The Cost of Equity in Latin America

Transcription

1 Working Paper Nº 12 The Cost of Equity in Latin America Martin Grandes, Demian Panigo and Ricardo Pasquini December 2005

2 The Cost of Equity in Latin America Martin Grandes The American University of Paris and CEF Demian Panigo PSE-ENS, Univ. de la Plata, CEIL-PIETTE and CEF Ricardo Pasquini CEF Abstract The aim of this paper is twofold. First, it applies standard Capital Asset Pricing Models (CAPM) to look into cross-section (at the rm and industry levels) and time series di erences in the opportunity cost of equity (COE) across seven major Latin American countries. Using an unbalanced panel spanning monthly observations for about 921 publicly traded rms in , it comes up with more than 312,000 COE estimates from 6 di erent econometric (rolling GMM) speci cations. Second, the paper statistically tests the econometric output obtained from those CAPM-type models to nd out how well and how much systematic risk (the single determinant of COE in CAPM) accounts for both, cross-section and time series variations in COE. JEL codes: G12, G15. Keywords: Cost of equity, CAPM, Latin America, rolling GMM, variance decomposition, systematic risk, idiosyncratic risk. We are grateful to the Swiss Agency for Development and Cooperation for generous - nancial support. We would also like to thank Alberto R. Musalem, Ricardo Bebczuck, Pedro Elosegui, Gisela Juliano and Horacio Pozzo for helpful comments and suggestions. Usual disclaimers apply. 1

3 Contents 1 Introduction 3 2 Survey of the Literature What do we know about emerging countries and in particular about Latin America? Stylized Facts, Data and Methodology Stylized facts for Latin America Dataset Econometric and statistical methodology to estimate the CAPM COE Data frequency Optimal sample size The assumption of real market integration Sovereign spreads calculation and pricing into the CAPM framework Risk-free interest rate and emerging market bond yield stability Corrections for illiquidity Beta (systematic risk loading) robustness or instability The econometric method Negative COE estimates Weighting strategies Variance Decomposition Empirical results for Latin American markets Asset pricing model speci cation The COE Derived from Black s CAPM Beta estimates The explanatory power of CAPM Variance Decomposition Results Conclusions 53 6 Appendix 63 2

4 1 Introduction The weighted average cost of capital (WACC) a combination of equity and debt costs paid by either public or private entities - is an important determinant of economic growth, in turn a necessary condition for poverty reduction (see Henry (2003) or Grandes and Pinaud (2004)). In Latin America, WACC, and in particular the opportunity 1 cost of equity capital (henceforth COE), has been generally relatively higher and volatile compared to OECD countries excluding Mexico. This may be attributable to a number of reasons beyond though not unrelated to- historically weak macroeconomic policy framework, macroeconomic volatility, external vulnerability, low national savings and investment rates and as a consequence a remarkable dependence on external nancing. Latin American stock markets are relatively underdeveloped and are characterized by: a) rather shallow markets (low market capitalization to GDP ratios, low volume of business, limited number of publicly traded rms and scant free oats), b) illiquidity (low traded volumes and many observations without any transaction), c) high average stock returns, d) stock return volatility,and e) and non-gaussian excess returns (see Wong Davila, 2003). Reducing the COE in Latin American countries should be a major developmental objective in the policy maker s agenda. There are several arguments underpinning the case for a sustained reduction in the COE and ultimately in WACC: First, a lower COE is critical to raise investment in both physical and human capital, hence inducing a higher rate of capital accumulation and faster economic growth. In other words, when the expected returns to equity are higher than COE, investment projects become pro table and more rms will be investing, thus driving investment rates higher. Second, reducing COE may create more opportunities for new rms not only large ones but also SME- to tap stock markets and raise funds at more affordable costs than other sources of nance such as banking loans. An increased number of rms raising capital in the (domestic) stock market favours capital markets development and provides additional opportunities for portfolio diversi cation, fostering e cient allocation of capital. As a result, nancial market development should be enhanced. Third, the COE is a key variable to corporate nance management. The relative (to debt) COE is always necessary to obtain the optimal capital structure of any publicly traded rm, i.e. the capital structure which minimizes WACC (see Harris and Raviv, 1991; or Elton and Gruber, 1995). Please also note that 1 In contrast to an accounting cost, the opportunity cost stands for the notion of the rate of return that capital providers will expect to receive if they would invest the capital in the most valuable alternative. 3

5 lower COE would lead rms to operate with lower leverage thereby contributing to improve rms resiliance to demand, interest rate or other shocks. Last, but not least, it stands out in the context of the post-monterrey discussions on providing developing countries with cheaper and sustainable sources of nancing for development. Moreover, decreasing WACC and in particular COE could contribute to achieving the Millennium Development Goals. The main objective of this paper is to shed some light on the pricing of Latin American stocks and the COE for Latin American rms in seven countries: Argentina, Brazil, Chile, Colombia, Mexico, Peru and Venezuela. More speci cally, this contribution presents a unique panel database of COE estimates by country, sector and rm for the period using di erent versions of Capital Asset Pricing Models (CAPM), which assume all rm idiosyncratic risk can be diversi ed away. In addition, the paper tests the hypothesis of real market integration ( home bias ), it examines whether COE is procyclical in Latin American stock markets (i.e. lower COE in recession times) and nally assesses the breakdown between systematic (or CAPM-explained COE) and idiosyncratic risk the unexplained variance of COE. The main conclusions drawn from this study are the following: 1. The positively sloped relationship between COE (expected returns) and risk across rms, sectors and countries is con rmed. On average, the highest COE estimates are found in Venezuela and Argentina (35% and 28% respectively) while the lowest COE are in Chile and Peru (roughly 16%). Pension Funds, Textiles and Agriculture & Fishing are the sectors which display the lowest COE. On the other hand, Construction, Oil & Gas and Telecommunications have the highest COE. 2. Lack of real market integration (home bias e ect), i.e. global portfolio risk and real currency risk do not generally add explanatory power to local portfolio market risk, thus domestic CAPM would be the "right " model to price Latin American stocks and determine COE. 3. COE is statistically signi cantly acyclical for a majority of countries. Bad times do not mean lower COE. 4. For Latin America as a whole, on average 32% of the variability in COE can be attributable to (domestic) systematic risk. This raises questions about the remaining 68% which is accounted for by purely idiosyncratic risk or other systematic risk factors not captured by traditional CAPM nor explicited in this paper (see Fama and French, 1992 and 1997). The paper is organized as follows. Section 2 surveys the literature on di erent approaches to the measurement and determinants of COE, focusing on the advantages and disadvantages of di erent CAPM versions. Section 3 presents 4

6 the database and introduces the econometric methods adopted by this study. The econometric outcome and discussion follow in Section 4, including model speci cation tests, COE estimates and variance decomposition results. Section 5 puts forward some concluding remarks and some issues for further research. 2 Survey of the Literature The main foundations of asset pricing theory were laid by Harry Markowitz (1959), who developed the portfolio choice theory, widely known as meanvariance approach. In his theory, risk adverse investors, with a one-period investment horizon and looking at di erent asset returns correlations will choose mean-variance e cient portfolios. E cient portfolios are di erent combinations of available assets which minimize the portfolio variance for a given portfolio return or maximize the portfolio return for a given portfolio variance. Perhaps the main corollary of this theory is the so-called e cient frontier of portfolios, along which investors will select their optimal portfolio depending on their preferences (i.e. their risk tolerance). Yet, Markowitz s focus isn t on how this portfolio is priced on the market. Building on Markowitz s assumption of mean-variance investors and the existence of an e cient frontier of portfolios, Sharpe (1964) and Lintner (1965) developed the rst asset pricing theory, namely the Capital Asset Pricing Model, or CAPM. CAPM has become a milestone in asset pricing theory, not least because it has provided an intuitive and simple way of estimating the COE. CAPM makes three critical assumptions: 1) investors have identical perceptions of the future joint distribution of assets returns, 2) idiosyncratic risk is fully diversi able and 3) investors can borrow and lend unlimitedly at a risk-free rate. As a result, it follows that in equilibrium, all investors hold the same optimal mean-variance portfolio of risky assets, which amounts to an equal fraction of the market portfolio. The latter must be on the e cient frontier for assets market to clear. The pricing relation of CAPM is displayed in Equation 1. This relationship allows to determine the COE de ned as the expected return on an asset, e.g. a rm stock. The pricing equation relates the excess return on an asset (the return over the risk-free rate) to (only) the excess return on the market portfolio, through a coe cient beta which captures the covariance or systematic risk of that speci c asset (undiversi able risk) 2. E(R i ) R f = im [E(R M ) R f ] 8 i = 1; :::; N (1) According to Equation 1, for a given rm or asset COE can be calculated as the risk-free rate plus a risk premium equal to the rm s asset systematic risk 2 One possible interpretation is that Beta coe cient captures the risk that each dollar invested in a particular asset contributes to the market portfolio. 5

7 multiplied by the market premium (or excess return on the market portfolio). Intuitively, all investors will evaluate the risk of holding a security in terms of how it contributes to the risk of the market portfolio, hence riskier securities (and therefore rms) will be associated with a higher COE. When implementing this equation using actual data, the rst question that arises is which could the market portfolio be. The usual answer is that a proxy for this portfolio is given by a local market index that tracks the most representative stocks in terms of trading, capitalization, etc. 3 We will come back to this issue below. Later, Black (1972) showed that CAPM ndings could also be replicated by relaxing the free borrowing and lending assumption and instead assuming that there is unlimited short sale of risky assets. In other words, in Black s framework investors are able to undertake short positions in risky assets, i.e. they are able to borrow these assets, sell them on the market and repurchase them at an (expected) lower price in the future. In 1976, Ross (1976) developed the second milestone in the asset pricing theory, namely The Arbitrage Pricing Theory (APT). This theory begins with a less restrictive assumption. It assumes that there are no arbitrage opportunities in the market, in the sense that assets prices will adjust to the level of its expected prices. APT focus is di erent than CAPM s. While CAPM focuses on how investors choose a portfolio from an existing available group of assets, APT focuses on how the available investment opportunities in the market are a ected by exogenous factors 4. In particular, APT assumes that there are N factors which a ect the systematic changes in expected returns. The pricing relation of APT (Equation 2) associates the expected return on an asset, and hence COE with an undetermined N number of exogenous factors, i.e. the determinants of COE. R i = E [R i ] + i1 [F 1 ] + i2 [F 2 ] + ::: + ik [F K ] + i 8 i = 1; :::; N (2) According to Equation 2, for a given rm or asset COE can be calculated as the expected risk-free interest rate plus several terms each equal to a factor loading multiplied by the factor estimate itself. Now, the question becomes: which factors, how many, why? APT has given rise to an emerging empirical literature that searches which and how many factors a ect stock returns. Typically these factors are macroeconomic factors such as: innovations in in ation expectations, innovations in the Gross National Product or GDP estimates, unexpected changes in investor s con dence and unexpected shifts in the yield curve. 3 Equation 1 is typically tested using the following linear econometric models: R i;t = i + i RM;t + i;t or R i;t R f;t = i RM;t R f;t + i;t (depending on whether the risk free rate is assumed to be constant or not), where i and i are estimated using time series regressions for each individual stock. 4 Economists can think about this di erence as a demand side and a supply side approach. 6

8 While both CAPM and APT are the main foundations of the Modern Asset Pricing Theory, thus far the CAPM model appears as the model most widely used by almost all practitioners in the world when valuating an investment project 5. Undoubtedly, the main theoretical weakness of the APT lies in the fact that the N explanatory factors are not predetermined by the model. By contrast, CAPM assumes a strong speci cation of the relationship among asset returns, yet straightforward and intuitive. Moreover, the stock prices and volumes used by CAPM to compute the market portfolio are measured with very little error. Notwithstanding this, Roll (1977) raised perhaps one the most important theoretical critics to CAPM. He argued that CAPM could not ever be tested because of the unobservability of the market portfolio. In principle, the market portfolio should consider the stocks available in the capital market of our interest. Therefore, the proxy to be used should be the stock market index of the market in question. But, should the model include other than nancial assets, for instance real estate assets or human capital? If so, the elusive nature of the market portfolio would make the model untestable and would generate inexact and ine cient COE estimates. Confronted with Roll s critic of CAPM, researchers have chosen a more pragmatic view: wherever they nd a proxy for the market portfolio that do have certain properties predicted by CAPM, they will conclude that the underlying model is true and they will use it for pricing, COE estimation and ultimately for investment project valuation. That is why today the penetration of CAPM into the business arena remains sizeable. Important theoretical extensions were built on and followed CAPM framework with the aim of making its assumptions more realistic. One of this extensions was Merton s (1973) Intertemporal CAPM (ICAPM). The distinctive feature in Merton (1973) is that, unlike a single-period maximizing investor who, by de nition does not consider events beyond the present period, an intertemporal maximizer in selecting his portfolio will take into account the relationship between current and future returns 6. In other words, if the available investment opportunity set changes over time, there is some reason to believe that investors will price this in their portfolio choice. As the market interest rate is an element of the available investment opportunity set, the observation that the interest rate changes stochastically over time represents evidence that the available opportunity set changes over time. As a result, in equilibrium investors 5 In a survey for 27 U.S. companies, Bruner et al. (1998) reported that 85% use regularly CAPM for estimating the cost of capital. Looking into an emerging market, in a survey for Argentina, Galli and Pereiro (2000) reported that 68% of corporations, 64% of nancial assessors and 67% of banks and insurance companies use regularly CAPM for estimating the cost of capital. 6 Quoting Merton: Suppose that the current return on a particular asset is negatively correlated with changes in yields (capitalization rates). Then, by holding the asset the investor expects a higher return on the asset if, ex post, yield opportunities next period are lower than were expected 7

9 are now not only compensated for bearing systematic risk but also for bearing the risk of unfavorable (on the aggregate) shifts in the investment opportunity set. This additional source of risk can be re ected through Equation (3), which relates the excess return on an asset to the excess return on the market portfolio and the excess return on an asset (or portfolio of assets 7 ) that is supposed to capture the shifts in the investment opportunity set. E(R i ) R f = im [E(R M ) R f ] + N [E(R N ) R f ] 8i = 1; :::; N (3) Equation (3) states that, for a given rm or asset COE can be calculated as the risk-free rate plus two risk premia: 1) equal to the rm s asset systematic risk multiplied by the market premium (or excess return on the market portfolio) as in CAPM, and 2) equal to the rm s asset risk due to unfavorable shifts in the investment opportunity set multiplied by a corresponding excess return factor. Notice we have assumed that a single state variable is su cient to describe changes in the opportunity set. In general, Merton s intertemporal CAPM states that the expected excess return on any asset is given by a multi-beta version of CAPM with the number of betas equal to one plus the number of state variables needed to describe the relevant characteristics of the investment opportunity set. In his innovative CCAPM (Consumption CAPM) model, Breeden (1979) adopted the same assumptions as Merton (1973) and extended the latter model by allowing for investment and consumption choices in an intertemporal setting. Breeden s contribution is supported by the observation that the dollar value of an asset payo and real aggregate consumption are always perfectly negatively correlated. This observation arises because real aggregate consumption is perfectly negatively correlated with the marginal utility of an additional dollar of wealth invested. As a result, an asset s covariance with aggregate real consumption is all that is needed to price a rm s asset or to calculate its COE. CCAPM involves a single beta equation, where the instantaneous expected return on any security is proportional to its beta (or covariance) with respect to real aggregate consumption alone. In the new pricing equation (see Equation (4), R C represents a security the return of which is perfectly correlated with changes in aggregate consumption over the next instant. The main virtue of this model is that it does not su er from a critic like Roll s as the main variable, real aggregate consumption, is in fact observable 8. 7 Merton suggested a long term bond portfolio. Empirical ndings of Black and Scholes (1972) suggested a long term bond portfolio which is highly correlated with a signi cantly positive portfolio, constructed such that there would be zero correlation with the market. 8 It is worth nothing that both Merton s and Breeden s models are powerful theoretical tools, but they may be quite di cult to implement. In the case of Merton s ICAPM, the model su ers from the same problem of APT: state variables are not easily identi ed. Then, while quite important from a theoretical point of view, it is neither tractable for empirical testing, nor really useful for nancial decision making. The case of Breeden s CCAPM model is di erent. While it is relatively easy to test, data avalability is scarse, especially in emerging markets. Instantaneous consumption rates are not measured while weekly and monthly rates 8

10 E(R i ) R f = ic [E(R C ) R f ] 8 i = 1; :::; N (4) Another important extension of CAPM owes to Solnik (1974), Sercu (1980), Stulz (1981) and Adler-Dumas (1983) in what is known as the International CAPM. As mentioned earlier, one of the main ideas behind CAPM was that beta captures what each security contributes to the undiversifable risk of the market portfolio. This relationship enables the pricing so long as the chosen stock market index is indeed broadly perceived as the economy market portfolio. The di erent versions of the International CAPM recognize that as a country opens up its capital markets to foreign investors and let its residents invest abroad; the residents of the country no longer had to bear all the risks associated with the economic activities of that speci c country 9. It follows that in a freely mobile capital world investors will hold an internationally diversi ed portfolio of risky assets and will regard the risky security choices by how (in terms of risk and returns) they contribute to their internationally diversi ed portfolio. This has clear implications for the estimation of COE, as will be seen below. The International CAPM recognizes an additional risk due to the di erent currency denomination of nancial assets held by global investors. Investors holding a long position in a foreign stock have to short that currency to eliminate foreign exchange risk. This means that foreign exchange risk can be priced. A multifactor model that it is consistent with these assumptions would be one that contains a risk premia based on the covariances of assets with exchange rates, in addition to the traditional premium based on the covariance with the market portfolio. The International CAPM pricing equation (see Equation (5)) relates the expected excess return of an asset ( i ) with the expected excess return of a global portfolio ( G ) and with the nominal exchange rate returns of the other countries considered ( s j0 with j = 1; 2;?; n 10 ). Summing up, Equation (5) states that, for a given rm or asset COE depends on the risk-free rate and two systematic risk factors: 1) global market portfolio risk, and 2) currency risk (as long as this risk is not fully diversi able). E(R i ) r 0 =[E(R G ) R f ] ig + E [s 10 + r r 0 ] i1 + (5) ::: + E [s n0 + r r 0 ] in From a practitioner s perspective, the question of whether these models provide substantially di erent COE estimates is straightforward. In the last years are di cult to obtain. Additionally, available data contain considerable measurement error and include the consumption of nondurable goods, which is not compatible with the design of the model. 9 As Stulz puts it A country might have bad news on one day, but another might have good news. Because of diversi cation resulting from access to global markets, domestic investors can construct a portfolio of equities that has less risk for the same expected return. 10 Notice that all this variables are expressed respectively to a numeraire currency. Please refer to the methodological section for a discussion over real exchange risk incorporation. 9

11 a signi cant number of studies tried to provide an answer. Stulz (1995) derived two formulas for the di erence in the estimation of a rm s beta when the COE is computed with the domestic CAPM as compared to the single factor International CAPM. He analyzed the case of the Swiss multinational Nestlé and found a substantial pricing error. His study concludes that the International CAPM should be used in small economies instead of the domestic CAPM version. Koedijk et al (2002) derived a test to compute the pricing error between the domestic CAPM and the multifactor International CAPM (i.e. an International CAPM adding multilateral currency risk to global market portfolio risk). Equation (6) shows the resulting nested model. R i;t = i + im [R M;t ] + ig [R G;t ] + imner [R MNER;t ] + i;t (6) Unlike previous CAPM versions, the dependent variable is now expressed in terms of assets returns instead of excess returns. The nested model relates the stock return with a constant term (which captures the risk free rate), the local and the international market portfolios returns at time t ( R M;t and R G;t ) and nally R MNER;t, which is the multilateral nominal exchange rate return at time t. Using data from rms with foreign equity listings, Koedijk et al (2002) conclude that, although di erent COE estimates are signi cant for only 12 percent of the sample, the size of the cost of capital di erential between CAPM and the multifactor ICAPM goes up to 50 basis points for the US, 80 basis points for the UK and 100 basis points for France 11. Irrespective of the speci c CAPM version to be used for asset pricing and for COE estimation, it is always important to have a measure of how much of expected (excess) returns and consequently COE remain unexplained in these models. CAPM models share the assumption that the variability in expected returns that fails to be explained by the market risk factor is not priced because it is assumed to be diversi ed away. This crucial hypothesis relies on the e ciency of the market portfolio. As should be clear at this point, multifactor e cient models such as Merton s or Ross APT show how, as some assumptions in the CAPM setting are relaxed, the market portfolio turns out insu cient to capture all the variability in expected (excess) returns attributable to systematic risk. It follows that introducing appropriate state variables in the CAPM pricing equation may help account for some systematic risk that is not captured by the market portfolio. The consequence of disregarding this additional information 11 Another example is Mishra and O Brien (2001) who provided more evidence on the difference in estimation with these alternative models. Comparing the local CAPM with the two versions of the international CAPM (the single market factor and the version allowing currency risk) they estimate COE di erences of 48 and 61 basis points respectively for a US sample of stock, di erences of 76 and 47 basis points respectively for a 70 developed markets sample of ADRs and di erences of 57 and 70 basis points respectively for a 48 emerging markets sample of ADRs. 10

12 will be translated into a misspricing error, proportional to the weight of the unexplained risk in the (total) variance of returns (or excess returns, depending on model speci cation). Contributions to the empirical literature starting from the late 1970 s pointed out that some rm speci c variables could account for misspricing errors. These studies evidenced how when sorting stocks according to di erent rms attributes new estimates of future expected returns di er from the regular CAPM estimates. Basu (1977) showed that stocks with high earnings-price ratios had higher future returns than predicted by regular CAPM. Banz (1981) demonstrated that the same happened with those stocks with lower market capitalization. Bhandari (1988) used debt to equity ratios and found that stocks associated with relatively high debt to equity ratios yielded higher returns than those estimated using standard CAPM. This is intuitive as higher debt to equity ratios mean higher leverage, hence higher (default) risk as the rm builds up debt. Finally, Statman (1980) and Rosenberg, Reid and Landstein (1985) found identical results for returns on stocks with high book to market equity ratios, i.e. low book-to-market value stocks displayed higher returns. Fama and French (1992 and 1996) synthesized this approach within a COE model, broadly known as the three factor model. Supported by the nding of higher average returns on small stocks (in terms of market capitalization) and on high book to market value stocks in the US, they gured out an additional source of systematic risk not captured by previous CAPM frameworks through local market beta. Therefore, in addition to local market portfolio risk they included these attributes in a CAPM based equation, as displayed in Equation (7). Speci cally, Fama and French introduced diversi ed portfolios associated with the above mentioned attributes, and su ciently di erent from the market portfolio as new factors together with the market portfolio in the CAPM equation. Equation 7 illustrates the three factor model. E(R i ) R f = im [E(R M ) R f ] + is [E(SMB t )] + ih [E(HML t )] (7) In the pricing equation, expected returns (and COE) are now explained by the excess return on the market portfolio and two additional factors: SM B (small minus big) is the di erence between the returns on diversi ed portfolios of small and big stocks. HML (high minus low) is the di erence between the returns on diversi ed portfolios of high and low book to market stocks. The new betas will indicate the sensitivity of the particular asset to the additional systematic risk that is captured by each of the two new attributes. Fama and French s results suggested that US stock markets were not e cient (in the semi-strong sense) as there were additional sources of risk not priced in by the local market portfolio. Later research extended this nding to di erent samples Using a sample of stocks from the Tokyo Stock Exchange from 1971 to 1988, Chan, Hamao, 11

13 But in addition to the new sources of systematic risk found by Fama and French (1992 and 1996), there can be a second reason why part of the expected (excess) returns and consequently COE may remain unexplained by CAPM idiosyncratic risk. All CAPM versions share the common hypothesis that only systematic risk is priced in the market because ( rm or country-speci c) idiosyncratic risk can completely be diversi ed away. If this assumption were not true, idiosyncratic risk should be explicitely priced by way of including appropriate variables re- ecting this source of risk. As a result, disregarding these variables could cause a potential misspricing error proportional to the weight of the unexplained risk in the (total) variance of expected (excess) returns. A wealth of recent studies have given rise to discussions about whether there is a role for idiosyncratic risk in explaining returns or excess returns and ultimately COE. The main questions raised by this literature are: why idiosyncractic risk matters? how much risk not priced in stock markets is idiosyncratic? What variables are used to proxy for this source of risk? In a recent paper, Goyal and Santa Clara (2003) have found evidence that idiosyncratic risk is indeed priced in the market. Using CRSP stocks data for the US, they show how idiosyncratic risk can be captured through a measure of average stock risk 13 and then how this measure successfully predicts the return on the market in an econometric regression. Furthermore, in order to test the robustness of these results, they use Fama-French three factor model residuals and construct an alternative idiosyncratic variance measure. This measure is also found to forecast the return on the market. Additional recent evidence for the U.S. market highlights the fact of little diversi cation. Barber and Odean (2000) report that the mean household s portfolio in a large discount brokerage dataset held 4.3 stocks (worth 47,334 dollars), and the median household held 2.61 stocks (worth 16,210 dollars). Goetzmann and Kumar (2001) examined portfolios of more than 40,000 equity investment accounts from a large discount brokerage. Their ndings suggest little diversi - cation and a large amount of idiosyncratic risk undertaken by investors. They also suggest that investors are aware of the bene ts of diversi cation but they appear to adopt a "naïve" diversi cation strategy where they form portfolios without giving proper consideration to the correlations among stocks. Benartzi and Thaler (2001) ndings give further reasons to believe that diversi cation may be imperfect or incomplete. Their experimental and archival evidence and Lakonishok (1991) explore Japanese stocks. They estimate predictive regression of returns to the following variables: earning yield, size, book to market ratio and cash ow yield. Their cross-sectional regressions reveal a signi cant relationship of the selected fundamental variables and expected returns. Overall, of the four variables, the book to market ratio and cash ow yield have the most signi cant impact on expected returns. Capaul, Rowley, and Sharpe (1993) nd similar e ects in four European stock markets and in Japan. 13 We apply this measure to our sample in section 4. 12

14 for U.S. retirement saving plans also suggests naïve diversi cation in investor s strategies. People are found to spread their contributions evenly across investment options (a 1 n heuristic) irrespective of the particular mix of options they face. Theoretical fundaments for limited diversi cation are neither new. Levy (1978) and Merton (1987) had already built the rst theoretical extensions of CAPM where investors hold undiversi ed portfolios. Merton stressed the incomplete information problem that could lead to undiversi ed portfolios. Levy, probably inspired by the role of transaction costs and taxes that restrict portfolio diversi cation, assumed an imperfect market and imposed a constraint on the number of securities that an individual could hold in his portfolio 14. The empirical implications of these models support the role of idiosyncratic risk in stock pricing and consequently in COE estimation 15. Another possible reason for idiosyncratic risk pricing is that investors hold nontraded assets which add background risk to their portfolio decisions. When the risk of non traded assets increases, the investors are less willing to hold other traded risky assets. Investors then require an increase in expected returns (a higher COE) to be persuaded to hold the market portfolio of traded stocks. Mayers (1976) introduces a human capital factor in a CAPM setting and obtains similar implications to that of Merton and Levy 16. Other models allow for investor heterogeneity (Constantinides and Du e (1996)). Here, individuals are subject to idiosyncratic income shocks. The result is that, in equilibrium, risk premia depends on the cross-sectional variance of consumption growth among investors. Finally, the contigent claim analysis (Merton (1974) can also explain why idiosyncratic risk may be priced. This approach consists in considering equity and debt as contingent claims on the assets of a company. If equity is seen 14 For example, employee compensation plans often give workers stock in their rms but restrict their capacity to sell their holdings, thereby leading to a concentrated exposure. 15 Levy s model implementation isn t straightforward. It requires information about the number of securities that investors could hold and the wealth fraction they would be willing to allocate in order to purchase those securities in the stock market. However, some additional implications of the model allow Levy identify an impact of idiosyncratic risk. For example, his model suggests that the variance of each security is a key factor for pricing, especially for those securities that are less held. Levy exploits this relationship and incorporates a variance _ term together with the systemic risk (beta) in cross-section regression, namely: R i = 1 ^ i. The empirical results support the model predictions and the key role of idiosyncratic risk. In the case of Merton s model,the assumption of incomplete information implies that an investor will face an additional cost for not knowing a security. This cost is translated into the emergence of a new term in the pricing relation that captures the cost of incomplete information over all securities. The implementation of this model can be associated with the standard security market line test (see for example Roll (1977)): R i R F = i [R M R F ]+ i where the null hypothesis is i = 0 and i = 1 : : : n: Once again, as this model predicts, the rejection of the null is consistent with an ine cient market portfolio, as reported by Blume and Friend (1973), Black Jensen and Scholes (1972), and Fama and Macbeth (1973) 16 Nontraded assets that have been studied extensively in the literature are private businesses. 13

15 as a call option on the rms s assets value, then as assets volatility heightens, the value of equity goes up at the expense of the debtholders (i.e. debt prices decline and default premia widens). 2.1 What do we know about emerging countries and in particular about Latin America? The literature on emerging-market stock pricing (and COE) has looked into a handful of issues related to 1) how much correlation there is between developed and emerging stock market (excess) returns or within emerging stock markets (and individual securities) returns, 2) the extent to which this correlation is relevant for portfolio diversi cation and investors strategies. These issues include a) some analyses of risk-return (and COE) trade-o s in developed and emerging economies, b) the normality assumption of stock (excess) returns, c) the scope for portfolio diversi cation between emerging stock markets and d) how multifactor models such as Fama and French (1992, 1998) may explain emerging stock market (excess) returns and (excess) returns correlations. Major empirical ndings on these issues are surveyed next. Several authors have found that emerging stock market returns are higher than developed ones (Harvey (1991) and (1995), Fama and French (1998)). For instance, Fama and French (1998) report that for a sample of 13 developed markets between 1975 and 1995 the annual dollar return in excess of U.S. T-Bill rate is 9.6% on average, while for a sample of 16 emerging markets from 1987 to the average increases to 27.36%. A closer look at Fama and French s tables shows annual dollar average excess returns of 42.2% in the case of 6 Latin American countries covered by their study. These and other authors 18 have also realized that emerging stock markets are more volatile (see Bekaert and Harvey (1997a)). Fama and French (1998) report that standard deviations of annual dollar excess returns over the same periods were 15,67% and 67,87% in developed and emerging stock markets respectively. Most remarkably, for those Latin American countries included in their sample the standard deviation reached 97.34%. Even though the periods over which the gures are computed are not strictly comparable, the relationship between mean excess returns and risk (measured as the standard deviation of annual dollar excess returns) carries a meaningful implication: risk-adjusted returns (RAR) are lower in Latin America (0,43) than in developed stock markets (0,6). Relatively low RAR on Latin American (and other emerging-market) stocks may disincentivate the demand for this asset class. We will discuss this further in Section 4. In addition to the trade-o between risk and returns (COE), another stylized fact that has been con rmed in several studies is the abnormal statistical distribution of emerging stock market returns (see Wong Dávila (2003) for ev- 17 The sample period di er for some countries. See Fama and French (1998). 18 See Bekaert and Harvey (1997a) among others. 14

16 idence on Latin America). In this regard, an interesting observation is that, in order to account for downside risk (the risk of obtaining returns lower than the mean), some authors have documented that while for some developed countries semi deviations are lower than standard deviations, for emerging countries semi deviations are generally higher than standard deviations (see for example Grootveld and Salomons (2002)) As mentioned earlier, one theoretical implication of nancial market integration is the enlargement of the diversi cation opportunities set. These additional opportunities should enable investors to reduce portfolio risk for a given level of expected (excess) returns (Stulz (1999)). A key feature of the study of diversi- cation bene ts is the analysis of (excess) return correlations. As Stulz puts it little e ect of nancial integration should be expected if the local market and the world market are perfectly correlated. In fact, several authors including Bekaert et. al. (1998) and Harvey (1995) document low correlations between emerging markets and developed market returns. Furthermore, an element that increases the attractiveness of investing in emerging markets is that correlations within these markets are also generally low (Wong Dávila (2003)). Harvey (1991), for example, reports that the average cross-country correlation of developed markets returns during the 70 s and the 80 s was 41 percent, while for emerging markets the correlation was only 12 percent. Moreover, in order to compute more precisely the bene ts of diversi cation in emerging markets, Harvey tests whether adding emerging market assets to a mean-variance portfolio problem signi cantly shifts the investment opportunity set. He nds that the addition of emerging market assets signi cantly enhances portfolio diversi cation opportunities. Some empirical studies have extended these correlation analyses to recent years. In the case of Latin American markets correlations over the last decade, Wong Dávila (2003) points out that, while the sub-periods , 1995 and show statistically insigni cant cross country-correlations, the latter became larger and statistically signi cant during the sub-periods (Mexican Crisis) and (South East Asia, Russian and Brazilian Crises). Other authors have focused on the impact of nancial liberalizations, occurred during the late 80 s and early 90 s, on emerging stock markets correlations. The e ect of nancial liberalization on cross market correlations is key to measuring the bene ts of portfolio diversi cation because, as Bailey and Lim (1992) and Bekaert and Urias (1996) put forward, correlations may increase as a result of nancial opening, therefore reducing the bene ts of diversi cation and hence the scope for bringing down the cost of capital in emerging markets. Using data from 1976 to 1995, Bekaert and Harvey (2000) nd small correlations between emerging and developed markets for the entire period but also a slight tendency to increase in the wake of nancial liberalization episodes. This last observation suggests that the bene ts of diversi cation may still high. The degree of international nancial diversi cation has direct implications 15

17 for the choice of the reference portfolio (market portfolio) as well as on the speci cation of the asset pricing model (and by way of this on COE estimation). Evidence on this issue is presented in Bekaert and Harvey (2000). They nd that nancial liberalization brought about a stronger impact (i.e. beta) of global market portfolios on emerging markets (excess) returns: global betas jumped from 0,06 to 0,105 in the post-liberalization period. A similar example is found in Mishra and O Brien (2004), where an investability index is included to better di erentiate stocks which are fully open up to global investors from those which are not. Using data from years 1990 to 2000, in a regression of ex-ante 19 COE estimates on global betas, they nd that, for those emerging market equities with a substantial share of equity capital legally accessible to foreign investors, global CAPM betas do add some explanatory power to domestic portfolio risk (local betas). Rouwenhorst (1999) also looks into the realized increase in correlations though resorting to a slightly di erent approach. First, when he introduces portfolios sorted by size and book to market value into COE regressions for 20 emerging markets (including 6 from Latin America over the period ) he corroborates that the Fama and French three- factor model e ectively provides a signi cant explanation of returns 20 : Second, he notices that the cross-country correlations between these factor-based portfolios didn t increase signi cantly in the last years. Finally, he concludes that the factors responsible for the increase in emerging-market returns correlations are di erent from those that drive di erences in returns within these markets. The ndings revealing that Latin American returns are not robustly correlated with international portfolios are generally interpreted as signs of market segmentation. In this respect, Bekaert and Harvey (1995) explain that in these cases a stronger relationship should be observed between domestic stock returns and local market volatility. In the case of Mishra, D. R., O Brien, T. J. (2004) this appears to be the case as they nd a signi cant relationship between ex-ante COE estimates and stock return volatility (i.e.: total risk). 3 Stylized Facts, Data and Methodology In this Section, we present the stylized facts for Latin American stock markets over the period Then we introduce the dataset and analyze some statistical properties of our data, and lastly we explain and discuss the econometric estimation procedure conducive to CAPM COE estimates. 19 Ex-ante valuation models such as Gordon (1997) incorporate investor s expectations data on of stock prices in pricing formulas. 20 Fama and French (1998) show that value and size premia are also pervasive in emerging market returns, including Latin America. They report that the average high minus low book to market portfolio return is 16.9% (value weighed countries) and 14.13% (equally weighed countries), while the average small minus large caps returns is 14.89% (value weighted countries) and 8.7% (equally weighted countries). 16

18 3.1 Stylized facts for Latin America In Latin America, it has been typically the case that rms have been reliant on (short-term, sometimes dollar-denominated) banking nance or own cash- ows to fund their investment projects, the more so the smaller the rm and the less they had access to international capital markets. Local equity nance, let alone bond nance, have represented a minor share in total nance available for domestic rms. Yet local stock markets have experienced some positive developments since the early 1990s. For a while, the Brady debt swaps in the late 1980s and early 1990s alongside massive privatizations programs carried out by several Latin American countries in the early 1990s favoured the expansion and short-term development of domestic stock markets. Still, long-term stock market development in most countries analyzed in this study remain poor by developed-country standards. Figures 1 and 2 illustrate this observation plotting the stock market capitalization as a % of GDP. This measure, which re ects the importance of stocks markets in an economy, is computed for three groups of countries in Figure 1; while Figure 2 shows the same information for the seven Latin American countries studied in this paper in The rst fact is that Latin American stock markets capitalization in terms of GDP do not stand comparison with Emerging Asian and G-7 stock market capitalization, being Chile the only clear-cut exception (Figure 2). Indeed, Chile displays capitalization ratios above the Asian average and near G-7 ones in some years. Second, the early growth in capitalization ratios recorded early in the nineties bolstered by the Brady plans, the privatization programs and successful macroeconomic stabilization plans- was short-lived. With the exception of Brazil, whose relative stock market capitalization kept on growing over the whole decade, the other countries capitalization growth attened (Argentina, Chile) or even decreased (Colombia, Peru, Mexico and Venezuela). In spite of the structural reforms 21 carried out from the early nineties onwards, the development of Latin American stock markets has been dissapointing. Evidence in this way is presented by De la Torre and Schmukler (2004). They assess whether there is a gap between the extent of the reforms carried out in these markets, on the one hand, and the actual outcomes, on the other. Running panel regressions for 82 countries where the dependent variable are two alternative measures of stock market development, namely stock market capitalization and volume traded, against a set of economic fundamentals they nd that the predicted levels of development for Latin American countries are signi cantly 21 These included domestic nancial liberalization, the opening of the capital account, social security regimes reform (from the pay-as-you go to a private capitalization system), the creation of exchange commissions and improvements of the regulatory and supervisory framework, such as laws intended to protect minority shareholder rights. 17

19 160% 140% 120% 100% 80% 60% 40% 20% 0% Latin America Emerging Asia Developed Markets Figure 1: Aggregated Stock Market Capitalization as Share of Aggregated GDP by Selected Groups. Latin America is Argentina, Brazil, Chile, Colombia, Mexico. Emerging Asia is Korea, Malaysia, Singapore and Thailand. Developed Markets are Canada, Germany, Italy, Japan, UK and US. Considered Exchanges: Buenos Aires, Sao Paulo, Santiago, Bogota, Mexico, Lima, Seul, Kuala Lumpur, Singapore, Bangkok, Borsa Italiana, Deutsche Börse, London, Amex, Nasdaq, NYSE and Tokyo. Source: World Federation of Exchanges, IFS-IMF and SourceOECD. 18

20 120% 100% 80% 60% 40% 20% 0% Argentina Brazil Chile Mexico Peru Colombia Venezuela Figure 2: Domestic Companies Stock Market Capitalization as Share of GDP for Selected Latin Amercian Economies. Note: Colombia and Venezuela include foreign companies. Source: FIAB and World Federation of Exchanges higher than the levels actually attained as seen, for instance, in Figure 2. Third, an alternative measure of stock market development, namely the number of listed rms, has declined in almost all Latin American markets in our sample, as shown in Figure 3. This nding is also supported by De la Torre and Schmukler (2004). They show evidence pointing to an increasing internationalization trend in Latin American rms publicly traded in stock markets 22. By the year 2000, 18.2% of Latin American traded rms had gone international whereas only 11.6% and 7.7% of its G-7 and East Asian counterparts, respectively, had internationalized. An observer may wonder if the delisting phenomenon in Latin American markets is in fact associated with an internationalization process ending in a migration to developed markets, as sometimes happens, for example, when rms substitute their domestic share issuances for American Deposits Receipts. Fourth, liquidity in Latin American stock markets is another issue of concern. The consequences of shallow and illiquid stock markets are well known (Levine 1997 and others). A common measure of liquidity is the total (nominal) trading volume as a percentage of GDP. Figure 4 depicts this indicator spanning Market liquidity for the countries in our sample grew until and 22 According to De la Torre and Schmukler (2004), international rms are those identi ed as having at least one active depositary receipt program at any time in the year, or having raised capital in international markets in the current or previous years, or trading in the London Stock Exchange, New York Stock Exchange, or NASDAQ. 19

21 Argentina Brazil Chile Colombia Mexico Peru Venezuela Figure 3: Number of Listed Companies in Selected Latin American Stock Markets. Note: Excluding Pension Funds. Sources: FIAB and World Federation of Exchanges. then dropped to levels sometimes similar to those observed in Further evidence supporting the illiquidity phenomena in Latin America is shown in Table 1. For a sample 23 of more than observations, we calculate for each country the percentage of observations without trade, a usual proxy for illiquidity. 24 Figures averaging 20% suggest that illiquidity in these markets is signi cant and therefore diversi cation might become problematic. Typical practices in Latin American markets make diversi cation troublesome. From a supply side perspective, the diversi cation problem is worsened by ownership concentration and the limited share of publicly traded stocks as a percentage of the rm s capital. From a demand side perspective, the problem is exacerbated by common buy and hold investment strategies pursued by institutional investors. 23 An description of the data is presented in next section 24 See gure 14 in the appendix for a comparison between volume and nontrading observation measures. While overall the patterns displayed by the two measures are consistent, Brazil appears to be the odds. 20

22 25% 20% 15% 10% 5% 0% Argentina Brazil Chile Mexico Peru Colombia Venezuela, Rep. Bol. Figure 4: Total Value of Share Trading in Percentage of GDP for Selected Latin American Economies year AR BR CL CO MX PE VE TOTAL Table 1: Percentage of Observations without Trade. Source: Economatica. Fifth, Latin American stock markets are more volatile than mature ones. Limited (actual) diversi cation opportunities and illiquidity could be among the main factors driving stock return volatility (we will come back to this in Section 4). Figure 5 displays annualized average dollar stocks returns over the period Comparing Latin American stock market returns with developed markets returns (e.g. US stocks tracked by the Dow Jones index), it turns out that Latin American stocks are substantially more volatile than their US counterparts. A further observation is that Latin American stock market returns exhibit some degree of comovement though with a few exceptions pairwise market return correlations are generally low but positive (see Table 13 in the appendix). These relatively low correlations support the argument for 21

23 portfolio diversi cation between developed and emerging countries securities (Bekaert et al.(1998) and Harvey (1995)) or across emerging market securities (Wong Dávila (2003), see Section 2.1). Table 2 summarizes total returns statistics. Total market return volatility is visibly higher for Latin American indexes than Dow Jones s volatility. As economic theory predicts, Latin American stock returns consistently display higher mean return values. Another typical stylized fact regarding nancial and stock market returns in particular is that returns are not normally distributed, i.e. stock market returns are skewed and high leptokurtic. Moreover, normality tests reject the null hypothesis of normal distribution in all cases (also observed in estimated kernel densities of Figure 6 in the appendix). Finally, on the whole, Latin American stock market returns do not appear to be highly auto-correlated. For the cases of Chile, Colombia and Mexico, however, positive auto-correlation coe cients are signi cantly di erent from zero. 22

24 m1 1995m1 2000m1 2005m1 date Dow Jones IBC Venezuela MERVAL Argentina IGBC Colombia m1 1995m1 2000m1 2005m1 date IPSA Chile IGBVL Peru IPyC Mexico BOVESPA Brazil Figure 5: Across-country comparison of local market annualized total returns (12 month moving average, in USD). Source: Economatica. 23

25 Stock Market Index N Min Max Mean Median Std Mean/Std Skewness Kurtosis Norm. Pr First O. AC MERVAL Argentina BOVESPA Brazil IPSA Chile * IGBC Colombia * IPyC Mexico * IGBVL Peru IBC Venezuela DOW JONES USA Table 2: Descriptive Statistics of USD Total Returns from US and selected Latin American Stock Markets ( ). Note: * stands for significant autocorrelation coefficients at Source: Economatica. 24

26 3.2 Dataset Our dataset is an unbalanced panel spanning monthly observations for 921 publicly traded rms in ,000 observations- from the largest Latin American stock markets: Argentina, Brazil, Chile, Colombia, Mexico, Peru and Venezuela (Table 5 below illustrates this fact). However, as we will see later on, the estimation of CAPM COE will be performed on the basis of a restricted sample ( ) in order to come up with comparable gures. We gather data from Datastream, Economatica, Morgan Stanley, and regional central banks. The dataset includes individual stock variables such as share prices, total annualized returns, volume and the number of traded shares, as well as related macroeconomic or global variables. The latter are: the 30-year US Treasury bond yield to maturity, sovereign spreads -JP Morgan EMBI+ 25 -, MSCI 26 total returns, local market total returns 27 and multilateral real exchange rates. For the sake of comparison, all data but the number of traded shares and the rate of depreciation of the multilateral real exchange rate are expressed in current US dollars. From Table s 3 and 4, we can see that Brazilian stocks account for a third of the total number of stocks and near 40% of the total number of non-missing observations. Di erences between Figures in Table s 3 and 4, i.e. stock number and observation number distributions across countries and sectors, owe to the unbalanced nature of our panel database (see Table 5). For instance, while some Brazilian stocks have non-missing data since 1986, Colombian stock information is not available prior to Regarding across sectors distributions (Table 4), we observe that Finance & Insurance, Food & Beverages, Steal & Metal Products and those stocks labeled as "Others" explain more than 35% of the total number of observations. 25 Because J.P. Morgan EMBI+ data are not available for the whole sample period, we complement available information with country speci c parametric estimations following Druck and Morón (2001). Further details about the econometric speci cation are provided in the following sub-section (3-3). 26 As usual, the Morgan Stanley Capital International index is used as a proxy of the global market portfolio. 27 For Argentina, Brazil, Chile, Colombia, Mexico, Peru and Venezuela local market total returns are obtained using MERVAL, BOVESPA, IPSA, IGBC, IPyC, IGBVL and IBC indexes, respectively. 25

27 AR BR CL CO MX PE VE TOTAL Agriculture & Fishing Chemicals & Chemical Products Construction Electrical Equipment & Electronic Products Electricity Finance & Insurance Food & Beverages Machinery & Equipment Mining Motor Vehicles & Related Non-Metallic Mineral Products Non-specified 4 4 Oil & Gas Others Paper & Paper Products Pension Funds Software & Data Steal & Metal Products Telecommunications Textiles Transportation & Storage Wholesale & Retail Trade TOTAL Table 3: Number of listed stocks included in the sample by country and sector (unbalanced database, ) 26

28 Sector AR BR CL CO MX PE VE TOTAL Agriculture & Fishing Chemicals & Chemical Products Construction Electrical Equipment & Electronic Products Electricity Finance & Insurance Food & Beverages Machinery & Equipment Mining Motor Vehicles & Related Non specified 508 Non-Metallic Mineral Products Oil & Gas Others Paper & Paper Products Pension Funds Software & Data Steal & Metal Products Telecommunications Textiles Transportation & Storage Wholesale & Retail Trade TOTAL Table 4: Number of non-missing observations by country and sector (unbalanced database, ) Year AR BR CL CO MX PE VE TOTAL TOTAL Table 5: Number of observations by country and year 27

29 Additional variables such as CAPM rolling parameters (betas, alphas, R squared, t-values, Wald p-values, etc.), Vasicek adjusted values, COE estimates, etc., where including using the following econometric and statistical procedures. 3.3 Econometric and statistical methodology to estimate the CAPM COE In this Section, we deal with a number of model estimation and speci cation issues associated with the CAPM framework already discussed in Section 2 28 : 1. Data frequency, 2. Optimal sample size, 3. The assumption of real market integration or "home bias e ect" in stock princing, 4. Sovereign spreads calculation and pricing, 5. Risk-free interest rate and emerging market bond yield stability, 6. Corrections for illiquidity, 7. "Beta" (systematic risk loading) robustness and instability, 8. Heterocedasticity and serial correlation in regression residuals, 9. The presence of outliers, 10. Treatment of negative COE estimates 11. Weighting strategies Data frequency There is one fundamental reason to grasp why we use monthly instead of daily stock return observations. First, in the case of emerging markets daily observations are particularly characterized by illiquidity (non-trading). 29 Should we use such data, both beta coe cients and consequently CAPM-COE would be under-estimated because an illiquidity downside bias in the estimated covariances -between illiquid stock and local market excess returns- would come out. 28 We suggest the non-dedicated reader to skip this section without any loss of generality and move on to section 4 29 In the case of developed-country stock returns, Daves et al. (2000) show that high frequency data (daily returns) "provide a smaller standard error of the estimated beta than do weekly, two-weekly, or monthly return". However, this is fully explained by the higher number of observations they use in daily-return estimations and not by frequency choices. Furthermore, Daves et al (2000) prove that a larger return interval (low frequency data) smooths out some of the noise a ecting the return generating process. In other words, they suggest a trade o between degrees of freedom (smaller standard deviation of betas) and noise (larger standard deviation of betas) 28

30 Assuming that the lower the frequency the lower the expected number of observations without trade, it is clear that the illiquidity downside bias can be strongly reduced by using monthly returns, without a signi cant loss in terms of degrees of freedom (which could be the case when using quarterly or annual data) Optimal sample size The sample size choice is a controversial issue on its own. There is no clear consensus concerning the optimal sample size on the basis of which CAPM betas should be estimated because of the potential trade-o between e ciency and the likelihood of structural breaks (i.e. parameter instability). The larger the sample size the lower the variance of beta estimates given the higher degrees of freedom, but the higher the probability of biased betas so long as the earliest observations turn out irrelevant for expectational purposes. Altman, Jacquillet, and Levasseur (1974), Baesel (1974), Gonedes (1973), Roenfeldt, Griepentrof, and P aun (1978), Smith (1980), Alexander and Chervany (1980), and Daves et al. (2000) conclude that the optimal estimation period ranges from four to nine years. Like in Fama and MacBeth (1973), we use a four-year rolling window sample because it is consistent with the average length of the business cycle in the largest Latin American countries (see Carrera et al., 1998). Therefore, we use 48-months rolling windows to estimate CAPM betas and subsequently CAPM COE for the countries in our sample The assumption of real market integration To test the null hypothesis of "real" market integration, we follow Koedijk et al. (2002) who derive a nested (domestic-global) CAPM equation à la Stultz (1995) from which we are able to perform the test. Before presenting the nested equation, a caveat is in order. Real market integration is not a synomym of nancial market integration or nancial opening. By real market integration we mean that global factors such as international portfolio returns or multilateral exchange rate returns are relevant to price domestic stock returns. Put di erently, if the null hypothesis of real market integration is accepted, there is some risk diversi able in the local market which contains a global risk component which is systematic. By contrast, nancial market integration is associated with full capital mobility, i.e. the inexistence of barriers to nancial in ows and out ows (capital controls, foreign exchange regulations, dual exchange rate regimes, taxation on capital ows, etc). That is, while markets may be nancially integrated (absence of barriers to capital ows) investors could still price local stocks disregarding global factors, i.e. international portfolio returns or multilateral exchange rate returns will not add signi cant information to the domestic market portfolio when computing local stock returns ("home equity 29

31 bias") As noted in the literature survey, Koedijk et al. (2002) derive their nested equation from a generalization of Stultz (1995), combining the multifactor International CAPM equation of Solnik (1983) and Sercu (1980) R i;t = i + ig [R G;t ] + imer [R MER;t ] + i;t (8) (where R i;t, R G;t and R MER;t stand for asset i, global portfolio and multilateral nominal exchange rate returns, respectively) with the standard Sharpe-Lintner s domestic CAPM equation R i;t = i + im [R M;t ] + i;t (9) (where R M;t is the return of the local market portfolio). Using 8 to price the local market portfolio, we get: R M;t = M + MG [R G;t ] + MMER [R MER;t ] + e i;t (10) Then, plugging 10 in 9 yields a modi ed CAPM which takes into account the global factors set out in ICAPM: R i;t = i + M im + MG im [R G;t ]+ imer im [R MER;t ]+ im e i;t + i;t (11) Equalizing 11 and 8 yields the testable hypothesis, namely: H 0 : MG im = ig and imer im = imer which, in the case of acceptance would imply that domestic CAPM alone would su ce to price any stock i or that i;t is ortogonal to R G;t and R MER;t i.e. global factors (see Section 2, Equation 6) are not correlated with the residuals backed out from a domestic CAPM equation. Koedijk et al. (2002) demonstrate that testing the latter is equivalent to run the nested model presented earlier in Section 2: R i;t = i + im [R M;t ] + ig [R G;t ] + imner [R MNER;t ] + i;t (12) to test the null hypothesis H 0 : imrer = ig = 0 (using standard Wald or Log-likelihood tests). This enable us to to assess the likelihood of the global factors orthogonality condition, The non-rejection of H 0 would mean that global factors are irrelevant for pricing purposes because all the risk that could be diversi able domestically could also be diversi able globally. In such a case, there would be no misspricing error in the CAPM domestic speci cation. This would yield evidence in favor of the lack of real capital market integration or home bias puzzle (see Gri n and Karolyi, 1998). In this paper we apply a slightly modi ed version of Equation 12. Instead of using nominal exchange rate returns, we use multilateral real exchange rate 30

32 returns, assuming a) deviation from the PPP (as in Adler and Dumas, 1983) and b) that asset returns (in local currency) are partially correlated with in ation rates. R i;t = i + im [R M;t ] + ig [R G;t ] + imrer [R MRER;t ] + i;t (13) where R MRER;t stands for the rate of change in the multilateral real exchange rate Sovereign spreads calculation and pricing into the CAPM framework In emerging countries, COE estimates are strongly dependent on sovereign spread calculation and pricing. Since major nancial institutions provide widely accepted data on emerging markets sovereign spreads in hard currency typically in the form of bond spread or total returns indexes, most practitioners make use of it in order to estimate modi ed domestic CAPM betas. However, this data has been only recently available in some Latin American countries for two reasons. First, secondary government bond markets for long maturities were nearly inexistent before the Brady Plans. Second, comprehensive indexes are only available since 1993 (e.g. JP Morgan EMBI+). Moreover, some Latin American countries like Chile have not had benchmark government bonds in hard currency until Given the constraint on sovereing spread data availability, we proceed to complete the actual dataset, namely JP Morgan EMBI+ indexes for Argentina, Brazil, Colombia, Mexico, Peru and Venezuela and JP Morgan EMBI Global indexes for Chile, with parametric estimations based on Druck and Morón s (2001) single equation model. Druck and Moron (2001) set out a "con scation risk model" from which they derive a sovereign spread equation with four types of covariates: "(1) those that re ect the safe asset return, (2) those that are idiosyncratic to each particular economy, (3) those a ecting the probability of an adverse shock, and the government s decision to whom should be con scated in case the bad shock arises, and 4) those variables measuring the balance sheet e ect". As proxies of these covariates they use (1) the yield to maturity on the 30-year US government bond, (2) the return of the domestic stock exchange measured in dollar terms and lagged one period, (3) the ratio M2 to foreign reserves as well as the variation of foreign exchange reserves; the lagged endogenous variable and (4) the ratio of Foreign Liabilities over the sum of Demand Deposits, Time, Savings and Foreign Currency Deposits. More formally: SS j;t = j + j X 0 j + j SS j;t 1 + j;t (14) 31

33 where j ; j and j are the parameters for country j, SS j;t and SS j;t 1 stand for actual and lagged sovereign spreads, j;t represents estimated residuals in t and Xj 0 is a vector of covariates including the 4 groups of variables introduced above. Depending on data availability in each country we may use a slightly modi ed version of Equation 14 excluding the lagged dependent variable from the speci cation. We rst estimate parameter vectors j ; j and j using standard OLS regressions. Then, we use these parameters as well as the covariates series represented by Xj 0 to ll all gaps in sovereign spreads since 1986 and until the rst actual observation of sovereign spread available for each country. Figure 6 shows that Latin American sovereign spreads are well tted by Druck and Moron s single equation model, with an average R-squared of 0.8. Finally, we apply an unseasonal two-parameter Holt-Winter exponential smoothing algorithm to reduce excessive noise in the tted sovereign spread series. The extent to which sovereign spreads are actually priced in stock markets returns (or excess returns) has also been discussed in the academic literature. Modi ed versions of domestic CAPM applied to emerging markets often include sovereign spreads in COE estimates (see, for instance, Mariscal and Lee, 1993). However, there is no general agreement on how much of this "government bond risk" is already priced in local market indices. Most practitioners assume that government bond excess returns (sovereign spreads) are not priced in local stock markets. Therefore, sovereign spreads should be additive. In this case, the following CAPM-COE speci cation obtains 30 : COE i;t = R f;t + a i [R M;t R f;t ] + SS j;t (15) where COE i;t is the rm i s estimated COE at t, R f;t is the risk-free interest rate (30 year US government bond yield to maturity), a i stands for the rm i s Beta parameter obtained from a standard Black s version of the domestic CAPM 31, [R M;t R f;t ] is the local market excess return (over the risk free interest rate) and SS j;t is the country j sovereign spread in t. Notice that if sovereign spreads are not priced in local stock markets, Equation 15 will overestimate COE. 32 In other words, if sovereign spreads are already priced in R M;t, they are also priced but twice in COE i;t. Here, we assume that R M;t includes SS j;t and then, a proper estimation of COE should be conducted by subtracting the sovereign spread from the local market excess return and adding it to the latter plus the risk free rate as shown in Equation 16: 30 Fornero (2002) equation 10 or Rodriguez Pardina (2005) pp Using the following equation: R i;t R f;t = a i RM;t R f;t + i;t : 32 See Erb, Harvey and Viskanta (1995). 32

34 Argentina R 2 : Brazil R 2 : Residual (left scale) Actual (right scale) Fitted (rigth scale) Chile R 2 : Residual (left scale) Actual (right scale) Fitted (right scale) Colombia R 2 : Residual (left scale) Actual (right scale) Fitted (right scale) Mexico R 2 : Residual (left scale) Actual (right scale) Fitted (right scale) Peru R 2 : Residual (left scale) Actual (right scale) Fitted (right scale) Residual (left 3000 scale) Actual (right scale) 2500 Venezuela R 2 : Fitted (right scale) Residual (left scale) Actual (right scale) Fitted (right scale) Figure 6: Latin American sovereign spreads: Actual values from Datastream. Fitted and residual values from Druck and Moron (2001) s single equation model. Note: All series but Chilean ones are JPM EMBI+ values. Chilean sovereign spreads comes from the JPM Global index. Sources: Datastream and Central Banks. 33

35 COE i;t = R f;t + b i [R M;t R f;t SS j;t ] + SS j;t (16) Note that b i is obtained from a modi ed Black s version of the domestic CAPM equation, namely: (R i;t R f;t SS j;t ) = b i [R M;t R f;t SS j;t ] + i;t (17) Intermediate alternatives propose that only a share (ranging from 0.3 to 0.7) of the sovereign spread is actually priced in local stock markets. Along these lines, authors as Godfrey and Espinosa (1996) propose to include a correction factor in (15) to avoid the "double pricing bias" in COE. Unfortunately, there are no previous studies on Latin American countries allowing a proper identi cation of the share of sovereign spreads that is actually priced in these markets. For this reason, we nally use Equations 16 and 17 to obtain our COE estimates Risk-free interest rate and emerging market bond yield stability The question about how much the sovereign spread is already priced in stock market indices could have been dismissed should we have used Sharpe-Lintner s CAPM speci cation. Assuming that sovereign spreads are constant over time (at least for a given sub-sample or moving window), it is possible to derive COE estimates by using the following equations: R i;t = i + c i [R M;t ] + i;t (18) where i ' R f + SS j is a regression intercept comprising both the risk-free interest rate ( R f ) and the share of the sovereign spread that is actually priced in the local market ( SS j ). COE i;t = E (R i;t ) = i + c i [R M;t ] (19) Notwithstanding this simpli cation, the constant government bond yields hypothesis can be safely and clearly rejected in our sample. As shown in Table 6 most Latin American countries have extremely volatile values. These results strenghten the case for using Black s version(s) of CAPM, where both, the sovereign spread and the risk free rate are stochastic and variable over time. 34

36 Country Mean Std. Dev. Min Max Argentina Brazil Chile Colombia Mexico Peru Venezuela US Table 6: Descriptive statistics of Government Bonds annualized yields (in USD, ) Corrections for illiquidity In we pointed out that low frequency data (e.g. monthly data) tend to reduce the incidence of the "illiquidity downside bias" in CAPM-Beta estimates. In spite of this, there are so many non-trading days in our database that many Latin American stocks have several observations with no recorded trading even on a monthly basis. Following Damodaran (2002), this non-trading problem can be addressed in one of two ways. One way is to work with even larger return intervals. However, quarterly and annual returns strongly reduce the number of observations and therefore the sample size. The second way is to estimate betas using monthly returns, and then adjusting these betas for the extent of the non-trading. Regarding the second way, there are two well-known adjustment mechanisms to deal with the problem of non-trading observations. The rst, put forward by Scholes and Williams (1977) propose the following adjustment equation: S W = k=1 X k= 1 i;t+k (1 + 2) (20) where S W is the rm i s adjusted CAPM Beta, is the rst order autocorrelation coe cient of local market returns and i;t+k are the slope coe cients from three separate regressions, R i;t = i;t 1 + i;t 1 [R M;t 1 ] + i;t (21) R i;t = i;t + i;t [R M;t ] + i;t R i;t = i;t+1 + i;t+1 [R M;t+1 ] + i;t Damodaran (1996) suggests that this procedure allows the beta estimate "to re ect the spill over of returns that often occurs around non-trading". The second adjustment mechanism is the "Dimson Beta adjustment" (see Dimson and Marsh, 1983). This adjustment consists in summing the slope 35

37 coe cients on the ve lagged, ve leading and contemporaneous returns on a stock market index in the following regression: and then R i;t = i + k=5 X k= 5 i;t+k [R M;t+k ] + i;t (22) D = k=5 X k= 5 i;t+k (23) Both adjustment mechanisms have been intended for high frequency data (daily data). However, as they are applied to low frequency data they become less e cient because of two di erent reasons. The Dimson s adjustment is too demanding in terms of degrees of freedom. There are 12 parameters in Equation 22 and we have only 48 monthly observations for each rolling window. On the other hand, Scholes and Williams approach su ers from "frequency-dependent autocorrelation". The lower the frequency, the lower the expected autocorrelation coe cient of local market returns because of a higher probability of "momentum" changes. When autocorrelation coe cients becomes negligible or even negatives, the "spill over e ect" of returns around non-trading is unlikely to happen and beta adjustments based on "spill over e ects" become much less e ective. In this paper, we use a third alternative adjustment process. We assume that investors form expectations using a simple and single rule: factor loadings on systematic risk (beta parameters) are better represented by high-trading observations. If we equally weight high and low-trading (including non-trading) observations we would add noise on beta expectations because we would have a higher probability of hazardous returns in low-trading days. Therefore, we need a weighting matrix to correct for illiquid stocks. The chosen matrix is one where the number of monthly traded shares is the weighting variable. In this way, liquid observations (associated with non-hazardous returns) drive beta estimates reducing the "illiquidity downside bias" Beta (systematic risk loading) robustness or instability The instability of beta estimates is another critical problem we encounter when estimating CAPM COE for Latin American rms. Individual stock illiquidity, changes in the market indexes (owing to delisting, mergers & acquisitions, etc.) and macroeconomic uncertainty result in highly volatile CAPM Beta estimates. Extremely unstable betas cannot be used to derive robust COE estimates. In the Appendix, we show average CAPM betas time series by country and sector (Figures 16 to 22). It is worth noting that these estimates are more robust in low-volatility countries such as Chile, Mexico or Peru (less volatile countries 36

38 since 1997, our benchmark period) than in Argentina, Colombia, Brazil 33 or Venezuela. The di erences look sharper at the rm level due to segmented liquidity. High-volume rms display less volatile betas and largely represent the average estimates by sector. On the contrary, low-volume stocks (a majority in Latin America) are associated with noisy betas because of disproportionate nontrading observations. Vasicek (1973) proposed an estimator to deal with this shortcoming. Basically, this estimator improves the mean reversion trend of individual betas allowing for both individual and sectoral beta dispersion. When the uncertainty about the estimate of the individual beta is high compared to the uncertainty about the average beta estimate, the beta forecast is adjusted strongly towards the average beta (e.g. average beta by sector). On the other hand, when the uncertainty about the estimate of the individual Beta is small compared to the uncertainty in the estimate of the average beta, then the beta forecast is adjusted strongly towards the individual beta. Formally, Vasicek s (1973) adjusted beta is a weighted average between individual and sector betas where beta variances (the measure of the uncertainty about betas) are the weights: V i A s i = i + s + s i s + i (24) where V i A is the rm i s Vasicek s adjusted beta, i is the rm i s CAPM standard beta, s is the sector s s across- rm average beta (with rm i belonging to sector s ), i is the rm i s standard deviation of beta estimate and s is the sector s s across- rm standard deviation of betas. We use this approach instead of other often used ad-hoc corrections toward one The econometric method The classical estimator for beta is the well-known ordinary least squares (OLS). However, it has been documented that in studies of nancial assets returns the OLS estimator su ers from several de ciencies: it has a mean reversion 33 Note that most Brazilian Betas are particularly low. This is not surprising because Bovespa index is mostly explained by Telebras. Damodaran (2002) show that "Telebras is 40% or more of the Bovespa, and this has some strange consequences. The rst is that the beta estimates for all other Brazilian stocks essentially become regressions of those stocks against Telebras, rather than a diversi ed stock index. The second is that more than 90% of all stocks on the Brazilian index were reporting betas less than one at the time of this regression. Since it is the weighted average beta that is one, and Telebras has a beta greater than one, this asymmetry in beta estimates becomes possible. The third and most troubling consequence is that it is the smallest, riskiest companies in the Brazilian market that have the lowest betas, while the largest and most estabilished rms have the highest betas. There are still many who argue that this is, in fact, the best measure of risk in these rms, and that the marginal investor s portfolio in Brazil is likely to be weighted heavily with Telebras. This argument may have resonance in markets where investors invest only in domestic stocks...". Moreover, because none of our regional stock market indices is a weighted portfolio of all local stocks, even weigthed average Betas could be either higher or lower than one. 37

39 Kernel Density Unit Root Probability from ADF tests with 12 lags Figure 7: Kernel density of Unit Root probabilities from ADF tests (applied rm by rm) with 12 lags in the ADL (autorregresive distributed lags) speci cation. tendency, it is ine cient when returns (or excess returns) distributions are abnormal, and also introduces signi cant biases when shares are poorly and thinly traded 34. To overcome these shortcomings, GMM speci cations have become popular as they do not rely on the normality, homoskedasticity, or the lack of serial correlation assumptions held by OLS. Indeed, GMM estimators 35 can a ord distribution of returns which are heteroskedastic, serially dependent and non-gaussian. The only required assumptions are that returns are stationary with nite fourth moments (see Ferson and Jagannathan, 1996 and Fernandes, 2004). Table 2 above, shows that all Latin American stock market returns but Colombian ones have very small rst order autocorrelation coe cients and none of them appear to be close to the unit root. Furthermore, we show in Figure 7 that the results of the Augmented Dickey-Fuller (ADF) tests (without using structural breaks in order to allow for a higher probability of non rejection of the unit root hypothesis) do not support the null hypothesis of the existence of a unit root. Indeed, 90 to 95 per cent of these results (depending on whether we use 12 or 4 lags in the ADF test) rejects the null hypothesis as GMM assumptions prescribe. Lastly, given the lack of a widely-accepted underlying theory supporting a conditional GMM equation (a GMM equation with instrumental variables for local market excess returns), we use the unconditional equation yielding GMM 34 See Lam (1999), Lally (1998), or Boabang (1996). 35 See Hansen (1982). 38

40 estimators that are the same as the OLS estimators. Nevertheless, GMM procedures leads to heteroskedasticity and autocorrelation consistent standard deviations, which is particularly important for speci cation purposes. Furthermore, GMM estimates were improved by ruling out outliers at the country level. Observations in the upper and bottom tails (2 percent) of total return distributions (by country) were treated as outliers Negative COE estimates In developed countries, negative COE estimates are rare (e.g. some cases of negative betas in a sample period with high local market excess returns and low risk-free interest rates). In emerging economies, negative COE estimates can be a more regular output from CAPM regressions. Most Latin American countries negative COE estimates owe to mediumterm sizeable negative excess returns. True, it is always possible to extend the sample in order to obtain rolling windows with strictly positive average excess returns. However, it is well-known that the higher the sample size the higher the probability of non-representative betas because of changing fundamentals over time. A way to deal with negative COE estimates has been put forward by Barnes and Lopez (2005) and Hail and Leuz (2004). According to this literature, it su ces to apply a simple trimming rule setting at 0 all negative COE estimates. Because of the systematic origin of Latin American negative COE values, this trimming rule ensures that relative COE estimates (e.g. across sectors) will not be signi cantly modi ed (even when the country level average COE signi cantly increases with the number of trimmed observations) Weighting strategies Unlike the bulk of empirical contributions to stock pricing and COE estimation, we use volume (in US current dollars) instead of market capitalization as across- rm weighting variable (e.g. to obtain weighted average COE estimates by sector or country ) 36. In this way, weighted averages become market representative in a proper sense. Big rms with high market capitalization but low trading activity (low volume) must be highly weighted when stock variables are taken into account but only high volume rms (irrespective of whether they are big or small in terms of market capitalization) should be highly weighted when ow variables are analyzed. Because COE estimates are obtained from a ow of traded shares, volume-weighted strategies improve both sector and country average reliability. 36 The standard distinction is between equal and market value-weighted averages. See for example Bennet and Sias (2004),Cao, Simin and Zhao (2005) or Lettau and Ludvigson (2002). 39

41 3.4 Variance Decomposition Almost all previous methodological issues focus on COE estimates without paying especial attention to variance decomposition procedures. The breakdown of the total variance of (excess) returns is important to assess how much risk is systematic. systematic risk should be the only source risk priced in CAPM. To analyse the variance of (excess) returns we follow Goyal and Santa Clara (2003). Consider the following measure of total risk in a country. First, compute the variance of a stock (or collection of stocks) p using a 12 months moving window as: V pt = 11X i=0 r 2 pt i (25) Where r p;t i is stock p return in month t. Then compute the average stock variance as the arithmetic average of the N 12-month window variances of each stock return. V t = 1 N t " XN t 11X rpt 2 i i=1 i=0 # (26) Where N t is the number of stocks in the country of interest at each t. 37 This is a measure of total risk, including systematic and idiosyncratic components. Now consider a portfolio that equally weights all stocks for a speci c country at each moment in time t. Call this portfolio the equally weighted portfolio (ew). This portfolio, by construction, will capture the systematic risk of the market. Using (25) we can compute a time series for the variance of this portfolio (V ew ). Formally: 11X 1 NX V ew = rp;t 2 i (27) N i=0 t i=0 Analyzing together both measures, we obtain the share of the total variance V of returns explained by idiosyncratic risk, namely 1 ew V t. With the size of this "residual" variable we get a measure of the potential miss-pricing error in CAPM models if underlying assumptions do not hold. 4 Empirical results for Latin American markets Before estimating the contribution of systematic risk (betas) to account for asset returns (or excess returns) and hence be able to obtain COE estimates, it is necessary to identify the appropriate econometric speci cation of the underlying asset pricing model. 37 Note that this measure is not, strictly speaking, a variance measure since returns are not demeaned. However, the impact of subtracting the mean is minimal, or you can safely assume mean returns normalized to zero.. As Goyal and Santa Clara (2003) suggest, the expected squared return overstates the variance by less than one percent of its level. 40

42 4.1 Asset pricing model speci cation Following Stultz (1995) and Koedijk et al (2002), we use a nested International CAPM-Domestic CAPM equation in order to test whether global portfolio risk and (multilateral) real exchange rate uctuations add some signi cant information to the domestic CAPM model (see Section 3.3.3). Recall Equation 28 below which suggests that a rm s asset return (i.e. its COE) can be accounted for by: the risk-free rate, local market portfolio risk, global market portfolio risk, and multilateral real exchange rate returns (or "real" currency risk, as long as this risk is not fully diversi able or hedged against currency exposures are limited). R i;t = i + im [R M;t ] + ig [R G;t ] + imrer [R MRER;t ] + i;t (28) In order to gure out which model speci cation should be adopted to estimate expected (excess) returns and COE, we perform di erent individual and joint statistical tests under the null hypothesis that either global market portfolio risk (Global Returns) or multilateral (real) exchange rate returns (RER), or both are statistically insigni cant in Equation (28); in other words, we are testing the null hypothesis that Domestic CAPM is the right model. Table 7 displays the results of these tests: we can conclude that both Global Returns and RER are almost never signi cant and therefore Domestic CAPM overwhelmingly turns out to be the relevant econometric speci cation we should adopt. Global Returns RER returns Join test Country (1) (2) (1) (2) (1) (2) Period AR BR CL CO MX PE VE Latin America Table 7: Percentage of Wald Test rejecting the null of non significant global instruments Running more than nested equations (84359 for unweighted GMM speci cations and for weighted GMM models, using monthly traded shares as weights) we nd the rejection percentages in the case of the joint test under the null hypothesis that: both Global Returns and RER coe cients are non signi cant in the nested equation) are always below 40%. Moreover, taking Latin America as a whole these percentages decrease up to 19 and 28%, depending on the econometric speci cation In Columns (1) of Table 7 percentages are taken from non weighted GMM speci cations 41

43 Weigthed GMM Non-Weighted GMM Critical value for rejection 0 Jan- 90 May- 91 Sep- 92 Jan- 94 May- 95 Sep- 96 Jan- 98 May- 99 Sep- 00 Jan- 02 May- 03 Sep- 04 Figure 8: Average Wald test p-values in Latin America for the null Hypothesis: Global returns and RER returns do not explain individual stock total returns. Note: weighted GMM econometric speci cation uses traded shares as within rm weights for each rolling window of 48 monthly observations. Regarding the Wald Test dynamic properties, we nd that Latin American average p-values (i.e. the probability that the null hypothesis is rejected) are slightly decreasing over time but they always remain well above the usual 0.05 critical value for rejection (see Figure 42). For most Latin American stock markets we nd increasing rejection percentages since 2000 (see Table 8). Notwithstanding this fact, none of these values is on average higher than 0.5. Therefore, and taking into account that a single econometric speci cation is required in order to produce both time-series and cross-section comparable COE estimates, we nally reject the null hypothesis that global components (i.e. Global Returns and RER) are statistically signi - cant in the ICAPM-CAPM nested equation. In other words, the only relevant factor to account for variations in expected (excess) returns the COE- in our sample of Latin American countries is local market portfolio risk (and sovereign spreads), like in the single factor or Domestic-CAPM (Equation 1 above). while in Columns (2) values have been obtained from weighted GMM models using monthly traded shares as within weights. 42

44 Arg. Bra. Chile Col. Mex. Peru Ven Whole Sample Table 8: Percentage of Wald Test rejecting the null of non significant global instruments. Yearly averages by country obtained from non weighted GMM specifications Using within rm weighted GMM instead of unweighted versions of the nested equation, we obtain similar results as we can see from Figure The COE Derived from Black s CAPM Beta estimates Using the Black s CAPM beta estimates (Equation 29, reproduced below) we have got from GMM rolling regressions, we compute alternative estimates of the COE. (R i;t R f;t SS j;t ) = b i [R M;t R f;t SS j;t ] + i;t (29) Indeed, we calculate 8 di erent COE estimates depending on whether the Vasicek adjustment 39 is allowed for, and on the di erent weighting mechanism in both the GMM rolling regressions (with or without within- rm weights - the weight being the number of traded shares in each observation) and crosssectional averages (with or without between- rm weights, the latter being the (nominal) monthly volume 40 ). Each COE estimate is the result of summing the risk-free rate, the appropriate sovereign spread (see Section 3.3.4) and a term equal to Black s CAPM beta multiplied by the local market portfolio premium (or excess return on the market portfolio). In Table 9 and Figure 39 See Equation 24 in Section See Section

45 Average COE by sector ( ) VE 30 AR 25 CO BR MX 20 PE 15 CL COE std by sector ( ) Figure 9: COE in Latin America. Cross-plot of average COE and standard deviation by country (annualized values, in percentages) 9, we present the annualized average COE by country (and their associated standard deviations) for the period Country Overall averages Mean Std AR BR CL CO MX PE VE Table 9: Black's Model Cost of Equity estimates by country (in percentage). Overall averages for the whole sample period (1997 to 2004) Not surprisingly, the riskiest stock markets (Venezuela and Argentina) are also those with higher average COE estimates, while the less risky country, Chile, exhibit the lowest rates of stock returns and hence COE estimates. Notwithstanding this nding, the risk-return (COE) relationship found in the case of Peru deserve further discussion. Peruvian COE estimates are lower than expected -after all Peru is an speculative grade country, and its stock market remains underdeveloped/illiquid and the average COE observation is below the 44

46 tting curve. However, the Peruvian macroeconomic outlook has been steadily improving since Indeed, average in ation in is the lowest in Latin America and the average real GDP volatility in Peru is also relative small since 1997 and well below those of Argentina, Venezuela, Colombia, and even Mexico. Why should then rational (but to some extent backward-looking) investors require higher returns on a Peruvian stock? This remains an open question to debate and further research. Figure 9 depicts a mean-variance COE trade-o which is quite in line with Markowitz s predictions. Average COE estimates seem to be relatively high on an absolute basis 41. However, this is not surprising because of the sample period and methodological features. Most Latin American nancial crisis takes place in this period (including the Mexican one -Tequila- 42 ). Furthermore, it is worth noting that setting at 0 all negative COE estimates (the standard criterion 43 ) yields higher average COE values (because Latin American stocks show many observations with negative COE estimates in this period). Allowing for negative observations reduces Latin America average COE estimates by 25% (on average), but do not qualitatively changes the relative structure of data (neither across countries nor across sectors). From a time series perspective, our CAPM COE estimates share some common features with regional stock markets returns: high return volatility and some degree of co-movement (compare Figures 10 and 5). In spite of these commonalities, when we look at COE over time we realize two di erent patterns emerge. On the one hand, Argentina, Brazil and Venezuela share a high overall volatility alongside higher but decreasing COE estimates since January On the other hand, more stable patterns in the evolution of COE arise in the cases of Chile, Colombia, Mexico and Peru. Although COE estimates remain lower than those of the rst group, they have been steadily increasing since It is interesting to notice that Latin American COE are a-cyclical (see Figure 11) and not pro-cyclical as is generally the case in developed, mature stock markets. This is because GDP growth is negatively correlated with sovereign spreads which only play a role in emerging markets. When the sovereign spread GDP-elasticity is higher than that of total market returns, COE estimates can even be counter-cyclical (e.g. Argentina or Colombia). Looking at the country level, only Mexican COE estimates are signi cantly pro-cyclical (with a correlation coe cient of 0.48). A critical question arises from the previous results: Why should Latin American rms increase their use of equity nance if it is very expensive (as usual) 41 For the sake of comparison with developed-country stocks, see for example Khothari et al. (1995), Fama and French (1997) or Hauptman and Natella (1997). Also see section Remember that cross-country comparable COE estimates start in 1997, but were obtained using information from 1993 to 2004 (i.e. a minimum of 48- month or 4-year moving window is required to estimate beta and COE). 43 See the methodological section. 45

47 AR BR VE Jan-97 Mar-98 May-99 Jul Sep-01 Nov-02 Jan-04 CL CO MX PE Jan-97 Mar-98 May-99 Jul-00 Sep-01 Nov-02 Jan-04 Figure 10: Evolution of the COE by country (Black s model 12-month rolling moving overall-averages) 46

48 Average COE (annualized values) COE = *GDP growth R2 = Country Correlation Coeff. (COE-GDP growth) Argentina Brazil 0.03 Chile Colombia Mexico 0.46* Peru 0.19 Venezuela 0.25 Note: * stands for significant correlation coefficients at 5% Real GDP growth (YoY, as %) Figure 11: The acyclical pattern of the COE in Latin American countries. Cross-Plot and across country comparison of average correlation between COE and GDP growth ( , Quarterly data) and does not provide a "bene cial" pro-cyclical pattern? Risk-averse managers would be willing to pay a market premium to obtain equity nance if COE estimates were pro-cyclical (because of the pro t-smoothing properties of such a behavior). But it is no longer true when COE estimates become a- cyclical. Therefore, Latin American stock market underdevelopment can also be explained by this feature. When examining the average COE estimates by sector, we nd that Pension Funds and Agriculture & Fishing stocks have the lowest estimates in the sample while Oil & Gas, Telecommunication, Electricity and Construction rms display the highest values across sectors (see the last column in Table 10). Pension Funds have the lowest COE because they hold more diversi ed investment portfolios than other sectors. Low COE estimates for Agriculture & Fishing are due to the relatively low return volatility of this sector (sales -in US current dollars- of this tradable sector are much more stable than those of non-tradable ones). On the contrary, Construction rms are highly volatile (and thus risky) because of their high sensitivities to the business cycle (which is priced in higher expected returns and then relatively higher COE). COE estimates for Telecommunication and Electricity rms are surprisingly high because these rms have relatively stable sales (in domestic currency). However, expected pro ts in US current dollars are particularly uncertain because of country speci c regulations and high exchange rate volatility in most Latin American countries. Oil & Gas COE results could have a di erent nature. Impressive COE estimates would be explained by gradually increasing pro t expectations rather 47

49 Average COE by sector ( ) Agriculture & Fishing Pension Funds Finance & Insurance Oil & Gas Telecommunications Construction COE std by sector ( ) Figure 12: COE in Latin America. Cross-plot of across-country overall averages and standard deviations by sector (annualized values) than by excessive pro t uncertainty. Put it di erently, high COE estimates owe to progressive upward corrections and not to symmetric volatility. The mean-variance trade-o observed across-countries is also reported acrosssectors (see Figure 12 and Figure 31 in the appendix), with Oil & Gas, Telecommunications and Construction being representative to the upper-right panel (high mean - high variance) and Pension Funds and Agriculture & Fishing (amongst others) belonging to the lower-left one. The majority of sectors report the lowest COE estimates in Peru and, mainly, in Chile, while the highest are almost always associated with Venezuelean rms. Venezuela and Colombia display the highest cross-sector COE dispersion while Chile and Mexico show the lowest ones. 48

50 Sector AR BR CL CO MX PE VE Average Agriculture & Fishing (0.27) (0.30) (0.15) (0.20) (0.19) (0.17) (0.22) Chemicals & Chemical Products (0.33) (0.34) (0.12) (0.18) (0.21) (0.23) (0.47) (0.32) Construction (0.39) (0.43) (0.17) (0.27) (0.62) (0.50) Electrical Equipment & Electronic Products (0.27) (0.35) (0.25) (0.40) (0.34) Electricity (0.43) (0.44) (0.21) (0.29) (0.10) (1.20) (0.44) Finance & Insurance (0.61) (0.36) (0.15) (0.30) (0.35) (0.21) (0.47) (0.39) Food & Beverages (0.37) (0.25) (0.19) (0.46) (0.27) (0.31) (0.16) (0.28) Machinery & Equipment (0.22) (0.27) (0.28) (0.13) (0.29) Mining (0.23) (0.21) (0.32) (0.20) (0.37) (0.14) (0.26) Motor Vehicles & Related (0.59) (0.26) (0.23) (0.32) Non-Metallic Mineral Products (0.44) (0.31) (0.15) (0.38) (0.33) (0.28) (0.58) (0.34) Oil & Gas (0.42) (0.42) (0.21) (0.55) (0.42) Others (0.44) (0.31) (0.17) (0.32) (0.32) (0.20) (0.34) (0.32) Paper & Paper Products (0.20) (0.28) (0.24) (0.09) (0.27) (0.55) (0.29) Pension Funds (0.18) (0.02) (0.18) Software & Data (0.28) (0.05) (0.24) Steal & Metal Products (0.86) (0.35) (0.35) (0.30) (0.40) (0.90) (0.41) Telecommunications (0.69) (0.41) (0.30) (0.11) (0.28) (0.25) (0.66) (0.43) Textiles (0.21) (0.24) (0.07) (0.22) (0.12) (0.16) (0.75) (0.27) Transportation & Storage (0.04) (0.16) (0.19) (0.17) (0.60) (0.27) Wholesale & Retail Trade (0.33) (0.40) (0.27) (0.16) (0.27) (0.31) (0.30) Table 10: Overall Average Cost of Equity by country and sector (annualized values for the whole sample period: ) The highest across-country COE dispersion is obtained for Construction and Electricity stocks, while Mining and Electrical Equipment & Electronic Products stocks appear to have very similar COE in all Latin American countries studied in our sample. Finally, we observe that extreme values of COE by country are very di erent 44. In Argentina, Brazil, Chile, Colombia, Mexico, Peru and Venezuela, the sectors with the highest COE estimates are Steal & Metal, Agriculture & Fish- 44 More details on COE estimates by country and sector are presented in gures 22 to 28 in the appendix. 49

51 ing, Steal & Metal, Oil & Gas, Non-Metallic Mineral Products, Construction and Electricity respectively. Conversely, Transportation & Storage, Transportation & Storage, Textiles, Telecommunications, Textiles, Pension Funds, and Agriculture & Fishing exhibit the lowest COE estimates in Argentina, Brazil, Chile, Colombia, Mexico, Peru and Venezuela, respectively. 4.3 The explanatory power of CAPM How well does Black-CAPM regressions t (excess) returns? How much of (excess) returns remain to explain? Are Black-CAPM beta and COE estimates mispricing systematic risk? To answer these questions we will rst take a look at how much of the stock (excess) returns variance remains unaccounted for by Black-CAPM regressions. Should Black-CAPM regressions provide a poor explanation of (excess) returns variability, it could be the case that CAPM assumptions are wrong and hence misspricing errors huge. For instance, investors may not be able to fully diversify portfolios and idiosyncratic variables may in fact matter. It is clear at this point that understanding how large idiosyncratic relative to systematic risk is in each country is a key issue. In Section 4.4 we provide an alternative measure of the variance decomposition that may be useful to determine the relative importance of these sources of risk. Econometric techniques enable us to isolate the percentage of the risk which is not accounted for by the explanatory-variable set. In our study, these are the proxies for the domestic market portfolio (see Section 3.3 and 4.1). As mentioned earlier, if these market portfolios are e cient (something that we are not testing here), they should (fully) capture the systematic component of risk. It follows that Black-CAPM regressions allow us to isolate the percentage of the total variance of (excess) returns explained by systematic risk, what amounts to computing the R-squared or goodness of t. Figure 13 shows the R-squared which averages out all individual R-squared obtained through the 8 di erent econometric speci cations as set out in Section 3.3. The sample covers all stock returns on Latin American rms in the selected countries over The black solid line indicates the overall (across-econometric model) average R-squared while the dotted lines depict the individual R-squared values at +- 1 standard deviation away from the mean. 45 Figures 32 to 35 in the Appendix report average R-squared values on a country basis. Like in the full sample case, these measures of the goodness of t 45 Out of 8 possible CAPM econometric speci cations, the highest individual R-squared obtains where within and between rm weights are used (Vacisek-adjusted betas). In principle, the result that weighting rms by their average traded volume increases the explanatory power of the market portfolio, and therefore the stock return variability accounted for by systematic risk, is not surprising. This happens as in our sample there is an apparent correlation between market capitalization and the average traded volume. Market capitalization is generally well tracked by the market portfolio or its proxy. A chart displaying the best t and other R-square values is available upon request. 50

52 CAPM R2 (across model overall mean) for Latin America +/- 1 std Jan-97 Mar-98 May-99 Jul-00 Sep-01 Nov-02 Jan-04 Figure 13: R-Squared overall mean across di erent CAPM-GMM speci cations. L.A. sample correspond to Black-CAPM regressions where within and between rm weights are used (Vacisek-adjusted betas). The country reporting the highest average R-squared is Argentina (44,4%), followed by Mexico (43.9%), Venezuela (40%), Colombia (39,7%), Peru (29,4%), Chile (32,2%) and Brazil (22,6%). The best Black-CAPM model speci cation accounts for, on average, 32% of the variance of (excess) returns for the whole sample of Latin American countries. Why the remaining 68% is not explained by the best model speci cation is subject to discussion. If all Black-CAPM assumptions held true, then, for Latin America, 32% of the variance of returns would be attributable to systematic risk, and 68% to idiosyncratic, fully diversi able risk. However, it may be the case that Black-CAPM assumptions could be wrong, for example, if there were intertemporal investment choices not captured by the domestic market portfolio (as Merton s (1973) model suggested), or if investors were not able to fully diversify portfolios (as Levy (1978) or Merton (1987), among others, demonstrated). In any of these cases, the important 68% of (excess) return (and COE) volatility that remains unexplained represents a huge potential misspricing error of the cost of capital. Either additional systematic risk factors (Fama and French 1992, 1996 and 1997) or rm-idiosyncratic variables, or both, could be added to Black-CAPM so as to reduce the potential misspricing error. 46 An interesting question related to the foregoing analysis is how large idiosyncratic relative to systematic risk turns out in each country. Our Black-CAPM 46 This is subject of ongoing research by the authors. 51

53 regressions suggest that idiosyncratic risk accounts for a percentage close to 68% of total (excess) returns variance, i.e. the average R-squared is There are some disadvantages to the use of R-squared though. The rst is that it is model dependent. Another disadvantage of R-squared is that it is only a relative measure, so it does not say anything about the absolute magnitude of the variance. It may re ect whether systematic risk is relatively higher than idiosyncratic risk in a country with respect to another country, but it does not say anything about the absolute magnitude of systematic risk in either country. Next Section presents an alternative approach to deal with these disadvantages. 4.4 Variance Decomposition Results An alternative approach to breaking down total risk (i.e. the total variance of (excess) returns and COE)) consists in, rst, estimating the cross-sectional variance of stock (excess) returns in a given country at time t (Section 3.4) to capture the systematic component of stock (excess) return volatility, and, second, to divide the latter by the average total stock risk. Table 11 presents some descriptive statistics of these two measures, i.e. total and systematic risk. Recall that these are 12-month rolling window standard deviations. Figures 36 to 39 in the appendix plot the evolution of those variances by country, over the period Table 12 compares the R-squared obtained from Black- CAPM regressions as discussed in Section 4.3 with the share of systematic risk in total risk measured according to the methodology laid out in Section 3.4. Country Total Risk (V t ) Systematic Risk (V ew ) Mean Median Std Dev Mean Median Std Dev Argentina Brazil Chile Colombia Mexico Peru Venezuela Table 11: Standard Deviations on Total Returns by country for the whole sample period: Table shows that, on average, systematic risk accounts for 30% of the total variance in (excess) returns. This gure is actually close to the average R-squared -32%- we have got from the best Black-CAPM econometric speci - cations. Also, consistent with the ndings from the Black-CAPM regressions, the share of systematic risk increases in the cases of Argentina and Venezuela, this time to 41% and 37%, respectively. 47 Note that Column 1 in table 12 is the result of dividing the square of the gures in column 4 by the square of the gures in column 1 in table

54 Country Systematic Risk / Total Risk Overall average R2 Argentina Brazil Chile Colombia Mexico Peru Venezuela Table 12: Alternative Systematic Risk Measures. Overall averages for the whole sample period: It is interesting to note that the country displaying the lowest R-squared in Black-CAPM regressions (23%), Brazil, has nevertheless the higher absolute systematic standard deviation with a value of 18.22% (see Table 4.4). Brazil has also the largest absolute total variance measure. In relative terms, Brazil s systematic risk share (33%) is not the highest and has a comparable level to that of Mexico(29%) or Chile(28%). 5 Conclusions This paper provides a unique dataset of comparable COE estimates for Latin America. The dataset includes 921 rms listed in 7 stock markets (Argentina, Brazil, Chile, Colombia, Mexico, Peru and Venezuela) and looks at the intertemporal ( ), cross-country and cross-sectoral dimensions of COE. In order to obtain homogeneous (and robust) CAPM-COE estimates for these Latin American publicly-traded rms, we introduce a number of methodological considerations, some of which are "innovative" in the literature of emerging-market stock pricing (test of real market integration or "home bias e ect" in stock princing, an alternative method to price sovereign spreads into COE, adjustment for illiquidity, beta robustness and instability, treatment of negative COE estimates and weighting strategies; see Section 3.3), Our main results can be summarized as follows: 1. Risk-adjusted returns on Latin American stocks are signi cantly lower than those observed in developed countries. However, Latin American COE estimates (CAPM required returns) are much higher than those in mature markets, reaching an annualized regional average of 24.06% (in US dollars). 2. These results are mainly explained by the underlying extreme uncertainty in Latin American stock markets, in turn related to periods of heightened macroeconomic volatility. 3. Despite the recent increase in nancial globalization, we nd a lack of real market integration ("home bias e ect") in the case of Latin American 53

55 stocks. Therefore, COE estimates should be derived from domestic CAPM speci cations instead of international versions.notwithstanding the implications of the latter, we found that "home bias" in stock pricing is slightly decreasing over time. 4. In line with Markowitz s predictions, there is a clear-cut risk-return (standard deviation-mean) positive trade-o in COE estimates. This is not surprising because a strong relationship between returns and local portfolio risk should be expected when markets are segmented. As a result, the riskiest stock markets (Venezuela and Argentina) are also those associated with higher average COE estimates, while Chile (the Latin American "paradigm" in terms of capital market development and stability) exhibits the lowest risk/return values. The positive risk-return trade-o is also reported across-sectors, with Oil & Gas, Telecommunications and Construction displaying the highest COE means and standard deviations and Pension Funds and Agriculture & Fishing the lowest. 5. Latin American COE estimates are not generally pro-cyclical, which comes in sharp contradiction with the theoretical insights in the literature on developed countries. This is because GDP growth is negatively correlated with sovereign spreads which are an important component of total nancing costs in emerging markets. If sovereign spread GDP-elasticities are higher in absolute value than those of local market (excess) returns, COE estimates can even be counter-cyclical (e.g. Argentina or Colombia). Put di erently, when there is a recession in Latin American countries, the reduction in the local market premium is o set by a rise in the sovereign spread, yielding a-cyclical COE estimates. 6. Using two di erent measures of variance decomposition we nd that individual returns, and hence COE are mainly driven by idiosyncratic shocks (even in Venezuela or Argentina, the countries with the largest shares of systematic risk in total risk). Consequently, CAPM-COE estimates should be cautiously interpreted because 60% to 70% of the total variance is not explained by the model. In a context of low probability of complete diversi cation, this may lead to signi cant misspricing errors. Our main results may shed light on the causes of Latin American stock market underdevelopment. On the demand side, excessive systematic risk reduces the risk-adjusted return on Latin American stocks below the level of developed markets. Therefore, why should risk-averse investors hold Latin American stocks in their portfolios if they o er relatively small risk-adjusted returns?. On the supply side, excessive macroeconomic volatility drives high and a- cyclical COE estimates. Then, why should Latin American private sector man- 54

56 agers tap stock markets to raise equity nance if COE estimates are neither low nor exible?. In the light of the foregoing results, a policy concern should be to dampen the excessive macroeconomic volatility -typically associated with country riskobserved in some Latin American countries studied in this paper, thereby reducing the systematic component of risk and ultimately COE. This would make more advantageous for investors to hold Latin American stocks as their riskadjusted returns would increase and for rms to raise cheaper equity nance as COE might fall. Lower COE is a necessary condition for higher investment, sustained long-term growth and poverty-reduction enhancing. As said before, however, systematic risk in the context of our Black (domestic) CAPM regressions only accounts for 30% to 40% of total risk, i.e. it only explains less than half of COE. Other potential sources of systematic risk dealing with size (capitalization) and book to market value ratios (Fama and French 1992, 1996 and 1997) or rm-speci c variables (idiosyncratic risk not priced in Black-CAPM COE estimates) or both could help explain the remaining 60% to 70% of total variability in COE. An ongoing extension of this research project is looking into the latter potential sources of misspricing. 55

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64 6 Appendix Percentage of Observations Without Trade (Iliquidity Measure) 0,4 0,35 0,3 0,25 0,2 0,15 0,1 0,05 0 Argentina 0 0,05 0,1 0,15 0,2 0,25 Total Trading Volume as Percentage of GDP (Liquidity Measure) Percentage of Observations Without Trade (Iliquidity Measure) 0,3 0,25 0,2 0,15 0,1 0,05 0 Brazil 0 0,05 0,1 0,15 0,2 0,25 Total Trading Volume as Percentage of GDP (Liquidity Measure) Percentage of Observations Without Trade (Iliquidity Measure) Percentage of Observations Without Trade (Iliquidity Measure) 0,25 0,2 0,15 0,1 0,05 Chile 0 0 0,05 0,1 0,15 0,2 Total Trading Volume as Percentage of GDP (Liquidity Measure) 0,5 0,4 0,3 0,2 0,1 0 Peru 0 0,02 0,04 0,06 0,08 Total Trading Volume as Percentage of GDP (Liquidity Measure) Percentage of Observations Without Trade (Iliquidity Measure) 0,5 0,4 0,3 0,2 0,1 Percentage of Observations Without Trade (Iliquidity Measure) 0,16 0,14 0,12 0,1 0,08 0,06 0,04 0,02 0 Percentage of Observations Without Trade (Iliquidity Measure) Venezuela, Rep. Bol. Mexico 0 0,05 0,1 0,15 0,2 0,25 Total Trading Volume as Percentage of GDP (Liquidity Measure) Colombia 0,4 0,35 0,3 0,25 0,2 0,15 0,1 0, ,00 0,02 0,04 0,06 0,00 0,01 0,01 0,02 0,02 Total Trading Volume as Percentage of GDP (Liquidity Measure) Total Trading Volume as Percentage of GDP (Liquidity Measure) Figure 14: Liquidity Measures Comparison ( ) 63

65 Stock Market Index (1) (2) (3) (4) (5) (6) (7) (8) MERVAL Argentina (1) BOVESPA Brazil (2) IPSA Chile (3) IGBC Colombia (4) IPyC Mexico (5) IGBVL Peru (6) IBC Venezuela (7) DOW JONES USA (8) * * 0.45* * * * 0.41* 0.49* * 0.24* 0.35* 0.23* 0.44* * 0.21* 0.22* 0.25* 0.24* * 0.44* 0.47* * 0.16* 0.21* 1.00 Table 13: Stock Market correlation matrix ( ). Note:* stands for significant autocorrelation coefficients at

66 Kernel Density DOWN JONES US MERVAL Argentina IBC Venezuela IGBC Colombia USD Monthly Total Returns Kernel Density BOVESPA Brazil IPSA Chile IGBVL Peru IPyC Mexico USD Monthly Total Returns Figure 15: Gaussian Kernel Densities of Total Returns by Country ( ) 65

67 Figure 16: Beta estimates by sector in Argentina from 1996-I to 2004-IV 66

68 Figure 17: Beta estimates by sector in Brazil from 1996-I to 2004-IV 67

69 Figure 18: Beta estimates by sector in Chile from 1996-I to 2004-IV 68

70 Figure 19: Beta estimates by sector in Colombia from 1996-I to 2004-IV 69

71 Figure 20: Beta estimates by sector in Mexico from 1996-I to 2004-IV 70

72 Figure 21: Beta estimates by sector in Peru from 1996-I to 2004-IV 71

73 Figure 22: Beta estimates by sector in Venezuela from 1996-I to 2004-IV 72

74 0.6 AR BR CL CO MX PE VE Critical value for rejection 0 Jan-97 Mar-98 May-99 Jul-00 Sep-01 Nov-02 Jan-04 Figure 23: Average Wald test p-values by country (using traded shares as weights in the GMM econometric specification) for the null H0: Global returns and RER returns do not explain individual stock total returns 73

75 Figure 24: 12-month moving averages Black s model COE estimates for Argentina 74

76 Figure 25: 12-month moving averages Black s model COE estimates for Brazil 75

77 Figure 26: 12-month moving averages Black s model COE estimates for Chile 76

78 Figure 27: 12-month moving averages Black s model COE estimates for Colombia 77

79 Figure 28: 12-month moving averages Black s model COE estimates for Mexico 78

80 Figure 29: 12-month moving averages Black s model COE estimates for Peru 79

81 Figure 30: 12-month moving averages Black s model COE estimates for Venezuela 80

82 Argentina Brazil Average COE by sector ( ) Textiles Transportation & Storage Telecommunications Steal & Metal COE std by sector ( ) Average COE by sector ( ) Agriculture & Fishing Textiles Transportation & Storage Electricity Construction COE std by sector ( ) Chile Colombia Average COE by sector ( ) Chemicals & Chemical Products Steal & Metal Products Average COE by sector ( ) Textiles Oil & Gas Textiles COE std by sector ( ) Telecommunic COE std by sector ( ) Mexico Peru Average COE by sector ( ) Construction Finance & Insurance Average COE by sector ( ) Electricity 0.10 Construction Steal & Metal Products Textiles COE std by sector ( ) 0.00 Pension Funds COE std by sector ( ) Venezuela 0.60 Electricity Average COE by sector ( ) Food & Beverages Agriculture & Fishing Steal & Metal Products COE std by sector ( ) Figure 31: Mean-Variance Trade-O in Latin American COE estimates. Cross-plot of average and std by country and sector (annualized values) 82

83 LA overall mean Argentina +/- 1 std Argentina Jan-97 Mar-98 May-99 Jul-00 Sep-01 Nov-02 Jan LA overall mean Brazil +/- 1 std Brazil Jan-97 Mar-98 May-99 Jul-00 Sep-01 Nov-02 Jan-04 Figure 32: CAPM models Explanatory Power: Overall average R-Squared (across di erent model speci cations) in Argentina and Brazil 83

84 LA overall mean Chile +/- 1 std Chile Jan-97 Mar-98 May-99 Jul-00 Sep-01 Nov-02 Jan LA overall mean Colombia +/- 1 std Colombia Jan-97 Mar-98 May-99 Jul-00 Sep-01 Nov-02 Jan-04 Figure 33: CAPM models Explanatory Power: Overall average R-Squared (across di erent model speci cations) in Chile and Colombia 84

85 LA overall mean Mexico +/- 1 std Mexico Jan-97 Mar-98 May-99 Jul-00 Sep-01 Nov-02 Jan LA overall mean Peru +/- 1 std Peru Jan-97 Mar-98 May-99 Jul-00 Sep-01 Nov-02 Jan-04 Figure 34: CAPM models Explanatory Power: Overall average R-Squared (across di erent model speci cations) in Mexico and Peru 85

86 LA overall mean Venezuela +/- 1 std Venezuela Jan-97 Mar-98 May-99 Jul-00 Sep-01 Nov-02 Jan-04 Figure 35: CAPM models Explanatory Power: Overall average R-Squared (across di erent model speci cations) in Venezuela 86

87 30 Total Risk Measure (V) Systematic (EW) Standard Deviation Measures Argentina Percent Jan2000 Date Jan Standard Deviation Measures Brazil Total Risk Measure (V) Systematic (EW) 25 Percent Jan2000 Date Jan2005 Figure 36: Variance Decomposition Results by Country 87

88 18 16 Standard Deviation Measures Chile Total Risk Measure (V) Systematic (EW) Percent Jan2000 Date Jan Standard Deviation Measures Colombia Total Risk Measure (V) Systematic (EW) Percent Jan2000 Date Jan2005 Figure 37: Variance Decomposition Results by Country (cont.) 88

89 24 22 Standard Deviation Measures Mexico Total Risk Measure (V) Systematic (EW) Percent Jan2000 Date Standard Deviation Measures Peru Jan2005 Total Risk Measure (V) Systematic (EW) Percent Jan2000 Date Jan2005 Figure 38: Variance Decomposition Results by Country (cont.) 89

90 30 25 Standard Deviation Measures Venezuela Total Risk Measure (V) Systematic (EW) 20 Percent Jan2000 Date Jan2005 Figure 39: Variance Decomposition Results by Country (cont.) 90