Consumption habit and international stock returns

Journal of Banking & Finance 29 (2005) 579–601 www.elsevier.com/locate/econbase

Consumption habit and international stock returns Yuming Li a, Maosen Zhong a

b,*

Department of Finance, College of Business and Economics, California State University, Fullerton, CA 92834, USA b UQ Business School, The University of Queensland, Brisbane, Qld. 4072, Australia Received 17 February 2003; accepted 19 January 2004 Available online 24 June 2004

Abstract We use the consumption-based asset pricing model with habit formation to study the predictability and cross-section of returns from the international equity markets. We find that the predictability of returns from many developed countries’ equity markets is explained in part by changing prices of risks associated with consumption relative to habit at the world as well as local levels. We also provide an exploratory investigation of the cross-sectional implications of the model under the complete world market integration hypothesis and find that the model performs mildly better than the traditional consumption-based model, the unconditional and conditional world CAPMs and a three-factor international asset pricing model. Ó 2004 Elsevier B.V. All rights reserved. JEL classification: G15; G12 Keywords: Consumption-based CAPM; Habit formation; International asset pricing

1. Introduction Time variation of equity returns in the international markets has been the subject of extensive empirical studies in the finance literature. The empirical research under the world market integration hypothesis documents that expected returns on different countries’ equity indices are related to the risk premiums associated with the aggregate world market portfolio and exchange rates. (See, for example, Harvey, *

Corresponding author. E-mail addresses: [email protected] (Y. Li), [email protected] (M. Zhong).

0378-4266/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jbankfin.2004.05.020

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1991; Ferson and Harvey, 1993, 1998; Dumas and Solnik, 1995; De Santis and Gerard, 1997, 1998). Furthermore, using consumption-based asset pricing models, researchers have shown that the behavior of international equity and currency returns are related to risks associated with consumption (e.g., Wheatley, 1988; Braun et al., 1993; Chue, 2002, in press; Sarkissian, 2003). In particular, Chue (2002, in press) finds that a world representative-agent model with habit formation in the form of Campbell and Cochrane (1999) under a complete world equity market integration hypothesis can generate substantial time-varying co-movements of the first two moments of international stock returns. Sarkissian (2003) reports that the heterogeneous-agent consumption-based model of Constantinides and Duffie (1996) under incomplete consumption risk sharing can explain the international currency premiums better than the world representative-agent model. In this article we provide an empirical investigation of the predictability and crosssection of returns from the international equity markets using the representativeagent, consumption-based asset pricing model (CCAPM) with habit formation. Given the recent empirical evidence on the importance of habit formation and incomplete risk sharing in the international markets, we examine the relation between expected returns from each country’s equity market and the time-varying prices of risks associated with the world as well as local consumption. We study the portions of the time variation in each country’s expected stock returns that are explained by the world and local measures of consumption relative to habit. To generate time-varying prices of risks endogenously, we adopt the infinite-horizon non-linear habit specification of Campbell and Cochrane (CC, 1999) and the finite-horizon linear habit specification of Li (2001) for the world and local consumption. We find that time-varying expected returns from developed countries’ equity markets are consistent to some extent with the implications of the world consumptionbased model with habit. But the predictability of returns is not explained entirely by the world representative-agent model under complete market integration. While expected returns for some countries are inversely and significantly related to the world consumption relative habit, local consumption relative to habit is still significant and inversely related to expected returns from most developed countries’ equity markets. In addition to the empirical analysis of time-varying expected returns, we provide an exploratory investigation of the cross-sectional implications of the world representative-agent model under complete world market integration hypothesis. Following the scaled factor model approach proposed by Cochrane (1996) and implemented in Lettau and Ludvigson (2001b), we transform the conditional world consumptionbased pricing model into an unconditional multifactor pricing model where risk premiums reflect compensation for the risk of changing expected returns, beta risk associated with world consumption growth and risk of changing beta. Results indicate that the model performs mildly better than the traditional, unconditional consumption-based model, the unconditional and conditional world CAPMs and a three-factor international asset pricing model in explaining the cross-section of expected returns in the international equity markets. The rest of the article is organized as follows. Section 2 presents the methods of estimating the consumption-based CAPM with habit formation. Section 3 describes

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data and provides evidence of predictability of international equity returns. Section 4 discusses the empirical results and the last section concludes the paper. 2. The models 2.1. The model for time-varying expected returns Under the joint hypothesis of complete international market integration and complete consumption risk sharing, asset prices from all countries are determined by a common stochastic factor (e.g., Stulz, 1981a,b). In particular, in a world representative-agent model expected returns from assets in the world economy are related to the aggregate world consumption risk. We assume that the preference of a representative agent in the world economy is given by E

1 X t¼0

ð1cw Þ

dtw

ðCwt  Xwt Þ 1  cw

1

:

ð1Þ

Here Cwt and Xwt denote per capita consumption and habit in the entire world, respectively. The coefficients dw and cw are respectively the world time discount factor and utility curvature parameter. The level of world habit Xwt is external (Abel, 1990), depending on current and past per capita world consumption. In particular, we assume that habit is given by either the infinite-horizon non-linear habit process of CC (1999) or the long-horizon, linear habit process studied by Heaton (1995), Li (2001), among others. The world surplus consumption ratio, 0 < Swt ¼ ðCwt  Xwt Þ= Cwt < 1, represents an indicator of the state of world economy. A high value of Swt is indicative of worldwide economic expansion while a low value of Swt signals a worldwide recession. Let Ri;tþ1 denote one plus the rate of return on any asset in country i from time t to t þ 1. Then Ri;tþ1 satisfies the Euler equation of the following form:  cw Cw;tþ1 Sw;tþ1 Et ½Mw;tþ1 Ri;tþ1  ¼ 1; Mw;tþ1 ¼ ; ð2Þ Cwt Swt where Et represents the expectation conditional on the information set as of time t and Mw;tþ1 is the intertemporal rate of substitution of consumption of the world representative investor. We assume that asset returns and world consumption growth are jointly lognormally distributed. Similar to Li (2001), the Euler equation (2) for the world representative-agent model implies that expected excess returns on any asset in country i can be expressed as 1 e Et ½ri;tþ1  ¼  r2it þ cw ½1 þ kðswt Þcovt ðri;tþ1 ; cw;tþ1 Þ: 2

ð3Þ

In Eq. (3) and thereafter, where a lower-case letter denotes the natural logarithm of an upper-case letter, the risk premiums on each asset are the world price of risk, cw ½1 þ kðswt Þ, times the conditional covariance of the asset’s returns with world

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consumption. The world price of risk depends on the world utility curvature parameter cw and the world sensitivity function kðswt Þ which measures the conditional sensitivity of Swt on Cwt . While cw is constant, kðswt Þ is inversely related to the world surplus consumption ratio Swt , implying that investors around the world require higher expected returns on assets in each country, when world consumption falls toward habit. If the international capital markets are completely segmented, asset prices from each country reflect the stochastic discount factor for the country. Similar to Eq. (3), the expected excess (log) returns from each asset in country i can be written as 1 e Et ½ri;tþ1  ¼  r2it þ ci ½1 þ kðsit Þcovt ðri;tþ1 ; ci;tþ1 Þ: ð4Þ 2 Expected excess returns on any asset in country i reflect compensation for the asset’s covariance with consumption growth in the country. The term ci ½1 þ kðsit Þ stands for the local price of covariance risk in country i, and kðsit Þ is the local sensitivity function representing the conditional sensitivity of Sit to Cit . Like the counterpart under complete integration, the local sensitivity function kðsit Þ is inversely related to the local surplus consumption ratio Sit , ceteris paribus. Similar to the market-based partial integration tests in the literature, 1 we consider a consumption-based analogue where expected excess returns in each country are expressed by the following econometric model: 1 e  ¼  r2it þ /it cw ½1 þ kðswt Þcovt ðri;tþ1 ; cw;tþ1 Þ Et ½ri;tþ1 2 ð5Þ þ ð1  /it Þci ½1 þ kðsit Þcovt ðri;tþ1 ; ci;tþ1 Þ: In Eq. (5), expected excess returns are a weighted average of those given by Eqs. (3) and (4) respectively. The weight 0 6 /it 6 1 stands for the fraction of country i’s expected returns at time t that are related to their covariance with world consumption. If the international equity markets are partially integrated, 0 < /it < 1. Eq. (5) suggests that expected excess returns in each country are inversely related to the lagged world and local surplus consumption ratios. Linear approximations to the sensitivity functions kðswt Þ and kðsit Þ imply that the expected excess return on each asset in country i can be written as e Et ½ri;tþ1  ¼ ai0 þ ai zt þ biw swt þ bii sit :

ð6Þ

In Eq. (6), the forecasting variables swt and sit represent the demeaned world and local log surplus consumption ratios, respectively, and zt is a vector of demeaned information variables. The slope coefficients biw and bii are constants. Here sit is orthogonal to swt , and zt is orthogonal to both swt and sit . The time-varying Jensen’ alpha, ai zt , captures the time-varying degree of integration and time-varying conditional variances and covariances as well as the linear approximation error in Eq. (6). In fact, the variances and covariances of international stock returns with world and local consumption growths are generally time-invariant in our data set (results are available upon request). 1 Empirical studies on integration include, e.g., Chan et al. (1992), Errunza et al. (1992), Bekaert and Harvey (1995), Carrieri et al. (2001), and Dumas et al. (2003).

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The model for expected one-period returns in Eq. (6) can be easily extended to a e e e model for expected returns over multiple periods. Let ri;tþ1;tþK ¼ ri;tþ1 þ þ ri;tþK denote the cumulative excess returns with continuous compounding for country i over K periods. If the surplus consumption ratios are highly persistent, they should be able to predict multi-period returns. More specifically, we write expected K-period excess returns as e Et ½ri;tþ1;tþK  ¼ aKi0 þ aKi zt þ bKiw swt þ bKii sit :

ð7Þ

In Eq. (7), aKi is a vector of constants and bKiw and bKii are constant slope coefficients. 2 In addition, expected returns at each horizon K should be inversely related to the lagged world and local log surplus consumption ratios, bKiw < 0 and bKii < 0 if biw < 0 and bii < 0, respectively. Under the assumption of complete market integration, expected returns in each country should be compensation for their covariance risks with world consumption only and consequently, time-varying expected returns in each country should reflect changing aggregate world price of risk rather than the local price of risk. In this case, bKii is zero and the last term in Eq. (7) vanishes. Otherwise, expected returns can also vary with the local price of risk: bKii 6¼ 0. Because the forecasting variables in the right hand side of (7) are orthogonalized, we can obtain the following variance decomposition of expected returns in each country: e varðEt ½ri;tþ1;tþK Þ ¼ varðaKi zt Þ þ varðbKiw swt Þ þ varðbKii sit Þ:

ð8Þ

Eq. (8) implies that the portions of the variation of expected K-period excess returns that is explained by the world and local log surplus consumption ratios can be measured respectively by the following variance ratios ðj ¼ w; iÞ: 0 6 VRKij ¼

varðbKij sjt Þ varðaKi zt Þ þ varðbKiw swt Þ þ varðbKii sit Þ

6 1:

ð9Þ

To assess the total portion of the predictable variation in each country’s equity market returns that is explained by the world and local surplus consumption ratios, we also calculate the total variance ratio as the sum of the world and local variance ratios, 0 6 VRKi  VRKiw þ VRKii 6 1:

ð10Þ

Under the null hypothesis that the world representative-agent model explains all of the predictability in each country, we have VRKii ¼ 0. In general, the larger is VRKii as compared to VRKi , the greater is the extent the international equity markets are explained by local habit formation. If habit formation explains all of the predictability in country i, we anticipate the total variance ratio to be unity: VRKi ¼ 1. We use the generalized method of moments (GMM) of Hansen (1982) to estimate Eq. (7) along with the local and total variance ratios given by Eqs. (9) and 2 Similar to Campbell et al. (1997), if sjt ðj ¼ w; i) follows an AR(1) process with an autocorrelation coefficient hj , then the law of iterated expectations implies bKij ¼ bij ð1  hKj Þ=ð1  hj Þ.

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(10) simultaneously for each country. Following Ferson and Harvey (1993) and Li (2001), we construct the following disturbance terms: e uK1t ¼ ri;tþ1;tþK  ðaKi0 þ aKi zt þ bKiw swt þ bKii sit Þ; 2

2

2

2

2

2

ð11Þ 2

uK2t ¼ ½ðaKi zt Þ þ ðbKiw swt Þ þ ðbKii sit Þ VRKii  ðbKii sit Þ ;

ð12Þ 2

2

uK3t ¼ ½ðaKi zt Þ þ ðbKiw swt Þ þ ðbKii sit Þ VRKi  ½ðbKiw swt Þ þ ðbKii sit Þ :

ð13Þ

We use orthogonality conditions, E½uK1t ð1; zt ; swt ; sit Þ ¼ 0 and E½uK2t  ¼ E½uK3t  ¼ 0, to construct an exactly identified system. The estimates of aKi0 , aKi , bKiw and bKii are numerically equivalent to OLS regression coefficients. The advantage of using the GMM system is that we can compute the asymptotically consistent standard errors for these coefficients as well as VRKii and VRKi . 2.2. Cross-sectional implications In addition to time-series implications for predictability of returns, the world representative-agent model with habit under the complete international market integration hypothesis should also help explain the cross-section of unconditional expected returns in the international equity markets. While one can take an unconditional expectation in Eq. (3) to obtain unconditional expected returns, we use a more general approach which does not rely on the existence of the riskfree rate. Following Cochrane (1996) and Lettau and Ludvigson (2001a,b), the stochastic discount factor given by Eq. (2) can be written, in a linear approximation, as Mw;tþ1 A0 ðswt Þ þ A1 ðswt ÞDcw;tþ1 ;

ð14Þ

where Dcw;tþ1 is the world consumption growth rate. To obtain a model for unconditional expected returns, we assume that A0 ðswt Þ ¼ a0 þ as swt and A1 ðswt Þ ¼ ac þ asc swt where coefficients a0 ; as ; ac and asc are constants. Then Eq. (14) can be rewritten as Mw;tþ1 a0 þ as swt þ ac Dcw;tþ1 þ asc ðswt Dcw;tþ1 Þ:

ð15Þ

While the approximation in Eq. (14) is in a conditional single-factor form, where the intercept and the fundamental factor Dcw;tþ1 are scaled respectively with time-varying coefficients, A0 ðswt Þ and A1 ðswt Þ, Eq. (15) is in a scaled multifactor form with constant coefficients. By substituting the right-hand side of Eq. (15) into Euler equation (2), one can obtain the following scaled multifactor beta pricing model, E½Ri;tþ1  ¼ k0 þ bis ks þ bic kc þ bisc ksc ;

ð16Þ

where bis , bic , and bisc represent constant factor sensitivities from the multiple regressions Ri;tþ1 ¼ bi0 þ bis swt þ bic Dcw;tþ1 þ bisc ðswt Dcw;tþ1 Þ þ ei;tþ1 :

ð17Þ

The intercept k0 is the expected return on the zero-beta portfolio. If a common riskfree rate exists in the international markets and the linear factor model is correctly

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specified, k0 should be the same as the riskfree rate. The other coefficients ks ; kc and ksc are constant premiums for the variable factors swt , Dcw;tþ1 and swt Dcw;tþ1 , respectively. Collecting terms on Dcw;tþ1 in Eq. (17), we obtain the conditional beta for country i’s returns on the world consumption growth as Biwt ¼ bic þ bisc swt . To ease interpretation, we assume that swt and Dcw;tþ1 are demeaned so time-varying expected international stock returns are captured by Et ½Ri;tþ1  ¼ bi0 þ bis swt . This implies that the scaled multifactor pricing model (16) is essentially a conditional CCAPM with timevarying betas and expected returns whose time-series fluctuations are driven endogenously by the world log surplus consumption ratio swt . The risk premiums in the model reflect compensation for the risk of changing expected returns, beta risk associated with world consumption growth and risk of changing beta. We estimate the scaled multifactor pricing model (16) using a two-pass time-series and cross-sectional regression method. Compared with alternative ways of estimating the model, this method is easy to implement, generating statistics with straightforward economic interpretations. Given that the coefficients in Eq. (17) are assumed to be constant, we first run a single time-series multiple regression with data throughout the full sample period to obtain estimates of bis ; bic , and bisc . Then we perform a single cross-sectional regression of time-series average returns from international stock indices on the estimated bis ; bic , and bisc . Following Jagannathan and Wang (1996), we use the R2 statistic of the cross-sectional regression to measure the goodness of fit of the model in explaining the cross-sectional variation of average returns. The conditional world consumption CAPM can be reformulated as the conditional world market-based CAPM. In the representative-agent model of CC (1999), consumption growth and consumption-claim returns are perfectly correlated, conditional on the lagged surplus consumption ratio since consumption growth is the only source of uncertainty. This suggests that the world consumption growth in the stochastic discount factor (14) and consequently in the scaled multifactor model (16) can be replaced with the return on the world market portfolio Rw;tþ1 . Further, if the preference of the world representative agent is simplified to the form of power utility, the coefficients in the stochastic discount factor (14) become constant. The conditional consumption CAPM (16) or the market-based CAPM are reduced to unconditional models. If time-varying investor risk aversion associated the habit-based utility preference is relevant for explaining the cross-section of returns in the international equity markets, the conditional consumption and market-based CAPMs should perform better than the corresponding static models. We use the two-pass regression technique described earlier to evaluate the performance of the alternative models plus a threefactor model similar to the multifactor model estimated by Ferson and Harvey (1993).

3. Data and preliminary evidence on predictability 3.1. Data We use quarterly data of 17 national stock price indices from the Morgan Stanley Capital International (MSCI) throughout the period 1969:Q4 to 2000:Q4. These

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indices represent value-weighted portfolios of large firms traded in the national equity markets. We calculate quarterly excess stock returns as quarterly gross returns in the US currency less the US 3-month Treasury bill rate. We also calculate annual excess returns by summing up four quarterly excess returns with continuous compounding. As our model of international partial market integration requires national and world consumption indices simultaneously, our study of the predictability of returns includes data from the 13 countries with local consumption data available for the period. Later in a cross-sectional analysis of international equity returns, we use data of stock market indices from all of the 17 countries plus the MCSI world index. Due to data availability, we use the non-durables and services consumption for the US to accord with most of studies of the US domestic equity markets. For the remaining countries, the consumption data of each country are household or private total consumption within the country. We construct a 13-country GDP-weighted world consumption index, analogous to the MSCI trade-weighted world stock market index. The quarterly growth rate of this index is a weighted average of the real per capita seasonally-adjusted consumption growth rates of the 13 countries mentioned above, with these countries’ shares in the aggregate Gross Domestic Product (GDP) in US dollars at the beginning of each quarter as weights. 3 We examine the predictability of international stock returns produced by the world and local information variables. Following the literature, we use the world information variables to capture the movements of the world business cycles and other global economic conditions. Similarly, we use the local information variables to capture the variation of expected returns with the local business cycles. In particular, we choose to include three world information variables and two local information variables in our analysis, motivated by previous studies on the US and international markets (e.g., Harvey, 1991; Bekaert and Harvey, 1995, 1997; Lettau and Ludvigson, 2001a). The world information variables are: (1) the US log consumption-wealth ratio (CWR); (2) the term spread (TRM), calculated as the US 10-year bond yield minus the 3month US bill rate; and (3) the relative 3-month Eurodollar rate (EUR), defined as the 3-month Eurodollar rate minus its one-year backward moving average. The local information variables are: (1) the domestic log consumption-price ratio (LCP), defined as the log of local consumption divided by the local stock market index; and (2) the domestic relative short-term rate (LRR), defined as the domestic short-term rate minus its one-year backward moving average. The appendix contains detailed descriptions of the sources and availability of data. 3.2. Summary statistics Panel A of Table 1 reports the summary statistics for excess stock returns and consumption growth rates for the 13 developed countries included in our study as well as the world equity or consumption index. We choose the moments of the con3

As discussed in Harvey (1990) and Sarkissian (2003), using this method of constructing world consumption index instead of simply aggregating the US dollar values of consumption from all countries avoids the extra volatility in world consumption growth rate induced by fluctuations in exchange rates.

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Table 1 Summary statistics Country

Excess returns Mean

Consumption growth Std. dev.

Autocorrelation

Panel A: Excess returns and consumption growth (%) Australia 0.301 12.515 )0.021 Austria 0.531 10.866 0.213 Canada 0.870 9.565 0.075 France 1.420 12.331 0.079 Germany 1.207 10.405 0.082 Italy 0.190 13.753 0.049 Japan 1.337 12.728 0.087 Norway 1.063 14.874 0.041 Spain 0.775 12.648 )0.074 Sweden 2.160 11.613 0.054 Switzerland 1.577 10.245 0.008 UK 1.375 11.271 0.072 US 1.269 8.301 0.055 World 1.011 8.197 0.015 Nonlinear model Mean Panel B: Surplus consumption Australia 6.543 Austria 12.425 Canada 5.970 France 8.756 Germany 18.671 Italy 7.763 Japan 11.430 Norway 11.847 Spain 6.967 Sweden 13.243 Switzerland 8.742 UK 10.179 US 2.809 World 3.669

Std. dev. ratios (%) 1.540 3.771 2.939 2.693 6.580 1.989 3.009 3.765 3.070 3.662 3.488 2.394 0.847 1.130

Mean

Std. dev.

Autocorrelation

0.449 0.626 0.424 0.426 0.492 0.703 0.557 0.531 0.581 0.393 0.328 0.568 0.529 0.499

0.898 1.910 1.001 1.261 2.341 1.160 1.612 2.111 1.137 2.063 1.285 1.423 0.443 0.529

)0.115 )0.384 0.114 0.021 0.135 0.315 )0.221 )0.339 0.124 )0.296 )0.235 )0.054 0.393 0.140

Mean

Std. dev.

Autocorrelation

5.184 6.233 4.615 4.513 4.861 6.490 5.495 6.183 5.312 4.813 3.715 5.783 5.568 5.453

1.457 2.087 3.120 2.525 4.857 3.361 2.563 3.551 3.462 3.274 2.055 3.093 1.438 1.468

Linear model Autocorrelation 0.897 0.964 0.972 0.962 0.852 0.920 0.943 0.941 0.971 0.930 0.967 0.905 0.912 0.928

0.775 0.606 0.752 0.556 0.673 0.824 0.734 0.599 0.799 0.617 0.680 0.789 0.945 0.890

The sample period is from the first quarter of 1970 to the fourth quarter of 2000. In panel A, all statistics are for excess log returns and log consumption growth rates. In panel B, means and standard deviations are for the surplus consumption ratios and the first-order autocorrelations and cross-correlations are for the log surplus consumption ratios. The nonlinear and linear habit processes with habit persistence u ¼ 0:95 are from Campbell and Cochrane (1999) and Li (2001), respectively.

sumption growth rates for each individual country’s or the world model to match the sample moments calculated from the observed data when the model is implemented based on the non-linear habit process of CC (1999). We pick the level of the habit persistence parameter u ¼ 0:95 for each country’s and the world model to

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correspond approximately to the median autocorrelation of the world and local information variables because the models used in the paper are intended to explain the return predictability associated with these variables. We assume that the utility curvature parameter cj ¼ 2 for the world and each country, as in CC (1999), Li (2001) and Chue (in press). For the linear habit model we calculate habit with the same level of the habit persistence and four-year lags of consumption so the level of habit moves slowly with past consumption. 4 The descriptive statistics for the surplus consumption ratios of each country’s and the world index are presented in panel B of Table 1. The autocorrelations are calculated with the log surplus consumption ratios. Based on the non-linear habit specification of CC (1999), the means and standard deviations of the surplus consumption ratios vary substantially across countries, while the first-order autocorrelations are close to the assumed habit persistence for most countries. With the linear habit process, we observe less dispersion in the means and standard deviations across countries but lower autocorrelations. Of particular interest is the world surplus consumption ratio. Based on non-linear and linear habit processes, on average 3.7–5.5% of world consumption is in surplus of the world habit and the autocorrelations of the calculated world log surplus consumption ratios fall within the range of 0.89–0.93. To what extent can the world and local information variables predict stock returns? Table 2 reports the estimated coefficients from multiple regressions using non-overlapping quarterly and annual data, p-values associated with v2 tests of excluding world, local or all information variables, and the adjusted R2 statistics of the regressions. Throughout the paper annual returns are calculated from the fourth quarter of each year to the third quarter of the next year to maximize the predictability of returns. In all tables hereafter, the estimated coefficients that are statistically significant at the 5% level and the p-values that are less than 5% are highlighted in bold. The standard errors of the estimated coefficients are not reported The statistical inferences in the regressions are adjusted for the heteroskedasticity of regression residuals. The exclusion tests of all information variables and the adjusted R2 statistics provide considerable evidence of predictability of international stock returns. The reported p-values show that the world and local information variables are jointly significant forecasters of quarterly returns from three countries (Spain, UK and US) and annual returns from eight countries. The adjusted R2 statistics for many countries are higher for annual returns than quarterly returns. In particular, while the adjusted R2 s from quarterly return regressions are less than 5% for all countries except Japan, regressions with annual returns produce adjusted R2 s exceeding 5% for nine countries. Further, for six of these countries (Australia, Italy, Japan, Norway, Spain and Switzerland), the adjusted R2 s are higher than 10%. The evidence indicates that the return predictability is economically significant in the international stock markets. 5 4

The empirical results are not particularly sensitive to the precise level of habit persistence and the number of lags used. In particular, with u ¼ 0:90 or 0.99, the results are similar. 5 We also perform the univariate variance ratio test of Lo and MacKinlay (1989) using quarterly, 1-, 2-, and 3-year horizons. These results (available upon request) generally reinforce the evidence of predictability of international stock returns.

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Table 2 Multiple regressions of non-overlapping excess returns on world and local information variables Country

p-Value for excluding Local

All

Adj. R2

Quarterly returns (K ¼ 1) Australia 0.048 Austria 0.718 Canada 0.565 France 0.235 Germany 0.272 Italy 0.780 Japan 0.047 Norway 0.115 Spain 0.489 Sweden 0.984 Switzerland 0.040 UK 0.008 US 0.003

0.201 0.638 0.134 0.252 0.697 0.096 0.055 0.074 0.007 0.925 0.480 0.769 0.235

0.107 0.666 0.402 0.111 0.227 0.325 0.056 0.254 0.033 0.993 0.079 0.036 0.002

0.033 )0.021 0.004 0.025 )0.003 0.009 0.057 0.018 0.036 )0.039 0.049 0.047 0.071

Annual return (K ¼ 4) Australia 0.046 Austria 0.043 Canada 0.707 France 0.123 Germany 0.003 Italy 0.341 Japan 0.000 Norway 0.077 Spain 0.469 Sweden 0.129 Switzerland 0.000 UK 0.142 US 0.221

0.016 0.084 0.091 0.345 0.419 0.014 0.001 0.010 0.026 0.507 0.032 0.290 0.843

0.103 0.133 0.041 0.262 0.001 0.004 0.000 0.009 0.011 0.037 0.000 0.263 0.188

0.155 )0.012 0.019 0.030 0.055 0.113 0.304 0.151 0.110 0.064 0.269 0.003 0.067

World

Exclusion tests are adjusted for heteroskedasticity and autocorrelation of residuals. The estimated coefficients significant at the 5% level and the p-values less than 5% for the exclusion tests are highlighted in bold. The world information variables in panel B include: (1) the US log consumption-wealth ratio (CWR); (2) the term spread calculated as the US 10-year T-bond yield less the 3-month US bill rate (TRM); and (3) the relative 3-month Euro dollar rate (EUR), calculated as the 3-month Euro dollar rate minus a one-year backward moving average. The local information variables in panel C are: (1) the domestic log consumption-price ratio (LCP), calculated as local consumption divided by the local stock market index; and (2) the domestic relative short-term rate (LRR), calculated as the short-term rate minus a one-year backward moving average. Annual returns are calculated from the fourth quarter of each year to the third quarter of the next year.

4. Empirical results 4.1. The results of estimating the partial integration model The results of estimating the CCAPM with world and local habit formation under the partial international market integration hypothesis using disturbance terms

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Table 3 The explanatory power of world and local log surplus consumption ratios in a partial integration model Country

World bKiw

Local bKii

1 qtr.

1 qtr.

1 yr.

Panel A: Nonlinear habit Australia 0.041 0.070 Austria 0.053 0.176 Canada 0.014 )0.037 France 0.015 )0.016 Germany )0.004 )0.068 Italy )0.009 )0.071 Japan 0.060 0.082 Norway 0.045 0.055 Spain 0.006 )0.047 Sweden )0.019 )0.169 Switzer0.010 )0.025 land UK )0.005 )0.048 US )0.026 )0.157 Panel B: Linear habit Australia 0.089 0.318 Austria 0.106 0.432 Canada 0.086 0.198 France 0.096 0.344 Germany 0.040 0.105 Italy 0.039 0.250 Japan 0.089 0.282 Norway 0.075 0.294 Spain 0.061 0.276 Sweden )0.007 )0.129 Switzer0.036 0.152 land UK 0.026 0.240 US )0.017 )0.004

Local VRKii

Total VRKi

p-Values for over-identification tests

1 yr.

1 qtr.

1 yr.

1 qtr.

1 yr.

1 qtr.

1 yr.

)0.077 )0.039 )0.019 )0.047 0.000 )0.104 )0.015 )0.017 )0.038 )0.034 )0.029

)0.082 )0.025 )0.053 )0.133 0.003 )0.596 )0.266 0.038 )0.135 )0.104 )0.110

0.24 0.14 0.17 0.19 0.00 0.33 0.00 0.03 0.19 0.31 0.17

0.01 0.00 0.06 0.09 0.00 0.43 0.03 0.01 0.17 0.10 0.12

0.37 0.58 0.22 0.21 0.00 0.34 0.19 0.19 0.19 0.45 0.18

0.03 0.20 0.08 0.09 0.07 0.45 0.05 0.02 0.17 0.37 0.13

0.960 0.175 0.000 0.265 0.000 0.021 0.420 0.326 0.000 0.762 0.828

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

)0.032 )0.050

)0.176 )0.109

0.05 0.21

0.15 0.08

0.05 0.31

0.17 0.42

0.200 0.154

0.150 0.000

)0.078 )0.023 )0.025 )0.007 )0.026 )0.053 0.007 0.004 )0.009 )0.005 )0.031

)0.042 )0.116 )0.019 )0.105 )0.025 )0.325 )0.043 )0.051 )0.028 )0.013 )0.188

0.29 0.05 0.23 0.01 0.23 0.39 0.01 0.00 0.03 0.11 0.34

0.01 0.06 0.02 0.11 0.03 0.48 0.00 0.04 0.02 0.01 0.61

0.59 0.79 0.59 0.34 0.39 0.44 0.29 0.17 0.21 0.14 0.41

0.28 0.55 0.28 0.59 0.15 0.63 0.11 0.25 0.23 0.09 0.72

0.857 0.193 0.044 0.036 0.607 0.015 0.497 0.076 0.363 0.207 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.538 0.000

0.023 )0.021

0.021 0.038

0.11 0.02

0.01 0.10

0.14 0.05

0.29 0.10

0.041 0.000

0.000 0.000

The following exactly identified system is estimated by the Generalized Method of Moments: Disturbance terms Orthogonal to e uK1t ¼ ri;tþ1;tþK  ðaKi0 þ aKi zt þ bKiw swt þ bKii sit Þ

uK2t uK3t

¼ ¼

½ðaKi zt Þ2 ½ðaKi zt Þ2

þ þ

ðbKiw swt Þ2 ðbKiw swt Þ2

þ þ

ðbKii sit Þ2 VRKii ðbKii sit Þ2 VRKi



ðbKii sit Þ2



½ðbKiw swt Þ2

1; swt ; sit ; zt 1 þ

ðbKii sit Þ2 

1

e represents the K-quarter non-overlapping excess return with continuous compounding in country ri;tþ1;tþK i. swt is the demeaned world log surplus consumption ratios based on the nonlinear or linear habit specification (persistence u ¼ 0:95). sit is the component of the local log surplus consumption ratio that is orthogonal to swt . zt includes the demeaned first lags of world and local information variables described in Table 1, orthogonal to swt and sit . VRKii (VRKi ) are the fractions of the variance of the K-quarter expected excess returns that are explained by sit (swt and sit ), respectively. The coefficients significant at the 5% level are highlighted in bold. The tests of overidentifying restrictions are conducted by including zt1 as additional instruments associated with disturbance term uK1t . With five information variables except the constant, the tests have five degrees of freedom.

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(11)–(13) are presented in Table 3. Let us first discuss the results in panel A, obtained by estimating the model with the non-linear habit process. If there is a representative agent in the fully integrated world markets, expected equity returns from each country should be inversely related to the lagged world surplus consumption ratio. For Germany, Italy, Sweden and US, the estimated coefficients bKwt are negative and statistically significant for the annual return horizon. For five other countries, the estimated bKwt are also negative but imprecisely estimated. As discussed earlier, if the world representative-agent CCAPM under the full integration hypothesis explains all predictability, we expect the local betas to be zero. In a striking contrast to this hypothesis, the estimated bKit in Table 3 are mostly negative and often significant for both quarterly and annual returns. Except for Germany and Norway, local betas are negative for both return horizons and significant for six countries at the quarterly horizon and 10 countries at the annual horizon. This implies that the local surplus consumption ratios are also informative about future stock returns from most countries. Further, the local variance ratios reported in panel A of Table 3 are non-negligible and statistically significant for many countries. They are 6% or higher and statistically significant for annual returns from five countries (i.e., Canada, Spain, Sweden, UK and US) but are relatively small or insignificant for the rest of countries. A comparison of the local and total variance ratios further reveals that the total variance ratios for a number of countries including US exceed local variance ratios by large margins, suggesting that habit formation and changing price of risk at the world level are important for explaining predictable variation of expected international stock returns associated with world business cycles. However, local habit formation makes significant marginal contributions for explaining the predictability for several countries, perhaps related to local business cycles. The results in panel B of Table 3 based on the linear habit process are less consistent with the inverse relation between expected returns and the lagged world surplus consumption ratio but still accord well with the inverse relation between expected returns and the lagged local surplus consumption ratios. The estimation results presented in the table are based on exactly identified systems. To conduct diagnostic tests of the model, we consider an over-identified system by including the second lags of the world and local information variables. With a total of five information variables, the system delivers over-identifying restrictions with five degrees of freedom. The two right columns of Table 3 report results of testing the over-identifying restrictions. For either the non-linear or linear habit specification, the restrictions are rejected for a few countries when the model is estimated with the quarterly data and all but one country when the model is estimated with the annual data. This suggests that the model does not explain all predictability, particularly for the annual return horizon. In the rest of the paper, empirical results will be based on the non-linear habit specification. 4.2. Evidence on international cross-sectional pricing We now move to the empirical investigation of the cross-sectional implications of the world CCAPM. For the sake of comparisons, we report in panel A of Table 4

592

Model

Risk premiums ( 100) for factors Const. k0

swt ks

cw;tþ1 kc

Panel A: World consumption-based model 1. 3.55 0.36 (4.94) (1.77) 2. 3.73 )11.52 0.45 (4.86) ()1.42) (1.85) 2a. 3.68 0.29 (4.81) (1.16) 2b. 3.36 )1.25 0.41 (4.61) ()0.14) (1.70) Panel B: World CAPM and multifactor models 3 2.08 (1.50) 4. 2.54 3.63 (1.66) (0.43) 5. 2.11 (1.66)

swt cw;tþ1 ksc

Rw;tþ1

swt Rw;tþ1

WEXB

WRB

0.07 (1.78) 0.06 (1.43)

1.89 (1.19) 1.28 (0.76) 1.82 (1.23)

0.58 (1.05) )0.03 ()0.05)

0.10 (0.51)

p-Value for

Cross-sectional

F-stat. v2 -stat.

R2 Adj. R2

Pricing error, % [p-val.]

0.088 0.076 0.117 0.083 0.081 0.349 0.180 0.405

0.551 0.523 0.704 0.641 0.595 0.541 0.256 0.157

0.542 [0.523] 0.440 [0.641] 0.515 [0.541] 0.698 [0.157]

0.132 0.233 0.094 0.493 0.112 0.617

0.192 0.142 0.330 0.186 0.257 0.098

0.728 [0.287] 0.663 [0.210] 0.698 [0.306]

Y. Li, M. Zhong / Journal of Banking & Finance 29 (2005) 579–601

Table 4 Risk premiums in factor pricing models from cross-sectional regressions

The risk premiums kj from the model E½Ri;tþ1  ¼ k0 þ bis ks þ bic kc þ bisc ksc are estimated from a cross-sectional regression using average returns from 17 countries (13 countries in Table 1 and Belgium, Denmark, Hong Kong (China) and Netherlands) plus the MSCI world index. Ri;tþ1 represents the quarterly US returns with simple compounding from the country or world index i. The coefficients bij are estimated in a single time-series multiple regression:

swt is the demeaned lagged world log surplus consumption ratio based on the nonlinear habit specification of CC (1999). Dcw;tþ1 is the demeaned current world consumption growth rate. The risk premiums in models 2a–2b are based on the same time-series regressions as for model 2 (e.g., for model 2a, bis 6¼ 0; ks ¼ 0). Model 3 is a world CAPM where Rw;tþ1 is the US dollar excess returns on the MSCI world index. Model 4 is a conditional CAPM where the scaled factors are swt , Rw;tþ1 and swt Rw;tþ1 . Model 5 is a three-factor model where the factors are world excess returns (Rw;tþ1 ), the first log difference in the trade-weighted average of US dollar prices of major currencies (WEXB), and the GDP-weighted average of the local real short-term interest rates from 17 countries (WRB). The Fama–MacBeth t-statistic is reported in parenthesis. The p-values in brackets for testing the joint significance of all risk premiums except the intercept are reported for the average F-statistic and the v2 statistic. R2 is the proportion of the cross-sectional variation of average returns that is explained by the crosssectional regression. The cross)sectional pricing error is the squared root of the average squared pricing errors across all portfolios. The p-value in bracket under the pricing error is for the v2 test of zero pricing errors for all portfolios.

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Ri;tþ1 ¼ bi0 þ bis swt þ bic Dcw;tþ1 þ bisc ðswt Dcw;tþ1 Þ þ ei;tþ1 ;

593

594

Y. Li, M. Zhong / Journal of Banking & Finance 29 (2005) 579–601

estimation results for the unconditional CCAPM (model 1), the scaled multiple factor model in Eq. (16) (model 2) and restricted versions of the model (models 2a and 2b) which are based on the same first-pass time-series regression as for model 2 but with the restriction that one of risk premiums is zero in the second-pass cross-sectional regression. Here our sample is expanded to include stock returns from all of the 17 countries plus the MSCI world index with data available from the beginning of the sample period. For each of the estimated coefficients of a model, we report the Fama–MacBeth t-statistic and the p-values associated with two statistics for testing the joint significance of risk premiums except the intercept: the average F-statistic and the v2 statistic. Next to the cross-sectional R2 and adjusted R2 is the cross-sectional pricing error, calculated as the squared root of the average squared pricing errors across all portfolios. The p-value under the cross-sectional average pricing error is for the v2 statistic testing the null hypothesis of zero pricing errors for all portfolios. The v2 tests of joint significance of risk premiums and pricing errors are multivariate generalizations to the Fama–MacBeth t-statistic. 6 First consider the results of estimating model 1: the unconditional CCAPM. The model indicates that the average zero-beta rate k0 , the implied risk-free rate, is positive. However, the estimated value of the average zero-beta rate k0 is large and precisely estimated according to the t-statistic, approximately twice the size of the average quarterly nominal US 3-month Treasury bill rate of 1.67% during the sample period. The inability of the model to explain the riskfree rate is found from estimating each of the models reported in Table 4 and consistent with findings from estimating domestic conditional asset pricing models by cross-sectional regression method (e.g., Jagannathan and Wang, 1996; Lettau and Ludvigson, 2001b). In addition to the average zero-beta rate, the CCAPM implies a positive risk premium kc for the world consumption risk. The estimate of kc is 0.36 with a t-statistic of 1.77, implying that the world consumption growth rate is priced at a 10% significance level in a two-tailed test and a 5% level in a one-tailed test. The R2 and adjusted R2 of the model are 55% and 52%, respectively, and the cross-sectional pricing error of the model is 0.54% with a p-value of 0.52. We now discuss the results of estimating model 2: the scaled multifactor model. The estimated coefficient ks is negative but imprecise while estimates of kc and ksc are positive and individually significant at a 10% level in a two-tailed test and a 5% level in a one-tailed test. The v2 test of joint significance rejects the hypothesis of zero premiums at the 10% level. The scaled multifactor model offers mild improvement in the goodness-of-fit, as the R2 and the adjusted R2 for the model are 70% and

6

Cochrane (2001) provides a detailed description of the test statistics in cross-sectional regressions. We also calculate t-statistic and v2 statistic with Shanken’s correction for errors in estimating the first-pass time-series regression coefficients. These statistics typically produce less significant results than those from the Fama–MacBeth procedure. However, since the assumptions of homoskedasticity and zero autocorrelation of residuals and factors underlying these asymptotically consistent statistics are violated by factors used here including swt , the Fama–MacBeth procedure does not necessarily overstate the significance of the estimated risk premiums (see Jagannathan and Wang, 1998).

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64%, respectively, which are higher than those from the unconditional CCAPM. The improvement in the performance can also be seen from the decline of the cross-sectional pricing error from 0.54% for model 1 to 0.44% for model 2. We find that much of the improvement vanishes if one imposes the restriction that the price ks for time-varying expected returns is zero. Indeed, the estimation of model 2a under this restriction generates a lower adjusted R2 statistics of only 54% and a higher cross-sectional pricing error of 0.51%. Alternatively, estimating model 2b under the restriction that the risk premium ksc associated with the time variation in the conditional betas is zero produces results that are less favorable than model 1. The results underscore the importance of risk premiums associated with both time-varying expected returns and time-varying conditional betas. To gain further insights, we provide scatter plots of average returns against each of the factor sensitivities in Fig. 1. Consistent with the coefficient estimates for model 2, there is an inverse relation between average returns and bis excluding Hong Kong but there are tendencies for expected returns to increase with bic and bisc . We note that while the estimated bic are mostly positive but the estimates of bis and bisc are not uniformly positive or negative. Changes in the signs of bis and bisc across countries indicate that the conditional expected returns, Et ½Ri;tþ1  ¼ bi0 þ bis swt , and consumption betas, Biwt ¼ bic þ bisc swt , are procyclical for some countries and countercyclical for other countries. Under the assumption that the world consumption growth rate is i.i.d., the conditional CCAPM implies that expected returns from all countries should be inversely related to swt , i.e., bis < 0. The positive estimates of bis may be evidence against the underlying assumption. Nevertheless, the difference in the cyclical variation of conditional expected returns or betas should help explain the cross-section of expected returns. To evaluate this effect, we report the component contributions (factor sensitivity times a factor risk premium) to average returns on all portfolios in Table 5. Overall, the last row of the table shows that cyclical variations in conditional expected returns Average Returns

Average Returns

Average Returns

8.0

8.0

8.0 Hong Kong

Hong Kong

Hong Kong 6.0

6.0

6.0 Sweden

Sweden

4.0

Sweden

4.0

4.0

Australia

2.0

0.0 -0.06 -0.04 -0.02 0.00 0.02 b(s)

0.04 0.06 0.08 0.10

2.0

-0.5

0.0 0.0

Australia

Australia

0.5

2.0

1.0

1.5 b(c)

2.0

2.5

3.0

3.5

0.0 -20.0 -15.0 -10.0 -5.0 0.0

5.0 10.0 15.0 20.0 25.0

b(sc)

Fig. 1. Average returns versus sensitivities to factors in the world conditional consumption-based model (model 2). b(s) is the sensitivity of returns to the lagged world log surplus consumption ratio. b(c) is the sensitivity of returns to current consumption growth. b(sc) is the sensitivity of returns to the lagged world log surplus consumption ratio times current consumption growth.

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Table 5 Component contributions to expected returns in the world conditional consumption-based model (model 2) Country

Average return

k0

bis ks

bic kc

bisc ksc

Pricing error

Australia Austria Belgium Canada Denmark France Germany Hong Kong Italy Japan Netherlands Norway Spain Sweden Switzerland UK US World Average

2.797 2.866 4.032 2.977 3.895 3.924 3.542 6.327 2.830 3.857 4.257 3.858 3.266 4.684 3.884 3.811 3.356 3.214 3.743

3.726 3.726 3.726 3.726 3.726 3.726 3.726 3.726 3.726 3.726 3.726 3.726 3.726 3.726 3.726 3.726 3.726 3.726 3.726

)0.482 )0.649 )0.168 0.017 0.016 )0.220 0.003 )0.907 0.067 )0.577 0.146 )0.595 )0.084 0.442 )0.035 0.100 0.376 0.102 )0.136

0.132 0.883 0.474 0.643 0.521 0.987 )0.088 1.414 0.187 0.210 0.177 1.365 )0.005 0.797 0.043 )0.115 0.032 0.121 0.432

)1.021 )0.540 )0.034 )0.657 )0.142 )0.682 )0.533 1.640 )1.054 0.597 )0.257 )0.496 0.173 )0.947 )0.475 )0.114 )0.316 )0.172 )0.279

0.442 )0.554 0.034 )0.752 )0.228 0.113 0.434 0.454 )0.096 )0.099 0.464 )0.142 )0.544 0.666 0.623 0.213 )0.464 )0.564 0.000

See notes to Table 4 for descriptions.

and world consumption betas make negative contributions to average returns, but an examination across countries reveals that the relative contributions vary substantially. For instance, given a negative risk premium ks , the large and negative bis produces a positive contribution (0.44) and the second highest high average returns from Sweden, while a positive bis generates a negative contribution ()0.48) and the lowest average returns from Australia. Additionally, the lowest returns from Australia and the highest returns from Hong Kong among the countries in our sample are explained in part by the estimated bisc for these two countries. Indeed, given the positive estimated risk premium kisc , a negative bisc makes a negative component contribution ()1.02) to Australia’s average returns and a positive bisc offers a positive component contribution (1.64) to Hong Kong’s average returns. The results, all together, indicate that the world CCAPM with habit formation performs better than the traditional CCAPM in explaining the cross-section of expected returns in the international equity markets. The cross-sectional analyses so far are limited to the consumption-based models. How does the performance of these models compare with that of the world CAPM or multifactor international models? To address this question, in panel B of Table 4 we report results of estimating the alternative models. Model 3 is an unconditional world CAPM where Rw;tþ1 is the US dollar excess returns on the MSCI world index. Model 4 is a conditional CAPM where the scaled factors are swt , Rw;tþ1 and swt Rw;tþ1 . Model 5 is a three-factor model where the factors are world excess returns (Rw;tþ1 ), the first log difference in the major currencies index (WEXM), and the GDPweighted average of the local real short-term interest rates from the 17 countries used

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in the cross-sectional regressions (WRB). The major currencies index, available from the US Federal Reserve Bank, represents a trade-weighted average of US dollar prices of major currencies of euro-area countries plus Canada, Japan, UK, Switzerland, Australia and Sweden. This three-factor model is similar to the multifactor model estimated by Ferson and Harvey (1993). It is noteworthy that the unconditional and conditional CAPM do not perform better than the corresponding consumption-based CAPM. The risk premiums in models 3 and 4 are not statistically significant individually or jointly at the 10% or lower levels. Although the conditional CAPM with the lagged log surplus consumption ratio as a conditional variable (model 4) outperforms the unconditional CAPM (model 3), the cross-sectional R2 statistic (33%) of the conditional CAPM are sharply lower than that of the conditional consumption-based CAPM (70% in model 2), with the cross-sectional pricing errors of the former notably higher than the later. The three-factor model (model 5) performs better than the unconditional CAPM (model 3) but worse than the conditional CAPM (model 4), based on the cross-sectional R2 and pricing errors. Indeed, none of the three factors appears to be priced as each of the risk premiums is imprecisely estimated. Scatter plots (available upon request) based on the results in models 3–5 further confirm that there are noticeable positive relations between average returns and the sensitivities associated with the world market portfolio returns and the interactions of the market returns with lagged world surplus consumption but the average returns are not related to risks associated with either exchange rates or real interest rates. Overall, the results suggest that the conditional world CAPM delivers moderate improvements in cross-sectional pricing over the unconditional CAPM and a three-factor model but fails to outperform the conditional world CCAPM. The results indicate that time-varying investor risk aversion, which is an essential feature in the conditional CAPM and CCAPM but not in the unconditional single or multifactor models, is important for explaining the cross-section of returns in the international markets.

5. Conclusion In this study, we use the consumption-based asset pricing model with habit formation to study the predictability and cross-section of returns from developed countries’ equity markets. We find that the predictability of expected returns from most of the developed countries’ equity markets are explained in part by time-varying consumption relative to habit associated with a common world stochastic discount factor. There is also evidence that time-varying expected returns from developed countries’ markets are related to consumption in surplus of habit within their own countries. More interestingly, our cross-sectional test shows that the conditional world consumption-based CAPM under habit formation outperforms a number of alternative models, including the unconditional world CCAPM and CAPM, conditional world CAPM and a three-factor international model incorporating returns on a world market portfolio, the exchange rate and the real interest rate as risk factors. The results

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suggest that the CCAPM under habit formation helps explain the behaviors of returns not only in the US but also in the international markets. The empirical finding of the paper provides some new insights into the issue of international asset market integration. The evidence that local habit formation helps explain predictability in addition to world habit formation suggests that the equity markets of developed countries might be imperfectly integrated, akin to some of the emerging market countries (e.g., Errunza et al., 1992; Bekaert and Harvey, 1995; Bekaert et al., in press). In this regard, the evidence presented here supports the theoretical notion (e.g., Errunza and Losq, 1985, 1989; Eun and Janakiramanan, 1986) that the equilibrium price of a security is determined jointly by its international and national risk premiums. However, interpreting the results as evidence of market segmentation is at odds with a significant literature on market integration based on multifactor pricing models (e.g., Hardouvelis et al., 2001; Dumas et al., 2003), which conclude that developed markets are integrated and the degree of integration has increased over time. In the earlier literature on international asset pricing, evidence of market segmentation has been attributed to barriers of cross-country investments (e.g., Stulz, 1981b, Errunza et al., 1992). Recently, however, Obstfeld (1994) observes that the integration among most of industrial countries increased after 1973 in terms of falling barriers to international investments, while the correlations of consumption growth rates still remain at low levels. Note that the world representative-agent model under the complete market integration hypothesis implicitly requires perfect cross-country consumption risk sharing so that the equilibrium of a world economy with heterogeneous investors facing country-specific risks is isomorphic in its pricing implications to the equilibrium of a representative-agent economy with only the aggregate world consumption risk (see Constantinides (1982, 2002) and Cochrane (2001) for discussions on the issue of consumption risk sharing). The empirical finding of explanatory power of the local consumption relative to habit in addition to the world counterpart may be explained by the existence of uninsurable country-specific idiosyncratic risks. Our findings are also complementary to the finding that incomplete risk sharing in domestic and the international markets has significant effects on asset pricing (e.g., Brav et al., 2002; Sarkissian, 2003), because the inability of investors to insure themselves against country-specific, idiosyncratic risks implies that investors in the international markets require compensation for local in addition to world consumption risk. The results of the paper present a challenge for the further development of an international asset pricing model to better understand the predictability and cross-section of international equity returns.

Acknowledgements The comments from participants at the 2002 European Finance Association Meetings in Berlin, Germany, the 2002 Financial Management Association Meeting and the 2002 Academy of Financial Service meeting in San Antonio, Texas, USA, and a seminar at the City University of Hong Kong are gratefully acknowledged.

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Helpful suggestions of two anonymous referees and Editor G.P. Szeg€ o are also appreciated. Part of the research was conducted when the first author was visiting University of California, Riverside and City University of Hong Kong. Appendix A. Data descriptions A.1. Real per-capital consumption The real per-capital consumption for each of the 13 countries excluding US is local consumption divided by the consumer price index (CPI) and the population. The consumption, population and CPI data are from the International Financial Statistics (IFS). The sample periods of consumption data for Australia, Canada, Japan, Norway, Sweden, UK and US are 1969Q4–2000Q4. For other countries, the sample periods are as follows: Austria (1969Q4–1999Q4), France (1969Q4– 1998Q4), Germany (1969Q4–1998Q4), Italy (1970Q1–1998Q4), Spain (1970Q1– 1998Q4), and Switzerland (1970Q1–2000Q4). Using regressions with seasonal dummy variables, we find that the quarterly consumption and GDP data obtained from IFS for three countries in our sample are not seasonally adjusted, including Austria, Norway and Sweden. We use the X11 procedure in the SAS program to convert these non-seasonally adjusted data into seasonally-adjusted units, to make them consistent with the data from US and other countries. 7 The annual population data for each country (in million) over 1969-2000 are interpolated to quarterly observations. The quarterly data of Gross Domestic Products (GDP) used to calculate the weights for the world consumption index are obtained from IFS. Most countries have GDP data over 1969Q4–2000Q4, except Sweden (1980Q1–2000Q4). We convert the GDP data into seasonally adjusted units if they are not already seasonally adjusted. We estimate Sweden’s seasonally adjusted GDP data for the period with missing data from the country’s seasonally adjusted consumption data under the assumption of a constant consumption/GDP ratio throughout the sample period because the observed data show little variability in the ratio. The exchange rates used to convert GDP data into US dollars are mainly obtained from IFS. Since January 1, 1999, the currency values of the 11 European countries have been fixed relative to that of euro. The exchange rates for country involved after this date are derived from the official fixed euro conversion rates obtained from the Federal Reserve Bank of St. Louis. A.2. Information variables The US consumption-price ratio is from Lettau and Ludvigson (2001a). The US 10-year Treasury bond yield, the US 3-month T-bill rate and the 3-month London Eurodollar rate are from the Federal Reserve Bank of St. Louis. The local 7 Ferson and Harvey (1992) examine asset pricing models using aggregate consumption data without seasonal adjustment.

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short-term interest rates are obtained from IFS. For Germany, Italy, Spain and Switzerland, the local short-term rates are not available for the full sample. We use the short-term rate of France as a proxy for these countries’ short-term rates because the short rate of France is more highly correlated with the short rates of these countries than the short rates of US, UK and other countries, during a sub-period in which the rates for all countries are available.

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