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 segmen-

tation 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 thankparticipants in the econometrics workshop at the University of Toronto. All remaining errors aremine.

†Alonso Gomez Albert, 150 St. George St., University of Toronto, Toronto, M5S3G7, Canada.Phone: (416)946-0455. Fax:(416) 978-6713. Email: agomez@chass.utoronto.ca.

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. In-

terest 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 per-

cent 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

1International Monetary Fund, World Economic Outlook: Growth and Institutions, WorldEconomic and Financial Surveys, April 2003.

1

the world market in emerging markets.

Beginning in 1989, Mexico experienced a transformation from a closed and pro-

tected 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 de-

valuation 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 condi-

tional expected return of a national markets index is equal to a weighted average of

2A striking increase of firms have undertaken ADRs programs, passing from 8 firms in 1992 to71 in 2001. Many of the ADRs are traded over the counter, but by 2001 there were 28 differentseries traded on major exchanges.

3Banco 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 time-

varying. 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 hy-

pothesis 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, in-

deed 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 sug-

gests 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 in-

vestors’ expectations of future average returns. To capture this variation, I assume

that the parameters of the stochastic discount factor depend on current-period in-

formation 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’ condi-

tioning 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 uncondi-

tional 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 R2s. 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 spec-

ifications, 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 sub-

stantial 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 cross-

6

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, div-

idends 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 infor-

mation set. Since Ωt is unobservable from a researcher’s perspective, expectations

4Also 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 can-

didates 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+1rt+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 + b′ft+1, where ft+1 is a vector

of size k of risk factors. In general, mt+1 can be written as mt+1 = mt+1 + εt+1

where mt+1 is the projection of mt+1 on the asset space and εt+1 is orthogonal to

8

the asset space, so E(mt+1εt+1) = 0. Any random variable orthogonal to returns

can be added to m, leaving the pricing implications unchanged.

In the case of conditional factor models, the coefficients at and bt vary over

time as a function of conditioning information, mt+1 = at + b′tft+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 Rft and the

factors, ft+1, yields:

ιk = Et(mt+1ft+1) and 1 = Et(mt+1Rft ) (4)

where ιkε<k is a vector with all of its components equal to one. Solving for at and

bt we obtain:

at =1

Rft

− Et(f′t+1)bt and bt = (V art(ft+1))

−1

(ιk − Et(ft+1)

Rft

)(5)

Equation (5) shows explicitly that both at and bt are functions of Rft , 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

5If ft+1 does not belong to the payoff space, we can replace it with ft+1 = proj(ft+1|X), whereX represents the asset space.

6Predictable movements in volatility may be a source of variation in bt, however they appearto be more concentrated in high-frequency data (see Cambell, Lo and MacKinlay (1997)) than inmonthly, or quarterly returns.

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 conse-

quence of the predictability of equity premia.

The beta representation for expected returns can be obtained by combining equa-

tion (3) with the linear specification of the SDF (at + b′tft+1):

Et(rt+1,i) = −Covt(rt+1,i, f′t+1)

Et(mt+1)bt ≡ −β′t,i

V art(ft+1)

Et(mt+1)bt ≡ β′t,iλt (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.

rt+1,i = ct,i + β′t,i (ft+1) + εt+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

of coefficients β′t,i represent risk exposures of portfolio excess returns to the factors

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(εt,ift+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,

Et(rt+1,i) = βt,i

′λt + αi,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 two-

pass 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 = D′iZt (9)

ct,i = c′iZt

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 = c′iZt + d′i(Zt ⊗ ft+1) + εt+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

7As shown in equation (5), at and bt are functions of conditional returns, therefore variablesthat can summarize variation in conditional moments are used as instruments Zt.

8V 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 cross-

section of returns, time-varying betas are recovered using the estimated version

of equation (9), βt,i = D′Zt and cross-section regressions of returns on βt,i are

estimated.

14

3 Data

The sample is limited to the period following the devaluation suffered by the Mex-

ican 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

9Mexican electronic provider of financial information.10In 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.11The 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 itsmaximum of 195 listed firms in 1998 and falling to 158 for 2003. Only about 60 percent of thesestocks trades at least once per week.

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 aggre-

gated 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 Produc-

tion, 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 liquid-

ity, 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 IPC 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: IPC is the monthly log-difference of the Mexican market in-

dex expressed in U.S. dollars, and in excess of the 30-day T-bill. The IPC 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, Diff , 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

12The IPC is the most important market index and is comprised of 35 stocks (see nex section).

17

dollars (UMS)13. Diff 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, Mkt, that is

13These bonds pay a fixed semi-annual coupon. The maturity of the bonds that I used to estimatea zero coupon structure are: 06-Apr-05 15-Jan-07 12-Mar-08 17-Feb-09 15-Sep-16 15-May-26

14One of the most questionable issues in the empirical international finance literature seeking tomeasure integration of national stock markets, is the use of the CAPM or ICAPM to explain inter-national 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.

15Given the differences in size between U.S. stock markets and the Mexican stock exchange, theU.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)

SMB (Small Minus Big) is the average return on three small portfolios minus the

average return on three big portfolios, and c) HML (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 infor-

mation 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 re-

turns. The first variable, ∆y, represents the monthly real growth rate of seasonally

adjusted labor income. The second variable, ∆FA 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 Diff , lagged Fama and French fac-

16See Fama and French (1993) for a detailed explanation of these portfolios.17The 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 maturitiesof 28, 91, 182, 364 and occasionally of 724 days

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 be-

tween 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 an-

nualized. 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 IPC.

Diff , the risk premium of Mexican sovereign debt measured by the spread be-

tween 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 Diff follows an AR(1)18.

Cross-correlations are presented in panel D of Table II. IPC is highly correlated

with both Mkt and Exch19.

18The first order autocorrelation is 0.81 while the second autocorrelation is of 0.64.19Remember that Exch is measured as the price of Mexican Pesos in U.S. dollars

21

4.2 Predictability and Description of Stock Portfolio Re-

turns

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 IPC on lagged information

variables Zt−1. The regressions produce significant t-statistics in many cases. The

R2 in the case of the IPC 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 IPC 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 Unconditional Factor Models

4.3.1 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 transporta-

tion 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 IPC

20I 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 andMexican pesos) as an additional local risk factor. This was motivated by the international financeliterature that explores integration with a weighted average of the ICAPM and CAPM, wheresystematic risk, under the hypothesis of segmentation, is quantify by the variance of the localmarket. However, risk exposures for idiosyncratic risk were not significant in any of the industrialportfolios.

21As noted in table 1, the transportation sector accounts for less than 2.4 percent of totaltransactions 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, Mkt, appears uniformly significant and positive for all

industrial portfolios. Risk exposures to SMB and HML, are also significant in

several industrial portfolios. An interpretation for HML, not universally accepted,

is provided by Fama and French (1995). They showed that HML acts as a proxy for

relative distress. Weak firms, with low earnings, tend to have low book-to-market

ratios and positive loadings on HML, whereas the contrary effect is observed for

strong firms. Therefore, slopes on HML can be interpreted as a measure of financial

distress. In all industrial portfolios, slopes on HML 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 SMB factor, coefficients are positive in all

portfolios. A common interpretation for SMB 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 SMB 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 R2s in all portfolios. From

a time-series perspective, it appears that the local-factor model measured by R2s,

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), Diff

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

22For testing linear restrictions in a SURE representation, the analogous F -statistic under GLS

assumptions is: F = (Rβ−r)′[RV ar(β)R′]−1(Rβ−r)/q

e′V e/(N−K), where V = Σ ⊗ I; Σ is the FGLS estimate of

the covariance matrix. N is the number of observations of each equation times the number ofequations and K stands for the number of parameters estimated in the system. An alternative teststatistic (Wald test), under the hypothesis that e′V e/(N −K) converges to one, that measures thedistance between Rβ and r is given by qF . This test statistic has a limiting χ2(q) distribution.

23Mexico implemented a dual exchange rate regime during the 1980’s and a semi-fixed exchangeparity 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

just λ = ET (ft+1) where the notation ET refers to the sample mean. However,

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 = β′iλt+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 un-

scaled factor model. Time-series averages of the cross-sectional regressions coeffi-

cients λt+1, Fama-MacBeth t-statistics for the coefficients and the time-series average

of R2s 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 IPC

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 Diff 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 partic-

ular, cross- section regressions of the form:

E(Rt+1,i) = β′iλ 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 45-

degree 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

24The Fama-French model performs better than the local-factor model when the betas usedin 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 Conditional Factor Models

4.4.1 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 pre-

dictability. 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 men-

tioned 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.25Equation 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

time-varying. R2

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 time-

varying 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 coeffi-

cients 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 asso-

ciated 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, cross-

section regression for the scaled factor version are performed, where betas are time-

varying:

Rt+1,i = β′t,iλ + αt+1,i i = 1, ..., N.

Table XIII summarizes the different versions of the cross-sectional regressions. Time-

series averages of the cross-sectional coefficients are shown along with their Fama-

MacBeth 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 R2s 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 pric-

ing 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 R2s 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 concern-

ing 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 indus-

trial 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 covari-

ance 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 alter-

native models to explain the pattern of returns. The Fama and French (1993) three

factor model, despite the controversy of whether these factors truly capture non-

diversifiable 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 cor-

responded 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 ex-

change 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 Amer-

ica 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 inte-

gration, 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 Re-

search 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 Econo-

metrics 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 Cross-

Listing and Order Flow Migration: Evidence from an Emerging Market, Jour-

nal 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, forthcom-

ing.

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 mar-

ket comovement in the Americas, Journal of Multinational Financial Manage-

ment 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 Polit-

ical 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.

Jan90 Jul92 Jan95 Jul97 Jan00 Jul02 Jan05−20

0

20

40

60

80

100

120Growth Rate of Foreign Capital Inflows to Portfolio Investment

38

Figure 2: Ratio of the Value of Holdings of Mexican Stocks by Foreign toDomestic Investors.

Jan90 Jul92 Jan95 Jul97 Jan00 Jul02 Jan050

10

20

30

40

50

60

70

80Ratio of Value of Mexican Stocks Holdings Foreign/Domestic

39

Figure 3: Ratio of the Value Traded in Mexican ADRs to the Value Tradedin Mexico.

Jan90 Jul92 Jan95 Jul97 Jan00 Jul02 Jan050.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5Ratio of Trading Value ADR/Mex

40

Figure 4: Realized vs. Fitted returns in unconditional model for 10 Indus-trial Portfolios. ET (rt+1,i) = βiλ + αi

−2 −1 0 1 2

−2

−1

0

1

2

CAPM

Fitted

Rea

lized

−2 −1 0 1 2

−2

−1

0

1

2

Local Factor

FittedR

ealiz

ed

−2 −1 0 1 2

−2

−1

0

1

2

Fama and French

Fitted

Rea

lized

−2 −1 0 1 2

−2

−1

0

1

2

Augmented Fama and French

Fitted

Rea

lized

41

Figure 5: Realized vs. Fitted returns in conditional model for 10 IndustrialPortfolios. ET (rt+1,i) = ET (βt,iλt) + αi

−2 −1 0 1 2

−2

−1

0

1

2

CAPM

Fitted

Rea

lized

−2 −1 0 1 2

−2

−1

0

1

2

Local Factor

FittedR

ealiz

ed

−2 −1 0 1 2

−2

−1

0

1

2

Fama and French

Fitted

Rea

lized

−2 −1 0 1 2

−2

−1

0

1

2

Augmented Fama and French

Fitted

Rea

lized

42

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

Beverages, Food 22 7.97 6.56 8.08 6.82 9.41 16.42 8.46 6.71

and Tobacco

Financial Ser- 18 7.51 2.85 3.23 3.30 3.47 3.88 6.89 9.61

vices

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

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

Panel A. Industrial Portfolios

Beverage, Food 1.96 33.48 -0.19 0.04 0.05 -0.17 0.11 -0.09

and Tobacco 0.03 0.47 0.29 0.06 0.32 0.11

Financial Services 7.55 53.38 -0.05 0.03 0.10 -0.26 0.05 -0.13

0.30 0.40 0.15 0.01 0.39 0.41

Building -7.01 39.86 0.01 -0.08 0.06 -0.07 0.00 -0.02

0.46 0.23 0.28 0.23 0.35 0.28

Conglomerates -8.84 42.10 -0.10 0.08 0.11 -0.14 0.06 -0.11

0.16 0.24 0.12 0.10 0.44 0.09

Media & Telecoms 10.52 38.08 -0.12 -0.02 0.09 -0.11 0.02 -0.06

0.13 0.36 0.21 0.19 0.34 0.20

Chemical & Metal -24.87 45.17 -0.03 0.09 0.09 -0.06 0.01 -0.12

0.40 0.19 0.19 0.25 0.45 0.08

Industrial -7.20 32.77 -0.08 -0.07 0.13 -0.23 0.10 0.12

0.23 0.22 0.12 0.01 0.32 0.27

Machinery & Equipment -21.72 54.43 0.19 0.10 0.05 -0.15 -0.06 0.07

0.03 0.26 0.44 0.04 0.45 0.38

Retailing 6.71 54.52 0.08 -0.01 0.05 0.00 0.03 -0.04

0.22 0.42 0.29 0.47 0.42 0.25

Transportation -6.77 43.50 -0.14 0.00 -0.06 -0.05 0.10 -0.10

0.09 0.41 0.27 0.24 0.13 0.20

Panel B. Risk Factors

IPC 5.03 34.39 -0.09 -0.05 0.10 -0.14 0.00 -0.06

0.18 0.29 0.19 0.12 0.44 0.10

Exch -4.55 8.92 -0.05 -0.15 0.01 0.10 0.09 0.10

0.31 0.06 0.48 0.23 0.41 0.48

Diff 3.08 0.43 0.81 0.64 0.48 0.37 -0.16 -0.07

0.00 0.26 0.26 0.32 0.28 0.45

Mkt 5.72 17.72 0.04 -0.08 0.01 -0.08 0.02 0.04

0.34 0.23 0.44 0.20 0.36 0.43

SMB -5.05 16.62 0.27 0.13 0.00 0.15 -0.02 -0.01

0.00 0.29 0.32 0.06 0.36 0.23

HML 10.28 15.11 0.27 0.11 0.20 0.13 0.05 -0.11

0.00 0.35 0.04 0.38 0.43 0.27

Panel C. Information Variables

∆y 6.24 9.77 -0.57 0.02 0.33 -0.33 0.40 -0.11

0.00 0.00 0.05 0.38 0.03 0.44

∆FA 6.82 3.69 -0.01 -0.08 -0.01 -0.09 0.33 0.20

0.46 0.22 0.44 0.16 0.00 0.20

CetSp 2.26 1.70 0.61 0.27 0.15 0.03 0.10 0.23

0.00 0.06 0.16 0.10 0.48 0.26

Panel D. Cross-Correlations

IPC Exch Diff Mkt SMB

Exch 0.67

Diff -0.14 -0.11

Mkt 0.72 0.38 -0.12

SMB 0.11 0.05 -0.08 0.09

HML -0.31 -0.16 -0.17 -0.51 -0.52

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, “∆FAt−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 ∆FAt−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 11.35

1.33 -4.76 1.49 -1.46 0.17 -5.26

Building 2.76 -1.67 1.98 -1.69 0.20 -0.23 11.18

1.52 -4.24 1.99 -2.68 0.17 -2.20

Conglomerates 1.25 -1.90 1.13 -0.80 0.18 -0.48 10.05

0.64 -4.50 1.06 -1.18 0.15 -5.27

Media & Telecoms 2.29 -1.33 1.11 -0.66 0.11 -0.44 5.59

1.24 -3.34 1.10 -1.04 0.08 -4.41

Chemical & Metal 1.54 -1.88 1.66 -1.60 0.17 -0.17 9.53

0.72 -4.10 1.44 -2.18 0.15 -1.70

Industrial 0.22 -0.99 1.77 -0.64 0.10 -0.29 4.98

0.14 -2.86 2.03 -1.16 0.07 -3.28

Machinery & Equipment -0.64 -0.75 1.61 -0.66 0.02 0.11 1.14

-0.23 -1.26 1.07 -0.69 -0.01 1.23

Retailing 2.78 -1.81 2.11 -1.30 0.12 -0.39 5.87

1.09 -3.27 1.51 -1.46 0.09 -3.97

Transportation 0.54 -0.97 0.11 -0.33 0.05 -0.46 2.17

0.25 -2.04 0.09 -0.43 0.01 -5.05

IPC 2.17 -1.44 1.28 -0.83 0.16 -0.46 8.75

1.34 -4.13 1.45 -1.48 0.13 -4.70

45

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 “IPC”, exchange

rate “Exch” and Diff 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 IPC Exch Diff 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

Financial Services 0.51 1.21 0.86 -0.02 0.78 -0.08 107.07

0.29 11.93 2.20 -0.04 0.77 -0.94

Building 0.94 0.86 0.85 -0.51 0.79 -0.08 115.11

0.75 11.63 3.00 -1.38 0.79 -1.00

Conglomerates 0.29 0.97 0.65 -0.38 0.80 -0.08 121.84

0.22 12.70 2.23 -1.02 0.80 -0.99

Media & Telecoms 0.60 1.15 -0.53 -0.13 0.92 -0.09 351.92

0.82 26.44 -3.18 -0.62 0.92 -0.88

Chemical & Metal 1.56 0.72 0.96 -1.16 0.52 0.00 32.32

0.72 5.64 1.97 -1.84 0.50 -0.05

Industrial -1.17 0.47 0.83 0.22 0.44 -0.06 23.38

-0.69 4.71 2.15 0.45 0.42 -0.76

Machinery & Equipment 2.78 0.76 -0.57 -1.67 0.22 0.05 8.57

0.84 3.90 -0.76 -1.72 0.20 0.65

Retailing 2.14 1.21 0.66 -0.60 0.72 -0.08 77.72

1.07 10.34 1.47 -1.03 0.71 -0.99

Transportation 3.75 0.25 1.29 -1.28 0.22 0.03 8.53

1.41 1.61 2.16 -1.65 0.20 0.36

46

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 “SMB”, and high minus low factor“HML” 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 Mkt SMB HML 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 14.64

-0.41 6.14 0.36 0.97 0.31 0.56

Building -1.66 1.59 0.71 0.71 0.42 0.18 21.62

-1.76 7.50 3.11 2.46 0.40 1.63

Conglomerates -1.63 1.59 0.70 0.50 0.42 0.18 21.60

-1.63 7.12 2.92 1.62 0.40 1.60

Media & Telecoms -0.13 1.69 0.06 0.26 0.55 0.06 36.68

-0.16 9.51 0.32 1.07 0.54 0.54

Chemical & Metal -3.09 1.48 0.87 0.79 0.30 0.29 12.89

-2.64 5.64 3.09 2.20 0.28 2.40

Industrial -1.47 0.99 0.39 0.65 0.21 0.19 7.99

-1.62 4.89 1.78 2.33 0.18 1.71

Machinery & Equipment -2.94 1.56 0.62 0.76 0.20 0.22 7.69

-1.95 4.60 1.71 1.64 0.18 1.90

Retailing -1.08 2.25 0.43 0.87 0.41 0.10 21.14

-0.83 7.72 1.38 2.19 0.39 0.93

Transportation -1.26 0.89 0.62 0.63 0.12 0.27 3.92

-0.99 3.11 2.03 1.61 0.09 2.34

47

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 “SMB”, and high minus low factor “HML” 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 Mkt SMB HML 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 28.63

0.93 4.58 0.11 0.75 7.11 0.54 0.13

Building -0.44 1.08 0.64 0.60 2.38 0.66 0.10 43.29

-0.60 6.26 3.67 2.70 8.18 0.65 1.13

Conglomerates -0.41 1.08 0.63 0.38 2.40 0.64 0.09 39.20

-0.51 5.74 3.34 1.58 7.55 0.62 1.04

Media & Telecoms 0.61 1.39 0.02 0.19 1.44 0.65 0.04 40.84

0.85 8.22 0.11 0.88 5.09 0.63 0.43

Chemical & Metal -1.95 1.01 0.81 0.68 2.24 0.47 0.17 19.52

-1.87 4.10 3.28 2.17 5.42 0.44 1.88

Industrial -0.62 0.64 0.34 0.57 1.67 0.39 0.11 13.93

-0.76 3.34 1.77 2.32 5.17 0.36 1.31

Machinery & Equipment -2.66 1.44 0.61 0.73 0.56 0.21 0.22 5.95

-1.74 3.99 1.67 1.59 0.92 0.18 1.90

Retailing 0.31 1.67 0.35 0.74 2.73 0.58 0.07 31.11

0.28 6.35 1.34 2.20 6.18 0.56 0.75

Transportation -0.38 0.52 0.57 0.54 1.73 0.22 0.12 6.36

-0.31 1.82 1.99 1.48 3.59 0.19 1.46

48

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 IPC and UMS 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 F -test Wald test F -test Wald test

IPC 244.33 2551.93

0.00 0.00

Exch 2.50 26.09 9.64 101.80

0.01 0.00 0.00 0.00

Diff 1.39 14.52

0.18 0.15

Mkt 11.69 122.08 9.42 99.51

0.00 0.00 0.00 0.00

SMB 2.49 26.04 2.94 31.02

0.01 0.00 0.00 0.00

HML 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 RegressionsUnconditional Model

Results for average λ estimates from monthly cross-sectional regressions for indus-

trial portfolios: Rt+1,i = β′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. “IPC”

is the excess return in U.S. dollars of the Mexican Stock Index over the 30 day T-

Bill, Mkt is the excess return of U.S. market over the 30 day T-Bill, “Exch” is the

US. dollar/Mexican peso exchange rate growth, “Diff” is the spread betweem UMS

bond and a T-Note of 5 years, “SMB” and “HML” are the Fama-French mimicking

portfolios related to size and book-to-market equity ratios. The table reports cross-

sectional regression using expanding sample (es) and rolling windows of 36 months

(rw) coefficients.Fama-MacBeth t-statistics are presented below the coefficients in

parenthesis.

Risk Factors R2

Model IPC Mkt Exch Diff SMB HML

CAPM λes 2.34 0.21

(1.29)

λrw 1.76 0.19

(1.15)

Local λes 2.97 0.31 -0.48 0.47

Factor (1.58) (0.42) (-0.62)

λrw 1.36 -0.16 -1.13 0.50

(0.82) (-0.25) (-1.80)

Fama and λes 0.50 -2.33 0.25 0.42

French (0.42) (-1.12) (0.12)

λrw -0.77 -2.87 2.16 0.42

(-0.73) (-1.47) (0.95)

Fama and λes -0.74 0.79 -3.95 1.88 0.54

French with (-0.40) (1.10) -(1.27) (0.76)

Exchange λrw -1.12 0.26 -4.01 3.51 0.54

(-0.79) (0.37) (-1.74) (1.18)

50

Table IX

Conditional Beta Regressions; Local Factors

Excess returns on 10 industrial portfolios are regressed on lagged instruments, “IPC” Mexican stock market

index multiplied by the instruments and a constant, “Exch” the exchange rate multiplied by the instruments

and a constant and, “Diff” 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 Panel B: Fixed constant

R2 R2 R2 R2

Time-varying Constant F -test Time-varying Constant F -test

Betas Betas (p-value) Betas Betas (p-value)

Beverage, Food & Tobacco 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 Panel B: Fixed constant

R2 R2 R2 R2

Time-varying Constant F -test Time-varying Constant F -test

Betas Betas (p-value) Betas Betas (p-value)

Beverage, Food & Tobacco 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 multi-

plied 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 Panel B: Fixed constant

R2 R2 R2 R2

Time-varying Constant F -test Time-varying Constant F -test

Betas Betas (p-value) Betas Betas (p-value)

Beverage, Food & Tobacco 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 F -test Wald test F -test Wald test F -test Wald test

IPC 0.9185 11.0930

(0.5938) (0.9993)

Exch 0.3177 3.8375 0.8773 11.1765

(0.9998) (0.9544) (0.6576) (0.3439)

Diff 0.4594 5.5491

(0.9947) (0.8516)

Mkt 1.7791 21.4879 1.7428 22.2024

(0.0064) (0.0179) (0.0083) (0.0141)

SMB 3.2200 38.8906 2.4226 30.8634

(0.0000) (0.0000) (0.0000) (0.0006)

HML 2.4939 30.1211 3.2043 40.8219

(0.0000) (0.0008) (0.0000) (0.0000)

Panel B: Tests on alphas

constant 0.7184 8.6773 0.4063 4.9069 0.3581 4.5617

alpha (0.8675) (0.5630) (0.9983) (0.8973) (0.9995) (0.9185)

zero 0.7968 9.6234 1.0893 13.1569 0.8340 10.6250

alpha (0.8134) (0.4741) (0.3264) (0.2150) (0.7589) (0.3875)

54

Table XIII

Cross-Section RegressionsConditional Model

Results for average λ estimates from monthly cross-sectional regressions for indus-

trial portfolios: Rt+1,i = β′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. “IPC”

is the excess return in U.S. dollars of the Mexican Stock Index over the 30 day T-

Bill, Mkt is the excess return of U.S. market over the 30 day T-Bill, “Exch” is the

US. dollar/Mexican peso exchange rate growth, “Diff” is the spread betweem UMS

bond and a T-Note of 5 years, “SMB” and “HML” are the Fama-French mimicking

portfolios related to size and book-to-market equity ratios. The table reports cross-

sectional regression using expanding sample (es) and rolling windows of 36 months

(rw) coefficients.Fama-MacBeth t-statistics are presented below the coefficients in

parenthesis.

Risk Factors R2

Model IPC Mkt Exch Diff SMB HML

CAPM λes 1.48 0.20

(0.86)

λrw 0.22 0.20

(0.16)

Local λes 2.60 1.08 -0.16 0.51

Factor (1.24) (1.40) -(0.23)

λrw 1.12 0.66 -0.78 0.47

(0.76) (1.60) -(1.81)

Fama and λes -1.38 -0.53 1.00 0.46

French (-1.06) (-0.36) (0.84)

λrw 0.11 -1.36 0.44 0.51

(0.10) -(1.15) (0.38)

Fama and λes -1.74 -0.07 -1.20 2.09 0.55

French with (-1.47) (-0.11) (-0.76) (1.60)

Exchange λrw -0.60 0.04 0.36 -0.81 0.59

(-0.54) (0.09) (0.33) (-0.72)

55

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