Multinationals and the gains from international diversification

Transcription

1 Review of Economic Dynamics 7 (2004) Multinationals and the gains from international diversification Patrick F. Rowland a, Linda L. Tesar b,c, a Financial Engines Inc., 1804 Embarcadero Road, Palo Alto, CA 94303, USA b Department of Economics, 611 Tappan Street, University of Michigan, Ann Arbor, MI 48109, USA c National Bureau of Economic Research, USA Received 9 December 2002; revised 28 May 2004 Available online 8 July 2004 Abstract This paper employs mean variance spanning tests to examine the diversification potential of multinational firms and foreign market indices from the perspective of investors in the G7 countries over the period. We find evidence that multinational corporations may have provided diversification benefits for investors in Germany and the United States. We find that the addition of foreign market indices to a domestic portfolio inclusive of multinationals provided substantial diversification benefits in all countries. The economic importance of the shift of the portfolio frontier varied considerably across markets Elsevier Inc. All rights reserved. JEL classification: F23; F36 Keywords: Diversification; Spanning; Home bias; Multinationals 1. Introduction Despite the benefits of global diversification, evidence on home bias suggests that investors in industrialized countries have been reluctant to hold more than a small fraction of their wealth in foreign assets (French and Poterba, 1991 and Tesar and Werner, 1995). * Corresponding author. address: ltesar@umich.edu (L.L. Tesar) /$ see front matter 2004 Elsevier Inc. All rights reserved. doi: /j.red

2 790 P.F. Rowland, L.L. Tesar / Review of Economic Dynamics 7 (2004) While investors have increased their holdings of foreign equity in recent years, the fraction of the portfolio invested abroad remains far less than the share implied by standard models of optimal portfolio choice. At the end of 1996, the share of national equity portfolios invested in foreign equity was 11.2 percent in Canada, 5.3 percent in Japan, 18.2 percent in Germany, 22.5 percent in the United Kingdom and 10 percent in the United States (Tesar and Werner, 1998). The extent of home bias in bond portfolios tends to be even larger than in equity portfolios. 1 This paper employs mean variance spanning tests to examine the diversification potential of multinational firms and foreign market indices from the perspective of investors in Canada, France, Germany, Italy, Japan, the United Kingdom and the United States over the period. We test whether the addition of multinationals and international equities to a broad-based portfolio of domestic equities significantly shifts the portfolio frontier. One possible explanation for the observed home bias in national portfolios is that investors can obtain the benefits of international diversification indirectly through multinational firms, and therefore do not need to hold foreign equity in their portfolios. Previous studies have generally concluded, however, that multinational firms do not provide diversification benefits. Jacquillat and Solnik (1978) regressed the returns of multinationals from nine countries on the set of market indices and found that multinational returns tended to covary most with the firm s home market. Senchack and Beedles (1980) contrasted the risk, returns and betas of portfolios of multinationals with portfolios of domestic and international equities and found that multinationals did not deliver diversification benefits. These studies presume that the appropriate domestic benchmark is the market portfolio. While in theory the value-weighted index of domestic equities should reflect the full benefits of investing in the home market, there is ample evidence that portfolios that deviate from the market can produce higher risk-adjusted returns (Roll, 1977). The advantage of the mean variance spanning methodology employed in this paper is that it imposes no restriction on the composition of the domestic portfolio or the international portfolio. Our testing procedure is comprised of two steps. We begin with a portfolio of purely domestic equities that excludes multinationals and cross-listed firms. In the first step we examine whether the addition of multinationals (headquartered in the investor s country of origin) to the set of domestic equities provides diversification benefits, controlling for the effects of industry classification and firm size. We find evidence that the addition of multinationals significantly shifts the domestic portfolio frontier for investors in Germany and the United States. Thus, we find little evidence that home bias due to indirect diversification through multinationals could possibly be rationalized for investors in most countries. The finding that multinationals may shift the portfolio frontier does not necessarily imply, however, that multinationals are a substitute for holding international assets. In the second step we examine whether the addition of international stock-market indices shifts the domestic portfolio frontier inclusive of multinational equities. We find that from the 1 The exception is the United Kingdom with foreign bond holdings at 37.5 percent of the portfolio in The allocation of bonds to foreign and domestic categories is particularly problematic for the United Kingdom due to the location of the eurobond market in London.

3 P.F. Rowland, L.L. Tesar / Review of Economic Dynamics 7 (2004) perspective of investors in every country the addition of an international market index to the set of domestic equities inclusive of multinationals significantly shifts the portfolio frontier. The results make clear that investors cannot exhaust the gains from diversification without turning to international markets. Finally we examine the welfare benefits of global diversification from the perspective of investors in each of the seven countries in our sample. While the mean variance tests provide information about the statistical significance of the shift in the portfolio frontier as assets are added to the benchmark set, the tests do not provide information about the magnitude of the shift in an economic sense. We calculate two measures of the magnitude of the shift in the efficient frontier. The first metric is the percentage change in consumption required to make the investor indifferent between holding the utility-maximizing portfolio comprised of the benchmark set of domestic assets and the utility-maximizing portfolio comprised of the set of domestic and international equities. The second is the change in mean return per unit risk, or the change in the Sharpe ratio. We find that the gains from international diversification vary dramatically across the seven countries. Interestingly, the marginal gains of adding international indices to a broadly-defined domestic portfolio inclusive of multinationals are small relative to the initial gains of adding multinationals to a set of purely domestic assets. Our paper is similar to the study by Errunza et al. (1999) although it differs in some important respects. Errunza et al. examine the gains from home-grown diversification from the perspective of investors located in the United States. The purpose of their paper is to see if US investors can exhaust the gains from diversification by holding only those securities that trade on US exchanges, inclusive of ADRs and country funds. In general, they fail to reject the null hypothesis that a broadly defined portfolio comprised of US industry indices, US multinationals, ADRs and country funds spans individual foreign country indices. Our study differs from theirs in three ways. First, because we wish to understand the problem of home bias, we exclude ADRs and country funds from the benchmark portfolio because these are by definition claims on foreign firms. The finding that a portfolio with ADRs and country funds spans foreign indices tells us little about marginal benefits of global diversification. Second, by excluding multinationals from the benchmark portfolio, we can test explicitly for the marginal benefits of diversification, if any, that can be obtained through multinationals. Finally, we examine the benefits of diversification for investors outside of the United States, where the ability to purchase claims on foreign firms in the home market may be more limited. 2 Because investors in different countries face different currency risks, we examine the gains from diversification from each investor s perspective by denominating all returns in their home currency. The paper is organized as follows. The specification of the generalized method of moments mean variance spanning test is discussed in Section 2. Section 3 presents our metrics for quantifying the magnitudes of the gains from diversification and Section 4 discusses our data set. The finite-sample properties of the test are discussed in Section 4 2 Excluding multinationals and cross-listed equities from the benchmark domestic portfolio requires us to create our own indices, as off the shelf industry and country indices contain a significant fraction of multinational and international stocks. The methodology we use to create the indices is described in Appendix A.

4 792 P.F. Rowland, L.L. Tesar / Review of Economic Dynamics 7 (2004) and Appendix C. Section 5 summarizes the diversification benefits of multinational firms. The marginal benefits of adding country indices are discussed in Section Generalized method of moments mean variance spanning test Throughout, we will refer to the set of domestic equities as the benchmark assets and the set of expanded investment opportunities as the extended set of assets. We perform mean variance spanning tests to determine if the portfolio frontier comprised of the benchmark and extended-set assets is statistically different from the portfolio frontier comprised of only the benchmark assets. In particular, the test provides evidence for determining whether the addition of the extended-set assets to the benchmark set of assets restricts the set of discount factors that price the benchmark assets alone (Hansen and Jagannathan, 1991). The advantage of the spanning test is that it does not require specification of a risk-free rate of return. The disadvantage, however, is that rejection of the null hypothesis that the portfolio frontiers are equivalent does not imply that the marginal diversification benefits are economically significant. We will address this problem in Section 3 by providing a utility measure of the benefits of an outward shift of the portfolio frontier. We follow the methodology described in DeSantis (1993) and Bekaert and Urias (1996) to test for mean variance spanning. Assuming frictionless markets, a common restriction on asset pricing models is E[R t+1 m t+1 ]=ι (2.1) where R t+1 is a n-dimensional vector of gross asset returns, m t+1 is the stochastic discount factor and ι is a vector of ones of dimension (n 1). 3 Explicit parameterization of m t+1 gives Eq. (2.1) an economic interpretation. For example, specifying m t+1 as a linear function of the return on the market portfolio yields the Capital Asset Pricing Model. Alternatively, if m t+1 is specified as the intertemporal marginal rate of substitution, the consumption CAPM is obtained. Following DeSantis and Bekaert Urias, let m t+1 be a candidate discount factor for R t+1 and assume m t+1 is a linear projection onto R t+1 such that m t+1 = c + [ R t+1 E(R t+1 ) ] β + εt+1 (2.2) where c is a constant, ε t+1 is the error term of the regression and is uncorrelated with R t+1 by assumption. In general, β cannot be estimated because m t+1 is unobserved. Nevertheless, if m t+1 is required to price R t+1, then substitution of Eq. (2.2) into Eq. (2.1) yields the unconditional asset pricing restriction, where 0 isa(n 1) vector of zeros: E { ([ c + R t+1 Rt+1 E(R t+1 ) ] )} β ι = 0. (2.3) Partition R t+1 such that R t+1 R B,t+1 R E,t+1 and partition β such that β [β B β E ]. The dimensions of R B and R E are (n B 1) and (n E 1), respectively. R B and R E 3 The derivation of the theoretical bounds for the first two moments of m t+1 are presented in Hansen and Jagannathan (1991) and the computational steps are discussed in DeSantis (1993).

5 P.F. Rowland, L.L. Tesar / Review of Economic Dynamics 7 (2004) correspond to the benchmark portfolio of n B assets and the extended-set portfolio of n E assets. The null hypothesis that R t+1 is priced by the subset of n B assets in R B,t+1 implies that R E,t+1 is redundant for asset pricing. Therefore, under the null hypothesis, the coefficients in β E are equal to zero and the unconditional asset pricing restriction may be rewritten as: E { R t+1 [ c + [ RB,t+1 E(R B,t+1 ) ] βb,1 ] ι } = 0. (2.4) Conditional on a given value of c and that R B,t+1 is a subset of R t+1, the restriction in Eq. (2.4) implies that the portfolio frontier comprised of the benchmark assets is tangent to the portfolio frontier comprised of the benchmark assets and extended-set assets at the point corresponding to the highest Sharpe ratio. 4 The two-fund separation theorem states that any frontier portfolio can be obtained as a linear combination of any two distinct frontier portfolios. Therefore, if the portfolio frontiers implied by R t+1 and R B,t+1 are tangent at two distinct points, then the two frontiers must coincide at all points. Let h T ( β B ) denote the 2n B sample moment conditions that are obtained as a generalization of Eq. (2.4), { [ Rt+1 c1 + [ R B,t+1 E(R B,t+1 ) ] ] } βb,1 ι h T ( β B ) = E [ R t+1 c2 + [ R B,t+1 E(R B,t+1 ) ] ] = 0, (2.5) βb,2 ι where β B =[β B,1,β B,2 ]. Denote b B =[b B,1,b B,2 ] as the vector of estimators of β B subject to the restriction that the coefficients corresponding to the extended-set assets are equal to zero. The vector b B is the solution to arg min b B = argmin h T (β) Ω T h T (β) subject to β E = 0 (2.6) where β E =[β E,1,β E,2 ] and Ω T is an optimally chosen weighting matrix. 5 The null hypothesis is that the frontiers coincide at all points (i.e. β E = 0). Under the null hypothesis, the generalized method of moments (GMM) test of over-identifying restrictions has a chi-square distribution with 2n E degrees of freedom. The order of the Newey West correction used in the GMM algorithm is equal to 4(T /100) 2/9 (see Newey and West (1992)). T [ h T ( b B ) ΩT h T ( b B )] χ 2 (2n E ). (2.7) The alternative hypothesis is that β E 0. Rejection of the null hypothesis implies that the variation in the returns of the benchmark assets does not explain the variation of the returns of the benchmark and extended-set assets. Failure to reject the null hypothesis provides evidence that the benchmark set of assets spans the risk-return opportunities offered by the extended set of assets. 4 See DeSantis (1993) for a detailed explanation of the relationship between the portfolio frontiers and the volatility bounds of m t+1. 5 See DeSantis (1993), Bekaert and Urias (1996) and Campbell et al. (1997).

6 794 P.F. Rowland, L.L. Tesar / Review of Economic Dynamics 7 (2004) Quantifying the gains from international diversification Rejection of the null hypothesis that the benchmark portfolio of domestic assets spans the extended-set portfolio does not provide information about the magnitude of the shift in the efficiency frontier, nor does it provide insight into whether the shift is economically significant. To give the shift in the portfolio frontier an economic interpretation, we quantify the gains from diversification in two ways. First, we calculate the gains in lifetime utility associated with expanding the portfolio to include the extended set of assets (Lewis, 2000). The utility gain is measured as the percentage reduction in permanent consumption that makes an individual indifferent between the optimal portfolio comprised of assets from the benchmark and the extended-set and the optimal portfolio comprised of assets from the benchmark set only. 6 Second, we report the change in Sharpe ratio resulting from the shift in the portfolio frontier. We use the country-specific mean LIBOR rate as a proxy for the risk-free rate in our calculation of the change in the Sharpe ratio. To measure utility gains, we follow Lewis (2000) by letting C t denote permanent consumption at time t of an individual holding the optimal portfolio of benchmark assets and letting Ct denote the permanent consumption at time t of an individual holding the optimal portfolio of benchmark and extended-set assets. The utility gain, δ, isgivenbythe relationship U 0 (C 0 ) = U 0 ( C 0 (1 δ) ). (3.1) We use the Epstein Zin Weil (see Epstein and Zin, 1989) specification for utility which allows the risk-aversion parameter, γ, to differ from the inverse of the elasticity of intertemporal substitution parameter, θ: U t = [ c (1 θ) t + β [ ( 1 γ )] (1 θ)/(1 γ) ] 1/(1 θ) E t U t+1 for γ,θ >0; γ,θ 1. (3.2) The utility maximizing portfolio is obtained by maximizing the utility function given in Eq. (3.2) subject to the portfolio frontier of available assets. Portfolio returns are assumed to be jointly log-normally distributed such that ln(r B,t ) N(µ B (1/2)σB 2,σ2 B ),and ln(r BE,t ) N(µ BE (1/2)σBE 2,σ2 BE ),wherer B,t and R BE,t are the vector of gross returns on the benchmark portfolio and the vector of gross returns on the portfolio that includes the benchmark and extended-set assets, respectively. The expected utility of consumption for an investor who is holding the optimal benchmark portfolio may be written as [ ( E t U(C t ) = W t {1 β exp (1 θ) µ B 1 (1/(1 θ)) 2 B)]} γσ2, (3.3) 6 The utility-gain metric has two shortcomings. First, the spanning test presented in Section 2 tests the hypothesis that the asset-pricing kernel is the same for the two sets of assets. If the asset-pricing kernel is not valid across the two sets of assets, then the utility-gain metric, which is a function of the mean and variance of the portfolios, is also not valid. Second, we do not consider the variance of the utility-gain metric. Despite these shortcomings, this metric provides an economically intuitive measure of the distance between portfolio frontiers.

7 P.F. Rowland, L.L. Tesar / Review of Economic Dynamics 7 (2004) Fig. 1. Utility improvement from expanding the set of available assets. and the expected utility of consumption for an investor who is holding the optimal portfolio of benchmark and extended-set assets may be written as [ ( E t U(C t ) = W t {1 β exp (1 θ) µ BE 1 (1/(1 θ)) 2 BE)]} γσ2, (3.4) where W t is equal to the individual s wealth at time t and is assumed to be exogenous. Figure 1 illustrates the utility gain from adding the extended set of assets to the portfolio of benchmark assets. Without the extended set of assets the investor maximizes utility subject to the portfolio frontier of benchmark assets. The optimal portfolio is obtained at the tangency labeled T B. If the set of available assets is expanded to include both the benchmark and extended-set assets, the investor increases utility by choosing the optimal portfolio at T BE. The utility gain is measured as the percentage reduction in permanent consumption that makes an individual indifferent between the optimal portfolio at T BE and the optimal portfolio at T B, as given in Eq. (3.1). Note that the inner brackets in Eqs. (3.3) and (3.4) indicate that utility maximization involves a trade-off between the mean return of the portfolio and its variance. As discussed in Lewis (2000), the portfolio allocation decision depends only on the coefficient of risk aversion and no other preference parameters. To compute welfare gains, we numerically solve for the optimal portfolio weights given the set of benchmark assets and the extended set of assets. We then use Eqs. (3.3) and (3.4) to compute the utility levels associated with the two portfolios. Finally we compute welfare gains using Eq. (3.1).

8 796 P.F. Rowland, L.L. Tesar / Review of Economic Dynamics 7 (2004) For the utility specifications in Eqs. (3.3) and (3.4), the admissible combinations of γ and θ are restricted such that the discount factor, β, is less than one: [ β 1 > exp (1 θ) (µ 12 )] γσ2. (3.5) We consider the utility gain from diversification for risk-aversion parameter (γ ) equal to 2 and an elasticity of intertemporal substitution parameter (θ) of five. 7 There is little consensus in the literature about the true magnitudes of risk aversion and intertemporal substitution. Our specification is intended to be suggestive of the possible gains from diversification, and the parameter values are chosen so that our measures can be compared to estimates in other studies. 4. Data description and finite sample properties of the test We consider the benefits of diversification through the addition of multinationals and the addition of foreign market indices from the perspective of investors from Canada, France, Germany, Italy, Japan, the United Kingdom and the United States. For each country in the sample, firm-level data is used to construct portfolios by industry classification, firm size and domestic/multinational status. The number of domestic portfolios ranges from 14 for Italy to 21 for the United States. The data is extracted from Datastream, a proprietary database. In instances where Datastream is not the primary source of the data, the primary source is cited. With the exception of Japan, the sample of equities includes firms that are currently traded or were previously traded. 8 International equities that are cross-listed on the domestic market are eliminated from the sample of domestic firms. The time series are sampled weekly and the data sample spans nearly a twelve-year period from January 4, 1984 to October 25, Domestic portfolios Within each country, equities are classified according to industry, firm size and domestic/multinational status. The four industry classifications are consumer goods and services, energy and utilities, finance and real estate, and industrials. Classification by firm size is based on firm market capitalization relative to industry capitalization. The three classifications are small, medium and large. In addition, each equity is classified as a domestic or a multinational equity. Therefore, each country s portfolio includes 7 Lewis (2000) discusses the relationship between the risk-aversion parameter and the elasticity of intertemporal substitution parameter. She reports findings for a broader set of parameter values for an investor who holds a portfolio of market indices. 8 Our sampling of Japanese companies from the Datastream database yielded no delisted or bankrupt firms and no firms were allocated to the other industry classification (see Appendix A). Given the Japanese business environment, financially distressed companies may be dissolved in ways other than through bankruptcy. The extent to which delistings and bankruptcies occurred in Japan and were not covered by Datastream would cause our results to overstate the benefits of holding Japanese equities.

9 P.F. Rowland, L.L. Tesar / Review of Economic Dynamics 7 (2004) Table 1.1 Summary statistics by firm classification, Canada Number in population Number in sample Sample mean return Sample standard deviation Return per unit risk Canada domestic Consumer goods and services small medium large Energy and utilities small medium large Finance and real estate small medium large Industrial small medium large Canada multinationals Consumer goods and services small medium large Industrial small medium large Notes. Unless otherwise noted, the sample period is from January 4, 1984 to October 25, The returns are stated in percent return per week in the local currency. The return per unit risk is the sample mean return divided by the sample standard deviation. a maximum of twenty-four categories: half of the categories are domestic equities and half of the categories are multinational equities. Ideally, the portfolios of individual firms categorized by size and industry should be based on the entire set of firms within each country-industry-size class. Given the large number of firms in some of the categories and the lack of documentation about the status of many firms, we form value-weighted portfolios based on a random sample of firms from each category. 9 Sources in addition to the information provided by Datastream were 9 In forming country-industry-size portfolios, we include up to 30 firms within each type of portfolio (by industry, size and country), where size is based on the cumulation of market capitalization. Given the skewness in the distribution of firm size in the population, the large firms are oversampled in the sense that a large firm will almost certainly be included in the large portfolio, whereas there is only a small chance that a particular small firm will be included. We were more concerned about the representation of firm size as a factor than about the representation of a particular firm in the portfolio.

10 798 P.F. Rowland, L.L. Tesar / Review of Economic Dynamics 7 (2004) Table 1.2 Summary statistics by firm classification, France Number in population Number in sample Sample mean return Sample standard deviation Return per unit risk France domestic Consumer goods and services small medium large Energy and utilities small medium 0 large Finance and real estate small medium large Industrial small medium large France multinationals Consumer goods and services small medium large Industrial small medium large Note. The sample period of French firms is truncated to the period from July 17, 1985 to October 25, used to verify the status of each firm in our random sample. The weights within the sample portfolio change over time as the market capitalization of the firms in the portfolio changes. This ensures that the returns of the sample portfolio for each category are value weighted over the full time series. Details of the equity classification and the construction of the portfolios are explained fully in Appendix A. A listing of the multinational firms by country is provided in Appendix B. 10 Tables 1.1 through 1.7 provide summary statistics of the portfolios by size and industry for each of the seven countries. The first column of each of the tables shows the number of firms per category. For example, there are 787 small, domestic, consumer-goods-and-services firms in Canada covered by the Datastream database. Notice that no country has firms in all of the categories. The United States 10 Various studies have used different indicators of multinational status, such as foreign assets, foreign sales or the number of foreign subsidiaries. Each of these indicators has its own strengths and weaknesses. In this analysis, we used the Hoopes (1994) to obtain a list of companies with foreign branch operations. There is considerable overlap between our list of multinationals and the list of companies in Datastream that have foreign assets, for example.

11 P.F. Rowland, L.L. Tesar / Review of Economic Dynamics 7 (2004) Table 1.3 Summary statistics by firm classification, Germany Number in population Number in sample Sample mean return Sample standard deviation Return per unit risk Germany domestic Consumer goods and services small medium large Energy and utilities small medium large Finance and real estate small medium large Industrial small medium large 0 Germany multinationals Consumer goods and services small 0 medium large Energy and utilities small 0 medium 0 large Finance and real estate small 0 medium 0 large Industrial small medium large has the most non-empty categories with 21. The maximum size of the random sample is 30. Column two reports the number of firms in the sample portfolio. For example, the sample portfolio for the small, domestic, consumer-goods-and-services category in Canada contains 30 firms. Columns three through five provide sample mean returns, sample standard deviations, and the mean return per unit risk in local currency units for each category over the January 4, 1984 to October 25, 1995 period Datastream incorporates the dividend payment by multiplying the return due to price appreciation by the most recent dividend yield.

12 800 P.F. Rowland, L.L. Tesar / Review of Economic Dynamics 7 (2004) Table 1.4 Summary statistics by firm classification, Italy Number in population Number in sample Sample mean return Sample standard deviation Return per unit risk Italy domestic Consumer goods and services small medium large Energy and utilities small medium large Finance and real estate small medium large Industrial small medium large Italy multinationals Industrial small 0 medium large Note. The sample period for Italian firms is truncated to the period from January 15, 1986 to October 25, Exchange rates The benefits of diversification are examined from the perspective of an investor domiciled in each of the seven countries in our sample in local currency units. 12 The time series of exchange rates for the seven sample countries are the Datastream weekly exchange rates. Table 2 shows the mean and standard deviation of the exchange rates relative to the pound for our sample countries (UK excluded). For ease of comparison, the exchange rates are stated in pounds per foreign-currency unit International indices In the tests for global diversification, the extended-set portfolio contains international market indices from the countries other than the benchmark country. We use the weekly 12 Alternatively, we could calculate all returns in US dollars and assume that investors hedge their portfolios against exchange rate risk. It is difficult to obtain clear evidence on the extent of hedging in global capital markets, but survey evidence suggests that investors do not hedge fully against exchange rate risk (Bodnar et al., 1998). Indeed there is evidence that exchange rate fluctuations provide some of the benefits of global diversification. We leave the question of the benefits of global diversification based on hedged returns to future research.

13 P.F. Rowland, L.L. Tesar / Review of Economic Dynamics 7 (2004) Table 1.5 Summary statistics by firm classification, Japan Number in population Number in sample Sample mean return Sample standard deviation Return per unit risk Japan domestic Consumer goods and services small medium large Energy and utilities small medium large Finance and real estate small medium large Industrial small medium large Japan multinationals Consumer goods and services small medium large Industrial small medium large total-return index for each sample country as calculated by Datastream. 13 The sample means and standard deviations of the return series for each country-specific index are reported in local currency in Table 3.1 and in US dollars in Table 3.2. The third column of each table shows the return per unit risk (Sharpe ratio). Table 4 shows the correlations between market indices in US dollars Finite sample properties of the test The size and power characteristics of our test are a concern because the number of test assets is large. In related research, Bekaert and Urias (1996) present Monte Carlo simulation results indicating that the empirical size and power of GMM-spanning tests are adversely affected by an increase in the number of assets in the benchmark and extendedset portfolios conditional on a given sample size. This suggests that, for a given number of benchmark (extended-set) assets, the size and power characteristics deteriorate as the 13 The total-return index is a value-weighted index that includes dividend reinvestment. Dividend disbursements are incorporated into the index return through the most recent dividend yield on the component security.

14 802 P.F. Rowland, L.L. Tesar / Review of Economic Dynamics 7 (2004) Table 1.6 Summary statistics by firm classification, United Kingdom Number in population Number in sample Sample mean return Sample standard deviation Return per unit risk UK domestic Consumer goods and services small medium large Energy and utilities small medium large Finance and real estate small medium large Industrial small medium large UK multinationals Consumer goods and services small medium large Industrial small medium large Note. The sample period for UK firms is truncated to the period from December 17, 1986 to October 25, number of extended-set (benchmark) assets increases. This is a concern for our test because some of the test cases include as many as 21 assets in the benchmark portfolio and nine assets in the extended-set portfolio. The degradation of the size and power properties is mitigated, however, because our sample size (617 observations) is more than four times larger than the sample size used in the Bekaert and Urias simulations. We investigate the size and power characteristics of the GMM-spanning test used in this paper following the simulation methodology of Bekaert and Urias. (See Appendix C for a complete discussion of the simulation methodology and our results.) As shown in Appendix C, if the simulation is conducted with a sample size of 152 observations, our size and power results are consistent with those reported in Bekaert and Urias. We find that as the number of extended-set assets increases the size of the test increases and the power of the test decreases. However, the simulation results based on our larger sample size of 617 observations indicate that the adverse effects of increasing the number of test assets are minimal. (For specific results, see Table C.1.) These simulation results provide us with a high degree of confidence in our test results.

15 P.F. Rowland, L.L. Tesar / Review of Economic Dynamics 7 (2004) Table 1.7 Summary statistics by firm classification, United States Number in population Number in sample Sample mean return Sample standard deviation Return per unit risk US domestic Consumer goods and services small medium large Energy and Utilities small medium large Finance and real estate small medium large Industrial small medium large US multinationals Consumer goods and services small medium large Energy and utilities small 0 medium 0 large Finance and real estate small medium 0 large Industrial small medium large Table 2 Summary statistics for exchange rates Canada France Germany Italy per 100 lire Japan per 100 yen United States Mean rate St. dev Notes. The exchange rates are stated as pounds per unit of local currency. The exchange rate for Italy and Japan are stated per 100 units of lire and yen, respectively. The sample period is from January 4, 1984 to October 25, 1995.

16 804 P.F. Rowland, L.L. Tesar / Review of Economic Dynamics 7 (2004) Table 3.1 Summary statistics for the returns on the international indices (local currency) January 1984 October 1995 Sample mean return Sample standard deviation Return per unit risk Canada France Germany Italy Japan United Kingdom United States Notes. The rates of return are stated in percent return per week in the local currency. The return per unit risk is the sample mean return divided by the sample standard deviation. Table 3.2 Summary statistics for the returns on the international indices (US dollars) January 1984 October 1995 Sample mean return Sample standard deviation Return per unit risk Canada France Germany Italy Japan United Kingdom United States Table 4 Sample correlations of the dollar-returns on the international indices Canada France Germany Italy Japan UK US Canada France Germany Italy Japan UK US 1.00 Note. The sample period is from January 4, 1984 to October 25, Do multinationals provide diversification benefits? In this section, we examine the diversification benefits of multinational equities from two perspectives. First, multinational equities are added to a portfolio of domestic equities. Setting up the spanning test in this way reveals the marginal benefit of adding multinationals to a portfolio of purely domestic equities. The second test adds multinational

17 P.F. Rowland, L.L. Tesar / Review of Economic Dynamics 7 (2004) equities to a portfolio that contains domestic equities as well as international equity market indices. This test reveals the marginal diversification benefits of multinational equities relative to all assets available to the investor. If, for example, the returns of multinational firms tend to mimic international markets, the null hypothesis of spanning would be rejected in the first test but not necessarily in the second. If, on the other hand, multinationals provide diversification benefits that are different from the benefits provided by international markets, the null hypothesis of spanning could be rejected in the second case. All returns are unhedged and in local currency units. The significance of the spanning test and the associated utility gain are considered jointly. If the null hypothesis is rejected, we evaluate the relative magnitude of the utility gain. If the spanning test fails to reject the null hypothesis that the benchmark portfolio spans the set of broader assets, measurement of the utility gain is meaningless because we cannot conclude with a high level of statistical significance that the portfolio frontiers are, in fact, different. In the first set of tests, the benchmark portfolio is the set of domestic equities and the extended-set portfolio is the set of multinational-corporation equities. The results of the tests are reported in Table 5.1. We fail to reject the null of spanning for Canada, France, Italy, Japan and the United Kingdom. We reject the null of spanning for Germany and the United States at the 0.02 percent and 0.06 percent levels of significance, respectively. In these two countries, multinationals appear to offer statistically significant diversification benefits. Table 5.1 also reports the utility gains resulting from the shift in the efficiency frontier as multinationals are added to the set of domestic assets. The utility gains from adding multinationals appears to be sizable ranging from 5.97 to percent of permanent consumption. 14 The US investor receives the largest utility gain from adding multinational equities. The finding that US investors could have obtained sizable benefits from holding Table 5.1 Mean variance spanning tests and the utility gain from MNC diversification Canada France Germany Italy Japan UK US Sample: January 1984 October 1995 test statistic p-value #obs df Utility gain (percent) (γ = 2,θ = 5) Sharpe ratio change percent change absolute change Notes. The benchmark set is the set of domestic assets in each country. The extended set is the set of multinationals in that country. 14 In general, we tend to find large utility gains from adding assets to the benchmark portfolio. Gains of this magnitude are consistent with those reported in Lewis (2000) based on equity returns.

18 806 P.F. Rowland, L.L. Tesar / Review of Economic Dynamics 7 (2004) Table 5.2 Mean variance spanning tests and the utility gain from MNC diversification Canada France Germany Italy Japan UK US Sample: January 1984 October 1995 test statistic p-value #obs df Utility gain (percent) (γ = 2,θ = 5) Sharpe ratio change percent change absolute change Notes. The benchmark set is the domestic assets and an equally-weighted portfolio of the six international indices. The extended set is the set of multinationals in that country. The sample data for France, Italy and the United Kingdom are not available for the entire time series. The data series for France begins on July 24, The data series for Italy begins on January 15, 1986 and the data series for the United Kingdom begins on December 24, multinationals may provide part of the explanation for home bias in the US, though it does not resolve the puzzle for other countries. The diversification benefits measured by the change in the Sharpe ratio are consistent with our utility-gain metric. Two of the three largest percentage changes in the Sharpe ratios are Germany and the US. Canada has the second largest percentage change in its Sharpe ration but we fail to reject that the Canadian portfolio frontiers are significantly different. In the second set of tests (Table 5.2), the benchmark portfolio is the set of domestic equity and the set of international equity market indices. The extended-set portfolio is the set of multinationals. The international market indices are included in the benchmark portfolio as an equally-weighted portfolio. We reject the null of spanning for Canada, Germany and the US. This result suggests that for investors in these countries, multinationals offer diversification benefits, but the diversification benefits obtained are not offered by domestic or international assets. We leave the question of identifying the source of the diversification benefits provided by multinationals to future research. 6. International diversification benefits of market indices In this section, we examine the benefits of adding international stock market indices to a benchmark portfolio of domestic equities. To ensure that the domestic portfolio captures all of the possible diversification benefits available on the domestic market, multinationals are included in the benchmark portfolio. The purpose of our study is to isolate domestic and foreign sources of diversification benefits. Therefore, we depart from Errunza et al. (1999) in that we exclude cross-listed securities, ADRs, GDRs and country funds from the domestic portfolio because these securities are claims on foreign firms. Including these foreign securities in the domestic portfolio blurs the distinction between foreign and domestic assets. Furthermore, if the gains from diversification stem from holding a portfolio that includes cross-listed securities, then failing to reject the null of spanning does not help to explain home bias.

19 P.F. Rowland, L.L. Tesar / Review of Economic Dynamics 7 (2004) We consider the benefits of diversification from the perspective of investors domiciled in each of the seven countries covered by our study. The six remaining country indices are added separately to the set of domestic assets in order to consider the diversification benefits of each country index in isolation. The test results for the individual indices are reported in columns one through seven of Tables 6.1 through 6.7. Note that the spanning test is not reported for the market index of the country under consideration. The domestic market index is a linear combination of the sub-portfolios of domestic equities and is, therefore, redundant by definition. 15 The indices are also added jointly to the set of domestic assets in order to consider the diversification benefits of the market indices as a group. The market indices are added under two alternative specifications. The first specification combines the six indices into an equally-weighted portfolio. 16 The results of the spanning tests with respect to the addition of the equally-weighted index are reported in column 8, which is labeled Equal-wt. index. The second specification does not restrict the portfolio weights on the market indices. In this case, the extended-set portfolio contains six separate assets. This specification allows the indices to be held in various proportions, including short positions, along the portfolio frontier. Because the portfolio weights are unconstrained, the diversification benefits associated with this specification are found to be substantially larger than the diversification benefits from the addition of the equally-weighted index. The results of the spanning tests with respect to the addition of the set of market indices are reported in column 9, labeled All indices. Before turning to the specific results, an important feature of the data is worth noting. Recall from Table 3.1 that the returns (mean returns and risk-adjusted returns) in the Canadian market are low relative to the other six markets. As a result, if the portfolio weights are not restricted, an investor is likely to short equities with a low return per unit risk and go long in other available assets. Thus, investors from Canada can obtain substantial gains from international diversification by taking short positions in the domestic market and taking long positions in other markets. Conversely, investors from other markets may obtain substantial diversification benefits by holding a short position in the Canadian index and long positions in the other available assets. This will be confirmed in the results reported below US investors The US equity market is the largest equity market in the world so reviewing the results for this market is an appropriate place to begin. Table 6.1 reports the results of the spanning 15 Specifically, the covariance matrix derived from the returns of the benchmark assets and the domestic market index is singular and, therefore, the test statistic is not defined. Test results confirm the conjecture that the covariance matrix is singular or near-singular and that the domestic index is a linear combination of the domestic securities. This provides evidence that we have a representative sample of firms in our industry-size portfolios. 16 The equally-weighted portfolio includes all of the indices accept the index for the country under consideration. Therefore, the equally-weighted portfolio contains six indices. 17 We do not report the portfolio weights of the utility maximizing portfolios in the tables. They are available from the authors upon request.