International Portfolio Diversification and Multilateral Effects of Correlations *

Transcription

1 International Portolio Diversiication and Multilateral Eects o Correlations * Paul R. Bergin University o Caliornia, Davis, and NBER Ju Hyun Pyun Korea University Business School October 05 Abstract Not only are investors biased toward home assets, but when they do invest abroad, they appear to avor countries with returns more correlated with home assets. Oten attributed to a preerence or amiliarity, this correlation puzzle urther reduces eective diversiication. We use a multi-country general equilibrium model o portolio choice to study how bilateral equity holding are aected by return correlations among alternative destination and source countries. From the theoretical model, we develop an empirical approach or estimating a gravity equation or equity holdings that incorporates the overall covariance structure in a theoretically rigorous yet tractable manner. Estimation using this approach resolves the correlation puzzle, and inds that international investors do seek the diversiication beneits o low cross-country correlations, as theory would predict. JEL code: F36; F4; G; G5 Keywords: Stock return correlation; Bilateral equity holdings; International portolio diversiication; Multi-country model; Equity home bias; Correlation puzzle; Financial integration; Output co-movement * We are grateul to Robert Feenstra or valuable suggestions. We also thank Colin Cameron, Chris Changwha Chung, Jaiho Chung, Kuk Mo Jung, Jinill Kim, Minsik Kim, Yuan Liu, Gabe Mathy, Chris Meissner, Jungbien Moon, Kevin Salyer, Liugang Sheng, Ina Simonovska, Nick Zolas and seminar participants at UC Davis Brown bag, INFINITI conerence, KIEP, Korea University, Korea University Business School, UNIST or helpul comments. We are indebted to a very diligent and patient reeree. Department o Economics, One Shields Avenue, Davis, CA 9566, USA, prbergin@ucdavis.edu, Tel: (530) , Fax: (530) Business School, Korea University, 45 Anam-Ro, Seongbuk-Gu, Seoul 36-70, jhpyun@korea.ac.kr, Tel:

2 . Introduction Home bias in equities is a longstanding puzzle in international inance: investors on average preer to hold too large a share o their portolios in domestic assets, given the diversiication beneits o assets abroad. Further, even when investors diversiy abroad, evidence suggests that they preer countries with a high correlation in returns to their home country. Because a high correlation lowers diversiication potential, this behavior compounds investor losses rom home bias. Some researchers have explained this second anomaly, termed the correlation puzzle, as a preerence or amiliarity when investing abroad. 3 Understanding the correlation puzzle requires a multi-country perspective, both theoretically and empirically. 4 In the context o a multi-country general equilibrium ramework, it becomes clear that the optimal share o country i s portolio in the assets o a oreign country j depends not just on the correlation o returns between countries i and j, but also on the broader set o correlations with other countries. As Okawa and van Wincoop (0) pointed out, existing empirical rameworks or estimating the eect o the bilateral correlation on portolio shares ail to control or the correlations with all other countries, and hence the existing empirical literature studying correlations lacks a theoretical oundation. Given that correlations are central to modern theories o portolio choice, there clearly is a need or an empirical approach or dealing with them. This paper uses an N-country general equilibrium model to understand how bilateral asset holdings are aected by the covariances among all potential destination and source countries. We use the model to derive an estimation equation that controls or the overall covariance structure in a theoretically rigorous yet tractable manner. The idea is to apply a second order Taylor approximation, widely used or dealing with the nonlinear Euler equations in portolio models, to the overall portolio solution as well. In this second-order approximation, the See French and Poterba (99); Coeurdacier and Rey (03). See Aviat and Coeurdacier (007); Coeurdacier and Guibaud (0). 3 See Huberman (00); Barberis and Thaler (004). 4 General equilibrium asset-pricing models have become widespread in international macro-inance research, with the development o higher-order approximation techniques, but these models are generally two-country rameworks. See Devereux and Sutherland (0) and Tille and van Wincoop (00) or a discussion o methodology, as well as Engel and Matsumoto (009), and Evans and Hnatkovska (0) or applications. The ew papers that model more than two countries in general equilibrium tend to assume the countries are symmetric and have independent returns, such as Baxter, Jermann and King (998), so these cannot study the choice o investors between alternative destination countries. Okawa and van Wincoop (0), discussed urther below, consider an extension with a general covariance structure, but their ocus is on the role o inancial rictions rather than heterogeneous correlations.

3 prolieration o covariances implied by the covariance matrix in the portolio solution o an N country model collapses down to several key average covariances: the covariance between the source country and destination country, the average covariance between source and other potential destination countries, the average covariance between the destination and other potential source countries, and the average covariance among countries other than the source and destination countries. Each o these groups o covariances has a distinct eect on bilateral equity holdings between a given pair o countries, so that the covariance structure can be summarized in the estimation equation by adding three new average covariance terms. In the absence o our recommended controls, where the only covariances included are the bilateral covariances between source and destination, estimation tends to relect the puzzle by predicting a preerence or high correlations. But the sign o the coeicient on the bilateral correlation becomes negative when including the other covariance terms recommended by our theoretical derivation. This suggests investors do preer destination countries with low comovement o returns with the home country, as theory would predict. We conclude that adequately controlling or the overall covariance structure is not merely a theoretical nicety, but has practical consequence in terms o helping uncover a statistically signiicant negative eect o bilateral returns comovement on bilateral equity holdings. Our empirical results are robust ater controlling or other amiliarity actors rom previous literature, such as distance, border, common language, etc, as well as controlling or legal restrictions on capital market openness. Our theoretical ramework is consistent with the model used in Okawa and van Wincoop (0), but we go beyond the general conclusion that the overall covariance structure matters, to make speciic predictions about how dierent groups o covariances have distinct eects on bilateral holdings, predictions which we can test in our empirical work. More crucially, we answer the challenge raised in Okawa and van Wincoop (0), to develop an empirical methodology that can deal with correlations in a theoretically rigorous yet tractable manner. Coeurdacier and Guibaud (0) oer an alternative explanation or the correlation puzzle, based upon the endogeneity o correlations. Our results are robust to controlling or endogeneity, and also suggest that the two explanations are complementary. Section introduces the N country portolio choice model with ull covariance structure and derives predictions regarding how covariances aect bilateral equity holdings. It presents simulations o a 3-country version o the model or intuition, and it also derives the theoretically-

4 based empirical equation. Section 3 describes data, with empirical results presented in section 4. Concluding remarks ollow.. Theory.. An N country, N+ Asset Model The model builds upon the two-country model o Devereux and Sutherland (0), but expands to an N-country setting, with non-zero covariance structure on incomes. Consider a consumer s dynamic optimization problem below. max E t k k U i, tk or i=,,n. () where s.t. N W i, t ji, tr j, t it R, t Yi, t Ci, t j where U i, t k () N Ci, tk and Wi, t ji, t it Y i, t is the endowment received by country i, W i, t is the total net claims o country i s agent on all oreign countries at the end o period t (i.e. net oreign assets o country i), holdings o country j s assets by country i, and We introduce an independent risk-ree asset, as this simpliies derivation o an empirical speciication later. 5 j ji, t is the real R j, t is the gross real returns o country j s assets. R,, as a risk-ree bond that is in zero net supply, t A country s output, Y it, ollows the process log Y i, t log Yi, t i, t where i.i.d. shocks are correlated across countries: or i=,,3,,n (3) 5 We assume a risk-ree bond in the same manner o Okawa and van Wincoop (0). This assumption can be justiied by the existence o nearly risk-ree assets such as insured bank deposits or government bonds. Above all, the assumption is useul to derive an empirical speciication or equity holdings. Without the risk-ree asset as an anchor asset, the optimal equity holdings would depend additively on the expected returns on all equity, thus making it harder to derive a simple orm o empirical speciication. Note that our real risk-ree bond is not related to exchange rate risk. While a bond is used to allow or hedging exchange rate risk in recent studies, Coeurdacier and Gourinchas (0) argue that equity holdings are not driven by real exchange rate risk, and Engel and Matsumoto (009) show similar results in a speciic model with nominal rigidities. 3

5 , N t, t 0 ~ N, 0 where The assets are assumed to be one-period equity claims on the home and oreign endowments, with the real payo to a unit o the equity o country i in period t deined to be N N NN. Y i, t. The real price o a unit o the equity o country i is denoted as E Zi t,. Thus, the gross real rate o return on the equity o country i is R i, t Y i, t or i=,,n. (4) E Zi, t The price o risk-ree bond is denoted as R Zt, t, and the real rate o return on the asset, Z t (5). Previous studies such as Kang and Stulz (997) and van Nieuwerburgh and Veldkamp (009) emphasized the role o inormation asymmetry on portolio choice. We ollow Okawa and van Wincoop (0), and introduce this inormation riction into a risk actor (variance o returns). Domestic agents are more inormed than oreigners about idiosyncratic payo innovations on domestic equity claims due to dierences in language and inancial system. So, rom the perspective o agents in country i considering an asset in a oreign country j, i, t has a mean o 0 and variance ij jj where ij. Equity home bias in our model arises rom this inormation asymmetry. Combine FOCs on N assets or country i, and write them in terms o the excess return o country j s asset, R R ) ( j, t, t E[ Ci, t ( R j, t R, t)] 0 or j=,,3,..n, (6) 4

6 where a risk-ree bond, is used as a numeraire, so R R ) measures the excess return on ( N, t, t asset N. Assets are assumed to be in zero net supply 6, so market clearing in the asset market implies For the risk-ree bond,, 0 or j=,,3,..,n. (7) j, t j, t jn, t, t 0. (7 ) Equilibrium consumption plans must satisy the resource constraint, C, t C, t CN, t Y, t Y, t YN, t. (8) Denote with (^) the log deviations o the variables rom the steady state equilibrium: x x xˆ where x is the value at the equilibrium. To solve or portolio holdings, we ollow x the approach o Devereux and Sutherland (0) and Tille and van Wincoop (00). A irstorder approximation o the non-portolio equations (equations () or each N country) and a second-order approximation o the Euler equations are needed to express the zero-order component ( x ) o equilibrium portolios. We ollow Devereux and Sutherland (0) in assuming symmetric steady state wealth among the countries, so that W 0 and 0 or i=,,n. and 0. (9), i, i N, i A irst-order approximation o a country i s budget constraint, equation (), implies 7 where Wˆ R R i N Wˆ ( Rˆ Rˆ ) Yˆ Cˆ. ( ) i, t ji j, t i, t i, t j ( W W ) C and ~ /( Y ). The zero-order components o asset returns are i, t i, t / constant, Rˆ ˆ, t R. ji ji (i=,,..n). Also the irst order component or risk ree bond is imposed to be 6 As in Devereux and Sutherland (0), we assume that the equity claims to income in a country are owned by deault by the residents o that country. As a result, we can treat equity claims to income as inside assets, i.e. assets are in zero net supply. This is purely an accounting convention that simpliies derivations. 7 Because 0 ~ ~ and Rˆ Rˆ 0 N j ji N, t, t ji j. 5

7 Take a second-order approximation o the country i s portolio condition, (6), to yield E ˆ ˆ ˆ ˆ ˆ ˆ ˆ t[ Rj, t R Rj, t R ] Et[ Ci, t ( Rj, t R )] or j=,,n. (6 ) From N equations o (6 ) or country i, we make pairs between country i and k, and derive N ( N ) equations like below E [( Cˆ Cˆ )( Rˆ Rˆ )] 0 or j=,,n, and i, k=, N, k i. (0) t i, t k, t j, t The irst order accurate solution or C ˆ Cˆ ) is also straightorward to derive rom ( ), ( i, t k, t which we substitute into (0). We ollow Okawa and van Wincoop (0) in imposing irst order components o asset prices where ˆ E ˆ Z jt, Z 0. So the irst-order approximations o (4) and (5) imply ˆ ˆ ˆ j, t j, t ( ) R R Y O (see technical appendix A). Hence, the distribution o irst order components o excess equity returns ollows that o irst order components o output, as introduced in equation (3), but where perceived variances o asset returns dier among countries due to inormation asymmetry. For instance, an agent in country aces Rˆ ˆ, t R 0 N Rˆ ˆ, t R 0 ~ N, σ where τ N Rˆ Rˆ 0 N N τ σ N, t N NN Based on equations (0) and ( ), we construct a matrix system to express the equity holdings (See technical appendix B). where A is an Α B N vector o equity holdings, B is an variance and covariance o the excess stock returns, and is an appendix B or a representation o the matrix). Α B (). N vector which consists o the N N matrix (see technical While a ull analytical solution to this system is not possible, () makes clear that portolio holdings in the vector A depend upon the ull set o covariances among all countries, 6

8 contained in the inverse o the ull covariance matrix ( covariance o a given source country and a given destination country. ), rather than just the bilateral.. Numerical Simulations Given that the system with general covariances is too complex to support analytical solutions, we demonstrate some key properties o the solution using numerical experiments. Consider a three country version o the model (N=3). See technical appendix C or an explanation o the ull model solution. The input to the simulation consists o inormation asymmetry parameter, τ ij and a 3 3 covariance matrix among asset returns across countries, 33. For illustration, we assume a uniorm unit variance or all assets, and a uniorm expected return or all assets, and choose values o the inormation cost τ =.3 when j i, τ = when j=i. The output consists o the 3 3 transormed equity share matrix, Α ~ 33. To help provide economic intuition, deine each ~ component o matrix Α 33 as the ratio o country j s equities held by country i to total equities o ji country i ( Y i ji ), where Yi is the total value o equity o country i (i=,,3) in our simulations. We add (endowment itsel) to the domestic equity holdings; thus, the sum o equity holdings o each country is equal to. International return correlations i) ii) iii) Equity Share ~ Α 33 = ~ Α 33 = ~ Α =

9 The simulation illustrates three key properties o the portolio solution. First, the bilateral equity holding between two countries is positively aected by a all in the bilateral stock return correlation. This property is apparent when comparing cases (i) and (ii) in the table above in regard to the relationship o countries and : a all in the correlation rom 0.8 to 0.6 raises equity holdings Α (,) 33 rom 0.54 to A second lesson is that a bilateral equity holding between two countries is negatively aected by a all in the bilateral stock return correlation o one o the countries with a third country. This property is apparent when comparing cases (ii) and (iii) in the table above: a all in the correlation between countries and 3 rom 0.4 to 0 lowers the equity holdings between countries and rom 0.46 to 0.4. Combining these two experiments and comparing case (i) to (iii) illustrates our claim that bilateral asset shares can appear to violate the irst lesson above, so that higher correlations sometimes are associated with higher rather than lower asset holdings. But these cases relect third country eects, and they are still consistent with a portolio that maximizes hedging beneits. Finally, we note that the degree o home bias 8 (represented in element Α (,) 33 ) aected the ull set o international correlations in this model: an improvement in the opportunities or diversiication as represented by a all in one or more bilateral correlations leads to a all in the degree o home bias in home equities. Finally, we summarize a more comprehensive set o simulations o the 3-country model to more broadly characterize the partial derivatives o portolio share with respect to bilateral and third-country correlations. 9 Figure reports the derivatives o the portolio share held by country o country equities with respect to the covariance o bilateral returns between countries and and the third-country covariance between country and 3. As in the simulations above, we calibrate.3, but we consider a range o values or the covariance 3 do demonstrate robustness. The igure shows that portolio holdings are everywhere monotonically decreasing in 8 For present purposes we deine the term home bias as the degree to which the share o home assets in the home portolio exceeds the share o home market capitalization in the world market. 9 Analytical derivatives are not possible in our N-country general equilibrium setting. In contrast with the model o Coeurdacier and Guibaud (0), third-country correlations aect also the degree o overall home bias, which complicates the task o assigning a sign to partial derivatives. While we are able to generate analytical expressions or these derivatives with the aid o computer sotware, the expressions are extremely long and impossible to sign, even in the case o N=3. 8

10 bilateral correlation between source and destination countries ( 0 ), and they are everywhere rising in correlation between source country and a third country ( 3 0 )..3. Derivation o the Estimation Equation and Some Theoretical Predictions The theoretical model shows the general equilibrium solution or the portolio and makes clear that an empirical equation explaining bilateral equity holdings should account or not just the covariance between source and destination countries, but also the broader covariance structure. However, the matrix algebra or portolios in equation () o an N country model does not produce a linear empirical speciication or equity asset holdings as shown in Okawa and van Wincoop (0). 0 We derive an estimable equation by taking a second order Taylor approximation. Given that a second order approximation was already employed to derive the Euler equation (6 ) used in constructing (), taking a second order Taylor approximation o the resulting equation () is a simple extension o this methodology, and is a logical approach to deriving a reasonable approximation to the theory that both captures the key predictions and is amenable to estimation. The equity share solution or a speciic source country i in an N-country world is written as ollows (see technical appendix D or derivation), where A () i i H () A () i ˆ ˆ ˆ ˆ i Et[ R t R ( R t R )] EX i... N i ˆ ˆ ˆ ˆ, EX E [ t Rt R ( Rt R )] H, i N i ii Ni EX N ˆ ˆ ˆ ˆ Et[ RNt R ( RNt R )] N N in NN. Multiply by Yi to change units rom portolio share to total equity holdings: 0 As shown in Okawa and van Wincoop (0), a model with a general covariance structure does not imply an estimation equation that is a true gravity equation, in which bilateral asset holdings are the product o country speciic variables and a bilateral riction. 9

11 A Y H ( ) i i i i i where ji jiyi and Ai. Ni This puts our let hand side variable in the usual units o the dependent variable rom previous empirical studies o the correlation puzzle, which will acilitate comparison o our results with the existing literature. Now consider the equity holdings o the source country i in a particular destination country j, ( ) [ ( ˆ ˆ )]. (3) N ji Yi i ( j, k) E Rk R k Next, take a second-order Taylor approximation o (3) with respect to all terms. For the point around which we construct the approximation, we choose a point where all countries are symmetric, so that, R ˆ k R ˆ, Y, ij, ii, ij (or i, j=, N), respectively. As derived in technical appendix E, the second order approximation is written: N N N N N G I J K L P Q ji ii jj kk ij ik jl mn k i, j k i, j li, j mi, j ni, j, nm N ( ij ) ( ik ) ( ) k i, j R S O (4) where G, I, J, K, L, P and Q are coeicients that are unctions o covariances o returns evaluated at the point o approximation (see the speciic ormula o each coeicient in technical appendix). Note that the equity holdings indeed depend on the ull covariance structure, in that all variances and covariances in the covariance matrix appear. A convenient property o i constructing the Taylor approximation around a point o symmetry is that the various covariances can be grouped into our categories, each o which is multiplied by the same coeicient in the Taylor approximation. The irst is the covariance between source country i and 0

12 destination j, ij, In the empirical equation (5) below, this regressor will be labeled EQCOV ij, and is o particular interest in our estimation. Technical appendix E-iii) provides a proo that the theoretical model implies the coeicient on this regressor should be negative. This represents the claim above that investors seek diversiication beneits in their choice o destination countries. The second set o regressors are the covariances between the source country i and countries other than j, ik.while each o these N- covariances can dier rom each other, the act we evaluate the Taylor approximation coeicient at a point o symmetry means that each o these covariances is multiplied by the same coeicient, which we label as L in equation (4). See technical appendix E-iv), v) and vi) or a proo o this claim, as well as the analogous claims or the other groups o regressors. This means we can sum up these covariances and actor out the common coeicient. In our estimation equation (5) below, this summation o covariances becomes a regressor we label as MT ij, representing multilateral eects o covariances in alternative destinations. A large value or MT ij indicates that there is a high correlation o returns between country i and all other countries other than j. So, it is expected that this MT term is positively associated with bilateral inancial asset holdings between countries i and j. Technical appendix E-iv) provides a proo that the theoretical model implies the coeicient on this regressor should be positive. The third group o regressors are the covariances between the destination country j and countries other than i, jl. Technical appendix E-v) again shows that even while these individual covariances will dier rom each other, they take the same coeicient in the Taylor approximation and thereore can be summed up to orm a regressor with a common coeicient. This regressor we label DT ij, representing destination eects. As shown in technical appendix E-v), the theoretical model implies an ambiguous sign or this regressor. Fourth are covariances between countries other than i and j. Again these (N-) covariances will dier rom each other in value, but they can be summed together as a single regressor, which while label as OT ij, representing other country eects. As shown in technical appendix E-vi), the theoretical model implies an ambiguous sign or this regressor. equation: To summarize, we rewrite the equity holdings solution (4) to orm the estimation

13 Equity EQCOV Var Var MT DT T. (5) ij ij i 3 j 4 ij 5 ij ij ij Each term in this estimation equation (5) corresponds to a term in the theoretical equation (4) above. The dependent variable, Equity ij, is the log o equity holdings. We take a log o equity holdings or scaling, which also makes our depending variable directly comparable to that usually used in the related empirical literature. This is easily incorporated in the Taylor approximation by writing the dependent variable as exp(log( )) beore taking derivatives. This simply introduces a constant actor o / which is included in each o the constants G, I, J,K,L, P, and, Q in the equation (4). In addition to the composite covariance regressors discussed above, the regressors Var i and Var j are the names we assign to the variances o returns terms ii and jj in (4). I one sums the our composite regressors, EQCOV ij, MT ij, DT ij, and OT ij, it becomes the sum o all elements except variance terms in the covariance matrix. This will be the same or all country pairs, and implies a colinearity problem. I the values o three variables out o the our variables are known, the value o any ourth variable is determined and the inormation on the ourth variable is redundant. Thus, in the regression analysis, we need to control or any three among the our variables, and we thereore will drop OT ij. This also applies ji to Var i, Var j and the sum o variances o third countries ( N k i, j kk ) because the sum o Var i, Var j and N k i, j kk (the sum o variances o all countries) are the same or all country pairs. Hence, we include Var i and Var j, not N k i, j kk in all speciications. In addition, we proxy or the inormation rictions ( ij and N k i, j ik ) in equation (4) with a vector T o common regressors, including distance, border, common language, etc. To represent the sum o rictions ( N k i, j ik ), which is conceptually similar to multilateral resistance in trade, we ollow the approach o Baier and Bergstrand (009) in that we construct this multilateral resistance term directly based on the theory. We select our representative direct barrier/riction variables on which we have an empirical measure geographical proximity (border, distance),

14 common language, and equity market liberalization and compute a direct measure o N k i, j ik or each country pair by summing the barrier measures or all countries outside the given pair. This produces our additional controls to include in the ull regression. This control or multilateral resistance is required because the benchmark model allows the inormation rictions, ij, to be heterogeneous among country pairs. This heterogeneity assumption actually is not necessary in our theoretical model or it to generate the theoretical predictions regarding covariances that we test. All that is required is that there be some inormation riction associated with purchasing assets outside the home country that dierentiates this rom purchase o a home asset; this riction can be homogeneous across countries. As a result, we will also report estimation results or an empirical equation that arises rom a version o the model where the inormation riction is homogeneous across countries. In this case the regressors in T ij relecting proximity and amiliarity drop rom the regression speciication. Although our empirical speciication rom the theory ocuses on cross-sectional variations o regressors to determine equity holdings, it is easily extended to panel data regression by adding time subscripts to all regressors and year ixed eects. For instance, a timevarying covariance and inancial rictions lead to time-varying MT and DT terms as well as timevarying multilateral resistance. We report results or panel estimation below, and or robustness, we report in the technical appendix the results or each o the cross-sectional estimations conducted or each year separately. 3. Data and Measurement This section discusses how data are used to measure the regressors in the estimation equation (5) above. 3. Main Variables Data or the bilateral portolio equity holdings, the dependent variable, come rom the Coordinated Portolio Investment Survey (CPIS) published by the International Monetary Fund (IMF). The survey has been conducted annually since 00 (and or the irst time in 997). The irst CPIS involved 9 source economies, while the CPIS has expanded participation up to 73 3

15 source economies in 006, including several oshore and inancial centers. In each case, the bilateral positions o the source countries in 8 destination countries/territories are reported. We select our sample beore 007 to avoid the global inancial crisis and post-crisis period. The CPIS provides a breakdown o a country s stock o portolio investment assets by country o residence o issuer. Lane and Milesi-Ferretti (008) point out the shortcomings o survey methods and under-reporting o assets by participating countries (see the details in Lane and Milesi-Ferretti, 008). Nevertheless, the survey presents a unique opportunity to examine oreign equity and debt holdings o many participating countries. We choose bilateral equity holdings or and take a log. We introduce stock market capitalization variables. The stock market capitalization variable is constructed by taking a log o product o source and destination countries market capitalization divided by world market capitalization. Domestic stock market capitalization data is available rom World Development Indicators. The measure or equity return variancecovariance (or correlation) o 33 countries (see technical appendix F or the list o countries) is constructed using equity total return indices collected rom the DataStream. We compute annual equity return variance-covariance over preceding 4-years rom 006, or each country pair, using bilateral monthly return data. To demonstrate robustness, we also use several alternative measures: equity return covariance constructed using equity price indices (EQCOV p ), equity return correlation (EQSYNC), and output co-movement (SYNC) 3 (see Portes and Rey, 005, and Lane and Milesi- Ferretti, 008, which also utilize both equity return correlation and output correlation). The SYNC measure is consistent with our theoretical endowment economy model, where the distribution o irst order components o excess equity returns ollows that o output. We also construct the multilateral correlation term using both measures: or each country pair i and j, we Equity holdings are reported in terms o millions o U.S. dollars. A unit is converted rom millions to thousands. So, in the expression o ln(equity+) means a thousand US dollars. All values are real: we convert nominal value into real term using US GDP delator (005=00). The reason why using the preceding 4 years data (48 monthly observations, ) or equity covariance is to make avoid extraordinary crisis events that may result in abnormal equity correlation or equity low patterns, such as Latin America economic crisis in the early 000s (00-00) and Asian Financial crisis in the late 990s ( ). In addition, previous study such as Longin and Solnik (995) presented equity return correlation computed using a 4 year rolling window. 3 EQSYNC is also computed over preceding 4-years with bilateral monthly return data and SYNC is using preceding 0-years real GDP data rom Penn World Table. 4

16 sum the (EQ)SYNC measure between the source country i and countries other than j: MT ( EQ) SYNC ij N ( EQ) SYNC ki, j ik and also obtain DT ( EQ) SYNC ij N ( EQ) SYNC. li, j jl 3.. Other Controls We include other important determinants o bilateral rictions (included in T in equation 5) identiied by previous literature, including speciic geographical, political and cultural actors. To control or explicit barriers to international equity investment, we consider a country s equity market liberalization index based on Bekaert and Harvey (004) and Bekaert, Harvey, and Lundblad (005). The oicial equity market liberalization indicator is coded as when a country s equity market is oicially liberalized oreign investors oicially have the opportunity to invest in domestic equity securities and zero otherwise. We construct bilateral equity market liberalization indicator by multiplying each equity market indicator in a country pair. However, in our sample period, equity markets o most developed and emerging economies are categorized as oicially liberalized and the measure has not much cross-sectional variation (The mean o the measure is 0.98 in our sample). Thus, or the robustness o the results, we introduce the alternative measures o capital account openness proposed by Quinn (997) and Quinn and Toyoda (008) and Chinn and Ito (006) respectively and construct bilateral measure by multiplication (see technical appendix). To measure geographical proximity, we use two variables rom Rose and Spiegel (004): (i) the log o bilateral distance between countries and (ii) a binary variable indicating a shared border. To control or cultural and historical ainities between countries that can aect crossborder asset holdings, we add binary variables or common language, or country pairs with a history o colonization, and or common colonizer. Common language may lower inormation costs between countries, so investors can more easily access each other s inancial market. The same colonial experience may predict more amiliar inancial institutions in another country. We include indicators or currency unions as they may decrease transaction costs and also remove risk rom exchange rate volatility (Coeurdacier and Martin, 009). Previous studies introduce a time zone dierence dummy to proxy or communication diiculties when the overlap between oice hours is limited (Portes and Rey, 005 and Lane and Milesi-Ferretti 5

17 008). We include the dierence in longitude between countries to measure time dierence, where the data is rom the CIA World Fact book. Lane and Milesi-Ferretti (008) ind that OECD countries and emerging market countries diered in the actors determining the pattern o equity investments. So we add an OECD dummy variable coded as i two countries in a pair are both OECD members. This variable also controls or income level and development o inancial institution o a country pair. A variable o common legal origin indicates i both source and destination countries have a legal system rom the same origin; English (Common), French, German or Scandinavian law. Common legal origin is likely to lead to similar institutions, regulation and custom or inancial transaction between countries. The inormation on legal origins is rom the Rose and Spiegel dataset. We also ollow Lane and Milesi-Ferretti (008) and Coeurdacier and Guibaud (0) in including an indicator variable i the source and destination countries have a tax treaty enacted prior to 00 and in orce until 006. This control varies by country pair. The data are available rom the IBFD Tax Treaty Database ( Lastly, we include a log o bilateral trade (sum o imports and exports between countries) divided by the sum o GDPs between two countries in line with Aviat and Coeurdacier (007) and Lane and Milesi-Ferretti (008). 4 We report summary statistics and correlation o key variables in Table A in technical appendix. 4. Empirical Results 4.. Main Results Coeicients rom panel estimation reported in Table support our main argument, that controlling or the overall covariance structure aids in uncovering a statistically signiicant negative eect o bilateral returns comovement on bilateral equity holdings, as predicted by theory. The irst two columns study our simplest model speciication. 5 Column (), which excludes controls or the overall covariance structure, shows that the estimated coeicient on international equity returns covariance (EQCOV) is signiicantly positive at the % critical level. 4 Our trade intensity measure relects trade relationships between countries that are not induced by countries sizes. Moreover, using other trade measures such as log o bilateral trade or log o trade over product o GDP does not aect our main results. 5 As described at the end o section above, this empirical speciication corresponds to the case o the theoretical model where there is a single homogeneous inormation riction o dealing with a oreign country. 6

18 This result echoes the results derived in previous papers noted above, suggesting an odd preerence by investors or countries with luctuations in returns that are similar to their home country. However, the result is transormed once we control or the general covariance structure by including the multilateral eects (MT) term and the destination eect term (DT) o returns covariance, which captures returns covariance with the multilateral partners. Column () shows that the estimated coeicient o EQCOV becomes signiicantly negative at the 0% critical level. Thus, we show that a higher return covariance lowers bilateral equity asset holdings once we adequately take into consideration covariances with third countries. Furthermore, the estimated coeicient o MT term is signiicantly positive, as our theory would predict. The remaining columns o Table report estimates or the more general model that includes additional variables representing bilateral and multilateral rictions across countries in terms o geography, language, and countries legal barriers to equity market investment (bilateral and multilateral equity market liberalization index). Also we control or variables that represent a country s culture, history, and countries real economic linkage such as trade in goods and services that previous studies considered. Column (3), excluding MT and DT controls, shows that the estimated coeicient o EQCOV is statistically insigniicant, with the point estimate positive as in column (). Column (4) show that the addition o MT and DT controls makes the estimated coeicient o EQCOV become negative and statistically signiicant at the % critical level. We conclude that adequately controlling or the overall covariance structure is not merely a theoretical nicety, but has practical consequence in terms o helping uncover a statistically signiicant negative eect o bilateral returns comovement on bilateral equity holdings. Column (5) shows that the result on EQCOV is preserved i the sample is expanded by deining the dependent variable as ln(equity+), to prevent observations rom dropping when taking a log o zeroes. We implement tobit estimation to consider let censored observations o the dependent variable, including MT and DT terms. The estimated coeicient o EQCOV is signiicantly negative at the % critical level. Also most o the estimated coeicients remain as the same as those o column (4). Throughout columns () to (5) in Table, other standard explanatory variables have the expected signs. Countries stock market capitalizations have a positive eect on bilateral equity holdings. Higher asset holdings are positively associated with common language in both countries, as are common colonizers and currency union. Distance has a negative eect. 7

19 Moreover, multilateral resistance terms o rictions show the opposite signs to bilateral rictions, which is consistent with theoretical prediction, i.e. the signiicant negative coeicient on the sum o border dummy to multilateral partners indicates that a country that is adjacent to third countries (has lower multilateral barriers) decreases investment in its bilateral partner. 6 Coeicients rom cross-sectional regressions estimated or each o the years separately are available in the appendix (see technical appendix Tables A-A7). Results are similar to those in the benchmark panel estimation, but we lose statistical signiicant in several o the cases. This is not surprising since the panel has the beneit o a larger sample. For example, we estimate a negative coeicient on EQCOV or the speciications in columns (), (4), and (5) or each o the years, but it is not uniormly signiicant or all o the years. We still have statistical signiicance or all o the years or column (5), hal o the years in column (4), and or only one o years in column (). 4.. An Instrumental Variable Approach The empirical investigation o the eects o equity returns covariance on equity asset holdings may encounter an endogeneity problem, as discussed in Coeurdacier and Guibaud (0). The causality can run in the opposite direction: inancial asset holdings between countries (inancial integration) may have either a negative or a positive eect on equity returns correlation. Hence, the ormer estimates o equity returns covariance on bilateral asset holdings might be biased. As a robustness check, this section implements an instrument variable (IV) approach, using past inormation on equity return correlation as an instrument, as suggested by Lane and Milesi-Ferretti (008) and Coeurdacier and Guibaud (0). 6 For completeness, the Technical Appendix reports results or regressions including a ull set o country-year ixed eects (see Table A7), even though the theoretical derivation does not call or them, since we control directly or multilateral inormation rictions ollowing the approach o Baier and Bergstrand (009). We note, irst, that a ixed eect speciication is not compatible with use o MT and DT controls, as the sum o EQCOV and MT is the same or all pairs involving any given source country, so there is exact multicollinearity with the set o source-country ixed eects. Similarly, the sum o EQCOV and DT is the same or all pairs involving any given destination country, so there is exact multicollinearity with the set o destination-country ixed eects. See Technical Appendix G or details. As a result Stata drops two o these three variables in columns () and (4) in Table A7. In particular, column (4) drops EQCOV, our primary variable o interest. We note, second, that results in columns () and (3) conirm that source and destination country-year ixed eects cannot substitute or MT and DT in resolving the correlation puzzle, in that coeicients on EQCOV are either positive or insigniicantly dierent rom zero. This result is consistent with our theory, since MT and DT terms vary over country-pair and year, rather than country and year. See Technical Appendix G or urther discussion. We emphasize that our theoretical derivation or the estimation equation does not require us to use ixed eects, as we control directly or multilateral rictions, an approach which should have superior eiciency. 8

20 Panel B o Table presents the irst stage regression o IV. We instrument EQCOV on its lagged inormation. The estimated coeicient o our instruments on current returns covariance (EQCOV) is reported in Panel B. F-test statistics on the irst stage regression all exceed the critical values at 0% maximal IV size which is 6.38 or weak instruments as reported by Stock and Yogo (00). Thus, we can reject the null hypothesis that the IV equation is weakly identiied. Panel A o Table reports estimates rom the second stage instrumental variable regressions. Estimates support our main conclusion, regarding the beneit o controlling or the overall covariance structure. The only speciications where the coeicient on EQCOV is statistically signiicantly negative are those that include our MT and DT controls, those in columns (), (4) and (5). We note that the coeicient on EQCOV is not statistically signiicant in either column () or (3), suggesting that controlling or endogeneity might be helping to oset the correlation puzzle. Further, we note that controlling or endogneneity enhances the statistical signiicance o the negative sign o EQCOV in column (), suggesting that the two explanations may be complementary Alternative Measures or Returns Comovement To reinorce the robustness o the results, we consider three alternatives to the EQCOV regressor. Table 3 uses EQCOV p, which is constructed using equity price indices rather than equity return indices. One beneit is that data are available or more countries. Table 4 uses equity return correlations (EQSYNC) rather than covariances. While our benchmark estimates use covariances because this is what was prescribed by the theoretical deviation o the estimation equation, previous studies have ocused on correlations. So we include this robustness check or comparison purposes. Table 5 uses output correlation instead o equity return correlation as another alternative measure. An advantage o the output measure is that it is available or a much wider set o countries, doubling the sample size (see technical appendix F or the list o countries in the sample). 7 For each o these three alternative measures o returns comovement, MT and DT are reconstructed accordingly to use the same data on comovement. 7 The inance literature has established the empirical relationship between stock returns and production growth rates (Fama, 990, and Schwert, 990, or the U.S., and Choi, Hauser, and, Kopecky, 999, or G-7 countries). For instance, the model o simple discounted cash low valuation maintains that stock prices relect investors expectations about the uture real economic variables such as corporate earnings, or its aggregate proxy, industrial 9

21 Results in all three tables are consistent with our main conclusion. While results vary somewhat, it remains true in each table that the only speciications where the coeicient on the returns comovement variable is statistically signiicantly negative are speciications that include our MT and DT controls. And in each table, two o the three speciications that include MT and DT controls (columns (), (4) and (5)) exhibit this result. 5. Concluding Remarks This paper studies how asset diversiication between a pair o countries is aected by correlations with third countries. Our N-country theoretical ramework oers one explanation or why recent empirical work has ound that higher return correlations are sometimes associated with higher portolio holdings, which is contrary to the pursuit o risk hedging. Because bilateral asset holdings depend not only upon bilateral stock return correlation with the destination country but on the ull covariance structure, the attractiveness o a oreign country as a hedge depends upon its hedging potential relative to other potential destination countries. The model suggests a means or controlling or third-country eects, and empirical speciications implementing these controls reverse this inding o preceding literature. This issue illustrates an advantage o taking a multi-country perspective in modeling bilateral asset holdings. production. I these expectations are correct on average, lagged stock returns should be correlated with the contemporaneous growth rate o industrial production. So, another beneit o using output growth correlation is that we avoid a simultaneity problem between stock return correlation and bilateral stock holdings because output comovement is highly correlated with the lagged stock return correlation. 0

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