A Global Equilibrium Asset Pricing Model With Home Preference

7/28/2019 A Global Equilibrium Asset Pricing Model With Home Preference

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MANAGEMENT SCIENCEVol. 58, No. 2, February 2012, pp. 273292ISSN 0025-1909 (print) ISSN 1526-5501 (online) http://dx.doi.org/10.1287/mnsc.1110.1361

2012 INFORMS

A Global Equilibrium Asset Pricing Model with

Home PreferenceBruno Solnik

Department of Finance, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong; andHEC Paris, 78350 Jouy en Josas, France, [email protected]

Luo ZuoSloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142,

[email protected]

We develop a global equilibrium asset pricing model assuming that investors suffer from foreign aversion,a preference for home assets based on familiarity. Using a utility formulation inspired by regret theory,we derive closed-form solutions. When the degree of foreign aversion is high in a given country, investors placea high valuation on domestic equity, which results in a low expected return. Thus, the model generates the

simple prediction that a countrys degree of home bias and the expected return of its domestic assets shouldbe inversely related. Our predicted relation between the degree of home bias and a countrys expected returnhas the opposite sign predicted by models that assume some form of market segmentation. Using InternationalMonetary Fund portfolio data, we find that expected returns are negatively related to home bias.

Key words : international asset pricing; home bias; familiarity; regretHistory : Received July 14, 2010; accepted March 14, 2011, by Brad Barber, Teck Ho, and Terrance Odean,

special issue editors. Published online in Articles in Advance June 24, 2011.

1. IntroductionAlthough there are many intuitive explanations forthe observed equity home bias, a major questionis what equilibrium asset pricing would be consis-

tent with such explanations. In this paper, we pro-vide a global capital asset pricing model (CAPM)that assumes a behavioral preference for home assets.Our model relies on two building blocks: familiarityand regret. Investors preference for home assets issupported by the concept of familiarity (see Huber-man 2001). In the model, we assume that investorsexhibit both traditional risk aversion and a prefer-ence for home assets (foreign aversion) using a for-mulation of their utility function inspired by regrettheory (Loomes and Sugden 1982, Bell 1982). Undersome assumptions, we are able to derive closed-

form solutions for the global asset allocation decisionin an N-country setting. Foreign aversion capturesinvestors preferences toward home assets and leadsinvestors to underinvest in foreign stocks in orderto reduce the potential for regret, thereby creatinga home bias. This result is no surprise and is notthe papers contribution. To draw a parallel, tradi-tional risk aversion implies that investors require ahigher expected return on risky assets than they doon risk-free assets. But the contribution of the tradi-tional CAPM is to derive equilibrium risk premiums

and portfolio holdings. Analogously, we derive mar-ket equilibrium results by assuming that investors ofall countries exhibit both traditional risk aversion and(possibly different or null) foreign aversion, and we

discuss how foreign aversion influences equilibriumexpected returns and holdings.

A main contribution of our paper is a discussion ofthe equilibrium relationship between the magnitudeof home bias in each country and global asset pric-ing. Two conclusions of our equilibrium asset pricingmodel are worth stressing:

(1) When foreign aversion is high in some coun-tries (i.e., a strong home bias) and low in others(i.e., a low home bias), there are pricing implications.A country with high foreign aversion will have ahigher demand for its local equity, resulting in a lower

expected return. Thus, the expected return on a coun-trys equity should be inversely related to the extentof home bias in that country. In other words, coun-tries with (relatively) high home bias should exhibit(relatively) low equilibrium expected returns.

(2) If all investors have a similar level of foreignaversion worldwide, assets would be priced accord-ing to the traditional CAPM (in which only traditionalrisk is priced), even though the home bias in holdingsis significant. So foreign aversion can introduce largehome biases without any asset pricing differential.

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Solnik and Zuo: A Global Equilibrium Asset Pricing Model with Home Preference274 Management Science 58(2), pp. 273292, 2012 INFORMS

A key assumption in our model is the concavityof the foreign-aversion function (i.e., regret aversion).Familiarity could also lead to several other behavioral

biases, including relative optimism, perceived compe-tence, and keeping up with the Joneses. All these

behavioral biases would induce some bias in equityholdings. However, in many such behavioral mod-els, home bias in holdings is derived from marketimperfections or some differing views on return dis-tributions. In contrast, our model assumes that mar-kets are frictionless and that return expectations arehomogeneous. This behavioral trait (i.e., regret) is alsodifferent from the psychological force in Cao et al.(2011), where investors pessimistically evaluate port-folio choice alternatives that deviate from the domes-tic portfolio. Both approaches rely on the familiarityconcept. However, in their model, home bias derivesfrom investors pessimistic beliefs about foreign assets(some form of model uncertainty) rather than theshape of the utility function, as in our setting. In addi-tion, they only model a simple two-country case. Ourutility formulation provides a distinct way of model-ing home bias that is parsimonious and tractable.

The asset pricing model offers interesting empiricalinsights. Even if only a few investors exhibit foreignaversion, they will affect equilibrium, as their biascannot be arbitraged away by other investors. Actu-ally, it is sufficient that investors from a single coun-try be foreign averse to induce a home bias in everycountry. Because foreign aversion is likely to evolveslowly, it is not surprising to find a slow evolution ofhome bias despite the rapid market liberalization ofrecent years. Gordon Brown, global chief investmentofficer of Fidelity International, even believes that therecent financial crisis will lead to an increase in homepreference: First, [I] expect the financial world to

become more local. Investors will favor local, home-country stocks over international investments as emo-tion overrides reason. Home is where the heart isand we should expect investors to feel safer in theirown backyards for a while. They will feel most con-fident holding domestic stocks where their govern-ments will protect both them and their institutions(De Ramos 2008).

An alternative explanation to the observed equityhome bias is the existence of international investment

barriers and institutional controls that lead to nationalmarket segmentation. Segmented CAPMs also pos-tulate, by construction, a home bias, but their ratio-nal pricing implications are quite different from ours.As discussed below, they predict a positive relation

between the extent of home bias and country expectedreturns. In the empirical section of this paper, weoppose the two major explanations of home biasand their pricing implications: one based on investor

behavior (which affects their utility function) and onebased on market imperfections (segmentation). But

both factors (foreign aversion and investment barri-ers) can be at play simultaneously.

Our models implications are tested using detailedinformation on actual global portfolio holdingsreported by the International Monetary Fund (IMF)and segmentation ratings. The home bias ratio (see

the definition below and in Kho et al. 2009) appearsto be extensive and varies widely among countries.In a traditional CAPM, the home bias ratio should

be 0%; in a fully segmented world with no foreignholdings, it should be 100%. Among developed coun-tries, the average ratio is around 70%; it ranges from37% for the Netherlands to 93% for Greece. The home

bias ratio for the United States is close to the average.Home bias is much higher among emerging markets.

We try to test whether a preference-based or seg-mentation-based approach provides a better explana-tion of international asset pricing based on observedhome biases. We conduct both a simple cross-sectional

test and some dynamic difference-in-differences tests.In the cross-sectional test, we use the long-run meanreturn as a proxy for the expected return and findthat expected returns and home bias are negativelycorrelated, after controlling for world beta and mar-ket segmentation. In the difference-in-differences tests,we examine how changes in a countrys home biaslead to changes in its expected returns relative to theworld return. We find that an annual decrease in home

bias is associated with a lower realized return in thatyear, after controlling for changes in segmentation andchanges in expected cash flows (proxied by changes individend yields). This finding suggests that if a coun-

trys home bias decreases in a given year, its expectedreturn will increase, which is achieved by a decrease inits local stock price. Moreover, we find similar resultsafter taking into account the asset pricing implica-tions of home bias changes in other countries. Overall,the empirical tests seem to provide support for ourmodels predictions.

2. Related LiteratureTraditional international CAPMs have fairly straight-forward conclusions (see Solnik 1974, Adler andDumas 1983). In frictionless markets where agentshave traditional utility functions, every investorshould hold a combination of their risk-free asset andthe world market portfolio even in the presence ofcurrency risk. Every portfolio should include domes-tic and foreign equity in proportion to their marketcapitalization. Pricing is such that the risk premiumon assets hedged against currency risk is proportionalto their covariances with the world market portfo-lio; hence the diversification benefits of internationalassets are valued.

Contrary to the predictions of international CAPMs,it has been repeatedly claimed that investors do not


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Solnik and Zuo: A Global Equilibrium Asset Pricing Model with Home PreferenceManagement Science 58(2), pp. 273292, 2012 INFORMS 275

hold the world market portfolio and have a biastoward home equity. Numerous tentative explana-tions have been provided for the observed equityhome bias (see reviews in Strong and Xu 2003, Karolyiand Stulz 2003, Bekaert and Wang 2009), with the twomajor justifications being institutional and behavioral.

The institutional explanation relies on explicit barriersto international investments (regulations, investmentconstraints, transaction costs, differential taxes). The

behavioral explanation depends on investors prefer-ence for home assets based on some behavioral traits(familiarity, relative optimism, perceived competence,keeping up with the Joneses). Other explanationshave also been provided: asymmetry of information(where local investors have better information ontheir home markets than foreign investors do); private

benefits for domestic insiders; and hedging motives(inflation, currency, and human capital risks). Actu-ally, numerous authors have questioned whether non-

behavioral explanations could justify the extent of theobserved home bias. French and Poterba (1991) sug-gest that explanations for the home bias puzzle must

be behavioral, not institutional. For example, global-ization has removed many barriers to internationalinvestments, at least in developed markets. Informa-tion is now widely and rapidly disseminated, at leastfor large firms that make up the bulk of world marketcapitalization. Currency risk can be easily hedged.

Although there are intuitive explanations for theobserved home bias, a major question is what equi-librium asset pricing would be consistent with suchexplanations. CAPMs have been developed to model

some common forms of barriers to internationalinvestment. These international CAPMs assume par-tial or full international market segmentation (e.g.,Stulz 1981, Errunza and Losq 1985, Chaieb andErrunza 2007), and they imply, by construction, home

bias. But the interesting contribution of segmentedCAPMs is to develop the pricing implications. Errunzaand Losq (1985) focus on the impact of barriers to freecross-border portfolio flows and develop an interna-tional asset pricing model. They state that the secu-rities inaccessible to a subset of investors command asuper risk premium (Errunza and Losq 1985, p. 105).Their conclusion, that the expected return should be

higher in countries with high investment barriers (andhence a high home bias) is the opposite of ours. Theintuition of the segmented CAPMs is quite straight-forward; consider, for example, Germany, where for-eign investment in many major German corporations(so-called national champions) is restricted by variousregulations and rules. Shares in these national cham-pions must be held by local investors, even if they donot willingly wish to do so. In equilibrium, this canonly be induced by a higher expected return (lowerprice) relative to traditional CAPM pricing. Foreigners

would like to invest in those attractive (cheap) nationalchampions, but are restricted from doing so. Natu-rally, the fact that national champions must be held bynationals also creates a local home bias. Hence, thereis a positive relation between the expected return ona country and its home bias ratio. Most tests of seg-

mentation have focused on the type of segmentationwith restriction on investment by foreigners, typicallyin emerging markets,1 and the general finding has

been a positive premium for such segmented markets(see references in Chaieb and Errunza 2007).

The segmentation envisioned above is one in whichforeigners are restricted from investing in the homesecurity. But the segmentation feature could be theopposite, namely that home investors are legallyforced to invest at home, while foreigners can investanywhere. Were home investors, for segmentation rea-sons, forced to stay home, home securities could alsocarry a higher expected return. This may happen

because domestic investors cannot diversify away thespecific country risk in the same way that foreigninvestors can, and thus require a higher rate of returnon domestic securities than foreign investors do. Lauet al. (2010) detail this risk diversification argumentand state that both Models (8) and (11) imply thatinvestors with concentrated domestic asset holdingswould need to be compensated with higher returns, asthere is less global risk sharing between domestic andforeign investors. Therefore, a larger degree of home

bias would lead to a higher cost of capital (p. 194).Rather than relying on some institutional mar-

ket imperfections, we model investors preferences

toward home assets and propose a global equilib-rium asset pricing model that is inspired by regrettheory. Regret theory has been applied extensivelywithin the decision sciences field, but it has beenmore sparingly employed in the area of finance. Forexample, Braun and Muermann (2004) apply regrettheory to demand for insurance, Muermann et al.(2006) to asset allocation in defined contribution pen-sion schemes, Michenaud and Solnik (2008) to cur-rency hedging, and Engelbrecht-Wiggans and Katok(2008) to auctions. Reviews of experimental workon regret can be found in Michenaud and Solnik(2008) and Bleichrodt et al. (2010). We assume that

investors treat domestic and foreign assets differentlyand experience regret when their foreign investmentposition underperforms domestic assets (foreign aver-sion). Kahneman and Lovallo (1993) suggest that deci-sion makers are excessively prone to treat problems asunique. Rather than looking at the whole portfolio asprescribed by traditional utility theory, investors tend

1 Even in developed countries, the typical restriction protects strate-gic industries from foreign ownership; it does not limit foreigncapital flows.


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to put different types of investments in different men-tal compartments, layers (see Statman 1999), or nar-row frames (see Barberis and Huang 2009). Investorshave a core portfolio made of domestic stocks. For-eign stocks are assigned to an unfamiliar asset classseparate from domestic stocks; investors care about

not only their absolute return and risk characteristics,but also their performance relative to that of the coredomestic asset class. When foreign stocks underper-form domestic stocks, investors feel the pain of regretof having invested abroad.

Investors tendency to prefer home assets is in-spired by the well-known concept of familiarity (seeHuberman 2001). Ackert et al. (2005) find experi-mental evidence that investors perceive themselvesas more familiar with local securities and investmore in them. International evidence suggests thatinvestors tilt their portfolios toward those stocksthat are most closely related to them (see Grinblatt

and Keloharju 2001, Massa and Simonov 2006). Thefact that investors tend to prefer local stocks is alsotrue within a country where distance seems to mat-ter, as shown by Coval and Moskowitz (1999), andIvkovic and Weisbenner (2005).2 But the lack of famil-iarity is likely to be more pronounced for stocks froma remote foreign country, which may have a differentlanguage and different reporting methods.

Familiarity could also lead to other cognitive biasesthat result in home bias, including relative optimism,perceived competence, and keeping up with the

Joneses. However, all these models rely on hetero-geneous beliefs or market frictions that we do notimpose. Strong and Xu (2003) use survey data of fundmanagers views on prospects for international equitymarkets and find that fund managers show signifi-cant relative optimism toward their home equity mar-ket. The influence of perceived competence on inter-national investing is evidenced in Kilka and Weber(2000) and Graham et al. (2009): investors believe thatthey are more competent in investing domesticallythan abroad and therefore treat foreign assets differ-ently for fear of showing incompetence. External habitformation models (keeping up with the Joneses)assume a behavioral bias and some market imper-

fection that leads to a home bias. In their approach,agents have exogenous preferences to mimic the con-sumption of people in their community (e.g., coun-try) and therefore agents tend to mimic the portfoliochoices of those living in their country. As stressed

by Gollier (2004), relative consumption preferencesare not sufficient to induce home bias. Generally, theresulting equilibrium will imply that everyone holds

2 Seasholes and Zhu (2010) find that the preference for local stockscannot be explained by an informational advantage.

the world market portfolio; agents do mimic the port-folio held by other nationals, but that portfolio isthe world market portfolio. To induce home bias,some exogenously specified financial market imper-fection must be introduced. This approach requiresthe ad hoc feature of exogenously specifying some

arbitrary level of home bias (or market imperfection)for a category of investors, which we do not haveto do. Regret theory offers a general formulation ofthe utility function that leads to market equilibriumunder frictionless financial markets. We are able tocharacterize the properties of the equilibrium solely asa function of the levels of risk and foreign aversions,and market observables.

A paper related to ours is Cao et al. (2011). Theyuse Gilboa-Schmeidler preferences and model famil-iarity bias in which individuals pessimistically eval-uate choice alternatives against the status quo (i.e.,the focal choice option). In the context of internationalfinance, they argue that because domestic assets startout by being domestically held, domestic investorsview them as the status quo and are reluctant toshift away from this initial position. This argument,that domestic investors perceive the domestic portfo-lio as focal and use it as the benchmark, lends sup-port to the benchmark choice in our paper (i.e., thedomestic portfolio). The intuition is similar: the fearof the unfamiliar makes investors reluctant to deviatefrom domestic assets. Cao et al. (2011) also concludethat equilibrium stock prices reflect an unfamiliaritypremium. However, there are two important differ-

ences between their approach and ours. First, the keyassumption in their model is investors pessimistic

beliefs (some form of model uncertainty) rather thanthe shape of the utility function, as in our setting.In our model, we assume that investors have perfectknowledge about all moments of stock returns, andforeign aversion does not come from any uncertaintyabout parameters. Second and importantly, whereasCao et al. (2011) model a two-country case, our utilityformulation is able to derive closed-form solutions foran N-country case with a risk-free asset. This providesus with the opportunity to derive the asset pricing

implications by taking into account the cross-countryeffect of changes in home biases. Regret theory is aparsimonious reduced form with attractive proper-ties, as outlined below.

Although some might disagree that investors havea preference for home assets, it would be sufficientthat some, but not all, investors exhibit home prefer-ence to make our extended global CAPM interesting.The tests conducted in the later part of this articleprovide some empirical support for the main impli-cations of our model.


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3. A behavioral Model of GlobalAsset Allocation Choices

We propose an extended-utility approach, in whichwe incorporate home preference using a formula-tion derived from regret theory. Following Loomesand Sugden (1982) and Bell (1982), we assume that

investors reach an optimal asset allocation by max-imizing expected utility. But their expected utilitytakes into account their foreign aversion, in addi-tion to traditional risk aversion. Loomes and Sugden(1982) and Bell (1982) derive an extended utility func-tion of final wealth x resulting from a given invest-ment choice, knowing that a different investmentchoice would have led to a final wealth y:

Uxy = vx + fvx vy (1)

where Uxy is the extended utility of achieving x,knowing that y could have been achieved, and vxis the traditional von NeumannMorgenstern utilityfunction, also called value function or choiceless util-ity. This traditional value function is assumed to bemonotonically increasing and concave (risk aversion),and its expected value reflects the return and riskof the overall portfolio. The difference vx vyis the value loss/gain of having chosen an invest-ment that yields x rather than a forgone choice thatyields y. The regret function f is monotonicallyincreasing and concave, with f 0 = 0. Note thatthe argument of f can be positive if the choseninvestment has a better outcome than the alternative.

Rejoicing, as named by Loomes and Sugden (1982),is the additional pleasure of knowing, ex post, thatthe best decision has been selected. Concavity of theregret function, f < 0, implies regret aversion (hereforeign aversion). Investors are regret sensitive (for-eign averse) only if the function is concave, just likethey are risk averse if the value function v is con-cave. This extended utility is defined over the ex post(final) outcomes of investment choices; and rationalinvestors would make choices ex ante by maximizingtheir expected utility:

EUxy = Evx + Ef vx vy (2)

Loomes and Sugden (1982) and Bell (1982, 1983)conclude that this is a well-behaved parsimoniousfunctional form that is consistent with empiricallyobserved deviations from traditional expected utilitytheory (e.g., violations of transitivity). It is a simplefunctional form based on two functions: a traditionalutility plus a function that captures regret. Our modelof home preference is a rather simple application ofregret theory formulation. Although the mathematicalformulation of regret theory inspired our modeling of

home preference, we do not claim to provide a full-fledged regret-theoretic model. We adopt this formu-lation because it is well adapted for modeling homepreference and has attractive properties. We incor-porate a foreign-aversion function that compares thereturn on the chosen global asset allocation to the

return that would have been achieved with a portfo-lio fully invested in domestic assets. In Equation (2),x is the outcome of the chosen global allocation andy is the outcome of a purely domestic allocation.Investors are assumed to treat foreign assets as a sep-arate asset class and our model restricts regret to befelt only on the return achieved on this foreign assetclass relative to the core, or domestic, portfolio. Usingfamiliarity parlance, our regret function simply statesthat investors are reluctant to deviate from familiardomestic assets for fear of the unfamiliar. Rememberthat all choices are done ex ante, not after observingthe ex post outcome. Here, we assume that investors

decide ex ante on their optimal asset allocation (withoutcome x taking into account potential deviationsfrom a purely domestic choice (with outcome y. Ifinvestors had no foreign aversion, this additional util-ity term would not be present. Obviously, such aspecification will necessarily lead to home bias, butthe papers contribution is to derive the equilibriumasset pricing implications and the relation betweenthe extent of home bias and asset pricing.

In the model, we have N countries and one assetper country (the countrys market portfolio). In addi-tion, we have a common risk-free asset with return R0.This means that there is no foreign exchange risk inour model. Although not having stochastic exchangerates is an apparent limitation of the model, tradi-tional CAPMs with currency risks conclude that cur-rency risks do not affect optimal equity holdings

because of the availability of currency hedging (e.g.,Solnik 1974, Adler and Dumas 1983). That is, withcomplete tradability of currency risk, all investors willhold the world market portfolio (hedged against cur-rency risk) and there is no home bias. Hence, cur-rency risk cannot explain the home bias in traditionalCAPMs.3 We assume that markets are frictionless andthat return expectations are homogeneous. This is in

contrast with other explanations of home bias thatrely on some market frictions, such as restrictions onforeign ownership or differential taxes, or on somediffering views on return distribution, such as relativeoptimism or information asymmetries.

3 The assumption of the complete tradability of currency risk isnot fully verified in the real world. Some currencies, mostly insmaller emerging countries, lack easily available forward currencycontracts, so there could be some home bias due to currency risk.This is a potential limitation of both the traditional CAPM andour model.


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This is a two-period model. In each country, 1 to N,there is a representative/aggregate investor. Investorslocated in the country called country i allocate theirwealth to equity assets, with realized return R andto the risk-free asset with a return R0. Investors fromcountry i have a wealth Wi and allocate

Ti 1Wi to

equity assets, and 1

T

i 1Wi to the risk-free asset.Final wealth W1i is given by

W1i = Wi1 + 1 Ti 1R0 +

Ti R

= Wi + WiR0 +Ti R 1R0

= Wi1 + R0 + WiTi r (3)

where all vectors in bold are N1 column vectors:i is a column vector of investment weights in equity,1 is a column vector of ones, R is a column vector ofrealized return on equity, and r is a column vector ofexcess return on equity (R 1R0.

The value (traditional utility) of final wealth, canbe written explicitly as a function of i, the vectorof decision variables, and of the vector of stochasticvariables r: viWi

Ti r. The extended utility function

reflecting the foreign aversion of investors from coun-try i is written as

UiW1

i = viWiTi r + fi

viWi

Ti r viWid

Ti r

(4)

where di is a column vector with zeros everywhereexcept 1 in the ith location. The extended utilityfunction incorporates a foreign-aversion function thatcompares the return on the chosen global asset allo-cation to the return that would have been achieved

with a portfolio fully invested in domestic assets. Riskconsiderations are taken into account in the valuefunction, but in addition, investors may experienceregret from their decision to invest abroad. Concav-ity in the regret function assures foreign aversion.Here we assume that fully foreign-averse investorswould choose ex ante the domestic market portfolio.One could argue that fully foreign-averse investorswould choose a combination of the domestic marketportfolio and the risk-free asset. Because we have onerepresentative investor per country, the choice of thedomestic market portfolio seems natural and allowsus to derive the intuition of the influence of home

preference in a simpler manner. One could argue thatthe theory is cheap in the sense that it directly pos-tulates home preference. But the derivations are verycomplex and the major attraction is to obtain equi-librium holdings and pricing results that are testableand opposed to conclusions of other rational modelsof home bias. Actually, the same criticism could beleveled at the traditional CAPM, which simply pos-tulates risk aversion; but the attraction of the CAPMlies in the conclusions on equilibrium holdings andpricing.

4. Optimal Portfolio Allocation withHome Preference

Investors maximize their expected utility:

EUiW1

i = EviWiTi r

+ EfiviWi

Ti r viWid

Ti r

(5)

This is a well-behaved optimization problem,because EUi is concave with respect to i.

4 Toderive analytical allocation rules, we need to makespecific assumptions about the functions vi andfi , as well as the distribution of r. If fi is lin-ear, then the problem is reduced to a traditionalexpected utility maximization, as the maximizationwith respect to i of the expected utility given in (5)reduces to the maximization of EviWi

Ti r. In gen-

eral fi is assumed to be concave (foreign aversion).Except for very particular and simplistic functionsvi and fi , we cannot derive explicit allocationrules and would have to resort to numerical solu-tions with little generality. The problem already arisesin the traditional maximization of expected utility inportfolio theory, but there are some interesting caseswhere explicit rules can be worked out.5 In our model,the problem is compounded by the presence of a con-cave foreign-aversion function defined over a valuefunction. An ad hoc assumption that would make themodel a bit more tractable could be to model theforeign-aversion term as defined over payoffs, notthe valuation of payoffs. But this simplification wouldnot be consistent with regret theory and would cost us

the theoretical and empirical appeal of this approach.An interesting alternative is to use the two-momentapproximation proposed by Pratt (1964). We use aTaylor expansion of (4) and take its expected value,ignoring moments higher than two. We then max-imize with respect to i and are able to deriveexplicit asset allocation rules with interesting eco-nomic interpretations. This two-moment ArrowPrattapproximation is very similar in spirit and results tothe multivariate normality assumption for return dis-tributions introduced in the finance literature (or log-normality in the case of continuous-time models). In

both cases, we end up with models that rely solely

on the first two moments of return distributions. Inour model, the extended utility function is complexwith two attributes, risk and foreign aversions. TheArrowPratt approach allows us to derive explicit

4 Various derivations are provided in the online appendix tothis paper. The online appendix is available at http://papers.ssrn.com/abstract=1778662.5 When the utility function belongs to the HARA (hyperbolic abso-lute risk aversion) class and asset returns are multivariate normallydistributed, there is a linear relation between optimal portfolioweights and wealth level.


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equilibrium results that lend themselves to economicinterpretations.6

For a given allocation i, we develop the Taylorexpansion around zero for small price movements.We expand the value function vi around zero andthe regret function fi around zero. So the implicit

arguments are zero for all derivatives of vi

andfi . Let r = Er and = ErrT. The optimal equity

allocation by investors of country i is given by

i =

1 r

i 1 i + idi (6)

where i = Wivi /v

i is the traditional measure of

relative risk aversion, and the parameter i can beregarded as the normalized home preference. Fol-lowing Bell (1983), we define i = Wiv

if

i /1 + f

i

as the foreign-aversion parameter and i = i/i/1 + i/i as the measure of home preference. Itshould be remembered that the home preference

parameter is solely influenced by the ratio of for-eign aversion to risk aversion, not by foreign aver-sion per se. The home preference parameter i hasa value of zero in the absence of foreign aversion;the value ranges up to one when foreign aversiondominates risk aversion. In the traditional case wherethere is no foreign aversion, fi = 0 (or fi is lin-ear), the optimal allocation to stocks by a regret-freeinvestor reduces to 1r/i. This is the standardresult under the assumption of multivariate normality(mean-variance result). On the other hand, if foreignaversion is extremely large relative to risk aversion(i/i = , home investors will hold no foreign assets

(i = 1, full home bias).

5. Global Market EquilibriumWe now aggregate asset demands and equate them tosupplies (market capitalization). We assume that allrisk parameters are exogenous and study the expectedexcess return r resulting from market equilibrium.Because the focus of our analysis is on the role offoreign aversion, we make the simplifying assump-tion that investors from the N countries have thesame traditional risk aversion i ,

7 but differentforeign-aversion parameters i, and hence different

home preference parameters i.

6 Strictly speaking, the ArrowPratt approximation is valid forsmall risks. The quality of the two-moment approximation dependson the actual return distributions and the shape of the utilityfunction. This has been extensively discussed in the literature,see Samuelson (1970), and Levy and Markowitz (1979). We thankChristian Gollier for his assistance in giving us a clearer view ofthis approach.7 Without that assumption, the asset pricing relation would be

based on some weighted-average risk aversion, as is the case in thetraditional CAPM, which would complicate the notations without

bringing any original insight.

5.1. Asset Pricing RelationWe define

W =N

i=1

Wi and M=N

i=1

Mi

where W is total wealth, M is total market capitaliza-

tion, and Wi and Mi are the wealth and market capi-talization of each country; in equilibrium M= W. Thevector M is the column vector of market capitalizationweights with the ith element mi = Mi/M= Mi/W Wealso denote relative wealth as wi = Wi/W. We definethe world-average home preference:

W =1

W

N

i=1

Wii =N

i=1

wii

This is the world average of home preferencesweighted by the wealth of investors. We also wishto measure how the home preference of investors of

country i differs from the world average. We definerelative home preference i as

i =1

1 Wwii miW (7)

Note that the is are weighted by the size of thecountry and that they sum to zero. The relative homepreference of country i is equal to the sum of allforeign js with a minus sign: i =

j=i j. In the

case of zero net foreign investment, we have i =mii W/1 W. We define as the column vec-tor with i as the ith element. The global asset pricingrelation is

r = M (8)

where , the column vector of is, can be consid-ered as a pure arbitrage portfolio because the is sumto zero and the weights of the market portfolio sumto one.

Let RW =N

i=1 miRi and R =N

i=1 iRi. For coun-try i, we have

ERi R0 = covRi RW covRi R (9)

This is the main asset pricing relation of our CAPMwith home preference. In the absence of foreign aver-sion (i = i = 0, the asset pricing relation (9) yields a

familiar result:8

ERi R0 = covRi RW (10)

All assets are priced according to their covarianceswith the world market portfolio. Risk diversifica-tion benefits are priced. The traditional result sug-gests that, ceteris paribus, the lower the covariance

8 Note that MTr = rW = MTM MT = 2W covRW R.

In the absence of foreign aversion ( = 0, we obtain the usualCAPM pricing relation: ERi R0 = ERW R0covRi RW/

2W.


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of foreign assets with the world market portfolio, thelower the expected return. Foreign assets that offergood diversification benefits for home investors jus-tify a lower expected return. But foreign aversion canaffect expected returns. The first term of Equation (9)is the traditional asset pricing relation and the second

term can be viewed as a home preference premiumor home bias premium. Assume, for the time being,that investors in all countries have zero net foreigninvestments (their wealth equals the market value oftheir domestic assets, Wi = Mi), as doing so simplifiesthe intuition.

First, assume that all investors exhibit the samelevel of home preference. Therefore, investors can

be foreign averse (i = 0 but with similar homepreference across the world (i = 0. In this case,asset pricing relation is identical to that found in thetraditional case (no home bias premium). The con-clusion is that foreign aversion does not affect asset

pricing, although it does affect asset holdings (see fur-ther discussion below). This is an important result.Asset pricing is not affected by the home bias per se;it is only affected by differences in home preferenceacross countries. When investors from different coun-tries have the same level of home preference, no pric-ing adjustment is needed. Relative to the traditionalCAPM, the underinvestment in foreign assets bydomestic investors is matched by the home preferenceof foreign investors for their local assets. So foreignaversion can introduce large home biases without anyasset pricing differential. Only when home preferencediffers across countries does a home bias premium

enter international asset pricing. This insight is quitedifferent from CAPMs derived with some form of seg-mentation, where investment barriers and home biasnecessarily lead to pricing biases. For example, assetpricing models developed under the assumption oftotal or partial segmentation conclude that restrictedsecurities should have a higher expected return inequilibrium than nonrestricted securities.

Detailing the second term of (9), we get

covRi R =N

j=1

covRi jRj

= i covRi Ri +j=i

j covRj Ri (11)

Note that covRi R in (11) is an increasing func-tion of i, so the home bias premium of a country isa decreasing function of its i. If investors from thecountry i have a higher home preference than aver-age (i > 0, the expected return on that countrysequity is generally going to be lower than in the tra-ditional case (negative home bias premium or home

bias discount). Ceteris paribus, investors from a moreforeign-averse country have a stronger demand for

domestic equity and are therefore willing to accept alower expected return. Of course, this lower expectedreturn will make their equity market less attractiveto investors from the other countries; hence foreigninvestors (foreign to country i will have a lowerdemand for equity i and will exhibit some home bias

that accommodates the home bias of country i inequilibrium.The absolute magnitude of the home bias premium

also depends on the diversification benefits providedto home investors by the foreign assets. The lowerthe covariance of foreign assets with home assets,the higher is the absolute value of the home biaspremium. Underinvesting in foreign assets that offergood diversification benefits must be compensated

by a larger home bias premium/discount. Hence, itis more costly to underinvest in assets that provideattractive diversification benefits. But the sign (direc-tion) of the home bias premium is determined by rel-

ative home preference, as discussed above.This can be illustrated in the simple case where allmarkets have the same variance of returns 2 andsimilar cross-country correlation . Remembering thatthe sum of national relative preferences must be zero(

j j = 0, the home bias premium for stocks of coun-try i is given by

covRiR = i covRiRi+

j=i

jcovRjRi

= i2 +2

j=i

j= i21

The premium will be negative for a country witha higher home preference, and its absolute valuedepends on the differential in home preference andthe correlation between markets. If the correlation islow, the benefits of international diversification arelarge and a higher home bias premium/discount isrequired in equilibrium to compensate the loss of riskdiversification.

Hence, the stylized prediction is that countrieswith lower expected returns are those with a higherhome preference and lower covariances with othercountries. Looking at Equation (8) also reveals thatthe international asset pricing implications of rela-

tive home preference are equivalent to a correctionof the market capitalization of each country by thevector of relative home preferences. This is a strik-ingly simple and intuitive result that shows how therelevant (or corrected) global market capitalizationhas to be adjusted for asymmetries in home prefer-ence. The correction is theoretically given by the rel-ative foreign aversion and empirically by the relativehome bias.9

9 Because relative home preference effectively withdraws somedomestic market capitalization from the global equity market, its


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5.2. Equilibrium Holdings and Home BiasIn equilibrium, the asset allocation to equity for in-vestors of country i is given by

i =

1 r

i 1 i + idi = M 1 i + idi

For the home allocation of country i residents, de-noted by hi, we get

hi = mi i 1 i + i (12)

The usual measure of home bias is the home biasratio (HB), which is calculated as one minus the ratioof the weights of foreign stocks in the investors port-folio and in the world market portfolio (see Kho et al.2009). This ratio would be zero in the absence of home

bias and one if no foreign assets were held (full homebias). Some statistics about national home bias ratiosare given in the empirical section (see Table 1). In

the notations above, the home bias ratio for country iwould be equal to

HBi = 1 1 hi1 mi

=hi mi

1 mi

In equilibrium, the home bias ratio is equal to

HBi = i i1i

1mi= W +i W

i1i

1mi (13)

We first assume that home preference is identicalworldwide (i = 0 i. Then, the home bias is identi-cal in every country and equals the universal measureof home preference W. Note that all investors havea home bias, with a similar HB equal to WHBi =

HBW = W, but that asset pricing follows the tra-ditional CAPM formula (10). This is a striking con-clusion of this work: home bias is consistent withassets being priced solely for their risk diversifica-tion properties. However, differential home preferencesaffect both asset pricing, as shown above, and equi-librium holdings. The second term of (13) is i W:investors will have a higher home bias ratio than theworld average if their home preference is higher thanthe world average. This is a natural result: the higher

the home preference, the higher the home bias.The last term of (13) is i1 i/1 mi andcan be regarded as a pricing adjustment. A countrywith a high home preference i > W will have ahigh demand for local equity; but that demand must

global asset pricing implications are related to those of large globalindex revisions that also modify the amount of freely traded globalequity contributed by each country; see Hau (2010). The fact thatother cross-sectional studies on large-scale asset supply shocks findstrong evidence in favor of the CAPM model lends some supportto our paper.

be accommodated by foreign investors. In equilib-rium, this will lead to a lower expected return (rel-ative to traditional CAPM pricing) for local equity.This lower expected return induces foreign investorsto underinvest in that particular local market andaccommodate the lower demand for foreign assets

from local investors. It will also make foreign assetsmore attractive in terms of expected returns for localinvestors and reduce local home bias ratio (pricingadjustment). In equilibrium, the home bias of localinvestors has to be accommodated by an offsettinghome bias in the holdings of all the other investors,

but that accommodation is spread across all the othercountries. An interesting implication is that it is suf-ficient that investors of a single country be foreignaverse to induce a home bias in every country. Giventhat one country has a small market capitalization rel-ative to the rest of the world, the pricing adjustmentterm should generally be small compared to

i

W.

This pricing adjustment term can be written (assum-ing for simplicity that mi = wi as mi/1 mi 1 i/1 W i W. All countries havea smaller market capitalization than the rest of theworld. For example, Germanys weight in world mar-ket capitalization is approximately 3.3%; hence theratio mi/1 mi is around 0.034.

It might be useful to go back to the relative roles ofrisk aversion and foreign aversion. In the traditionalCAPM, national risk aversion would not affect thecomposition of the equity portfolios held by nation-als. Assume that the Japanese are more risk averse

than the Americans. Nevertheless, the Japanese willstill hold the world market portfolio as their portfolioof risky assets. The proportion of Japanese equity inthe equity portfolio is the same for the Japanese or theAmericans. Nor would the fact that the Japanese havehigher risk aversion induce a higher expected returnon Japanese stocks. The only issue that matters is thecovariance of Japanese stocks with the world marketportfolio. This conclusion is quite different for foreignaversion, as outlined above. It could be that for cul-tural reasons, the Japanese also exhibit high foreignaversion (risk and foreign aversion could be corre-

lated), but what is important is the ratio of foreignaversion to risk aversion.

To summarize, a higher local home preference willgenerally simultaneously induce a lower expectedreturn on the local market and a higher local home

bias ratio. There should be a negative relation betweenthe expected return on a country and its home biasratio. This result is the opposite of that under seg-mented CAPMs, where there is generally a positiverelation between the expected return on a country andits home bias ratio.


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6. Data Description

6.1. DataData on global portfolio holdings, used to computehome bias ratios, is scarce and patchy. The U.S. Trea-sury has published statistics on the foreign hold-ings of U.S. investors since 1994, but similar data

for most other countries is lacking. Fortunately, theIMF has started to publish an annual Coordinated Port-

folio Investment Survey (CPIS) in recent years. Thefirst CPIS, conducted in 1997, had only 29 membercountries participating. Since 2001, the CPIS has beenundertaken on an annual basis and covers most IMFmember countries. The CPIS calls for data on hold-ings of securities at year-end, and provides detailedstatistics on the geographical breakdown of foreignequity holdings per country of origin and per coun-try of investment. The CPIS data used here weremade available in July 2010 and cover nine years (theyear 1997 and the 20012008 period). We restrict our-selves to countries for which we have CPIS data, evenif the data may be incomplete for some years.

Similar to any survey data, the CPIS data havebuilt-in limitations: in terms of comprehensiveness,some countries, notably China, are not (yet) report-ing; India did not report until 2004. In addition, theCPISs annual frequency is considered to be too lowin real-world applications and financial research thatuses daily or monthly price data. Its late availability,with a generally 18-month publication lag, also lim-its its interest for many studies. And, as with mostglobal data, there are some oddities. Within the Euro-

pean Union (EU), Luxembourg is an attractive placeto base mutual funds that can be subscribed to by EUresidents. However, as stressed by Kho et al. (2009),Luxembourg is simply a conduit to invest in othercountries, not a final investment destination. Thus, weshould interpret the CPIS data for such offshore coun-tries with caution. Because we lump together all for-eign investments from (to) a country irrespective ofdestination (origin), this indirect method of investingabroad through an offshore center poses fewer prob-lems to our study. We use CPIS data in our study

because it is the most detailed data source for analyz-ing equity home bias in a global context.10

We use total-return stock market indices from Mor-gan Stanley Capital International (MSCI) and its clas-sification of developed and emerging markets as of2008. MSCI calculates country indices since Decem-

ber 1969 for developed markets and since December

10 One possible alternative is to use information on mutual fundholdings available from Thomson-Reuters (e.g., Lau et al. 2010).However, measures based on such data also suffer from problems:(1) portfolio holdings of other domestic investors (i.e., individualand other institutional investors) are omitted; and (2) some foreigninvestors also hold domestic mutual funds.

1987 for emerging markets. As of 2008, MSCI cov-ers 23 developed markets and 25 emerging markets.Although CPIS covers all 23 of these developed mar-kets, we exclude Ireland and Hong Kong. Similar toLuxembourg, they are offshore countries that are thelisting bases for numerous foreign funds or securities

that are reported as domestic assets. The number ofemerging countries that we can use in this empiricalanalysis is limited by data availability; CPIS has nodata on China, Jordan, Morocco, Peru, and Taiwan.We end up with 21 developed markets and 20 emerg-ing markets, listed in Table 1. The panel of developedmarkets represents around 96% of the total marketcapitalization of all developed markets. The percent-age is smaller for emerging markets because of theexclusion of China.

A typical segmented CAPM suggests that coun-tries with high levels of segmentation should havehigher expected returns (lower stock prices). If the

home bias is caused by investment constraints ratherthan preferences, then the result would be the oppo-site of what we claimed earlier. Therefore, we wishto add a segmentation variable to control for seg-mentation. Consistent measures of investment con-straints do not abound across all countries. We usethe extent of national capital controls as a proxy forrelative segmentation. Each year, the IMF reports onup to 13 different types of international capital con-trols in its Annual Report on Exchange Arrangements andExchange Restrictions. These controls include restric-tions with respect to both inward and outward cap-ital flows or the holding of assets at home by non-

residents and abroad by residents. For each type ofcapital control, the IMF reports whether or not it islevied. The 010 rating used in this paper (i.e., Seg)is the percentage of capital controls levied as a shareof the total number of capital controls listed multi-plied by 10. This approach is used by the EconomicFreedom Network.11

Two data limitations need to be addressed: First,despite the fact that these 13 capital controls include

both forms of restrictions, namely, barriers to (i.e.,preventing foreigners from coming in) and barriersfrom (i.e., preventing domestic investment fromflowing abroad), we are not able to separate them. For

example, when assessing controls on direct invest-ment, the IMF refers to investment for the purposeof establishing lasting economic relations both abroad

11 The Economic Freedom Network (http://www.freetheworld.com)constructs a similar rating, where the 010 rating is the percentageof capital controls not levied as a share of the total number of cap-ital controls listed multiplied by 10. Hence, their rating is simplyequal to 10 minus our rating. Our segmentation rating increaseswith the level of segmentation; theirs decreases. We are grateful toRobert A. Lawson of the Economic Freedom Network for helpingus get this data.


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Table 1 Country-Level Statistics for Developed Markets and Emerging Markets

Developed markets Emerging markets

Country Market cap HB(%) Country Market cap HB(%)

Australia 749947 8141 Argentina 40159 7972

Austria 105156 5128 Brazil 501394 9879

Belgium 247353 4745 Chile 120775 8482

Canada 1206351 7136 Colombia 44843 9708

Denmark 159223 5955 Czech Republic 48000 8668

Finland 220515 6414 Egypt 64287 9850

France 1676673 7002 Hungary 26212 8741

Germany 1263225 5632 India 844916 9994

Greece 135468 9254 Indonesia 88968 9977

Italy 728518 5698 Israel 110642 9180

Japan 3434787 8711 Malaysia 189387 9789

Netherlands 588375 3720 Mexico 252288 9846

New Zealand 34167 6016 Pakistan 34655 9953

Norway 168152 4886 Philippines 44196 9953

Portugal 73815 6255 Poland 88975 9742

Singapore 253849 6925 Russia 388736 9973

Spain 951124 8693 South Africa 434449 8543

Sweden 381281 5841 South Korea 530516 9520

Switzerland 878151 5913 Thailand 110008 9885United Kingdom 2739821 6220 Turkey 122110 9990

United States 15498837 7169

Mean (equally weighted) 6450 9482

Mean (market-cap-weighted) 7057 9618

SD 1403 637

Notes. This table reports the average country-level statistics for the 21 developed markets and the 20 emerging

markets over the 20012008 period. The market capitalization data are in millions of U.S. dollars, as reported by

the World Federation of Exchanges.

by residents and in the country by nonresidents (asin the Compilation Guide of the IMF annual reports).Thus, if either restriction is levied by one country, the

IMF will report the existence of this type of controlin that country. As a result, the segmentation ratingconstructed in this paper measures the joint effect of

both forms of restrictions. Second, this rating may notfully capture the extent of market segmentation as itis solely based on the 13 capital transactions inves-tigated by the IMF. However imperfect such a rat-ing may be, we expect it to be positively correlatedwith other forms of market segmentation that it doesnot directly measure, and thus we use it as a con-trol variable in our empirical tests. To the extent thatour segmentation control is imperfect, it will maketesting implications of our preference-based model

more difficult as the two concepts, segmentation andpreferences, lead to opposite signs in the pricing rela-tion. If home bias only captures the effect of invest-ment constraints (rather than home preference), wewould expect the data to reject the implications ofour model. Most developed countries have relaxed oreliminated restrictions on foreign investments by itsresidents. However, such restrictions are still preva-lent in emerging countries. Therefore, being an emerg-ing market is in itself an indicator of segmentation.We will focus on the panel of developed markets

to minimize the potential segmentation effects, whilealso reporting results for the panel of emerging mar-kets and the joint panel.

6.2. Home Bias RatioWe use the extent of national home bias as a proxy forrelative foreign aversion. As mentioned previously,the usual measure of home bias is the home bias ratiocalculated as one minus the ratio of the weights offoreign stocks in the investors portfolio and in theworld market portfolio (see Kho et al. 2009). It is alsothe natural ratio to use given our theoretical results.This ratio would be zero in the absence of home

bias and one if no foreign assets were held (i.e., totalhome bias).

We compute the home bias ratio using CPIS portfo-

lio holdings data as well as data on stock market cap-italization from the World Federation of Exchanges(WFE), Euronext, the OMX Nordic Exchange, and theS&P Emerging Markets Database. All data are in U.S.dollars and at year-end. CPIS provides detailed statis-tics on the total foreign investment from country iFi and the amount of foreign investment to coun-try i from investors of all other countries (EFi. Wedo not have a direct measure of the total (domesticplus foreign) portfolio holdings of investors of coun-try i, but we can infer it by taking the national market


12/20


cap (Mi, adding foreign investments from country iFi and subtracting foreign investments to country iEFi Wi = Mi + Fi EFi. We can now compute thehome bias ratio (HB) as

HB = 1 % foreign portfolio investment

% foreign market cap

= 1 Fi/Wi

W Mi/W

There are two related measures of home bias devel-oped in the literature.12 The first one (HB1) is usedin Fontaine et al. (2010) and Morse and Shive (2011).It is computed as HB1 = Mi EFi/Wi Mi/W =W Mi/W Fi/Wi.

Our home bias ratio can be viewed as a normalizedversion of this HB1:

HB = 1 Fi/Wi

W Mi/W=

W Mi/W Fi/WiW Mi/W

=HB1

W Mi/W=

HB1

1 mi

We think that this normalization makes sense becauseit takes into account the scale of the market underconsideration. For the same HB, large countries havea lower HB1 than small countries. In our data, theUnited States has a HB1 of 41%, which is lower thanmost developed markets simply because of its size,although few would argue that U.S. investors havea much smaller home bias than others. In any case,the two measures are closely related and highly cor-

related in our sample (=

097).The second measure (HB2) is used in Lau et al.(2010). It is calculated based on domestic holdings:

HB2 =Mi EFi/Wi

Mi/W=

Wi Fi/WiMi/W

= 1 HB +HB

mi

According to this measure, size (per mi will stronglyaffect the measured home bias. For example, assumecountries where nationals hold no foreign assets.These countries have a full home bias, and HB will be100%. However, in such cases, HB2 is totally driven

by market size. For a large country with a market capmi = 40%, we get HB2 = 25; but for a small country

with mi = 005% we get HB2 = 2000, even though nei-ther country holds any foreign assets and both can beregarded as fully home biased. Similar strange con-clusions would arise with a home bias of 50%. A bigcountry would look much less home biased than asmall one. A log transformation, as performed in Lauet al. (2010), does not change the size bias; it simplyreduces the scaling a bit. Therefore, the effect picked

12 An earlier discussion of various measures and the importance ofsize bias can be found in Bekaert and Wang (2009).

up by HB2 is mainly a country-size effect and nothome bias per se. For example, based on our ratio HB,Switzerland has less home bias than the United States;whereas based on the other ratio, the United Statesis the least biased country in the world, with logHB2equal to 0.7, compared to 3.3 for Switzerland. This

seems implausible. LogHB2 has a weak correlationwith HB ( = 044) and a strong negative correlationwith market cap ( = 061).

For our panel of the 21 developed markets, wehave home bias ratios for all years from 2001 to2008, but are missing 1997 data for Germany, Greece,and Switzerland. Among our panel of the 20 emerg-ing markets, only seven countries reported in 1997.Although most countries started to report in 2001,Pakistan waited until 2002, Mexico until 2003, andIndia until 2004.

As an illustration, Figure 1 plots the average foreignmarket capitalization, foreign holdings, and home

bias ratios for the 21 developed markets over the20012008 period. The first bar gives estimates of theratio of foreign to investors total equity holdings.Foreign holdings in Figure 1 are not limited to thosein the other 20 countries, but include all foreign equityinvestments. The second bar indicates the ratio offoreign to world market capitalization for all coun-tries. For example, non-U.S. equity markets representsome 58% of world market capitalization, but U.S.investors only hold an average of some 16% in for-eign stocks in their equity portfolios. The home biasratio (HB) is the third piece of information reportedin Figure 1. The HB for U.S. investors over this period

is 1 16/58 = 72%.Equity home bias is not only prevalent in the

United States; investors from all countries exhibit alarge home bias. It is often argued in the media thatU.S. investors exhibit a very large home bias, imply-ing that home bias is smaller for other countries.In fact, the share of foreign stocks held by non-U.S.investors in their equity portfolio tends to be largerthan it is for U.S. investors, but their domestic equitymarket is much smaller, so the capitalization weightof foreign stocks from their local perspective is muchhigher. For example, British investors hold 35% oftheir equity portfolio in foreign stocks, whereas the

capitalization weight of foreign stocks from a Britishperspective is 93%. The HB for British investors is62%. It ranges from 37% for Dutch investors to 93%for Greek investors.

Table 1 reports the average HB by country overthe 20012008 period. For developed markets, themean HB is 65% with equal weighting and 71% withmarket-cap weighting; its standard deviation is 14%.The United States has a HB close to the average. Thehome bias is much larger for emerging markets thanit is for developed markets. Emerging markets have a


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Figure 1 Ratio of Foreign Equity Holdings to Total Equity Holdings per Nationality of Investor

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Australia

Austria

Belgium

Canada

Denmark

Finland

France

Germany

Greece

Italy

Japan

Netherlands

New

Zealand

Norway

Portugal

Singapore

Spain

Sweden

Switzerland

UnitedKingdom

UnitedStates

Foreign market cap Foreign holdings Home bias ratio

Notes. This figure plots the average foreign market capitalization, foreign holdings, and home bias ratios for the 21 developed markets over the 20012008

period. For investors from each country, the first bar gives the ratio of foreign to world market capitalization as reported by the World Federation of Exchanges.

The second bar gives the ratio of foreign to total equity holdings of national investors calculated using the data reported by the IMF in their CPIS database for

the same period. The third bar gives the home bias ratio (which would be zero if foreign holdings were in proportion to world market capitalization).

mean HB of 95% with equal weighting and 96% withmarket-cap weighting; its standard deviation is 6%.There is little doubt that investment restrictions playa significant role among most emerging markets.

It would be expected that HB gets reduced overtime. We plot the (simple) mean home bias ratiosover time from 1997 to 2008 in Figure 2. We computethe average HB separately for developed markets and

Figure 2 Home Bias Trend

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1990 1996 2000 2002 2004 2006 2008 2010

Developed market

Emerging market

Note. This figure plots the (simple) mean home bias ratios over time from

1997 to 2008, both for developed markets (denoted by diamonds) and for

emerging markets (denoted by squares).

emerging markets. As we can see in the figure, thehome bias ratio tends to decrease over time, especiallyfor the 21 developed markets. For these markets, the

(simple) average HB decreases from 81% in 1997 to55% in 2008. For emerging markets, the reduction in

HB over time is small; the average HB decreases from96% in 1997 to 92% in 2008.

Table 2 reports the summary statistics on the HBchanges (HB). First, we can see that most of thereduction in home bias comes between 1997 and 2001(12.80% for developed markets, and 0.57% foremerging markets). In 2001, all developed countriesexhibit a decrease in home bias from 1997, rangingfrom 34.45% for Austria to 2.57% for the UnitedStates. We also find that the mean and median ofHB are almost always negative, suggesting a general

trend of decreasing home bias. There is also hetero-geneity across countries within a given year: withineach year from 2002 to 2008, there are always coun-tries whose home bias decreases and countries whosehome bias increases simultaneously, though the mag-nitudes of home bias increases are generally rela-tively small.

7. TestsOur first test is a crude cross-sectional regression

between a proxy for expected return and home bias


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Table 2 Summary Statistics on Changes in Home Bias ( HB)

Year Obs. Mean Median SD Min Max

Panel A: Summary statistics on changes in home biasfor developed markets

2001 18 1280 1128 886 3445 257

2002 21 237 191 446 1022 881

2003 21 021 064 298 935 3192004 21 024 045 322 515 762

2005 21 158 143 393 1224 637

2006 21 093 088 281 734 377

2007 21 146 210 378 796 963

2008 21 728 579 873 3769 187

Panel B: Summary statistics on changes in home biasfor emerging markets

2001 7 057 050 280 637 175

2002 17 053 024 363 1266 653

2003 18 150 005 394 254 1235

2004 19 008 005 166 375 432

2005 20 056 005 128 295 091

2006 20 118 029 240 876 182

2007 20 096 011 178 537 091

2008 20 112 018 349 1166 482

Notes. This table reports the summary statistics on HBchanges (HB) over

the years from 1997 to 2008, both for developed markets (in panel A) and for

emerging markets (in panel B). Note that for 2001, the number represents the

change from 1997 to 2001. For subsequent years, the numbers are annual

changes. The home bias ratio (HB) is in percents.

ratio, using world beta and segmentation rating ascontrol variables. With limited time-series data avail-able on home bias and a small number of countries,we cannot perform sophisticated conditional tests. Forthe home bias ratio, we only have eight annual obser-vations from 2001 to 2008, and one additional obser-vation for 1997 with some missing countries. Hence,we cannot perform a FamaMcBeth methodology orother conditional tests. We are well aware of the lim-itations of unconditional tests where we use simpleproxies for expected returns and risk variables, butcannot find alternatives. Despite its limitations, thistest is presented for illustrative purposes and for com-parison with past research. In our second test, we usea difference-in-differences approach and examine howchanges in home bias of a country lead to changes inits expected returns relative to the world return.

7.1. Cross-Sectional TestsWe estimate the cross-sectional regression:

MeanRetit = a+b Betait +c HBit +d Segit +it (14)

In our unconditional test, a natural proxy forexpected return is the mean return over a very longtime period. As Lundblad (2007, p. 146) suggests, alarge data span is required to reliably detect the riskreturn tradeoff. Thus, we cannot use our full countrypanel because MSCI only starts to cover some marketsin the mid-1990s. MSCIs starting date for emerging

markets is 1987, and so we focus on the 17 classi-cal developed markets13 and 11 emerging markets14

for which we have MSCI stock index data from thatdate. We will use our full panel for the difference-in-differences tests that do not require a proxy forexpected returns. We compute the average return in

dollars over the whole period (from December 1987to December 2008) for all markets as well as theirworld beta. We have data on portfolio holdings fornine years and hence the HB data from various years.

One option could be to simply use the home biasratio estimated for one single year (e.g., the last year,2008). But estimates for any single year are subject tospecific events taking place in that market, as well assampling errors. To minimize this problem, we usea panel econometric method that includes all years.Table 3 reports estimates of Equation (14) using yearfixed effects and robust standard errors. It is a crudeand dirty test but one that allows the estimation of

the magnitude of the effect and comparison with tra-ditional CAPM tests.

We control for segmentation as it can partly explainthe observed home bias. Within developed markets,the correlation between HB and Seg using all yearlyobservations is 0.20. Within emerging markets, thecorrelation between HB and Seg is higher and equalto 0.54. If we pool developed markets and emerg-ing markets together, the correlation increases to 0.70.This can be explained by the very different charac-teristics of developed markets and emerging marketsas shown in Table 1: developed markets tend to havea much lower home bias than emerging markets, so

we are pooling together two different types of coun-tries. The crude correlation estimates suggest that seg-mentation partly explains the observed home bias.However, the correlation is still low, especially amongdeveloped markets, and there can be other explana-tions for the observed home bias, such as investorspreferences, as described in our model. It is also pos-sible that Seg is a noisy and imperfect measure ofsegmentation and HB may pick up the true segmen-tation. However, in that case, we would expect a pos-itive relation between HB and MeanRet, which is theopposite of our prediction.

13 The 17 developed markets have been covered by MSCI since itsinception in 1969. They represent about 95% of the total marketcapitalization of all developed markets. The four developed mar-kets not covered are Finland, Greece, New Zealand, and Portugal.14 The 11 emerging markets are Argentina, Brazil, Chile, India,Indonesia, Malaysia, Mexico, the Philippines, South Korea,Thailand, and Turkey. For India, we only have MSCI index datasince 1992. Nevertheless, we keep India because it has been consid-ered a classical emerging market and has been covered by the S&PEmerging Market Indices since their inception in 1975. For India,we chain link the MSCI index data from 1992 with S&P/IFCG(Global) index data from 1987 to 1992.


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Table 3 Cross-Sectional Relation of Mean Country Returns and

Home Bias

(1) (2) (3)

Beta 00013 00099 00012

134 400 123

HB 00099 00429 00088

503 364 433Seg 00005 00003 00004

473 057 320

EM 00369

433

EM Beta 00087

332

EM HB 00337

292

EM Seg 00007

152

Constant 00146 00512 00142

881 588 855

Obs. 151 89 240

Adjusted R2 (%) 20.9 18.8 52.0

Notes. This table reports the results for the regression (14). Column (1)

presents the results for the 17 developed markets, column (2) presents the

results for the 11 emerging markets, and column (3) presents the results

for the joint panel. We use the average monthly return over the period from

December 1987 to December 2008 as a proxy for expected return (Mean-

Ret), and compute their world beta (Beta) over that period. HB is the home

bias ratio and Seg is the segmentation rating. EM is a dummy variable that

equals one for emerging markets. All tests are unconditional using year fixed

effects and robust standard errors. The t-statistics are reported in parenthe-

ses below the coefficients., , and denote significance at the 10%, 5%, and 1% levels,

respectively.

We use the three distinct panels described above:the 17 developed markets, the 11 emerging mar-kets, and the joint panel of developed markets andemerging markets. Column (1) of Table 3 gives theresults for developed markets where the assumptionof frictionless markets is more likely to be valid. Allcoefficients have the expected sign. World beta andsegmentation are positively linked to expected return(as expected in segmented CAPM) and HB is nega-tively linked to expected return (as expected in ourpreference-based CAPM). The constant is a monthlyexpected return of 1.46%. The estimated world mar-ket risk premium equals 0.13% per month (approxi-mately 2% per year), but the t-statistic is low, whichis not surprising given the results of past uncondi-tional tests of global CAPM. The home bias premiumis a monthly 0.99%. It is negative, as implied by ourmodel, and statistically significant at the 1% level. Thecoefficient on segmentation ratings (Seg) is 0.05% andsignificant at the 1% level. Despite the positive corre-lation between the segmentation variable and the HBreported above, the two variables enter with oppositesigns in the regression, suggesting that the HB cap-tures more than segmentation effects. In untabulated

results, when we include either HB or Seg separatelyin the regression, each of them has the expected sign:the coefficient for HB is 0.79% and significant at the1% level; and the coefficient for Seg is 0.02% and sig-nificant at the 5% level.

The next column reports the results for emerging

markets. Our model fares quite well and the extentof home bias still has a negative influence on meanreturn (4.29%, significant at 1%). However, the seg-mentation variable shows up with a slightly nega-tive but statistically insignificant coefficient (0.03%,with t-statistic 0.57). This is a bit surprising. Thethird column reports the results when we include

both developed and emerging markets. Because of thevery different nature of the two types of market, weadd a dummy variable for emerging markets (EM),and its interaction with Beta, HB, and Seg. In essence,these coefficients test the differences in coefficients

between columns (1) and (2). The emerging markets

dummy has a positive coefficient of 3.69%; hence(segmented) emerging markets have higher returnsthan developed markets. It could be that our proxyvariable for segmentation is imperfect and that otherforms of segmentations are picked up by the emerg-ing markets dummy. As mentioned above, it couldmean that being classified as an emerging market is

by itself a good indicator of high investment con-straints and hence segmentation (not picked up byour IMF rating). Other omitted variables (e.g., eco-nomic growth and improved political climate) couldalso explain the importance of this emerging mar-kets dummy. The interaction term of EM with HB is

negative and significant (3.37%, significant at 1%),lending some support to our preference-based impli-cation, even for emerging markets. As expected, the

HB still has a negative coefficient (0.88%, signifi-cant at 1%): the higher the home bias, the lower theexpected return.

In a robustness check, we conduct tests basedonly on past available information for each observa-tion period. Although it is arbitrary, we assume thatexpected returns are measured using all past avail-able information and that world betas are measuredusing the past 10 years of data (120 monthly obser-vations). For example, we use the 2001 HB, the mean

return over 19872001, and the world beta computedover 19922001. Results (untabulated) are fairly simi-lar and lend support to the predictions of our model.

7.2. Difference-in-Differences TestsBecause we have consecutive annual observations forthe HB from 2001 to 2008, we can design dynamicdifference-in-differences tests where we examine howchanges in a countrys HB lead to changes in itsexpected returns relative to the world return. Oneappealing econometric advantage of this difference-in-differences approach is that we can eliminate all


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country-level fixed effects, which should substantiallyreduce the omitted-variable problem. Furthermore,we do not have to rely on a crude proxy for expectedreturn. We first present a difference-in-differences testin which only changes in home bias of the home coun-try are considered, and then a more sophisticated test

in which both own-country and cross-country effectsare considered.Because of the discontinuity of the HB data, we

exclude the 1997 observation.15 We end up with,at most, seven annual observations for the changein HB. With only seven annual returns, we cannotdevelop a full-fledged asset pricing methodology la FamaFrench. Nevertheless we can conduct somedifference-in-differences tests. If the HB of a countrydecreases in a given year, our asset pricing model sug-gests that its expected return should increase. Ceterisparibus, this would be achieved by a decrease inthe local stock price. Of course, everything is rela-

tive to the world return. So an annual decrease in HBshould be associated with a negative relative returnin that year. Because the annual excess return of acountry also captures its cash-flow news, we shouldeither control for expected cash flow changes directly,or decompose stock returns into a cash-flow compo-nent and an expected-return component and look atthe latter. In our regression, we control for expectedcash-flow changes by using the dividend yield change(relative to that in the world index) as a proxy. Thedividend yield data are deduced directly from thecum and ex dividend MSCI indices. We could imple-ment a vector autoregressive system to do the return

decomposition. However, with a few annual stockreturns, the estimated parameters are quite noisy.Nevertheless, with monthly data, previous researchfinds that expected-return news causes much morevariation in stock returns than does cash-flow news(e.g., Campbell 1991). Thus, if we find an association

between the annual excess return of a country and thechange in its HB, it is likely to be caused by expected-return innovations, instead of cash-flow innovations.

7.2.1. Test I. The first series of tests is con-ducted by simply extending the previous economet-ric methodology to a dynamic setting. We regress theannual excess return of a country over the world

index (denoted by ExRet) on the change in the coun-trys HB (denoted by HB), controlling for the changein Seg (denoted by Seg) and the change in dividendyields (denoted by Dividend):

ExRetit = a + b HBit + c Segit

+ d Dividendit + it (15)

15 When we include the data of 1997 and define the change in HBin 2001 as the difference between HB in 2001 and HB in 1997, wefind similar results (untabulated).

We use year fixed effects and Rogers standard errorswith country clustering. The use of year fixed effectsand country clustering is logically dictated by ourdata set. Results are reported in columns (1)(3) inTable 4. Recall that our major panel is the 21 developedmarkets where the assumption of frictionless markets

is more likely to be valid. Column (1) of Table 4 reportsthe results for the developed markets. We find a strongpositive association between annual relative returnand the change inHB. The regression coefficient equals1.22 and is statistically significant at the 1% level. Thissuggests that a 1% change in the home bias ratio isassociated with approximately a 1.22% annual relativereturn in that country. We also find a negative associa-tion between annual relative return and the change inSeg (0.015, with t-statistic 1.42), which is consistentwith the explanation that a lower price is needed toinduce local investors to hold stocks in a country thatimposes more capital controls. The opposite signs of

the coefficients on HB and Seg suggest thatHB cap-tures more than segmentation effects. Consistent withthe existing literature, the coefficient on Dividend ispositive (8.69) and significant at the 1% level.

The next column reports the results for the20 emerging markets. Again, we find a relativelystrong positive association between annual relativereturn and the change in HB (1.48, significant at 10%).However, the R2 (4.1%) is much lower comparedwith that associated with developed markets (28.5%).We find similar results in the joint panel where weinclude both developed markets and emerging mar-kets. In particular, we find a positive coefficient for

HB (1.46, significant at 1%), a negative coefficientfor Seg (0.034, significant at 5%), and a positivecoefficient for Dividend (2.99, significant at 10%).

A potential concern with this simple difference-in-differences test is that an excess realized return caused

by some omitted factor could lead to a mechani-cal adjustment to HB (own-price pressure effect)if investors do not rebalance their portfolio accord-ingly, for example, because of investment constraintsor other factors/motivations. Changes in dividendyield partly controls for other factors and will pickup some mechanic effect of price adjustment (short-term changes in dividend yield is strongly influenced

by price movements as dividends are fairly stable).16

16 In addition, we include some technical control variables and findsimilar results (untabulated). We define Outflowsi = Fi/EFi. Consideran exogenous shock (not endogenous as in our model) in the formof a drop of domestic stock prices relative to other markets. With-out a voluntary rebalancing of portfolio holdings, Outflows shouldincrease. That is because foreign holdings by domestic residents arenot affected by this domestic market drop, whereas foreign hold-ings of domestic securities are affected. This price adjustment ispurely technical and changes in Outflows can be used to control forsuch mechanical price pressure effect. Our results are robust aftercontrolling for changes in outflows.


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Table 4 Cross-Sectional Relation of Annual Country Excess Returns and Changes in Home Bias

(1) (2) (3) (4) (5) (6) (7)

HB 12152 14757 14637

505 177 549

OwnHB 04428 03630 04451 04621

458 938 902 816

OtherHB 02705 01387 02346 02485

207 227 317 323

Seg 00154 00029 00343 00003 00109 00312

142 010 215 003 044 207

Dividend 86885 24409 29884 88870 24091 28516

421 178 179 467 181 180

Constant 00962 02434 01703 01457 02383 01951 01882

751 860 893 398 750 754 720

Obs. 147 134 281 147 134 281 281

Adjusted R2 (%) 28.5 4.1 9.5 30.6 14.2 22.8 18.1

Notes. This table reports the cross-sectional relation of annual country excess returns and changes in home bias. The period is from December 2001 to

December 2008. Columns (1)(3) report the results for the regression (15) where we regress the annual excess return of a country over the world index (ExRet)

on the change in the country HB(HB), controlling for the change in Seg(denoted by Seg) and the change in dividend yields (Dividend). Columns (4)(7)

report the results for the regression (17) where we regress ExRet on OwnHB and OtherHB, controlling for Seg and Dividend. Both OwnHB and

OtherHBare multiplied by 10,000. Columns (1) and (4) present the results for developed markets, columns (2) and (5) present the results for emerging

markets, and columns (3), (6), and (7) present the results for the joint panel. We use year fixed effects and Rogers standard errors with country clustering.

The t-statistics are reported in parentheses below the coefficients., , and denote significance at the 10%, 5%, and 1% levels, respectively.

Next, we expand the model to take into account theeffects of changes in the home bias of other countries,where a potential own-price pressure effect doesnot apply.

7.2.2. Test II. So far, we only tested the influenceof a change of foreign aversion in the home coun-try. Another econometric improvement comes from

a tighter testing of the theory itself by introducingthe cross-country effect of changes in national homebiases. We recall our main pricing equation (8):

r = M

It can be written (in time differences) as

rt = Mt Mt1 t t1

= Mt Mt1 t t1

t t1

where the matrix is a diagonal matrix with the diag-onal elements of the covariance matrix .

We now wish to introduce the home bias ratio (HB)as a proxy for relative home preference (), but theyare not related in a simple manner. In the previoussection, we used the property that home bias increaseswith relative home preference to conduct a linear test

between the domestic market return and the domestic(own)

Documents

A Global Equilibrium Asset Pricing Model With Home Preference