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Integration of the Mexican Stock Market∗ Alonso Gomez Albert† Department of Economics University of Toronto Version 02.02.06 Abstract In this paper, I study the ability of multi-factor asset pricing models to explain the unconditional and conditional cross-section of expected returns in Mexico. Two sets of factors, local and foreign factors, are evaluated consistent with the hypotheses of segmentation and of integration of the international finance literature. Only one variable, the Mexican U.S. exchange rate, appears in the list of both local and foreign factors. Empirical evidence suggests that the foreign factors do a better job explaining the cross-section of returns in Mexico in both the unconditional and conditional versions of the model. This evidence supports the hypothesis of integration of the Mexican stock exchange to the U.S. market. JEL Classification: G12, G15, F36. Keywords: Integration of Financial Markets, Linear Factor Models, Fama and French Factors, Unconditional Pricing, Conditional Pricing. ∗ I am grateful to Angelo Melino for helpful comments, suggestions and guidance. I also thank participants in the econometrics workshop at the University of Toronto. All remaining errors are mine. † Alonso Gomez Albert, 150 St. George St., University of Toronto, Toronto, M5S3G7, Canada. Phone: (416)946-0455. Fax:(416) 978-6713. Email: [email protected] 1 Introduction The purpose of this paper is to study the determinants of equity returns in Mexico. The pricing performance of two sets of factors, inspired by the hypotheses of segmentation and integration of the Mexican stock exchange to the U.S. stock market, are evaluated. I examine the ability of multi-factor asset pricing models to explain the unconditional and conditional cross-section of expected returns of industry portfolios in Mexico. In the process I provide evidence on the integration of the Mexican and the U.S. stock markets. Financial markets have become steadily more open to foreign investors over the last forty years. Markets are considered integrated if assets with the same risk have identical expected returns regardless of their national status or where they are traded. Integrated capital markets provide the opportunity for better diversification and risk sharing and can lower the cost of capital for firms in emerging markets. Interest in emerging markets has rapidly grown in recent years as investors seek higher returns and international diversification. The average net capital flows to emerging market economies from 1995 to 2003 was 103.12 billion U.S. dollars, of which 8 percent was portfolio investment1 . Foreign investment can have a significant impact on returns in emerging markets because they are generally small and illiquid compared to more mature international markets. Bekeart and Harvey (2000) present evidence of a negative relation between the cost of capital and the degree of integration with 1 International Monetary Fund, World Economic Outlook: Growth and Institutions, World Economic and Financial Surveys, April 2003. 1 the world market in emerging markets. Beginning in 1989, Mexico experienced a transformation from a closed and protected economy to one of the most open economies in Latin America (see Bekaert, Harvey and Lundblad (2003)), what increased the participation of foreign investors in Mexico. Figure 1 presents the growth in portfolio investment by foreigners from the beginning of 1990 to the end of 2005. By 1994, after the Mexican Peso’s devaluation of almost 70%, control of the exchange rate was eliminated. Domestic companies sought to broaden their shareholder base by raising capital abroad. An increasing number of firms started listing in foreign equity markets, in particular, in the U.S.2 . Foreign investors accounted for over 30 percent of holdings3 and up to 80 percent of trading in Mexican stocks since 1990. Figures 2 and 3 present the ratio of the value of holdings of Mexican stocks by foreign investors to domestic investors, and the ratio of the value of volume traded in ADRs to their Mexican counterpart respectively. The large role played by foreigners in Mexican stocks, the recognition hypothesis, provides support for the hypothesis of integration. A considerable number of empirical studies have focused on measuring the degree of integration of capital markets by the correlation between a local market index return and a proxy of the world market return, see the survey article by Karolyi (2003). In a seminal study, Bekaert and Harvey (1995) assumed that the conditional expected return of a national markets index is equal to a weighted average of 2 A striking increase of firms have undertaken ADRs programs, passing from 8 firms in 1992 to 71 in 2001. Many of the ADRs are traded over the counter, but by 2001 there were 28 different series traded on major exchanges. 3 Banco de Mexico, Development of Equity Markets, 2003. 2 the covariance between the world market and the national index returns, and the variance of the country’s returns. These authors defined a time-varying measure of integration given by the weighting factor that is applied to the covariance and variance nesting the domestic and international version of the capital asset pricing model (CAPM). Using this measure, Bekaert and Harvey (1995) report considerable variability over time in the degree of integration between the Mexican stock index return and a proxy for the global stock market. With a sample of 12 emerging countries, including Mexico, they concluded that the degree of integration is timevarying. However, the empirical specification was rejected for many of the tested countries. Their diagnostic tests suggest that rejection of the model was as a result of omitting important local factors. In a closely related study, but with a more recent sample, Alder and Qi (2003) estimated a time-varying measure of integration between the Mexican stock index and the U.S. market. These authors, like Bekaert and Harvey (1995), assumed that the conditional expected return of the Mexican market is a time-varying weighted average of the covariance of the market index with the North American market return, and the variance of the Mexican market. In addition to the domestic and foreign market risk, they included exchange rate risk as an additional factor. Alder and Qi also concluded that the degree of integration is time varying and that exchange risk is priced in the case of the Mexican Stock Exchange. Even if the Mexican market is integrated to the world capital market, theoretical and empirical evidence suggests that exchange rate risk is priced and should be included as a source of systematic risk. Whenever a domestic investor holds a foreign 3 asset, her return in domestic currency depends on the exchange rate and therefore bears exchange rate risk. Ferson and Harvey (1993), Brown and Otsuki (1993), Ferson and Harvey (1994), Bekaert and Harvey (1995), Dumas and Solnik (1995), De Santis and Gerard (1998), Karolyi and Stulz (2003) and references therein, find that the price of currency risk, from the U.S. perspective, is significantly different from zero. Therefore, models of international asset pricing that only include proxies of the world market as the only risk factor are misspecified. This paper contributes to the international finance literature in testing the hypothesis of integration of the Mexican stock market to the U.S. market from a cross-section perspective. I examine the cross-section of returns of industry-based portfolios of Mexican equities. Data and studies of the Mexican stock market, indeed of any Latin American capital market, are scarce. To my knowledge, this is the first paper that examines whether international factors affect the cross-section of expected returns in Mexico. I explore the relative ability of two sets of factors, local and foreign, to explain the cross-section of returns. Following Bailey and Chung (1995), the local-factor model includes as factors the local market risk, exchange rate risk and political risk as the only sources of systematic risk in expected returns in Mexico. Fama and French U.S. portfolios were selected as the set of foreign factors used to explain the cross-section of returns in Mexico. In response to the failures of the CAPM in explaining the cross-section of expected returns sorted by size and book-to-market in the U.S., alternative models have been suggested to explain the pattern of returns. Fama and French (1993) developed a three-factor model, with 4 factors related to market risk, book-to-market and firm size, that has proved to be successful in capturing the cross-section of average returns in the U.S.. I compare the power of the Fama and French factors relative to the local factors for explaining the cross-section of expected returns. Empirically, I infer integration of the Mexican stock exchange to the U.S. market if the Fama and French factors synthesize better the risk exposures of the cross-section of returns in Mexico relative to the local factors. Finally, taking together the hypothesis of integration and the evidence that suggests that exchange rate risk is priced, a hybrid model that incorporates the Fama and French factors together with exchange rate is evaluated. I search for both unconditional and conditional versions of the local-factor model and Fama and French model. In the unconditional model, risk premia are assumed to be constant. For the conditional model, factors in the stochastic discount factor are expected to price assets only conditionally, leading to time-varying rather than fixed linear factor models. If risk premia are time-varying, the parameters in the stochastic discount factor will depend (among other conditional moments), on investors’ expectations of future average returns. To capture this variation, I assume that the parameters of the stochastic discount factor depend on current-period information variables, as in Cochrane (1996), Ferson and Harvey (1999) and Lettau and Ludvigson (2001). Factors are scaled by variables (instruments) that are likely to be important in summarizing variation in expected future returns. A conditional linear factor model can be expressed as an unconditional multi-factor model on the scaled factors. However, the choice of conditioning variables is of central importance 5 for this approach. The fact that expected returns are a function of investors’ conditioning information, which is unobservable, represents a practical obstacle in testing conditional factor models. In order to address this problem, a set of conditioning variables are selected based on their empirical performance in forecasting returns. The empirical results from cross-section regressions suggest that the unconditional model using the Fama and French factors does a good job explaining the cross-section of Mexican stock returns (see Figure 1). This result is consistent with the hypothesis of integration of the Mexican market to the U.S. market. Compared to the Fama and French model, the local-factor model was not able to capture the cross-section of average returns (see upper-right graph of Figure 1). In time-series regressions, I observed that portfolio returns appeared to be highly correlated with local factors, yielding high R2 s. However, on cross-section regressions, these risk exposures have low explanatory power when compared to the Fama and French risk exposures. Results for the conditional asset pricing models suggest that risk premiums can be significantly time-varying in the case of Fama and French factors, whereas in the local-factor the hypothesis of time-varying risk exposures was rejected. In both specifications, unconditional and conditional, Fama and French specification dominates the local-factor specification. The conditional version of the Fama and French model does not provide a substantial improvement with respect to its unconditional version. However, when the exchange rate is included, the conditional version of the Fama and French model outperforms all of the other specifications by explaining 60 percent of the cross6 section of expected returns compared to a 47 percent for the local-factor model. The evidence supports the hypothesis of integration of the Mexican stock exchange. Global factors, in particular, the Fama and French factors and exchange rate risk appear to be more important in explaining the cross-section of returns than local factors. The paper is organized as follows. In section 2, I give a brief summary of factor pricing models and address the difference between conditional and unconditional asset pricing. A detailed description of the data used in this paper is given in section 3. Section 4 presents the empirical results. Conclusions are presented in the final section. 2 Empirical Methodology 2.1 Linear Factor Model In the absence of arbitrage, we have the fundamental equation: Pt = Et (mt+1 (Pt+1 + Dt+1 )) (1) where Pt is a vector of asset prices at time t, Dt+1 represents a vector of interest, dividends or other payments at t+1, and mt+1 is the stochastic discount factor (SDF)4 . Et represents the conditional expectation with respect to Ωt , the market-wide information set. Since Ωt is unobservable from a researcher’s perspective, expectations 4 Also known as the pricing kernel or intertemporal marginal rate of substitution. 7 are usually conditioned on a vector Zt of observable variables (instruments) that are contained in Ωt . Equation (1) can be expressed in terms of returns. While no arbitrage principles place a restriction on mt+1 , in particular strict positivity, more structure is needed in order to explore the model empirically. Multiple factor models for asset pricing follow when mt+1 can be written as a function of several factors. The notion that the SDF comes from an investor optimization problem, and is equal to the growth in the marginal rate of substitution, suggests that likely candidates for the factors are variables that can proxy consumption growth or wealth, or any state variable that affects the marginal rate of substitution in an optimal consumption-investment path. In terms of returns, investors are willing to trade off overall performance to improve it in “bad” states of nature. If equation (1) holds it implies that: Et (mt+1 rt+1,i ) = 0 i = 1, ..., N (2) where rt+1,i are excess returns. Expanding equation (2) in terms of the covariance: Et (rt+1,i ) = Covt (rt+1,i , −mt+1 ) Et (mt+1 ) i = 1, ..., N (3) The conditional covariance of the excess return with the SDF is a general measure of systematic risk. In standard economic models, it measures the component of returns that is related to fluctuations in the marginal utility of wealth. A linear factor model is of the form: mt+1 = a + b0 ft+1 , where ft+1 is a vector ct+1 + εt+1 of size k of risk factors. In general, mt+1 can be written as mt+1 = m ct+1 is the projection of mt+1 on the asset space and εt+1 is orthogonal to where m 8 the asset space, so E(md t+1 εt+1 ) = 0. Any random variable orthogonal to returns c, leaving the pricing implications unchanged. can be added to m In the case of conditional factor models, the coefficients at and bt vary over time as a function of conditioning information, mt+1 = at + b0t ft+1 . To illustrate this heuristically, I assume that the factors ft+1 are returns on tradeable assets5 . Imposing the condition that the model correctly prices the risk free rate Rtf and the factors, ft+1 , yields: ιk = Et (mt+1 ft+1 ) and 1 = Et (mt+1 Rtf ) (4) where ιk ²<k is a vector with all of its components equal to one. Solving for at and bt we obtain: Ã 1 Et (ft+1 ) 0 at = f − Et (ft+1 )bt and bt = (V art (ft+1 ))−1 ιk − Rt Rtf ! (5) Equation (5) shows explicitly that both at and bt are functions of Rtf , and the conditional moments Et (Rt+1 ), Et (ft+1 ), and V art (ft+1 ). Therefore, if conditional moments are time-varying, the parameters in the stochastic discount factor will not be constant in general. Following Cochrane (1996), Ferson and Harvey (1999) and Lettau and Ludvigson (2001), I assume that the denominator in bt is not likely to be highly variable6 . On the other hand, a large body of literature has documented If ft+1 does not belong to the payoff space, we can replace it with fd t+1 = proj(ft+1 |X), where X represents the asset space. 6 Predictable movements in volatility may be a source of variation in bt , however they appear to be more concentrated in high-frequency data (see Cambell, Lo and MacKinlay (1997)) than in monthly, or quarterly returns. 5 9 that excess returns are predictable to some degree using monthly or quarterly data. Therefore, in this paper I assume that the only source of variation in bt is a consequence of the predictability of equity premia. The beta representation for expected returns can be obtained by combining equation (3) with the linear specification of the SDF (at + b0t ft+1 ): Et (rt+1,i ) = − 0 Covt (rt+1,i , ft+1 ) 0 V art (ft+1 ) 0 bt ≡ −βt,i bt ≡ βt,i λt Et (mt+1 ) Et (mt+1 ) (6) where βt,i are the population time-varying regression coefficients of a regression of rt+1,i on ft+1 , and are the loadings or risk exposures to ft+1 risks. λt are the associated prices of risk for each unit of risk exposure. Following Cochrane (1996) and Lettau and Ludvigson (2001), the conditional factor pricing model given above is implemented by explicitly modeling the dependence of the parameters in the stochastic discount factor, at and bt , on time-t information variables, Zt , where Zt set of variables that help forecast excess returns. To evaluate differences in exposures to risk factors, I measure risk exposures with time-series regressions of industrial portfolio excess returns on contemporaneous risk factors. 0 rt+1,i = ct,i + βt,i (ft+1 ) + ²t+1,i , i = 1, ..., N (7) where rt+1,i are excess returns over a one-month government zero coupon bond yield, and ft+1 is a vector of excess returns of economic risk factors. The vector 0 represent risk exposures of portfolio excess returns to the factors of coefficients βt,i ft+1 . In section 2.2 above, I further describe the scaled factor approach in order to 10 estimate βt,i of equation (7). The property Et (²t,i ft+1 ) = 0 captures the fact that the coefficients βt,i are the conditional betas of the returns. The idea behind the beta representation (6) is to explain the variation in excess returns across assets where betas are a measure of risk compensation between assets, and the λ are the reward per unit of risk. Equation (6) can be estimated with a cross-sectional regression, 0 dλ +α Et (rt+1,i ) = β t,i t i,t i = 1, ..., N (8) where the betas are the right-hand variables that come from (7), the factor risk premia λ are the regression coefficients, and αi are the pricing errors (differences between expected and predicted returns). This method is also known as a twopass regression estimate. In applying standard OLS formulas to cross-sectional regressions, it is implicitly assumed that the right-hand variables (in this case β) are fixed. However, in this case, the β is the estimate of a time-series regression and is therefore not fixed. Shanken (1992) provides the corrected asymptotic standard errors for λ and for α (see Cochrane (2001)). 2.2 Unconditional and Conditional Factor Pricing Models As mentioned above, the betas are the variables that explain the variation in average returns across assets. Therefore, the general model for expected returns should have betas that vary asset by asset. To evaluate if expected returns and risks are time varying, I first estimate the unconditional version of equation (7) and (8) where the coefficients are assumed to be constant through time. The unconditional approach 11 will not be adequate if risk exposures of a financial asset or portfolio vary in a predictable manner, for example, with the business cycle. In order to test for time-varying risk exposures, the unconditional version of the model is taken as the null hypothesis, and different specifications of the conditional model, where risk exposures are allowed to be time-varying, are set as the alternative. To proceed, I must specify the risk factors. Two sets of factors are used to explain the cross-section of returns in Mexico. The first set correspond to the hypothesis of segmentation of the Mexican stock exchange to the U.S. stock market. Under this hypothesis, risk exposures on the Mexican stock market are represented only by local factors. The vector of local factors is composed by the local stock market return, the exchange rate risk and a proxy of political risk. The second set of factors, correspond to the hypothesis of integration between the Mexican stock exchange and the U.S. market. Given the ability of Fama and French (1993) factors to explain the cross-section of expected returns in the U.S., under the hypothesis of integration, these factors appear as good candidates to synthesize risk exposures in the Mexican stock market. Therefore, not only the pricing performance of the two sets of factors is evaluated, but also the hypothesis of integration measured by the ability of the Fama and French factors to explain the pattern of returns in Mexico. Consequently, I conclude that the Mexican stock market is highly integrated if its risk exposures are better summarized by the Fama and French factors than by the local factors. 2.2.1 Scaled Factors Approach 12 A popular and simple approach to incorporate conditioning information is based on scaled factors. As shown above (equation (5)), in a conditional setting, the coefficients associated with the discount factor mt+1 are time-varying and depend on the time-t information set. A partial solution is to model the dependence of the betas in (8) with a subset of variables that belong to the time-t information set. Furthermore, if a linear specification is assumed, we can write βt,i = Di0 Zt (9) ct,i = c0i Zt where Zt is an L × 1 vector of information variables (including a constant) known at time t, and the elements of the matrix Di are fixed parameters to be estimated. In choosing the instruments, Zt , I focus only on variables that can forecast conditional returns7 . Conversely, the unconditional factor model is characterized by fixed betas and is a special case of equation (9), in particular when Zt is only a constant. Combining equations (7) and (9), the time series regressions to obtain betas is given by rt+1,i = c0i Zt + d0i (Zt ⊗ ft+1 ) + ²t+1,i (10) where every factor is multiplied by every instrument, and di is given by V ec(Di )8 . It is worth mentioning that the coefficients di in expression (10) are linear and fixed 7 As shown in equation (5), at and bt are functions of conditional returns, therefore variables that can summarize variation in conditional moments are used as instruments Zt . 8 V ec(A) is the operation represented by the vectorization columnwise of matrix A. 13 on the scaled factors (Zt ⊗ ft+1 ), so the conditional version of the factor model can be viewed as an unconditional factor model over scaled factors. In order to evaluate the ability of the scaled-factor model to explain the crosssection of returns, time-varying betas are recovered using the estimated version c0 Z and cross-section regressions of returns on β are of equation (9), βt,i = D t t,i estimated. 14 3 Data The sample is limited to the period following the devaluation suffered by the Mexican peso at the end of 1994; it runs from May 1995 to October 2003. Mexican stock prices and Mexican bond returns were obtained from Infosel Financiero9 . The rest of the variables were obtained from the Central Bank of Mexico, the Board of Governors of the Federal Reserve System web page, and the Fama and French web page. The data comprise two types of series: financial and macro variables, and are used to construct portfolio returns, risk factors, and information variables. 3.1 Returns on Mexican Portfolios To construct monthly returns, log differences of end-of-month closing prices were calculated. If the end-of-month price was not available, the closest quote preceding the end-of-month was used. There are a total of 101 months in the sample. Stock prices were adjusted for splits and dividends10 . I compute returns for all Mexican stocks that traded between 1995 and 2003 and the Mexican stock index. The average number of firms listed in the Mexican stock exchange during the sample is of 124, peaking in 1998 with 131 stock series11 , and the Mexican stock index. I applied some 9 Mexican electronic provider of financial information. In the sample analyzed, very few stocks payed dividends before 2001. However, by the end of the sample a high proportion of stocks were paying dividends. 11 The average number of series traded daily in the Mexican Stock Exchange between 2000 and 2003 is around 70 stocks. However, the total number of firms listed in 1995 is 185, reaching its maximum of 195 listed firms in 1998 and falling to 158 for 2003. Only about 60 percent of these stocks trades at least once per week. 10 15 filtering rules and summarized the stock returns by returns on industry portfolios. In order to evaluate the pricing performance of different sets of factors (in a common currency, and from a U.S. perspective), nominal log returns in Mexican pesos were converted to U.S. dollar returns. Excess returns of Mexican industrial portfolios were computed and are defined as the difference between its log U.S. return and the 30-days T-bill return. Given the thinness of trading in many of the Mexican stocks in the sample, and in order to help address potential problems such as survivorship bias, missing observations for individual stocks, and noise in individual security returns, I aggregated individual stocks into industrial portfolios. The industrial categories resemble the official categories defined by the Mexican Stock Exchange and are given by: 1) Beverages, Food Products and Tobacco, 2) Financial Services, 3) Building Products, that includes engineering, construction and the real state sectors, 4) Conglomerates, 5) Media, entertainment and telecommunications, 6) Chemical and Metal Production, 7) Industrial, that contains the paper and pulp products industry, textiles industry, glass production and tubes production, 8) Machinery and Equipment, 9) Retail Services and 10) Transportation. Table I presents a summary of the number of firms that comprise each portfolio, as well as the relative annual average liquidity, measured as the value of the transactions of the portfolio to the value of all transactions of the market. Industrial portfolios are formed using weights based on the previous year’s annual average liquidity and are re-balanced each January. The weights for each stock in each industrial portfolio are given by the relative annual average volume of the stock to the annual average volume of the portfolio. The 16 cross-section of the sample includes many industries and all of the components of the IP C index12 . 3.2 Risk Factors As mentioned above, I specify two sets of factors, ft+1 , that represent potential sources of rewarded risk in the Mexican stock. The choice of each set of factors is based on different assumptions concerning the degree of integration of the Mexican market to the North American market. In what follows, the factors will be divided into two categories: a) Local Factors and b) Foreign Risk Factors. Local Factors: IP C is the monthly log-difference of the Mexican market index expressed in U.S. dollars, and in excess of the 30-day T-bill. The IP C is the most important index of the Mexican Stock Market (BMV) and is computed as the weighted average price of 35 of the most liquid stocks listed on the BMV. It represents a broad sample of industries. Exchange rate risk, Exch, is computed as the log-difference of the “fix” exchange rate (in terms of U.S. dollars/ Mexican pesos). The “fix” rate is determined on a daily basis by the central bank and is computed as the interbank market exchange rate at the close. As a proxy of political risk, the spread between the 5 year yield of the UMS and the matching maturity of a U.S. Treasury note, Dif f , was computed. To obtain this spread, I calibrated a time series of a zero-coupon term structure at fixed terms from the observed prices of Mexican government bond issued in US 12 The IPC is the most important market index and is comprised of 35 stocks (see nex section). 17 dollars (UMS)13 . Dif f reflects perceived national credit risk, and is assumed to be highly correlated with political risk. Changes in sovereign yield spreads, like credit ratings, generally reflect changes in bond markets’ perceptions of an indebted country’s credit worthiness. Sudden increases are usually followed by a drying up of liquidity and a flow out of national equity markets. Alder and Qi (2003) interpret sovereign default risk as a measure of relative segmentation. Their rationale is that when sovereign default risk cannot be completely diversified, and hence is a priced factor, international investors will respond to an unexpected increase in default risk by liquidating their positions of assets subject to default risk. The same effect, they argue, will occur if the market becomes suddenly segmented. Foreign Factors: If the Mexican Stock Exchange is integrated to the U.S. stock markets, a linear pricing representation that has been successful in explaining the cross-section of different sorts of U.S. portfolios should be successful in explaining the cross-section of Mexican portfolios14 . Following this line of thought, the U.S. Fama and French factors are assumed to be the relevant risk exposures in Mexican industrial portfolios if these markets are integrated15 . The Fama and French mimicking portfolios related to market, size and book-to-market equity ratios are: a) Market risk, M kt, that is 13 These bonds pay a fixed semi-annual coupon. The maturity of the bonds that I used to estimate a zero coupon structure are: 06-Apr-05 15-Jan-07 12-Mar-08 17-Feb-09 15-Sep-16 15-May-26 14 One of the most questionable issues in the empirical international finance literature seeking to measure integration of national stock markets, is the use of the CAPM or ICAPM to explain international returns. Given the documented empirical failure of the CAPM in a domestic environment, a multi-factor approach appears to be more appropiate in an international setting. 15 Given the differences in size between U.S. stock markets and the Mexican stock exchange, the U.S. Fama and French factors are a good proxy of a weighted portfolio of Mexican and U.S. factors, where the weights are proportional to the capitalization of the U.S. and Mexican markets. 18 the monthly return of the U.S. market portfolio in excess of the 30-days T-bill, b) SM B (Small Minus Big) is the average return on three small portfolios minus the average return on three big portfolios, and c) HM L (High Minus Low) is the average return on two value portfolios minus the average return on two growth portfolios16 . 3.3 Information Variables In order to evaluate the scaled factor model, I must specify the relevant information variables Zt that track variation in risk exposures to explain returns in time t + 1. These variables are assumed to be known by investors in time t, and are used to assess the significance of time-varying market risk premiums. In the BMV three information variables are useful predictors of one-period ahead expected returns. The first variable, ∆y, represents the monthly real growth rate of seasonally adjusted labor income. The second variable, ∆F A is the monthly real growth of holdings of financial assets, and at last, the third information variable is CetSp that measures the term premium of the Mexican government term structure, and is given by the spread between the one year Cetes(Certificados de la Tesoreria) and the 28 days Cetes17 . Following previous studies (see Campbell (1987), Harvey (1989)), I also explored various other candidates. For example, the ex-post real return of the 28-days Cetes, the lagged exchange rate, lagged Dif f , lagged Fama and French fac16 See Fama and French (1993) for a detailed explanation of these portfolios. The Cetes is a zero coupon bond auctioned weekly by the Mexican Treasury that represents the leading interest rate in Mexico. Typically, the term structure is composed of bonds with maturities of 28, 91, 182, 364 and occasionally of 724 days 17 19 tors, lagged U.S. Momentum factor, the U.S. term premium, measured by the spread between the five-year and one-month Treasuries rates, and a short term spread between a T-bill and Cetes were evaluated. None of these variables appeared to have strong forecasting power on returns, except the spread between T-bill and 28-days Cetes that has explanatory power in the Beverage, Food and Tobacco portfolio. 20 4 Empirical Evidence 4.1 Summary Statistics Table II presents summary statistics for the portfolios’ excess returns, risk factors and information variables; the means and standard deviations for returns are annualized. The Media & Telecoms portfolio is not only the most liquid portfolio, but also the one with the highest average excess return over the sample, with an annualized average excess return in U.S. dollars of 10.52 percent. This sector is dominated by the telephone company monopoly, privatized at the beginning of the 90’s. It represents the most active stock in the BMV, and is the leading stock in the composition of the IP C. Dif f , the risk premium of Mexican sovereign debt measured by the spread between the 5 years yield of the UMS and the U.S. Treasury note of the same maturity, has an average of 3.08 percent. Autocorrelation coefficients for this variable suggest that Dif f follows an AR(1)18 . Cross-correlations are presented in panel D of Table II. IP C is highly correlated with both M kt and Exch19 . 18 19 The first order autocorrelation is 0.81 while the second autocorrelation is of 0.64. Remember that Exch is measured as the price of Mexican Pesos in U.S. dollars 21 4.2 Predictability and Description of Stock Portfolio Returns To implement the conditional asset pricing model, a set of instrument variables Zt−1 that capture the dependence of at and bt on the information set Ωt has to be defined. Since only variables that forecast returns and/or the stochastic discount factor, mt+1 , add information to the pricing problem (see equation (5)), I concentrate on a small set of variables that have the ability to forecast future returns. Table III summarizes the results of forecasting time-series regressions of the excess returns on the 10 industrial portfolios and the Mexican market index IP C on lagged information variables Zt−1 . The regressions produce significant t-statistics in many cases. The R2 in the case of the IP C is of 16 percent. The F -statistic for the joint hypothesis of zero coefficients is rejected in 10 of the 11 portfolios. In addition, the F -test associated with the joint hypothesis of zero coefficients in all portfolios was rejected with a p-value of 3.5×10−3 . To further evaluate the ability of these information variables Zt−1 to forecast returns, and to mitigate possible problems concerning data mining, I conducted the forecasting exercise with out-of-sample returns on the IP C using a sample from January of 1982 to August of 2004. An R2 of 5 percent was obtained for the whole sample and of 10 percent using a subsample from January of 1982 to January of 1991. Despite the structural transformation experienced in Mexico during the last 20 years, Zt−1 appears to have forecasting power on stock returns over these years. The hypothesis of a change in the value of the coefficients associated with the forecasting variables 22 between 1982-1995 and 1995-2003 was conducted. Statistical evidence of parameter constancy between samples was rejected. 4.3 4.3.1 Unconditional Factor Models Time-Series Evidence of the Factor Model Results for time-series regressions on contemporaneous factors ft+1 , as described in equation (7), assuming that both at,i and βt,i are constant, are presented from Table IV to Table VI for the the local-factor model, the Fama and French model and an extended version of the Fama and French with exchange rate respectively. The objective of regressions on contemporaneous factors is to measure risk exposures to the proposed factors. In other words, we are trying to measure if risk factors can account for the variability in the cross-section of returns. In the next section I evaluate if these risks are priced. Table IV presents results for the local-factor model20 . Excluding the transportation sector21 , the R2 coefficients for the local-factor model range from 51 percent in the Industrial sector to 87 percent for the Beverage, Food and Tobacco sector. The two most important factors in the local-factor model are the market return IP C 20 I included the local market stochastic volatility (that is a measure of market idiosyncratic risk, measured as both the squared sum and absolute value of daily returns in both U.S. dollars and Mexican pesos) as an additional local risk factor. This was motivated by the international finance literature that explores integration with a weighted average of the ICAPM and CAPM, where systematic risk, under the hypothesis of segmentation, is quantify by the variance of the local market. However, risk exposures for idiosyncratic risk were not significant in any of the industrial portfolios. 21 As noted in table 1, the transportation sector accounts for less than 2.4 percent of total transactions in the BMV. 23 and the exchange rate (Exch). For all portfolios, the constant term appears not significant. Table V shows the results for the Fama and French factor model. The slope on the U.S. market factor, M kt, appears uniformly significant and positive for all industrial portfolios. Risk exposures to SM B and HM L, are also significant in several industrial portfolios. An interpretation for HM L, not universally accepted, is provided by Fama and French (1995). They showed that HM L acts as a proxy for relative distress. Weak firms, with low earnings, tend to have low book-to-market ratios and positive loadings on HM L, whereas the contrary effect is observed for strong firms. Therefore, slopes on HM L can be interpreted as a measure of financial distress. In all industrial portfolios, slopes on HM L are positive giving evidence that financial distress is an important risk factor to explain the cross-section of industrial returns in Mexico. With respect to the SM B factor, coefficients are positive in all portfolios. A common interpretation for SM B is that is a factor that captures common variation of small stocks, not explained by the market portfolio. Given the size of Mexican stocks relative to U.S. firms, under the integration hypothesis, it is not surprising that the U.S. portfolio SM B is an important factor. Compared to the local-factor model, the R2 for the Fama and French model are often lower, however, constant terms appear insignificant in almost all portfolios. Finally, and following the international finance literature where the exchange rate has proven to be an important risk factor within an international setting, I extended the Fama and French model by including exchange rate risk. In general, the coefficients associated with the Fama and French factors are very similar when 24 Exch is included (Table V and Table VI). Exch appears significant and positive in all portfolios, resulting in a significant improvement of R2 s in all portfolios. From a time-series perspective, it appears that the local-factor model measured by R2 s, does a better job in explaining the pattern of industrial returns in Mexico. In the following section, however, cross-section regressions give evidence that regardless the high R2 in time-series regression for the local-factor model, betas from the Fama and French model do a better job in explaining the cross-section of returns in Mexico. To complement these results and to assess the relative importance of each risk factor, I performed F -tests22 to test the joint significance of each risk factor in all industrial portfolios. Table VII presents results of the different specifications (local factor, Fama and French and Fama and French with Exchange rate). In the local-factor model, and as observed in the time-series regressions (Table IV), Dif f factor is statistically insignificant. These results do not differ from a previous study by Bailey and Chung (1995). These authors, using a sample from 1988-1994 where Mexico had a fixed exchange rate regime, observed that the official exchange rate and the sovereign default risk were not significant factors in explaining portfolio returns. However, the spread between the official and a “market” exchange rate23 appeared to be driving returns. For the Fama and French model and Fama and French that 22 For testing linear restrictions in a SURE representation, the analogous F -statistic under GLS 0 −1 b 0 b b ⊗ I; Σ b is the FGLS estimate of assumptions is: Fb = (Rβ −r) [RV0 ar(β)R ] (Rβ −r)/q , where Vb = Σ bb b eV e/(N −K) the covariance matrix. N is the number of observations of each equation times the number of equations and K stands for the number of parameters estimated in the system. An alternative test statistic (Wald test), under the hypothesis that eb0 Vb eb/(N − K) converges to one, that measures the distance between Rβb and r is given by q Fb. This test statistic has a limiting χ2 (q) distribution. 23 Mexico implemented a dual exchange rate regime during the 1980’s and a semi-fixed exchange parity starting in the 1990’s that ended at the end of 1994. 25 includes exchange, all factors are jointly significant. Panel B of Table VII tests the hypothesis of zero intercept (omitted risk factors). Interesting and surprising, the test of zero intercept in not rejected for any of the three specifications. 4.3.2 Cross-Section of Expected Returns To evaluate the performance of the different models (i.e. local-factor vs. Fama and French) in explaining expected returns, cross-sectional regressions were performed. “First pass” time-series regressions are sufficient when factors are portfolio returns in the asset space. If this is the case, the estimate of the factors risk premia is b = E (f ) where the notation E refers to the sample mean. However, just λ T t+1 T when risk factors are not returns in the space of the tested portfolios, cross-sectional regressions must be performed in order to estimate risk premia for each factor and the respective pricing error (equation (8)). The cross-section regressions are given by: Rt+1,i = βi0 λt+1 + αt+1,i i = 1, ..., N, where λt+1 is the vector of risk prices, αt+1,i is the pricing error. The βi are the betas from time-series regressions using information up to time t. Table VIII summarizes the results for the cross-sectional regressions for the unscaled factor model. Time-series averages of the cross-sectional regressions coefficients λt+1 , Fama-MacBeth t-statistics for the coefficients and the time-series average of R2 s for the cross-sectional regressions are presented. The betas were estimated using expanding samples and moving windows of 36-months prior to the estimation 26 period. To form a basis of comparison of the different factor models, results for the domestic CAPM are also showed. The first four rows of Table VIII presents results for the CAPM where the IP C is used as a proxy for the unobservable market return. The low average of the R2 reflects the bad performance of the CAPM in explaining the cross-section of returns. With the inclusion of exchange rate, Exch, and political risk Dif f as additional factors, Local-factor model, there is a significant improvement in the performance of the pricing model. On average, 60 percent of the cross-sectional variation in returns is explained by local factors. Fama and French factors explain on average 55 percent of the cross-sectional variation in returns. Finally, the last columns correspond to the results for the Fama and French model with Exch. For these factors, on average 65 percent of the cross-sectional variation in returns in Mexico is explained. Figure 1 summarizes the above results for the different factor models. In particular, cross- section regressions of the form: E(Rt+1,i ) = βi0 λ i = 1, ..., N, were computed, where E(Rt+1,i ) is the sample average of industrial returns, βi are the betas of time-series regressions using the whole sample. If the proposed model fit perfectly expected returns, all the points in the figure would lie along the 45degree line. The figure shows clearly that few do, and that both local factor models (CAPM and local-factor) have small power in explaining returns in Mexico24 . The 24 The Fama-French model performs better than the local-factor model when the betas used in the cross-section regressions are estimated using the whole sample, and where the dependent 27 above results give support that the Fama and French factor model with exchange rate does a better job in capturing the pattern of average returns in Mexico than the other specifications, therefore, supporting the hypothesis of integration of the Mexican stock exchange with the U.S. market. In other words, and in the context of linear pricing methodology, a linear pricing kernel with fixed coefficient that is approximated by the Fama and French factors and exchange rate, does a better job in pricing the cross-section of returns in Mexico than a specification that uses local risk factors. 4.4 4.4.1 Conditional Factor Models Time-Series Evidence of the Factor Model As mentioned above, lagged instruments track variation in expected returns. In this context, conditional asset pricing presumes the existence of some return predictability. That is, there should exist some instruments Zt for which E(Rt+1 |Zt ) or E(mt+1 |Zt )25 are not constant. In the context of industrial portfolio returns, Fama and French (1994) argue that since industries wander between growth and distress, it is critical to allow risk exposures to be time-varying. In this paper, and as mentioned above, time-variation in conditional betas was achieved by allowing betas to depend linearly on instruments Zt . variable is the sample average of industrial returns, than using Fama-MacBeth methodology. 25 Equation 2 suggests that in the case of a risk free asset, all we require is realized risk free asset prices to vary over time. 28 Tables IX to XI present results from testing the hypothesis of time varying betas for the local-factor model and both versions of Fama and French model. These tests summarize the power of the instruments Zt to track variation in risk exposures. I performed F -tests for the hypothesis of time-varying betas. Under the null, the coefficients associated with the scaled factors, (Zt ⊗ ft+1 ) in equation (10), are restricted to be jointly equal to zero. Panel A of tables IX to XI present results from testing the hypothesis of time-varying betas when the constant is allowed to be 2 time-varying. R of the unrestricted and restricted models are presented in the first two columns, together with the p-values of the F -tests that compares both models (restricted and unrestricted) in the third column. The hypothesis of fixed betas, conditional on time-varying intercepts, is not rejected for all industrial portfolios in the local-factor model. For Fama and French factor model, strong evidence on timevarying betas conditional on time-varying intercepts is observed. Panel B presents results to test the hypothesis of time-varying betas conditional on a fixed intercept. Evidence on time-varying betas is found only for the Fama and French factors. These results give evidence that it may be appropriate to allow for time-varying risk exposures in the case of Fama and French factors. Table XII extend the above results by testing the joint hypothesis of zero coefficients associated with scaled factors. Results for the local factor model are consistent with those obtained in Table IX. That is, the hypothesis of zero coefficients associated with scaled factors, and therefore time-varying coefficients, for all portfolios is not rejected. However, for the the Fama and French factors, the hypothesis of time-variation is not rejected. 29 4.4.2 Cross-Section of Expected Returns To evaluate the ability of the different set of factors to explain the cross-section of industrial returns in Mexico, and to measure the performance of the scaled version of the factor model against the unconditional version, cross-sections regressions were performed. As in the unconditional version of the model presented above, crosssection regression for the scaled factor version are performed, where betas are timevarying: 0 Rt+1,i = βt,i λ + αt+1,i i = 1, ..., N. Table XIII summarizes the different versions of the cross-sectional regressions. Timeseries averages of the cross-sectional coefficients are shown along with their FamaMacBeth t-ratios. As in Table VIII, the betas were estimated either by using an expanding sample or a rolling window, 36-month prior estimation. In the context of the scaled factor model, conditional betas were used. An estimate of the explanation power of cross-section regressions R2 is computed as the average of individual R2 s of the above regressions. Results again reveal, as in the unconditional framework, that the Fama-French factors, together with the Exchange rate, perform the best in pricing the cross-section of returns in Mexico, supporting the hypothesis of integration of the Mexican stock exchange. Cross-section results confirm the time-series evidence obtained above concerning the hypothesis of time-varying risk exposures for the Fama and French factors. For the local-factor model, no significant differences are observed between the conditional and unconditional version of the models, i.e., average R2 are very similar for both 30 representations. However, in the case of the Fama-French factors, and consistent with the hypothesis of time-varying risk exposures, there is a significant improvement of using scaled-factors in terms of R2 s from cross-section regressions. 4.5 Pricing Errors The theoretical content of the factor model relies on whether the alphas or pricing errors are jointly equal to zero. Figures 4 and 5 provides a visual representation of the relative empirical performance of the unconditional and conditional versions of each model. Two measures of the performance of the factor models are presented in the last two rows of Panel A and Panel B on Table XIV. Average, is the average of the norm of the pricing error vector, and χ2 is the result of an asymptotic Wald test of the null hypothesis that the pricing errors are jointly zero. The table shows that the hypothesis of zero pricing errors is not rejected using expanding sample betas and unscaled factor models in all models. However, this result should be interpreted carefully. Lettau and Ludvingson (2001) make reference to several studies (e.g. Burnside and Eichenbaum (1996); Hansen, Heaton and Yaron (1996)) that have found that these tests, that rely on the variance-covariance of pricing errors, have very poor small-sample properties. Results from average pricing errors confirm the results mentioned above concerning the performance of the different set of factors. In the case of the local factor model, pricing errors are smaller for the unscaled version than when the betas are time-varying. A possible reason for this, is the fact that local factors and industrial returns are closely related (see Tables IV-VI), therefore, local factors could be 31 capturing time variation in risk exposures. In contrast, in the Fama and French factor model it is necessary to incorporate conditional information in the form of instruments to explicitly capture time-variation in risk exposures. As stated in equation (3), expected returns are determined by the conditional (on some state variable) covariance between asset returns and the stochastic discount factor that reflects time variation in risk premia. If conditionality is important empirically, and if the selected instruments, Zt−1 , are powerful forecaster of excess returns, it should be captured by scaling the factors. No significant improvement in the scaled version of the local factor model is observed by allowing the covariance of returns be state dependent. In this paper, the instruments were selected based on empirical evidence, in particular forecasting power. However, instruments that take into account empirical evidence and also reflect investors expectation of future expected returns should be better candidates for conditional models than the instruments selected only by their power to forecast returns. 32 5 Conclusions After the failure of the CAPM to explain the cross-section of expected returns sorted by size and book-to-market in the U.S. stock market, researchers have seeked alternative models to explain the pattern of returns. The Fama and French (1993) three factor model, despite the controversy of whether these factors truly capture nondiversifiable risk, proved to be successful in capturing the cross-section of returns sorted by size and book-to-market in the U.S.. In this paper, I investigated which factors explain the cross-section of returns in a particular emerging market, Mexico. Much of the work in empirical asset pricing has focused on developed markets, in particular, the U.S. stock market. Few studies have concentrated in studying the cross-section in a developing market or, the degree of integration of an emerging market taking into account the pattern of cross-section returns. To test the factor model, two sets of factors were evaluated. The first set corresponded to local factors. Under this specification, the underlying hypothesis was of segmentation of the Mexican stock market to the North American market. The local factors were chosen based on a previous study by Bailey and Chung (1995), and following much of the international finance literature that has concentrated on explaining returns in developing countries. In this literature, factors such as exchange rate risk, and political risk are used frequently to explain returns in national markets, and to evaluate the degree of integration of national markets to the world market. To study the hypothesis of segmentation, a local-factor model that is an ex- 33 tension of the CAPM that includes exchange rate risk and political risk is evaluated. Meanwhile, integration of the Mexican stock market to the U.S. market is evaluated using foreign factors that appeared to be successful in explaining the cross-section of returns in the U.S.. In this context, the Fama and French factors appeared as natural candidates to explore the hypothesis of integration. In order to incorporate the possibility of time-varying risk premia, the factor models were evaluated in both their unconditional and conditional or scaled versions. To evaluate the conditional version, the factors were scaled with instruments that incorporate investors’expectation of future expected returns. The instruments were the lagged real growth in labor income, the lagged real growth in holdings of financial instruments and the lagged term spread of Mexican government zero coupon bonds, Cetes. The empirical evidence suggests that the Fama and French factors can explain a substantial fraction of the cross-sectional variation in average returns sorted by industry. The hypothesis of time-varying risk exposures for the local-factor model was rejected but for the Fama-French factor models the evidence was supportive of time-varying risk exposures. Evidence for both unconditional and scaled factor models reveals that the augmented Fama and French with exchange rate does a better job in explaining the cross-section of returns than the local-factor model. These results seem to be especially supportive of the hypothesis of integration. 34 6 References 1. Alder, Michael and Rong Qi, 2003, Mexico’s integration into the North America capital market,Emerging Markets Review 4, 91-120. 2. Alexander, Gordon, Cheol S. Eun and S. Janakiramanan, 1987, Asset Pricing and Dual Listing on Foreign Capital Markets: A Note, Journal of Finance 42, 151-158. 3. Ang, Andrew and Geert Bekaert, 2001, Stock Return Predictability: Is it there?, Working Paper, Columbia University. 4. Bailey, Warren and Peter Chung, 1995, Exchange rate fluctuations, political risk, and stock returns: Some evidence from an emerging marketJournal of Financial and Quantitative Analysis 30, 541-561. 5. Bekaert, Geert and Campbell Harvey, 1995, Time-varying world market integration, Journal of Finance 50, 403-444. 6. Bekaert, Geert and Campbell Harvey, 2000, Foreign Speculators and Emerging Equity Markets, Journal of Finance 55, 565-613. 7. Bekaert, Geert,Campbell Harvey and Christian T. Lundblad, 2003, Equity Market Liberalization in Emerging Markets, The Journal of Financial Research XXVI, 275-299. 8. Brown, Stephen J., and Otsuki Toshiyuki, 1993, Risk premia in Pacific-Basin capital markets, Pacific-Basin Finance Journal 1, 235-261. 35 9. Campbell, John Y., Andrew W. Lo, and A. Craig MacKinlay, 1997, The Econometrics of Financial Markets, Princeton University Press, Princeton, NJ. 10. Cochrane, John, 2001, Asset Pricing, Princeton University Press, Princeton, NJ. 11. Domowitz, Ian, Jack Glen and Ananth Madhavan, 1997, Market segmentation and stock prices: Evidence from an emerging market, Journal of Finance 52, 1059-1085. 12. Domowitz, Ian, Jack Glen and Ananth Madhavan, 1998, International CrossListing and Order Flow Migration: Evidence from an Emerging Market, Journal of Finance 53, 2001-2027. 13. Fama, Eugene F. and Kenneth R. French, 1993, Common Risk Factors in the Returns on Stocks and Bonds, Journal of Finanial Economy 33, 3-56. 14. Ferson, Wayne E., 2003, Tests of Multifactor Pricing Models, Volatility Bounds and Portfolio Performance, Handbook of the Economics of Finance, forthcoming. 15. Ferson, Wayne E. and Campbell Harvey, 1999, Conditioning Variables and the Cross Section of Stock Returns, Journal of Fiance 54, 1325-1358. 16. Ferson, Wayne E. and Campbell Harvey, 1994, Sources of risk and expected returns in global equity markets, Journal of Banking and Finance 18, 775-803. 36 17. Ferson, Wayne E. and Campbell Harvey, 1993, The Risk and Predictability of International Equity Return, Review of Financial Studies 6, 527-566. 18. Harvey, Campbell, 1995, Predictable risk and returns in emerging markets, Review of Financial Studies 8, 773-816. 19. Johnson, Robert and Soenen Luc, 2003, Economic integration and stock market comovement in the Americas, Journal of Multinational Financial Management 13, 85-100. 20. Karolyi, Andrew G. and Rene Stulz, Are financial assets priced locally or globally?, Handbook of the Economics of Finance, forthcoming. 21. Lettau, Martin and Sydney Ludvigson, 2001, Resurrecting the (C)CAPM: A Cross-Sectional Test When Risk Premia Are Time-Varying, Journal of Political Economy 109, 1238-1287. 22. Solnik, Bruno, 1983,International arbitrage pricing theory, Journal of Finance 38, 449-457. 37 7 Figures Figure 1: Growth in Portfolio Investment in Mexico by Foreigners. Growth Rate of Foreign Capital Inflows to Portfolio Investment 120 100 80 60 40 20 0 −20 Jan90 Jul92 Jan95 Jul97 38 Jan00 Jul02 Jan05 Figure 2: Ratio of the Value of Holdings of Mexican Stocks by Foreign to Domestic Investors. Ratio of Value of Mexican Stocks Holdings Foreign/Domestic 80 70 60 50 40 30 20 10 0 Jan90 Jul92 Jan95 Jul97 39 Jan00 Jul02 Jan05 Figure 3: Ratio of the Value Traded in Mexican ADRs to the Value Traded in Mexico. Ratio of Trading Value ADR/Mex 5.5 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 Jan90 Jul92 Jan95 Jul97 40 Jan00 Jul02 Jan05 Figure 4: Realized vs. Fitted returns in unconditional model for 10 Industrial Portfolios. ET (rt+1,i ) = βi λ + αi Local Factor 2 2 1 1 Realized Realized CAPM 0 0 −1 −1 −2 −2 −2 −1 0 Fitted 1 2 −2 2 2 1 1 0 −1 −2 −2 −1 0 Fitted 1 1 2 0 −1 −2 0 Fitted Augmented Fama and French Realized Realized Fama and French −1 2 −2 41 −1 0 Fitted 1 2 Figure 5: Realized vs. Fitted returns in conditional model for 10 Industrial Portfolios. ET (rt+1,i ) = ET (βt,i λt ) + αi Local Factor 2 2 1 1 Realized Realized CAPM 0 0 −1 −1 −2 −2 −2 −1 0 Fitted 1 2 −2 2 2 1 1 0 −1 −2 −2 −1 0 Fitted 1 1 2 0 −1 −2 0 Fitted Augmented Fama and French Realized Realized Fama and French −1 2 −2 42 −1 0 Fitted 1 2 8 Tables Table I Composition of Industrial Portfolios Composition of industrial portfolios in the sample. The column labelled Firms gives the maximum number of firms used to construct each portfolio. The average relative liquidity measures the share of the value of the total trading within the sample of firms. Industrial Firms Average Relative Liquidity of Industrial Portfolios Sector Year 1995 1996 1997 1998 1999 2000 2001 2002 22 7.97 6.56 8.08 6.82 9.41 16.42 8.46 6.71 18 7.51 2.85 3.23 3.30 3.47 3.88 6.89 9.61 Building 21 31.26 19.34 26.04 20.02 17.88 15.70 14.22 9.38 Conglomerates 18 15.69 8.88 10.50 10.59 9.76 9.73 9.03 4.70 Media & Telecoms 10 24.53 24.10 16.90 12.52 13.47 17.83 24.58 27.86 Chemical & Metal 11 1.28 8.29 11.44 6.38 4.80 2.42 3.15 5.03 Industrial 13 2.53 2.08 3.64 5.09 3.14 3.82 2.42 3.29 Machinery & Equipment 5 0.00 0.22 0.01 0.01 0.03 0.02 0.00 3.50 Retailing 17 8.88 27.51 19.69 32.95 37.78 29.98 31.21 29.62 Transportation 3 0.35 0.16 0.48 2.32 0.27 0.20 0.05 0.31 Beverages, Food and Tobacco Financial Services 43 Table II Summary Statistics Returns are in U.S. dollars and measured in excess of the 30 days T-bill. All sample means and standard deviations are annualized. The sample period is March 1995 to October 2003. In panels A-C, the sample autocorrelations, ρj , are presented in the first row, and p-values of the Ljung-Box statistic for testing the joint significance of the autocorrelation coefficient up to the corresponding lag are presented in the second row. Panel D presents the sample correlation matrix of selected factors. Mean Std. Dev. ρ1 ρ2 ρ3 ρ4 ρ12 ρ24 33.48 -0.19 0.04 0.05 -0.17 0.11 -0.09 0.03 0.47 0.29 0.06 0.32 0.11 -0.05 0.03 0.10 -0.26 0.05 -0.13 0.30 0.40 0.15 0.01 0.39 0.41 Panel A. Industrial Portfolios Beverage, Food 1.96 and Tobacco Financial Services Building Conglomerates Media & Telecoms Chemical & Metal Industrial Machinery & Equipment Retailing Transportation 7.55 -7.01 -8.84 10.52 -24.87 -7.20 -21.72 6.71 -6.77 53.38 39.86 42.10 38.08 45.17 32.77 54.43 54.52 43.50 0.01 -0.08 0.06 -0.07 0.00 -0.02 0.46 0.23 0.28 0.23 0.35 0.28 -0.10 0.08 0.11 -0.14 0.06 -0.11 0.16 0.24 0.12 0.10 0.44 0.09 -0.12 -0.02 0.09 -0.11 0.02 -0.06 0.13 0.36 0.21 0.19 0.34 0.20 -0.03 0.09 0.09 -0.06 0.01 -0.12 0.40 0.19 0.19 0.25 0.45 0.08 -0.08 -0.07 0.13 -0.23 0.10 0.12 0.23 0.22 0.12 0.01 0.32 0.27 0.19 0.10 0.05 -0.15 -0.06 0.07 0.03 0.26 0.44 0.04 0.45 0.38 0.08 -0.01 0.05 0.00 0.03 -0.04 0.22 0.42 0.29 0.47 0.42 0.25 -0.14 0.00 -0.06 -0.05 0.10 -0.10 0.09 0.41 0.27 0.24 0.13 0.20 -0.09 -0.05 0.10 -0.14 0.00 -0.06 0.18 0.29 0.19 0.12 0.44 0.10 -0.05 -0.15 0.01 0.10 0.09 0.10 0.31 0.06 0.48 0.23 0.41 0.48 0.81 0.64 0.48 0.37 -0.16 -0.07 0.00 0.26 0.26 0.32 0.28 0.45 0.04 -0.08 0.01 -0.08 0.02 0.04 0.34 0.23 0.44 0.20 0.36 0.43 0.27 0.13 0.00 0.15 -0.02 -0.01 0.00 0.29 0.32 0.06 0.36 0.23 0.27 0.11 0.20 0.13 0.05 -0.11 0.00 0.35 0.04 0.38 0.43 0.27 -0.57 0.02 0.33 -0.33 0.40 -0.11 Panel B. Risk Factors IP C Exch Dif f M kt SM B HM L 5.03 -4.55 3.08 5.72 -5.05 10.28 34.39 8.92 0.43 17.72 16.62 15.11 Panel C. Information Variables ∆y 6.24 9.77 Table III Predictability of Industrial Portfolios Monthly excess returns are regressed on a set of lagged instruments. The instrumental variables are “∆yt−1 ” the lagged real growth in labor income, “∆F At−1 ” the lagged real growth in asset holdings, and CetSp is the lagged spread between the one year and one month cetes. HAC consistent t-ratios are on the second line below the coefficients. R2 is the coefficient of determination, with the adjusted R2 on the second line. ρ is the first order autocorrelation of the regression residual, with its t-value in the second column. F is the F -statistic of testing the hypothesis of zero coefficients in each regression. Const ∆yt−1 ∆F At−1 CetSp R2 ρ F Beverage, Food 1.05 -1.65 1.85 -0.55 0.22 -0.51 12.67 and Tobacco 0.69 -5.04 2.24 -1.06 0.19 -5.88 Financial Service 3.20 -2.49 1.96 -1.22 0.20 -0.49 1.33 -4.76 1.49 -1.46 0.17 -5.26 2.76 -1.67 1.98 -1.69 0.20 -0.23 1.52 -4.24 1.99 -2.68 0.17 -2.20 1.25 -1.90 1.13 -0.80 0.18 -0.48 0.64 -4.50 1.06 -1.18 0.15 -5.27 2.29 -1.33 1.11 -0.66 0.11 -0.44 1.24 -3.34 1.10 -1.04 0.08 -4.41 1.54 -1.88 1.66 -1.60 0.17 -0.17 0.72 -4.10 1.44 -2.18 0.15 -1.70 0.22 -0.99 1.77 -0.64 0.10 -0.29 0.14 -2.86 2.03 -1.16 0.07 -3.28 -0.64 -0.75 1.61 -0.66 0.02 0.11 -0.23 -1.26 1.07 -0.69 -0.01 1.23 2.78 -1.81 2.11 -1.30 0.12 -0.39 1.09 -3.27 1.51 -1.46 0.09 -3.97 0.54 -0.97 0.11 -0.33 0.05 -0.46 0.25 -2.04 0.09 -0.43 0.01 -5.05 2.17 -1.44 1.28 -0.83 0.16 -0.46 1.34 -4.13 1.45 -1.48 0.13 -4.70 Building Conglomerates Media & Telecoms Chemical & Metal Industrial Machinery & Equipment Retailing Transportation IP C 45 11.35 11.18 10.05 5.59 9.53 4.98 1.14 5.87 2.17 8.75 Table IV Risk Factors Regressions, Local Factors Model Monthly data from March 1995 to October 2003. Excess returns in U.S. dollars are regressed on the excess return on the the Mexican stock index “IP C”, exchange rate “Exch” and Dif f is the UMS spread. HAC consistent t-ratios are on the second line below the coefficients. R2 is the coefficient of determination, with the adjusted R2 on the second line. ρ is the first order autocorrelation of the regression residuals, with its t-value in the second column. F is the F -statistic for the hypothesis of zero coefficients in each regression. Const IP C Exch Dif f R2 ρ F Beverage, Food -0.28 0.84 0.39 0.08 0.87 -0.09 202.59 and Tobacco -0.34 17.18 2.06 0.32 0.87 -0.95 0.51 1.21 0.86 -0.02 0.78 -0.08 0.29 11.93 2.20 -0.04 0.77 -0.94 0.94 0.86 0.85 -0.51 0.79 -0.08 0.75 11.63 3.00 -1.38 0.79 -1.00 0.29 0.97 0.65 -0.38 0.80 -0.08 0.22 12.70 2.23 -1.02 0.80 -0.99 0.60 1.15 -0.53 -0.13 0.92 -0.09 0.82 26.44 -3.18 -0.62 0.92 -0.88 1.56 0.72 0.96 -1.16 0.52 0.00 0.72 5.64 1.97 -1.84 0.50 -0.05 -1.17 0.47 0.83 0.22 0.44 -0.06 -0.69 4.71 2.15 0.45 0.42 -0.76 2.78 0.76 -0.57 -1.67 0.22 0.05 0.84 3.90 -0.76 -1.72 0.20 0.65 2.14 1.21 0.66 -0.60 0.72 -0.08 1.07 10.34 1.47 -1.03 0.71 -0.99 3.75 0.25 1.29 -1.28 0.22 0.03 1.41 1.61 2.16 -1.65 0.20 0.36 Financial Services Building Conglomerates Media & Telecoms Chemical & Metal Industrial Machinery & Equipment Retailing Transportation 46 107.07 115.11 121.84 351.92 32.32 23.38 8.57 77.72 8.53 Table V Risk Factors Regressions, Fama and French Factors Monthly data from March 1995 to October 2003. Excess returns in U.S. dollars are regressed on the excess return of the the standard’s and Poor Index “S&P ”, the small minus big factor “SM B”, and high minus low factor“HM L” of Fama and French. HAC consistent t-ratios are on the second line below the coefficients. R2 is the coefficient of determination, with the adjusted R2 on the second line. ρ is the first order autocorrelation of the regression residual, with its t-value in the second column. F is the F -statistic for the hypothesis of zero coefficients in each regression. Const M kt SM B HM L R2 ρ F Beverage, Food -0.75 1.41 0.32 0.44 0.46 0.11 25.50 and Tobacco -0.99 8.22 1.73 1.88 0.44 0.98 Financial Services -0.56 1.87 0.12 0.40 0.33 0.06 -0.41 6.14 0.36 0.97 0.31 0.56 -1.66 1.59 0.71 0.71 0.42 0.18 -1.76 7.50 3.11 2.46 0.40 1.63 -1.63 1.59 0.70 0.50 0.42 0.18 -1.63 7.12 2.92 1.62 0.40 1.60 -0.13 1.69 0.06 0.26 0.55 0.06 -0.16 9.51 0.32 1.07 0.54 0.54 -3.09 1.48 0.87 0.79 0.30 0.29 -2.64 5.64 3.09 2.20 0.28 2.40 -1.47 0.99 0.39 0.65 0.21 0.19 -1.62 4.89 1.78 2.33 0.18 1.71 -2.94 1.56 0.62 0.76 0.20 0.22 -1.95 4.60 1.71 1.64 0.18 1.90 -1.08 2.25 0.43 0.87 0.41 0.10 -0.83 7.72 1.38 2.19 0.39 0.93 -1.26 0.89 0.62 0.63 0.12 0.27 -0.99 3.11 2.03 1.61 0.09 2.34 Building Conglomerates Media & Telecoms Chemical & Metal Industrial Machinery & Equipment Retailing Transportation 47 14.64 21.62 21.60 36.68 12.89 7.99 7.69 21.14 3.92 Table VI Risk Factors Regressions; Fama and French and exchange rate Monthly data from March 1995 to October 2003. Excess returns in U.S. dollars are regressed on the excess return of the “S&P ” the standard’s and Poor Index, the small minus big factor “SM B”, and high minus low factor “HM L” of Fama and French and the exchange rate Exch. HAC consistent t-ratios are on the second line below the coefficients. R2 is the coefficient of determination, with the adjusted R2 on the second line. ρ is the first order autocorrelation of the regression residual, with its t-value in the second column. F is the F -statistic of testing the hypothesis of zero coefficients in each regression. Const M kt SM B HM L Exch R2 ρ F Beverage, Food 0.19 1.02 0.27 0.35 1.85 0.67 0.06 44.40 and Tobacco 0.31 7.06 1.83 1.91 7.63 0.65 0.67 Financial Services 1.04 1.21 0.03 0.25 3.15 0.56 0.01 0.93 4.58 0.11 0.75 7.11 0.54 0.13 -0.44 1.08 0.64 0.60 2.38 0.66 0.10 -0.60 6.26 3.67 2.70 8.18 0.65 1.13 -0.41 1.08 0.63 0.38 2.40 0.64 0.09 -0.51 5.74 3.34 1.58 7.55 0.62 1.04 0.61 1.39 0.02 0.19 1.44 0.65 0.04 0.85 8.22 0.11 0.88 5.09 0.63 0.43 -1.95 1.01 0.81 0.68 2.24 0.47 0.17 -1.87 4.10 3.28 2.17 5.42 0.44 1.88 -0.62 0.64 0.34 0.57 1.67 0.39 0.11 -0.76 3.34 1.77 2.32 5.17 0.36 1.31 -2.66 1.44 0.61 0.73 0.56 0.21 0.22 -1.74 3.99 1.67 1.59 0.92 0.18 1.90 0.31 1.67 0.35 0.74 2.73 0.58 0.07 0.28 6.35 1.34 2.20 6.18 0.56 0.75 -0.38 0.52 0.57 0.54 1.73 0.22 0.12 -0.31 1.82 1.99 1.48 3.59 0.19 1.46 Building Conglomerates Media & Telecoms Chemical & Metal Industrial Machinery & Equipment Retailing Transportation 48 28.63 43.29 39.20 40.84 19.52 13.93 5.95 31.11 6.36 Table VII Unconditional Pricing Tests Panel A presents the results from testing the joint hypothesis of zero coefficients on all portfolio for the different factors. The first two columns presents results for the local-factor models, the next two for the Fama and French and the last two for the Fama and French that includes the exchange rate. p-values for the F -tests and Wald tests are presented below the value of the test statistic. Panel B presents the results from testing the joint hypothesis of zero coefficients for the omitted factors in each model. The Fama and French factors for the local-factor model, the local-factors in the Fama and French model and IP C and U M S in the Fama and French with exchange. p-values are presented in the second line. Panel A: Tests on significance of risk factors Local Factors Fama and French Fama and French and Exchange Factor F -test Wald test IP C 244.33 2551.93 0.00 0.00 2.50 Exch Dif f F -test Wald test 26.09 9.64 101.80 0.01 0.00 0.00 0.00 1.39 14.52 0.18 0.15 M kt SM B HM L F -test Wald test 11.69 122.08 9.42 99.51 0.00 0.00 0.00 0.00 2.49 26.04 2.94 31.02 0.01 0.00 0.00 0.00 1.44 15.00 1.65 17.47 0.16 0.13 0.09 0.06 Panel B: Tests on omitted risk factors Const 0.75 7.85 1.20 12.49 0.86 9.13 0.68 0.64 0.29 0.25 0.57 0.52 49 Table VIII Cross-Section Regressions Unconditional Model Results for average λ estimates from monthly cross-sectional regressions for industrial portfolios: Rt+1,i = β 0 λ. The betas come from time-series regressions using information up to time t of industrial portfolios excess returns on the factors excess returns. Individual λi estimates for the beta of the factor listed are presented. “IP C” is the excess return in U.S. dollars of the Mexican Stock Index over the 30 day TBill, M kt is the excess return of U.S. market over the 30 day T-Bill, “Exch” is the US. dollar/Mexican peso exchange rate growth, “Dif f ” is the spread betweem UMS bond and a T-Note of 5 years, “SM B” and “HM L” are the Fama-French mimicking portfolios related to size and book-to-market equity ratios. The table reports crosssectional regression using expanding sample (es) and rolling windows of 36 months (rw) coefficients.Fama-MacBeth t-statistics are presented below the coefficients in parenthesis. R2 Risk Factors Model CAPM IP C λes M kt Exch Dif f SM B HM L 2.34 0.21 (1.29) λrw 1.76 0.19 (1.15) Local λes Factor λrw Fama and λes French λrw Fama and λes French with Exchange λrw 2.97 0.31 -0.48 (1.58) (0.42) (-0.62) 1.36 -0.16 -1.13 (0.82) (-0.25) (-1.80) 0.47 0.50 0.50 -2.33 0.25 (0.42) (-1.12) (0.12) -0.77 -2.87 2.16 (-0.73) (-1.47) (0.95) -0.74 0.79 -3.95 1.88 (-0.40) (1.10) -(1.27) (0.76) -1.12 0.26 -4.01 3.51 (-0.79) (0.37) (-1.74) (1.18) 50 0.42 0.42 0.54 0.54 Table IX Conditional Beta Regressions; Local Factors Excess returns on 10 industrial portfolios are regressed on lagged instruments, “IP C” Mexican stock market index multiplied by the instruments and a constant, “Exch” the exchange rate multiplied by the instruments and a constant and, “Dif f ” political risk multiplied by the instruments and a constant. R2 of this regression is presented in the second column. R2 of the restricted model (constant betas), where excess returns are regressed only on instruments and risk factors is presented in the first column. The p-value of an F -test that compares the two models is presented in the third column. The last three columns present similar results assuming a fixed constant. In the fourth column the R2 when excess returns are regressed on a constant and the local risk factors are multiplied by the instruments and the constant. The p-value of F -test that tests the significance of time varying betas is presented in the last column. Panel A: Time-varying constant R2 R2 Time-varying Constant Betas Beverage, Food & Tobacco Panel B: Fixed constant R2 R2 F -test Time-varying Constant F -test Betas (p-value) Betas Betas (p-value) 0.8809 0.8798 (0.3757) 0.8824 0.8667 (0.0131) Financial Services 0.7878 0.7762 (0.1283) 0.7948 0.7738 (0.0325) Building 0.7858 0.7956 (0.8636) 0.7778 0.7864 (0.8145) Conglomerates 0.7830 0.7967 (0.9672) 0.7848 0.7958 (0.9140) Media & Telecoms 0.9225 0.9185 (0.1406) 0.9202 0.9188 (0.3049) Chemical & Metal 0.4953 0.5051 (0.6262) 0.4809 0.5026 (0.8423) Industrial 0.3690 0.4136 (0.9876) 0.3722 0.4193 (0.9966) Machinery & Equipment 0.1963 0.1825 (0.3134) 0.2214 0.1962 (0.2145) Retailing 0.7189 0.7157 (0.3535) 0.7192 0.7122 (0.2579) Transportation 0.1917 0.2131 (0.6930) 0.2010 0.1955 (0.3839) 51 Table X Conditional Beta Regressions; Fama and French Excess returns on 10 industrial portfolios are regressed on lagged instruments and Fama and French factors multiplied by the instrumental variables and a constant. R2 of this regression is presented in the second column. R2 of the restricted model (constant betas), where excess returns are regressed only on instruments and the factors are presented in the first column. The p-value of an F -test that compares the two models is presented in the third column. The rest of the columns presents similar results when the constant is assumed to be fixed. The fourth column presents the R2 when excess returns are regressed on a constant and the factors multiplied by the instruments and the constant. The restricted version of this model is the unconditional model. The p-value that tests the hypothesis of constant betas is presented in the last column. Panel A: Time-varying constant R2 R2 Time-varying Constant Betas Beverage, Food & Tobacco Panel B: Fixed constant R2 R2 F -test Time-varying Constant F -test Betas (p-value) Betas Betas (p-value) 0.6246 0.5687 (0.0097) 0.5118 0.4414 (0.0095) Financial Services 0.5358 0.4329 (0.0012) 0.4250 0.3055 (0.0014) Building 0.6078 0.5246 (0.0015) 0.5036 0.3995 (0.0013) Conglomerates 0.6319 0.5017 (0.0000) 0.5140 0.3992 (0.0006) Media & Telecoms 0.6283 0.5791 (0.0156) 0.5864 0.5351 (0.0173) Chemical & Metal 0.4262 0.3630 (0.0292) 0.3324 0.2773 (0.0570) Industrial 0.3035 0.2312 (0.0349) 0.2755 0.1840 (0.0161) Machinery & Equipment 0.1765 0.1633 (0.3205) 0.2028 0.1775 (0.2179) Retailing 0.5326 0.4545 (0.0057) 0.4961 0.3939 (0.0016) Transportation 0.2571 0.0956 (0.0013) 0.2144 0.0860 (0.0053) 52 Table XI Conditional Beta Regressions; Fama and French and Exchange Excess returns on 10 industrial portfolios are regressed on lagged instruments, Fama and French factors multiplied by the instrumental variables and a constant, and “Exch” the exchange rate multiplied by the instruments and the constant. R2 of this regression is presented in the second column. R2 of the restricted model (constant betas), where excess returns are regressed only on instruments and the factors are presented in the first column. The p-value of an F -test that compares the two models is presented in the third column. The last three columns presents the results when the constant is assumed to be fixed. In the fourth column, the R2 when excess returns are regressed on a constant and the factors multiplied by the instruments and the constant is presented. The restricted version of this model is the unconditional model. The p-value that tests the hypothesis of constant betas is presented in the last column. Panel A: Time-varying constant R2 R2 Time-varying Constant Betas Beverage, Food & Tobacco Panel B: Fixed constant R2 R2 F -test Time-varying Constant F -test Betas (p-value) Betas Betas (p-value) 0.7430 0.7117 (0.0663) 0.7044 0.6512 (0.0202) Financial Services 0.6373 0.5890 (0.0543) 0.5990 0.5431 (0.0438) Building 0.7321 0.6773 (0.0146) 0.6944 0.6452 (0.0292) Conglomerates 0.7547 0.6636 (0.0006) 0.7032 0.6216 (0.0031) Media & Telecoms 0.6683 0.6468 (0.1739) 0.6545 0.6315 (0.1610) Chemical & Metal 0.4809 0.4765 (0.3985) 0.4464 0.4434 (0.4114) Industrial 0.3851 0.3588 (0.2454) 0.3926 0.3574 (0.1860) Machinery & Equipment 0.1546 0.1637 (0.5079) 0.1816 0.1756 (0.4013) Retailing 0.6151 0.5678 (0.0648) 0.6081 0.5643 (0.0728) Transportation 0.2653 0.1944 (0.1027) 0.2085 0.1873 (0.3034) 53 Table XII Tests for Time Varying Betas Panel A presents the results from testing the joint hypothesis of zero coefficients on all portfolio for the scaled factors ft ⊗ Zt . The first two columns present results for the local-factor models, the following two for the Fama and French and the last two columns for the Fama and French that includes the exchange rate. p-values for the F tests and Wald tests are presented below the value of the test statistic in parenthesis. Panel B presents the results from testing the joint hypothesis of constant alphas and zero alphas, p-values are presented in parenthesis. Panel A: Tests on significance of scaled factors Local Factors Fama and French Fama and French and Exchange Factor IP C Exch Dif f F -test Wald test F -test Wald test F -test Wald test 0.9185 11.0930 (0.5938) (0.9993) 0.3177 3.8375 0.8773 11.1765 (0.9998) (0.9544) (0.6576) (0.3439) 0.4594 5.5491 (0.9947) (0.8516) M kt SM B HM L 1.7791 21.4879 1.7428 22.2024 (0.0064) (0.0179) (0.0083) (0.0141) 3.2200 38.8906 2.4226 30.8634 (0.0000) (0.0000) (0.0000) (0.0006) 2.4939 30.1211 3.2043 40.8219 (0.0000) (0.0008) (0.0000) (0.0000) Panel B: Tests on alphas constant alpha zero alpha 0.7184 8.6773 0.4063 4.9069 0.3581 4.5617 (0.8675) (0.5630) (0.9983) (0.8973) (0.9995) (0.9185) 0.7968 9.6234 1.0893 13.1569 0.8340 10.6250 (0.8134) (0.4741) (0.3264) (0.2150) (0.7589) (0.3875) 54 Table XIII Cross-Section Regressions Conditional Model Results for average λ estimates from monthly cross-sectional regressions for industrial portfolios: Rt+1,i = β 0 λ. The betas come from time-series regressions using information up to time t of industrial portfolios excess returns on the factors excess returns. Individual λi estimates for the beta of the factor listed are presented. “IP C” is the excess return in U.S. dollars of the Mexican Stock Index over the 30 day TBill, M kt is the excess return of U.S. market over the 30 day T-Bill, “Exch” is the US. dollar/Mexican peso exchange rate growth, “Dif f ” is the spread betweem UMS bond and a T-Note of 5 years, “SM B” and “HM L” are the Fama-French mimicking portfolios related to size and book-to-market equity ratios. The table reports crosssectional regression using expanding sample (es) and rolling windows of 36 months (rw) coefficients.Fama-MacBeth t-statistics are presented below the coefficients in parenthesis. R2 Risk Factors Model CAPM IP C λes M kt Exch Dif f SM B HM L 1.48 0.20 (0.86) λrw 0.22 0.20 (0.16) Local λes Factor λrw Fama and λes French λrw Fama and λes French with Exchange λrw 2.60 1.08 -0.16 (1.24) (1.40) -(0.23) 1.12 0.66 -0.78 (0.76) (1.60) -(1.81) 0.51 0.47 -1.38 -0.53 1.00 (-1.06) (-0.36) (0.84) 0.11 -1.36 0.44 (0.10) -(1.15) (0.38) -1.74 -0.07 -1.20 2.09 (-1.47) (-0.11) (-0.76) (1.60) -0.60 0.04 0.36 -0.81 (-0.54) (0.09) (0.33) (-0.72) 55 0.46 0.51 0.55 0.59 Table XIV Pricing Errors Monthly pricing errors for the cross sectional regressions are reported. In each column, the average price for the unscaled and scaled versions for different models are compared: CAPM, Local Factors, Fama and French and Fama and French with Exchange are reported. The last two rows reports the square root of the average squared pricing errors across all portfolios and a χ2 statistic for the test that the pricing errors are zero. CAPM Local Factors Fama and French Fama and French with Exch Scaled Scaled Scaled Scaled Panel A. Expanding Sample Beverage, Food & Tobacco 0.03 0.07 0.15 0.57 0.04 0.28 0.54 0.04 Financial Services 0.77 1.51 0.41 0.67 0.38 0.60 -0.15 0.48 Building 0.11 0.18 0.26 -0.24 0.70 -0.43 0.55 -0.57 Conglomerates -0.79 -0.58 -0.51 -0.26 -0.08 0.31 -0.03 0.07 Media & Telecoms 0.74 0.78 0.46 1.27 0.25 0.63 0.56 0.93 Chemical & Metal -1.43 -1.26 -0.95 -1.01 -0.61 -0.91 -0.67 -0.80 Industrial 0.05 -0.12 0.34 -0.63 0.24 -0.05 0.58 -0.08 Machinery & Equipment -0.86 -1.49 -1.47 -0.51 -0.89 -0.51 -0.80 -0.33 Retailing 0.14 0.26 0.10 -0.44 -0.25 0.09 -0.33 0.22 Transportation 1.25 0.64 1.21 0.59 0.22 -0.01 -0.26 0.04 Average 0.62 0.69 0.59 0.62 0.37 0.38 0.45 0.36 χ2 3.31 5.75 2.91 6.22 2.99 6.08 3.57 9.03 Panel B. Rolling Windows Beverage, Food & Tobacco 0.08 0.01 -0.06 0.33 -0.04 0.51 0.16 -0.10 Financial Services 1.31 1.95 1.27 1.31 0.88 0.66 0.82 0.59 Building 0.08 0.09 0.04 -0.90 0.62 -0.39 0.35 -0.02 Conglomerates -0.87 -0.60 -0.17 -0.29 -0.22 -0.63 0.17 -0.40 Media & Telecoms 0.84 0.88 0.61 1.19 0.85 0.35 0.68 0.80 Chemical & Metal -1.43 -1.34 -0.99 -0.91 -0.53 -0.08 -0.24 -0.60 Industrial 0.09 0.11 1.02 -0.07 -0.16 0.36 0.19 0.08 Machinery & Equipment -1.04 -1.55 -1.18 -1.12 -0.18 -0.69 -0.89 0.22 Retailing 0.11 0.25 -0.52 0.07 -0.95 -0.08 -0.66 -0.37 Transportation 0.83 0.21 -0.03 0.40 -0.28 -0.01 -0.57 -0.20 Average 0.67 0.70 0.59 0.66 0.47 0.37 0.47 0.34 χ2 -3.25 7.81 6.97 11.47 9.71 5.01 8.48 5.47 56