"AN EMPIRICAL INVESTIGATION OF INTERNATIONAL ASSET PRICING" by Claude J. VIALLET* N 87 / 02. * Claude J. VIALLET, INSEAD, Fontainebleau, France

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1 "AN EMPIRICAL INVESTIGATION OF INTERNATIONAL ASSET PRICING" by Claude J. VIALLET* N 87 / 02 * Claude J. VIALLET, INSEAD, Fontainebleau, France Director of Publication : Charles WYPLOSZ, Associate Dean for Research and Development Printed at INSEAD, Fontainebleau, France

2 AN EMPIRICAL INVESTIGATION OF INTERNATIONAL ASSET PRICING Robert A. Korajczyk Kellogg Graduate School of Management Northwestern University Claude J. Viallet INSEAD November 1986 Comments Welcome "Do not quote" or reproduce without the authors' authorization.

3 An Empirical Investigation of International Asset Pricing Abstract We investigate several alternative asset pricing models in ternis of their ability to price assets in an international setting. We use data on a large number of common stocks traded in the United States, Japan, the United Kingdom, and France. The pricing modela together with the hypothesis of capital market integration imply testable restrictions on multivariate regression modela relating asset returns to various benchmark portfolios. We find that the mispricing of international modela is generally smaller Chan their domestic counterparts and that the multifactor modela tend to outperform single-index "CAPM"-type models. While there is some evidance against ail the modela, the evidence is generally consistent with nontrivial international influences in asset pricing.

4 It is common to test asset pricing theories in a closed economy setting, in which assets are priced relative to benchmark portfolio(s) constructed from assets trading in the same economy. Fama and MacBeth (1973) and Roll and Ross (1980) are well known examples of single economy tests of the Capital Asset Pricing Model (CAPM) and Arbitrage Pricing Theory (APT), respectively. A variety of anomalies, relative to standard asset pricing models have been uncovered in the markets studied here. In particular, seasonal, firm size, and dividend yield related mispricing have been documented. 1 In this paper we present the pricing performance of alternative international and domestic asset pricing models. The models are compared when pricing assets within selected closed economies and, in their international versions, when pricing the whole set of assets across economies. The pricing models together with the hypothesis of capital market integration imply testable restrictions on multivariate regression models relating asset returns to various benchmark portfolios. Conditional on capital market integration, the tests provide information on the validity of the modal. Conversely, given that the assumed type of model is correct, the tests provide information about integration across markets. We compare domestic and international versions of the single index CAPM 2 (using equal-weighted and value-weighted market portfolios); a multifactor model in which the factors are prespecified to be the market portfolio proxies from the different countries; and mulifactor (5 and 10) models in which the pervasive factors are estimated by an asymptotic principal components technique. 3 We are interested in whether the factor models have explanatory power over the CAPM in a domestic as well as in an international setting. Single economy applications of the APT have had some

5 2 success in explaining pricing anomalies. 4 The period of our study covers which we divide into three five year subperiods. In our tests we utilize a large number of securities from four different countries both for factor estimation and hypothesis testing. The countries are the United States, Japan, the United Kingdom, and France. The number of assets available for each time period and other information about the data are contained in Table 1. In a related study Cho, Eun, and Senbet (1986) reject an international version of the APT. The evidence presented here is consistent with their findings in that there is some evidence against the international APT. However, we wish to stress relative comparisons of alternative modela (e.g., domestic vs. international or APT vs. "CAPM"). Relative to the work of Cho, Eun, and Senbet (1986) our study may be somewhat less general sine we cover baver countries (four rather than ten). On the other band, for the countries which we do study we utilize many more securities. 5 The large number of cross-sections allows more precise estimation of the factors. Thus the studies are complementary in that they represent the tradeoff between breadth and depth of coverage. The next section of the paper contains a brief description of the alternative asset pricing modela. In Section II we describe the data used and the sources of the data. The techniques used to estimate the pervasive economic factors and test the alternative models are described in Section III while the empirical resuits are given in Section IV. A summary of our results and conclusions are given in section V. I. Alternative Asset?ricins Modela

6 3 We investigate the pricing performance of domestic and international versions of the CAPM and APT. The economic content of the CAPM [pointed out by Roll (1977)] or the APT (as used here) is that some particular benchmark portfolio or a linear combination of a group of benchmark portfolios lies on the minimum variance boundary of risky assets. 6 The domestic and international versions of the models differ in that only securities traded on the local exchange are included in the benchmark portfolios for the former modal while the benchmarks for the international versions include ail the assets in the semple. Since the basic models are rather well known we will merely state the implications of the models and concentrate our discussion on the problems associated with implementing the models empirically. The standard version of the CAPM postulates that the "market" portfolio is on the mean/variance efficient frontier which, in turn, implies that the expected return on each asset is linearly related to its "beta" (fl LM cov(r,r M )/var(r )). Assuming the existence of a riskless asset with return r F' we have that: E(r i ) r F ft [E(r ) - r F ] (1) LM or E(Ri) fliem where R i (r i - r F ) and y - [E(r M ) - r F In a closed economy setting the market portfolio, M, would be the portfolio of ail domestic assets weighted by their respective proportionate values. Extending (1) to an international setting generally involves more than replacing the domestic market portfolio with an international market portfolio. Exchange rate uncertainty and,

7 4 particularly, potential deviations from strict purchasing power parity can lead to incremental hedging demanda for assets. Under certain conditions 7 there is no excess demand for hedging exchange risks and we can proceed with a relation like (1). Note that in both domestic and international applications one is never able to obtain the true "market" portfolio relevant for the particular model. The tests of the pricing relation (1) for different proxies, M, are tests of mean/variance efficiency for these proxies. An assumption underlying the APT is that asset returns follow a factor modal: or r i g i + bilf1 + bi2f2 + r ii + b i f + c i + bikfk + c i where b ij is the sensitivity of asset i to factor j; E(f ) E(ci) E(f j c ) 0 for ail i and j; bi (bil,bi2... bik); and f (ff.,f k )'. The number of assets in the economy is assumed to be sufficiently large and the correlation across the idiosyncratic returns (ci's) is assumed to be sufficiently small that the idiosyncratic risk can be diversified away in large portfolios. Lack of arbitrage opportunities and existence of a riskless asset imply that or E(R i ) b i1 / 1 + bi b ikk (2) E(R i ) = b 7 where 7 (71,72,...,/k)s. Additional equilibrium conditions [as in Connor (1984)] can lead to the pricing relation (2) holding as an equality rather

8 5 than an approximation. Our empirical work below tests (2) as an equality. Solnik (1983) extends the APT to an international setting. With the assumption that exchange rates follow the same factor model as asset returns, Solnik (1983) finds that the standard APT pricing relation (2) can be applied directly in an international setting. 8 Table 2 presents the particular modela we test. Two of them, the CAPM- EW and the CAPM-VW, are models where the benchmark portfolios are the equalweighted and value-weightea portfolios, respectively. Another one, the 4- index modal, uses as benchmark portfolios the equally weighted indices from the four countries. This modal can be viewed as a version of (2) in which the factors are prespecified to be the four national indices. The last two, the APT-5 and APT-10 factor models, use statistically estimated factors. When possible, we investigated these models in 3 versions: domestic returns vs domestic benchmark portfolios, domestic returns vs international benchmark portfolios and international returns vs. international benchmark portfolios. In the first two versions, the models are applied to each country separately and in the third version to the whole set of asset returns in our semple. The domestic benchmark portfolios refer to each country indices or factors while the international benchmark portfolios refer to the whole semple indices or factors. II. Data Sources The selected countries, markets, and data sources are presented in Table 1. They are the result of a compromise between the data requirement of the asymptotic principal component analysis - a large number of securities in each country - and the availability of reliable data.

9 6 Reliable data bases on country security prices are not many. Further, existing data bases are usually limited to stock price data and cover different periods of time. Nevertheless we were able to collect data spanning 15 years of monthly stock returns for four countries, including the three world major markets: the New York Stock Exchange and the American Exchange, the Tokyo Stock Exchange, and the London Stock Exchange. The Paris Bourse was added in order to introduce in our sample a country with severe foreign exchange controls. The four markets represented nearly 65% of the world capitalization by the end of In order to take advantage of the increasing number of firms in individual country data bases over time and reduce the difficulties associated with parameter nonstationarity, the 15-year period was split in three subperiods of five years each, a period of time most common in empirical tests of asset pricing performed on monthly stock returns. As a result, our semple size increased by nearly 50% from the first to the last subperiod when the total number of securities represented 74% of the number of securities listed in the four exchanges. Our sample include only securities with non missing data over each subperiod. Returns from France, Japan, and the United Kingdom, adjusted for dividends, were transformed into dollar returns using end-of-month exchange rates from the Data Resources Incorporated data file. Excess returns were computed using the short term US treasury bill return from Ibbotson Associates (1985). III. Estimation of Pervasive Economic Factors and Hypothesis Tests A. Estimation of Pervasive Factors Our tests of the CAPM and the 4-factor market index model amount to

10 prespecifying the benchmark portfolios whose mean-variance efficiency is being tested. However, the assumed linear factor structure which underlies the APT Tends itself quit naturally to direct statistical estimation of the factors. In fact most empirical tests of the APT to date use standard factor analytic techniques to estimate either the factor ioadings or the factors. For our five and ten factor models we use the asymptotic principal components technique of Connor and Korajczyk (1986a). An advantage of their procedure is that it can utilize very large cross-sections to estimate the pervasive factors. Also, while the number of time periods, T, has to be larger than the number of assumed factors, k, it does not have to be larger than the number of assets, n. While maximum likelihood factor analysis is, in theory, more efficient than principal components, standard factor analysis packages cannot handle the number of cross-sections analyzed here (e.g., the international APT during the subperiod uses securities to estimate the factors). A brief outline of the asymptotic principal components technique is presented here. For full details, see Connor and Korajczyk (1986a). Assume that asset returns foliows an approximate k-factor model [in the sense of Chamberlain and Rothschild (1983)], that exact multifactor pricing holds (i.e., (2) holds as an equality), and that we observe the returns on n risky assets and the riskless interest rate over T time periods. Let Rn be the n x T matrix of excess returns; F be the k x T matrix of realized factors plus risk premia (i.e.,fit - f + lit) ; and B n be the n x T matrix of factor it loadings. The estimation procedure allows the risk premia, 7j t, to vary through time. Exact multifactor pricing implies that 7 Rn - BnF + en (3)

11 8 where: E(Fcn') 0 E(cn) 0 E(cncn') Vn. Define to be the T x T matrix defined by an x Rn/n and define Gn to be the k x T matrix consisting of the first k eigenvectors of an. Theorem 2 of Connor and Korajczyk (1986a) shows that Gn approaches a non-singular transformation of F as n 03. That is Gn LnF in where plim in O. The transformation Ln reflects the standard rotational indeterminacy of factor modela but is irrelevant for testing the multifactor pricing modal. In the empirical work that follows we assume that n is sufficiently large that we can assume that en is essentially the null matrix. Nota that, white we are working with cross-sections as large as 4757, the factor estimation method only requires the calculation of the first k eigenvectors of a T x T matrix. In our work T is equal to 60 (five year subperiods with monthly data). The necessary calculations can easily be done on a personal computer. For the domestic versions of the APT (ln is calculated over the assets traded on the domestic stock exchange. For the international version of the APT n n is calculatcd from the entire semple of assets. B. Tests of Alternative Modela Against General Alternatives The alternative asset pricing modela (1) and (2) each place testable restrictions on the relation between asset returns and the returns on the benchmark portfolios. If we let P dente the vector of returns on a generic benchmark proxy (i.e., the return on some market index for the CAPM or the return on either prespecified or estimated factors for the APT) then the

12 intercept in the regression of any asset's returns on P should be zero. Thus, given a sample of m assets and the regressions 9 R it a i + b i P t + it i 1, 2,* m; t 1, 2,...T (4) the pricing models imply the restriction H0* a 1 a 2 versus the general alternative hypothesis HA: a 1 o 0, a 2 s 0,... a m O. ' a m 0 (5) We will refer to a i as the mispricing of asset i relative to the benchmark P. We first test whether mispricing is non-zero across assets for each of our alternative benchmarks. Because of the well-documented January seasonal patterns in asset returns we also allow the mispricing of assets to differ in January from the mispricing common to all months. 9 This is done by estimating the regression R it alnj + a LJ DJt + bi P t + c it (6) where D is a dummy variable equal to 1 in January and zero otherwise. Jt Mispricing specific to January is measured by au while mispricing which is not specific to January is reflected in ainj. Naturally, the pricing models imply that both measures of mispricing are equal to zero. The specifics of the tests are presented in Section IV below. C. Tests Against a Specific Alternative -- Different Zero-Beta Rates An advantage of testing against general alternatives is that the test should reject any false null hypothesis, asymptotically. A disadvantage is that the tests may have low power in small samples. MacKinlay (1986) shows that testing against a specific alternative will, in some cases,

13 10 dramatically increase the power of the test. The specific alternatives. considered here is that the expected excess return on a zero-beta portfolio (relative to the international versions of the APT) is a) equal to zero for every country or b) equal across countries (but not necessarily equal to zero). If the asset pricing model is correct and international capital markets are fully integrated the implied zero-beta expected return should be equal across countries. Frictions across markets, on the other hand, can lead to different implied expected zero-beta returns. Let the expected excess zero-beta return be denoted as a E(Rz) - RF. In the appendix we show that (aven when a Id 0) the asymptotic principal components estimates of the factors converge to the true factors plus risk premia relative to the zero-beta return as long as the return on RF is well diversified. This implies that the intercepta in the regression (4) are equal to a. Our estimate a for each country is the intercept in a regression of the excess return of a domestic "market" portfolio on the international factors estimated using the technique described in Section III.A. Testing for equality, across countries, of the implied zero-beta excess return as well as testing I di 0 for each country is straightforward. D. Direct Comparison of Alternative Modela The above tests compare each modal to either general or specific alternative hypotheses but do not provide a direct comparison of the performance of two alternative modela (e.g., CAPM vs. APT or domestic vs. international). Such direct comparisons are difficult because the modela are non-nested, in general. Two modela are nested if one is a special case of the other. The CAPM is not a nested version of the APT nor are domestic modela nested versions of international modela (an exception here is the

14 11 single index CAPM models are nested within the four-index prespecified factor model). We use the non-nested hypothesis testing techniques of Davidson and MacKinnon (1982) to compare the performance of varions alternative models. The tests proceed as follows. We initially designate one model as the null model (e.g., the CAPM) and one as the alternative modal (e.g., the APT). Given a semple of m assets, the null and alternative models are estimated in a standard multivariate regression framework R (1 m P N )fl N + c (7) E(cc') (EN e IT) where: R the mt x 1 vector of asset returns; I m an m x m identity matrix; PN the T x kn matrix of benchmark proxies appropriate for the null hypothesis (P and k for the alternative); A A - the mkn x 1 vector of factor sensitivities (PA and ka for the alternative); c the mt x 1 vector of unexplained returns; e the Kronecker product. The fitted values from the multivariate regressions will be denoted by RN and RA while EN is the standard estimate of EN. The test of the null versus the alternative hypothesis suggested by Davidson and MacKinnon (1982) is a test of whether the fitted values from the alternative model can predict the residuals from the null model. That is, we test 0 0 in the regression

15 12 R - RN PNb + O(RA - RN) + y. (8) Where PN is mt x kn matrix formed by stack±ng PN m times, b is a kn-vector of coefficients and B is a single coefficient. Note that R - RN need note have zero mean sine the modela in (7) are estimated in their restricted forms (i.e., ai is constrained to equal zero). Under the null hypothesis bas a mean of zero and a covariance matrix of (EN 0 IT). Thus we can estimate (8) as a standard restricted "seemingly unrelated regression" casing EN as an estimate for MN. A value of 9 close to zero indicates that the alternative model has no explanatory power beyond that of the null model. The results of theses tests are presented in section IV below. IV. Empirical Results A. The Correlation Structure of Asset and Factor Raturas Before we proceed with the formel hypothesis tests we present some evidence on the covariance structure of asset returns across countries and evidence on the relation between market indices and our estimated factors. Table 3 is the semple correlation matrix of several national indices over the period. The index denoted US-CRSP is the equal-weighted index of NYSE and AMER stocks provided by CRSP. The other four indices are (insemple) equal-weighted indices of the assets used in this study. These assets are described in Table 1 and Section II of the paper. The CRSP index and the in-sample US index are very highly correlated (0.997). The correlations between the international indices range from 0.21 to 0.45 and are consistent with previous evidence. While there are important common movements in the various indices, there also appear to be substantiel

16 13 country specific components to the return series. Table 4.A provides some evidence on the relation between the country indices and our international factors estimated by the asymptotic principal components procédure. For each subperiod we use every asset with nonmissing data over the period to calculate fln Rn'Rn/n. This gives us a semple of 3225, 3829, and 4757 assets in the three subperiods, respectively. The eigenvectors of On are our estimates of the pervasive factors. Regressions of the excess returns of the national indices on the first five factors are reported in Table 4.A. The coefficients of determination (R 2 ) reported in the lest column indicate a very strong relation between the estimated factors and the indices for every country except France. Also, each of the five factors generally has significant explanatory power across ail countries (again with the possible exception of France). The resuits in Table 4..A and some extensive canonicat correlation analysis not reported here indicate that there are several common international factors across the countries investigated here. The estimated mispricing of each index relative to these five benchmark portfolios (in % per annum) is listed in the third column. The values of aree (economically) very negative but are not measured with much precision. Also, while the CRSP index and the in-simple US index are highly correlated (see Table 3) there seem to be some important differences in the estimated mispricing of these two indices. The estimated mispricing relative to the 10-factor APT is generally smaller (in absolute value). They are not reported in detail here in order to conserve space. We discuss these estimates of mispricing in more detail below. B. Tests of Mispricing versus a General Alternative As discussed in Section 111.B the asset pricing models imply the

17 14 intercepts are zero in a multivariate regression of asset returns on particular benchmark portfolios. One would normally proceed in testing the hypothesis of zero mispricing by estimating the restricted null model in the multivariate regression (equation (4) with the contraint ai O] and estimating the unrestricted version of (4) which allows the intercepta to be non-zero. Dente the restricted and unrestricted residual covariance matrix for the null hypothesis and general alternative as EN. Standard andega approaches to hypothesis testing in the multivariate regression model involve investigating the increase in the generalized variance (determinant) of the residual covariance matrix due to additional restrictions (as in likelihood ratio tests) or calculating quadratic forms relative to the inverse of E. Large values of m [i.e., many assets on the left band side (LHS) of equation (4)] present some difficulties in hypothesis testing. In particular, when m is larger than T the generalized variances are uniformly zero and the estimated residual covariance matrix is singular. There are several alternative techniques designed to avercome this problem. We use two different techniques -- grouping assets into portfolios and placing s priori restrictions on the residual covariance matrix. The most common approach is to group assets into portfolios on the basis of some instrumental variables. Thus, rather than having m individuel assets on the LHS of (4) we have p portfolios (with p «m). This makes testing feasible, allows more precise estimates of the parameters in (4), but also l'uns the risk of masking mispricing if the values of ai are uncorrelated with the instruments. The instrumental variable chosen here is the "size" of the firm as measured by the market value of the common equity at the beginning of the subperiod. 10 In the US firm size is correlated with

18 15 mispricing relative to a domestic CAPM [Benz (1981) and Keim (1983)] and some versions of a domestic A.PT (see footnote 4). An alternative to portfolio grouping procedures is to place, a priori, some restrictions on the form of the residual covariance matrix. The m x m unrestricted covariance matrix, E, has m(m+l)/2 distinct elements. By restricting the form of this matrix we can reduce the number of parameters which must be estimated. The particular restriction which we use in the assumption that E is diagonal. While it is unlikely that this assumption is strictly true (especially for the single index CAPM models) it may be a useful approximation. In addition, under reasonable conditions, 11 testing under this assumption will tend to reject too often. This implies that failure to reject the null using the diagonality assumption should not be reversed if one had the true E. On the other band, using the true E would be expected to reverse a number of rejections of the null. It may be possible to utilize the theory of multiple comparisons tests to get a bound in the other direction. We first test the null hypothesis (5) under this diagonality assumption. To do so we calculate the standard likelihood ratio (LR) statistic T-211(1D N 1/1 1) GA I] where D represents the estimate of E assuming diagonality and I I represents the determinant. Table 5 presents the number of subperiods for which the null hypothesis is rejected at the 5% level of significance. There are only a few

19 16 rejections of H0: a -0 across the four modela with the 4-index and APT-5 i models performing slightly botter than the others, especially when the benchmark portfolios are constructed acrosh countries. The hypothesis H0: a -0 is rejected nearly unanimously for ail the models, whatever the ij version, domestic or international: they seem to perform equally poorly with respect to the January effect. Most of the p-values, not reported here, cluster around zero when the hypothesis is rejected and around one when it is not. This clustering of the test statistics around the extrema ends of the distribution may be indicative of the non-diagonality of E causing large differences between the assumed and true sampling distributions of the LR statistic. The second «tries of tests of the null hypothesis (5) is performed using size portfolios. Since we do not have size data for the French stocks these tests are performed using US, UK, and Japanese stocks (the French stocks are included for the purposes of factor estimation). We rank stocks on the basis of market value on the month preceding the subperiod. For each country individually we form ton equally weighted domestic portfolios (the first containing the smallest 10% of the firms, etc.). We also create ton international size portfolios. To test for mispricing we use a modified likelihood ratio (MLR) statistic [set Rao (1973, p. 555)]. The MLR statistic for our hypotheses is given by [(IENI/IEGAI) - 1] ' (T kn 1 - P)/P (9) where T is the number of time series observations, kn is the number of benchmark portfolios, and p is the number of LHS assets. Under the null the MLR statistic has an F distribution with degrees of freedom equal to p and

20 T-kN+1-p. An advantage of the MLR over alternative test statistics (such as the Wald or unmodified LR statistics) is that its exact small semple distribution is known (when c has a multivariate normal distribution). We calculate the test statistic for each five year subperiod and each set of size portfolios. However, in order to conserve space we only report in Table 6 tests aggregated across the three subperiods and the number of rejections (at the 5% level). 12 When the alternative models are applied to each country's size portfolios separately, the p-values in panel A indicate a low level of rejection of H0: a i - 0 and H0: a LUJ 0 for ail iodais and of H U 0 for all modela 0: a except the CAPM-EW. The rejections are more frequent when the models are applied to the international size portfolios, 17 with the 4-index modal performing botter than the others when testing H0: a i - 0 and H0: a O. These results are insufficient to discriminate between LNJ the alternative modela. However, when the number of rejections over the subperiods are considered (panel B), it appears that the factor modela dominate the CAPMs when the modela are applied to domestic size portfolios. The 4-index modal is rejected the least often when the benchmark portfolios are international with the three other modela showing similar high frequencies of rejection. The power of the above tests increases with the number of assets in each size portfolio, ceterls paribus. Since the international size portfolios have many more assets than their domestic equivalents, a simple comparison of the test statistics may be insufficient to estimate the relative robustness of the different versions of the five modela. Hence, we present some graphical evidence of the relative magnitude of the mispricing of the alternative models in their three versions. Space limitations

21 prevent us from showing the whole set of graphs corresponding to each model and to each of their various versions. We choose to show only six graphs which best illustrate and summarize the most important and general findings of the detailed comparison. Figures 1 to 3 show the average over the three subperiods of the mean A of the absolute mispricing (lail) for the three versions of the modela presented in Table The graphs plot the mispricing for each size portfolio, from the smallest (Si) to the largest (S10). In all versions, mispricing is much langer for small size portfolios than for large size ones: actually none of our modes seem to fully explain the size related anomaly. Mispricing is relatively large (in economic ternis) for the CAPM-VW modal and varies considerably from one version to another in the CAPM-EW and the 4-index modela. On the other band, mispricing is relatively small and systematically smaller than in any other modal for the APT-5 and APT-10 modela. Differencas in mispricing between the five and tan factor modela are minimal, with the APT-10 modal showing the smaller mispricing, nearly systematically. When the three versions of this "best" modal are compared, the mispricing in the international version ( international returns vs international factors) is slightly loyer than in the two other versions. Although the process of averaging mispricing over the three country semples (United States, Japan and United Kingdom) could bide strongly divergent results across countries, this is not the case here. The same general conclusions hold for each of the three countries, individually. 18 Figures 4 to 6 plot the average January absolute mispricing (laul) for the saine size portfolios as in Figures 1 to They show four remarkable findings. First, whatever the versions of the alternative

22 19 models, the mispricing of the factor models are always smaller than of the CAPMs for ail size portfolios. Equivalent graphs on individuel countries show no CAPM with lover mispricing than the factor models. Second, the APT- 10 model is the only one for which there is no relation between mispricing and size in the three versions of the model. Third, this model shows the lowest January specific mispricing. These last two findings hold as well when each country is studied separately. In other words, the APT-10 modal seems to include seasonal factors not "picked up" by the alternative models. 15 Finally, the most general version of this modal show the lowest mispricing over the alternative versions. This is when the size portfolios are constructed on the whole set of assets from the four countries in our semple and regressed on the 10 pervasive factors extracted from this set. To summarize, although the statistics in Tables 5 and 6 failed to discriminate unambiguously between the alternative models when tispricing is considered, the analysis of the magnitude of mispricing in relation to firm size shows clearly the dominance of the factor models over the CAPMs. Moreover, the 10 factor models appears to be the only one among the alternative models to include factors with sufficient seasonality to "explain" January-specific asset return behavior. Finally, the international version of this model shows the lowest mispricing. C. Tests for Cross-Country Equality of Zero-Beta Returns As discussed in Section III.C, intégration of world capital markets and validity of the international APT imply that the expected zero-beta returns should be equal across countries. In addition, if the US treasury bill (used here as a proxy for the riskless interest rate) is a zero-beta asset, the implied zero-beta excess returns should equal zero. Let I dénote the

23 20 expected excess return on a zero-beta portfolio (I E(Rz) - RF). As shown in the appendix integration and the APT Lmply that ai a for every asset i regardless of the market in which the asse1 is traded. In this section, we test whether the data are consistent with equality of zero-beta rates across countries and whether the excess zero-beta return is zero. We utilize the regressions of market indices on the world factors reported in Table 4. Note that the OLS estimate of the intercept for country c (az) in the regression is an average of the individuai assets' intercept. Since, under the null hypothesis, ai a for ail i we have that a a for each country. In Table 4.B we present tests for equality of the c country intercepta and tests for equality of the (aus afr auk ajp) zero-beta returns to the US treasury bill rate (aus afr auk ajp 0) for the international APT-5 and APT-10 modela. There are tige sets of tests -- one in which the US index is the CRSP equal-weighted index and one in which the US index is the equal-weighted portfolio of in-sample assets. For the UK, Japan, and France the indices are equal-weighted portfolios of insample assets. Individually, vert' few of the intercepta are (statistically) significantly different from zero. The values of aus are significant relative to the 5 and 10 factor APT during the subperiod using the CRSP index while is never significant using the in-sample index. Our aus estimate of a is significantly positive relative to the 10 factor modal JP during The values of afr are large in economic ternis (from -1.05% to % per annum) but are measured with so little precision that they are not statistically significant. This Jack of precision for the French market index is reflected in the mach loyer values of R 2 relative to the

24 21 other indices. The persistent negative values of afr may be indicative of strong capital controls. When we test the hypotheses jointly across the indices we reject equality of the treasury bill and zero-beta mean returns for the first two subperiods using the CRSP index but only for the second subperiod using the in-sample US index. Equality of the zero-beta rates across countries is rejected for both factor modela in the subperiod and marginally rejected for the 10 factor model in the period using the CRSP index. Using the in-sample US index we reject equality across countries only for the APT-10 in the subperiod. We do not reject either of the hypotheses in the last subperiod from 1979 to The tendency to not reject the hypotheses in more recent periods may be evidence (albeit probably weak evidence) for a trend toward greater integration of these capital markets. D. Non-Nested Hypothesis Tests The above tests give us some idea of how each modal performs individually. Given two alternative modela (e.g., the domestic CAPM vs. an international CAPM) it is possible to reject both modela, accept (i.e., fail to reject) both modela, or accept one and reject another. In each case it is not generally possible to determine which model actually fits better 2n the basis of the test statistics clone. Even in the case where one modal is accepted and the other rejected, the rejected modal may fit the data better but be subjected to a test with greater power. The methods for testing non-nested alternative hypotheses described in Davidson and MacKinnon (1982) provide a way to directly compare to alternative models. As can be seen from (8) and the discussion in Section

25 22 III.D, the non-nested procedure tells us whether the fitted values from the alternative model can explain the residuals from the null model. The technique is not totally unambiguous sine a significant value of 0 in (8) does not imply that if we reversed the regression (i.e., investigated the explanatory power of the fitted values from the null on the residuals from the alternative) the value of 0 would be insignificant. In other words, it is possible for each model to have additional explanatory power over the other modal. Bearing this in mind we present the estimates of (8) which Davidson and MacKinnon refer to as the P test. As the dependent variables 0 on the LHS of (8) we use the sets of 10 size ranked portfolios used in section IV.B. Since size data are unavailable for our semple of French stocks, they are not included as LHS assets. They are used in the international market proxy or factor benchmark portfolios. Table 7 contains the P tests for domestic benchmark portfolios versus 0 their international équivalents. We investigate the equal-weighted CAPM, the 5 factor APT, and the 10 factor APT. For the CAPM-EW the values of 0 are very small and insignificant (except that the aggregated value for Japan borders on significance at the 5% level). The international 5 factor APT shows some additional explanatory power over the domestic APT-5 for the US and UK but not for Japan. The international APT-10 shows additional explanatory power over the domestic APT-10 for each country. Table 8 compares domestic and international versions of CAPM-EW to APT- 5 (panel A) and APT-10 (panel B). For the domestic benchmark portfolios the APT-5 has additional explanatory power, over CAPM-EW, only for the US assets while the APT-10 has significant explanatory power for the US and Japan. Using the international benchmark portfolios the APT-5 and APT-10 have very

26 23 significant explanatory power over the international CAPM-EW. While these tests are not totally unambiguous, they do suggest that international modela explain components of returns not explained by domestic models and the factor modela have explanatory power over the single-index CAPM modela. We are investigating alternative approaches to comparing these non-nested alternative modela. V. Conclusions We compare domestic and international versions of a several alternative asset pricing modela. The empirical results indicate that the mispricing of international modela is generally smaller than their domestic counterparts and that the multifactor modela tend to outperform single-index "CAPM"-type modela. There is some evidence against all of the modela especially in terme of pricing common stock of small market value firme. In addition, there is mixed evidence on the equality of zero-beta expected returns across countries in the international APT. However, the strongest evidence against equality of implied zero-beta rates is from the fixed exchange rate subperiod. The evidence is generally consistent with non-trivial international influences in asset pricing. Obviously, much remains to be done. We are currently investigating different econometric methods for comparing non-nested alternative asset pricing modela. Also, extensions of this work to additional markets may provide even stronger evidence for the importance of international considerations sine it is reasonable to expect that smaller open economies are influenced more strongly by international factors.

27 24 Appendix In some asset pricing models (particularly international models) the US treasury bill return is not the appropriate zero-beta return, i.e., rft E(rzt) - À. In this appendix we show that we need not assume that rpt - Xt or even that r is riskless in order to obtain valid estimates of the Ft pervasive factors and their associated risk premia (fit + Although r is riskless in nominal US dollar returns is easy to see that it may not Ft be riskless in real terms or relative to another currency. Under certain conditions we can use excess returns relative to any well diversified asset or portfolio. Let Rit rit - (i.e., we are calculating excess returns rat relative to asset 6). We assume that (a) rat is well diversified and (b) taking excess returns with respect to rat does not alter the basic nature of the factor structure (i.e., taking excess returns with respect to rat does not turn a k-factor model into a q-factor modal with q<k). These are stated more formally as: a) r + b f it St i t b) II(B*n'B*n) 1/4 5 c < for ail n where: B - B n - 0>" an n x 1 vector of l's; and B n is as defined in (3). Given these conditions, ail of the assomptions required by Connor and Korajczyk (1986a) hold and their Theorem 2 can be applied to show that Gn LnF + te with plim On - O. Now the pricing model Limites that E(rit) E(r zt ) b 7 and, hence, that E(r it ) E(r St ) - [E(r zt ) - E(r it )] + b i 7 - X t + b i 7. Under the assumption that 1 t 1, the intercept terms in (4) should

28 ail equal a as was stated in the text. If condition (b) does not hold then À will include the risk premier for the k-q factors that were eliminated. 25

29 26 REFERENCES Rolf W. Banz. "The Relationship Between Return and Market Value of Common Stocks." Journal of Financial Economics 9 (March 1981), "Evidence of a Size-Effect on the London Stock Exchange." Unpublished manuscript, INSEAD., 1985 Michael Beenstock and Kam-Fai Chan. "Testing Asset Pricing Theories in the U.K. Securities Market " Working paper *66, The City University Business School. Gary Chamberlain and Michael Rothschild. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets." Econometric4 51 (September 1983), Nai-Fu Chen. "Some Empirical Tests of the Theory of Arbitrage Pricing." Journal of Finance 38 (December 1983), D. Chinhyung Cho; Cheol S. Eun; and Lemme W. Senbet. "International Arbitrage Pricing Theory: An Empirical Investigation." Journal of Finance 41 (June 1986), D. Chinhyung Cho and William M. Taylor. "The Seasonal Stability of the Factor Structure of Stock Returns." Working paper *27, Department of Finance, Northwestern University, October Gregory Connor. "A Unified Beta Pricing Theory." Journal of Economic Theory 34 (October 1984), Gregory Connor and Robert A. Korajczyk. "Performance Measurement with the Arbitrage Pricing Theory: A New Framework for Analysis." Journal of Financial Economics 15 (Mardi 1986a),

30 27. "Risk and Return in an Equilibrium APT: Theory and Tests." Working paper *A, Department of Finance, Northwestern University, June 1986b. Russell Davidson and James G. MacKinnon. "Some Non-Nested Hypothesis Tests and the Relations Among Them." geview of Economic Studies 49 (October 1982), Phoebus J. Dhrymes. Introductory Econometrics. New York: Springer-Verlag, Pascal Dumontier. "Le modela d'evaluation par arbitrage des actifs financiers: une etude sur le marche financier parisien." Finance 7 (January 1986), Eugene F. Fama and Andre Farber. "Money, Bonds, and Foreign Exchange." American Economic Review 69 (September 1979), Eugene F. Fama and James D. MacBeth. "Risk, Return, and Equilibrium: Empirical Tests." Journal of Political Economv 71 (May/Juni: 1973), Frederick L. A. Grauer; Robert H. Litzenberger; and Richard E. Stehle. "Sharing Rules and Equilibrium in an International Capital Market Under Uncertainty." Journal of Financial Economics 3 (June 1976), Mustafa N. Gultekin and N. Bulent Gultekin. "Stock Market Seasonality: International Evidence." Journal of Financial Economics 12 (December 1983), "Stock Return Anomalies and the Asset Pricing Tests: The Case of the Arbitrage Pricing Theory." Unpublished Manuscript, University of North Caroline, October Gabriel Hawawini. Eurovean Eouity Markets: Price Behavior and Efficiency. Monograph *1984-4/5, Salomon Brothers Center for the Study of Financial

31 28 Institutions, New York University, Gur Huberman and Shmuel Kandel. "Mean Variance Spanning." Working paper *184, CRSP, Graduate School of Busineés, University of Chicago, July Ibbotson Associates. stocks. Bonds. Bills. and Inflation, 1985 yearbook. Kiyoshi Kato and James S. Schallheim. "Seasonal and Size Anomalies in the Japanese Stock Market." Journal of Financial and Quantitative Analysis, (June 1985), Donald B. Keim. "Size Related Anomalies and Stock Return Seasonality: Further Empirical Evidence." journal of Financial Economics 12 (June 1983), "Dividend Yield and Stock Returns: Implications of Abnormal January Returns." Journal of Financial Economics 14 (September 1985), Bruce N. Lehmann and David M. Modest. "The Empirical Foundations of the Arbitrage Pricing Theory I: The Empirical Tests." Research paper #291, Columbia University, August 1985a.. "The Empirical Foundations of the Arbitrage Pricing Theory II: The Optimal Construction of Basis Portfolios." Research paper #292, Columbia University, August 1985b. A. Craig MacKinlay. "On Multivariate Tests of the CAPM." Unpublished manuscript, Wharton School, University of Pennsylvania, June C. R. Rao. Linear Statistical Inference and its Abnlications, 2nd. ed. New York: Wiley, Richard Roll. "A Critique of the Asset Pricing Theory's Tests Part I: On Past and Potential Testability of the Theory." Journal of Financial

32 29 Zconomics 4 (Marck 1977), Richard Roll and Stephen A. Ross. "An Empirical Investigation of the Arbitrage Pricing Theory." Journal of'finance 35 (December 1980), Bruno H. Solnik. "An Equilibrium Model of the International Capital Market." Journal of Economic Theory 8 (August 1974), "International Arbitrage Pricing Theory." Journal of Finance 38 (May 1983), Rene M. Stulz. "A Model of International Asset Pricing." Journal of Financial Economics 9 (December 1981), Simon Wheatley. "Some Tests of International Equity Markets Integration." Working paper #44, Center for the Study of Banking and Financial Markets, GSB, University of Washington, 1986.

33 30 Endnotes 1. See, for example, Banz (1981) and Keim (1983, 1985) for evidence on US exchanges, Kato and Schallheim (1985) for the Tokyo stock exchange, and Benz (1985) for the London stock exchange. Seasonality in a number of international markets is documented in Gultekin and Gultekin (1983). 2. These tests amount to tests of mean-variance efficiency of the market proxy portfolio chosen. Only when we are willing to make specific assumptions about the relation between the proxy and the "true" market can these tests be regarded literally as tests of the CAPM. 3. We refer to these latter models as variants of the APT. 4. In the US, Chen (1983) finda that the size anomaly becomes insignificant when the APT is used while Lehmann and Modest (1985a) and Connor and Korajczyk (1986b) find a significant size affect remaining. Lehmann and Modest (1985a) do find that the dividend yield anomaly is no longer significant. In the UK, Beenstock and Chan (1984) find that the APT does significantly better than the CAPM in explaining asset returns, as does Dumontier (1986) using French stocks. 5. Compare the numbers in Table 1 to the number of securities used in Cho, Eun, and Senbet (1986) -- US (60), Japan (55), UK (48), and France (24). 6. See Huberman and Kandel (1986). 7. See, for example, Solnik (1974, pp ); Grauer, et al (1976, p. 241); and Fama and Farber (1979).

34 31 8. A consumption-based intertemporal international asset pricing model is derived in Stulz (1981). The model allows differing consumption/investment opportunity sets across countries. We do not e::amine consumption-based modela here. Wheatley (1986) performs tests of a consumption-based international asset pricing model. 9. We also test for an April seasonal in the United Kingdom. 10. Of:her common instruments include independent estimates of Pin (particularly in tests of the CAPM), dividend yield, and idiosyncratic risk [var(ci)]. 11. I.e., that the sign of a i a j is the same as the sign of cl ij 12. Several methods of aggregating F-tests have been suggested. We calculate the p-value (or right tail area) of our F-statisfic and find the value of x 2 random variable which has the same p-value (the degrees of freedom of the x 2 variable are equal to the numerator degrees of freedom of the F variable). We then sum the x 2 statistics across the subperiods. The aggregate statistic is compared to a x 2 statistics with degrees of freedom equal to the sum of the subperiod degrees of freedom 13. I.e., domestic size portfolios vs. domestic benchmark portfolios, domestic size portfolios vs. international benchmarks, and international size portfolios vs. international benchmarks. The value A of a for each size portfolio is an average of the estimates over the three subperiods. The mean absolute mispricing when domestic size portfolios are used is calculated as (lau la JP 1)/3. For the international size portfolios the mean absolute mispricing is

35 A merely the absolute value of a for that size portfolio For the United Kingdom, and contrary to the other two countries, we found that January mispricing as well as April mispricing tend to be independent of portfolio size, whatever the model. Further, UK January mispricing, across models, tend to be larger than the April mispricing. Hence, ve choose to average January mispricing across the three countries, including the United Kingdom. 15. This is consistent with seasonality is factor risk premia found by Gultekin and Gultekin (1985) and Cho and Taylor (1986).

36 Table 1 Exchange Market Data and Sample Data Summary COUNTRY UNITED STATES JAPAN UNITID KINGDOM FRANCE TOTAL EXchange Market Data NYSE & AMEX TOKYO LONDON PARIS Market Capitalization (12/83)a World Capitalization 43% 15% 6.1% 1% 65.1% Nunter of listel firme (12/83)a Sample Data Sanple source CRSP Japanese London Share Compagnie des Researdi Price Data Base Agents de Change Iristitute (JSRI) Frequency of returns Mbnthly Mbnthly Mbnthly Monthly Nimber of sample firms: Value-Weighted Index CRSP JSRI index Ail share index n.a. Equally-Weighted Index CRSP Fr am sample Fram sample From sample a: source - International Federation of Stock Exchange Statistics, 1983

37 Table 2 Mbdels Tested CAPM-EW CAPM-VW 4-INDEX APTL5 AFT-10 Bmigima redmark lignglamrk ikncks Penchmark Damestic Damestic Damestic Damestic Damestic Damestic Damestic Damestic Damestic Int'al Damestic Int'al Damestic Int'al Damestic Int'al Int'al Int'al Int'al Int'al Int'al Int'al Int'al Table 3 Sanple Correlation of Eglal-weighted National Market Index Portfolios US UK JAPAN FRANCE US-CRSP US UK JAPAN 0.377

38 Table 4 Regression of Market Index Excess Returns on Estimated International Factors Five Factor Modal A. Rit ai + flileit... flopst cit INDEX PERIOD mix x10 fli2x10 fli3x x10 8i5x10 R 2 US-CRSP UK JAPAN FRANCE US a b (-2.94) (128.48) (-21.92) (-5.46) (7.20) (1.01) (1.70) (106.23) (76.05) (-2.15) (-10.21) (5.10) (-0.55) (5.69) (-69.02) (-4.87) (-19.92) (-20.48) (1.53) (43.93) (46.64) (40.68) (-8.24) (6.51) (1.22) (113.37) (-61.15) (6.33) (-1.15) (8.19) : (0.57) (25.08) (-40.21) (-3.72) (3.73) (27.11) (1.09) (21.62) (39.72) (-34.35) (5.29) (-4.65) (1.76) (13.72) (-10.23) (-34.48) (-3.52) (-5.23) (-1.28) (16.42) (-25.36) (11.99) (43.04) (-10.42) (-0.14) (2.72) (4.22) (-0.09) (-1.09) (-2.69) (-0.90) (6.37) (-0.95) (-1.81) (-2.08) (-2.51) (-1.22) (0.74) (-3.57) (0.19) (1.19) (0.79) (-0.16) (124.63) (-21.63) (-3.78) (7.00) (0.18) (-0.07) (103.48) (73.52) (-0.97) (-15.15) (3.79) (-0.30) (5.57) (-63.21) (-3.99) (-17.89) (-19.58) 0.986

39 B. Tests for Equality of Implied Zero-Beta Returns from International APT. US-INDEX MODEL PERIOD Test (X3) egus-auk-ajp-afr Test (x 2 ) 4 aus-auk-ajp-afr- CRSP APT (0.003) (0.003) (0.514) (0.017) (0.543) (0.428) APT (0.004) (0.004) (0.042) (0.001) (0.572) (0.505) IN-SAMPLE APT (0.379) (0.126) (0.077) (0.041) (0.521) (0.457) APT (0.209) (0.057) (0.013) (0.001) (0.511) (0.560) Note: t-statistics in parentheses in Panel A, p-values in parentheses in Panel B. a: Unadjusted2R 2 b: Adjusted R

40 Table 5 Number of Rejections at the 5% level of significance of H : a = 0 in R = a + b P + e and R = O l l i l i INJ + a IJ D + b i P + ei over the three subperiods. E assumed diagonal CAPM-EW CAPM-VW 4-INDEX APT-5 APT-10 R 1 P oc1=0 a 1J =0 o _INJ =0 a 1 =0 a IJ =0 a INJ =0 a1=0 a 1J =0 a INJ =0 a1=0 a 13 =0 ainj «1 =0 a I3 =0 a inj =0 US US JP JP UK UK FR FR n.a. n.a. n.a US Int'l JP Int'l UK Int'l I FR Int'l Int'l Int'l

41 Table 6 Tests of H0: a - 0 for size portfolios in R - a + b P + c and Ri i i i i inj +a D+bP+ c Panel A: Tests aggregated over the three subperiodsa CAPM-EW CAPM-VW R i P a-0 i ai J-0 a iiij -.0 a i -0 aij-0 a -0 inj US US (.268) (<.001) (.428) (.154) (<.001) (.276) JP JP (.738) (.108) (.528) (.124) (.123) (.156) UK UK (.405) (.064) (.315) (.239) (.162) (.286) US Int'al (.182) (<.001) (.147) JP Int'al (.226) (.039) (.146) UK Int'al (.237) (.254) (.281) Int'al Int'al * * (<.001) (<.001) (<.001) 4-INDEX APT-5 APT-10 R i P ai-0 aij-.0 ailif0 ai-0 aiji.0 ainj-0 ai-0 an-0 US US (.015) (.160) (.061) (.011) (.043) (.072) JP JP (.467) (.139) (.332) (.265) (.225) (.184) UK UK (.633) (.009) (.503) (.797) (.239) (.758) US Int'al (.904) (<.001) (.966) (.523) (.001) (.678) (.180) (.180) (.082) SP Int'al (0.965) (0.289) (0.973) (.823) (.140) (.680) (.663) (.832) (.662) UK Int'al (.993) (.620) (.990) (.661) (.487) (.726) (.698) (.322) (.690) Int'al Int'al * * * * (.576) (<.001) (.788) (<.001)(.009) (<.001) (<.001) (0.979) (<.0011

42 Panel E: Number of rejections at the 5% level of significance over the three subperiods. CAPM-EW CAPM-VW R i P a i -0 ai J-0 a inj -0 a i -0 ai J-0 a -.0 LNJ US US JP JP UK UK US Int'al JP Int'al UK Int'al Int'al Int'al INDEX APT-5 APT-10 R i P aine cli.1.4 clinj- cli- œij- ceinj-0 ai- clij-o *Cr US US JP JP UK UK US Int'al JP Int'al UK Int'al Int'al Int'al a x 2 statistics with p-values in parentheses. *: F-statiscics too large to compute aggregate x 2 -statistic.

43 Table 7 Non-nested (P0) Tests of Domestic vs. International Asset Pricing Models Using Size Ranked Portfolios. A. CAPM-EW PERIOD A 9-UNITED STATES A 9-UNITED KINGDOM A 9-JAPAN (0.21) (0.91) (0.02) (0.23) (0.93) (0.13) (0.52) (0.52) (0.02) <.001 (0.67) (0.93) (0.64) AGGREGATED P-VALa (0.57) (0.93) (0.05) B. APT (0.28) (<.001) (0.22) (0.06) (0.01) (0.06) (0.05) (0.58) (0.26) AGGREGATED P-VAL (0.04) (<.001) (0.10) C. APT (0.01) (<.001) (0.03) (<.001) 0.16 (0.08) 0.07 (<.001) 0.03 AGGREGATE P-VAL (<.001) (0.16) (0.13) (<.001) (<.001) (<.001) Note: p-values in parentheses. a: Aggregated P-Values Test for 0-0 across three subperiods.

44 Table 8 Non-Nested (P0) Tests of CAPM-EW vs. APT Domestic and International \brsions. ALTERNATIVE MODEL PERIOD A 6-UNITED STATES A 9-UNITED KINGDOM A 9-JAPAN Domestic/APT (<.001) (0.86) (0.14) (<.001) (0.32) (0.26) (<.001) (0.83) (0.27) AGGREGATE P-VALa (<.001) (0.79) (0.19) International/ APT-5 (<.001) (<.001) (<.001) (<.001) (<.001) (<.001) (<.001) (<.001) (<.001) AGGREGATE P-VAL (<.001) (<.001) (<.001) Domestic/APT (<.001) (0.60) (<.001) (<.001) (0.11) (0.02) (<.001) (0.62) (<.001) AGGREGATE P-VAL (<.001) (0.38) (<.001) International/ APT-10 (<.001) (<.001) (<.001) (<.001) (<.001) (<.001) (<.001) (<.001) (<.001) AGGREGATE P-VAL (<.001) (<.001) (<.001) Note: P-values in parentheses a: Test of 0-0 aggregated across three subperiods.

45 Figure 1 Absolute Mispricing Domestic Portfolios vs Domestic Factors % per a nnum 1 I I sl s2 s3 s4 s5 s6 s7 s8 s9 s 'I 0 Portfolio AP I.A ENA/ + CAP tvt VW o APT-5 e APT 1 0

46 Figure 2 Absolute Mispricing Domestic Portfolios vs Int'al Factors per annum O 1 s1 s2 s3 s4 s5 s6 s7 s8 s9 s 1 0 Portfolio CAPM EW + 4 INDEX o APT-5 a APT 1 0

47 Figure 3 Absolute Mispricing Int'aI Portfolios vs Int'aI Factors % per annum 0 s1 s2 s3 s4 s5 s6 s7 s8 s9 s 1 0 Portfolio t CitaPt A ENA/ + 4 INE)EX o APT-5 e APT 10

48 Figure 4 January Absolute Mispricing Domestic Portfolios vs Domestic Factors % per annum Portfolio o CAPM EW + CAPM VW o APT-5 A APT-1 0

49 Figure 5 January Absolute Mispricing Domestic Portfolios vs Intial Factors % per annum s1 s2 s3 s4 s5 s6 s7 s8 s9 s1 0 Portfolio ri OAP M EVV + 4 INDEX 0 APT-5 A APT 10

50 Figure 6 60 Absolute January Mispricing Int'al Portfolios vs Int'aI Factors I % per annum 30-I T s1 s2 s3 s4 s5 s6 s7 s8 CAPM EW s9 810 Portfolio + 4 INDEX o APT-5 à APT-10

51 /04 Philippe A. NAERT "Market share specification, estimation and and Marcel WEVERBERGH validation: tovards reconciling seeeingly 84/01 Arnoud DE MEYER "A technological life-cycle to the divergent vievs". organisational factors determining gatekeeper activities", November /02 Jeffrey SACHS and Charles A. WYPLOSZ "La politique budgétaire et le taux de change réel", November /05 Ahmet AYKAC, Marcel CORSTJENS, David GAUTSCHI and Ira HOROWITZ "Estimation uncertainty and optimal advertising devisions", Second draft, April /03 Jeffrey SACHS and Charles A. WYPLOSZ 84/04 Gabriel A. HAWAWINI 84/05 Charles A. WYPLOSZ 84/06 Gabriel A. HAWAWINI 84/07 Gabriel A. HAWAWINI 84/08 Gabriel A. HAWAWINI, Pierre MICHEL and Claude J. VIALLET 84/09 Gabriel A. HAWAWINI, Claude J. VIALLET and Ashok VORA "Real exchange rate effects of fiscal policy", December "European equity markets: a reviev of the evidence on price behavior and efficiency", February "Capital controls and balance of payments crises", February "An uncertainty model of the professional partnership", November "The geometry of risk aversion", October /06 Kasra FERDOWS "The shifting paradigme of manufacturing: inventory, quality and nov versatility", March /07 Kasra FERDOWS, Jeffrey G. MILLER, Jinchiro NAKANE and Thomas E.VOLLMANN. 85/08 Spyros MAKRIDAKIS and Robert CARBONE 85/09 Spyros MAKRIDAKIS and Robert CARBONE 85/10 Jean DERMINE "Risk, Return and equilibrium of the NYSE: update, robustness of results and extensions" December /11 Antonio M. BORGES and Alfredo M. PEREIRA "Industry influence on firm's investment in vorking capital: theory and evidence", January /12 Arnoud DE MEYER "Evolving manufacturing strategies in Europe, Japan and North-America" "Forecasting vhen pattern changes occur beyond the historical data", April "Sampling distribution of post-sample forecasting errors", February "Portfolio optimization by financial intermediaries in an asset pricing model". "Energy demand in Portuguese manufacturing: a tvo-stage model". "Defining a manufacturing strategy - a survey of European manufacturers". 84/10 Gabriel A. HAWAWINI and Pierre A. MICHEL 84/11 Jean DERMINE 84/12 Antonio M. BORGES "Impact of the Belgian Financial Reporting Act of 1976 on the systematic risk of common stocks", January "On the measurement of the market value of a bank", April "Tex reform in Portugal: a general equilibrium analysis of the introduction of a value added tax", December /13 Arnoud DE MEYER 85/14 Ahmet AYKAC, Marcel CORSTJENS, David GAUTSCHI and Douglas L. MacLACHLAN 85/15 Arnoud DE MEYER and Roland VAN DIERDONCK "Large European manufacturers and the management of R & D". "The advertising-sales relationship in the U.S. cigarette industry: a comparison of correlational and causality testing approaches". "Organizing a technology jump or overcoming the technological hurdle". 84/13 Arnoud DE MEYER and Kasra FERDOWS 1985 "Integration of information systems in manufacturing", December /16 Herwig M. LANGOHR and Antony M. SANTOMERO 85/17 Manfred F.R. KETS DE VRIES and Danny MILLER "Commercial bank refinancing and economic stability: an analysis of European features". "Personality, culture and organization". 85/01 Jean DERMINE 85/02 Philippe A. NAERT and Els GIJSBRECHTS 85/03 Philippe A. NAERT and Els GIJSBRECHTS "The measurement of interest rate risk by financial intermediaries", December 1983, Revised December "Diffusion Bodel for nev product introduction in existing markets". "Towards a decision support system for hierarchically allocating marketing resources across and vithin product groups". 85/18 Manfred F.R. KETS DE VRIES 85/19 Manfred P.R. KETS DE VRIES and Dany MILLER 85/20 Manfred F.R. KETS DE VRIES and Dany MILLER "The darker side of entrepreneurship". "Narcissism and leadership: an object relations perspective". "Interpreting organizational texts".

52 85/21 Herwig M. LANGOHR and Claude J. VIALLET "Nationalisation, compensation and vealth transfers: France " 1, Final version July "Barriers to adaptation: personal, cultural and organizational perspectives". "The art and science of forecasting: an assessment and future directions". 86/10 R. MOENART, Arnoud DE MEYER, J. BARBE and D. DESCHOOLMEESTER. 85/22 Herwig M. LANGOHR and "Takeover premiums, disclosure regulations, B. Espen ECKBO and the market for corporate control. A comparative analysis of public tender of fers, controlling -block trades and minority buyout in France", July /11 Philippe A. NAERT and Alain BULTEZ 86/12 Roger BETANCOURT and David GAUTSCHI 85/23 Manfred F.R. KETS DE VRIES and Dany MILLER 85/24 Spyros MAKRIDAKIS 85/25 Gabriel HAWAWINI "Financial innovation and recent developments in the French capital markets", October /26 Karel O. COOL and Dan E. SCHENDEL 85/27 Arnoud DE MEYER /01 Arnoud DE MEYER "Patterns of competition, strategic group formation and the performance case of the US pharmaceutical industry, ", October "European manufacturing: a comparative study (1985)". "The R S D/Production interface". 86/13 S.P. ANDERSON and Damien J. NEVEN "Analysing the issues concerning technological de-maturity". "From "Lydiametry" to "Pinkhamization": misspecifying advertising dynamics rarely affects profitability". "The economics of retail firme, Revised April "Spatial competition à la Cournot". 86/14 Charles WALDMAN "Comparaison internationale des marges brutes du commerce", June /15 Mihkel TOMBAK and Arnoud DE MEYER 86/16 B. Espen ECKBO and Herwig M. LANGOHR 86/17 David B. JEMISON 86/18 James TEBOUL and V. MALLERET "Bov the managerial attitudes of firms with FMS differ froc other manufacturing firms: survey results", June "Les primes des offres publiques, la note d'information et le marché des transferts de contrôle des sociétés". "Strategic capability transfer in acquisition integration", May "Tovards an operational definition of services", /02 Philippe A. NAERT Marcel WEVERBERGH and Guido VERSWIJVEL 86/03 Michael BRIMM "Subjective estimation in integrating communication budget and allocation decisions: a case study", January "Sponsorship and the diffusion of organizational innovation: a preliminary viev". 86/19 Rob R. WEITZ "Nostradamus: a knovledge-based forecasting advisor". 86/20 Albert CORHAY, Gabriel HAWAWINI and Pierre A. MICHEL "The pricing of equity on the London stock exchange: seasonality and size premium", June /04 Spyros MAKRIDAKIS and Michèle HIBON "Confidence intervals: an empirical investigation for the series in the N- Competition". 86/21 Albert CORHAY, Gabriel A. HAWAWINI and Pierre A. MICHEL "Risk-premia seasonality in U.S. and European equity markets", February /05 Charles A. WYPLOSZ 86/06 Francesco GIAVAZZI, Jeff R. SHEEN and Charles A. WYPLOSZ 86/07 Douglas L. MacLACHLAN and Spyros MAKRIDAKIS 86/08 José de la TORRE and David H. NECKAR "A note on the reduction of the vorkveek", July "The real exchange rate and the fiscal aspects of a natural resource discovery", Revised version: February "Judgmental bisses in sales forecasting", February "Forecasting political risks for international operations", Second Draft: March 3, /09 Philippe C. HASPESLAGH "Conceptualizing the strategic process in diversified firms: the role and nature of the corporate influence process", February /22 Albert CORHAY, Gabriel A. HAWAWINI and Pierre A. MICHEL "Seasonality in the risk-return relationships some international evidence", July /23 Arnoud DE MEYER "An exploratory study on the integration of information systems in manufacturing", July /24 David GAUTSCHI and Vithala R. RAO 86/25 H. Peter GRAY and Ingo WALTER 86/26 Barry EICHENGREEN and Charles WYPLOSZ "A methodology for specification and aggregation in product concept testing", July "Protection", August "The economic consequences of the Franc Poincare", September 1986.