas s zero. We use an economy wth an ntal nformaton advantage but no learnng capacty as a benchmark. A 10% ntal nformaton advantage by tself generates a 5.3% home bas.