Working Paper Nº 12
Martin Grandes, Demian Panigo and Ricardo
The Cost of Equity in Latin America
The American University of Paris and CEF
PSE-ENS, Univ. de la Plata, CEIL-PIETTE and CEF
The aim of this paper is twofold. First, it applies standard Capi-tal 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 1986-2005, it comes up with more than 312,000 COE esti-mates 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 Introduction 3
2 Survey of the Literature 5
2.1 What do we know about emerging countries and in particular
about Latin America? . . . 14
3 Stylized Facts, Data and Methodology 16 3.1 Stylized facts for Latin America . . . 17
3.2 Dataset . . . 25
3.3 Econometric and statistical methodology to estimate the CAPM COE . . . 28
3.3.1 Data frequency . . . 28
3.3.2 Optimal sample size . . . 29
3.3.3 The assumption of real market integration . . . 29
3.3.4 Sovereign spreads calculation and pricing into the CAPM framework . . . 31
3.3.5 Risk-free interest rate and emerging market bond yield stability . . . 34
3.3.6 Corrections for illiquidity . . . 35
3.3.7 Beta (systematic risk loading) robustness or instability . . 36
3.3.8 The econometric method . . . 37
3.3.9 Negative COE estimates . . . 39
3.3.10 Weighting strategies . . . 39
3.4 Variance Decomposition . . . 40
4 Empirical results for Latin American markets 40 4.1 Asset pricing model speci…cation . . . 41
4.2 The COE Derived from Black’s CAPM Beta estimates . . . 43
4.3 The explanatory power of CAPM . . . 50
4.4 Variance Decomposition Results . . . 52
5 Conclusions 53
6 Appendix 63
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 opportunity1 cost of
eq-uity 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 macro-economic policy framework, macromacro-economic 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 pub-licly 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 devel-opmental 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 af-fordable 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 diver-si…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 rel-ative (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
1In 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.
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 discus-sions 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 coun-tries: 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 1997-2004 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¤er-ent approaches to the measuremdi¤er-ent and determinants of COE, focusing on the advantages and disadvantages of di¤erent CAPM versions. Section 3 presents
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.
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 mean-variance approach. In his theory, risk adverse investors, with a one-period in-vestment 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 re-turn or maximize the portfolio rere-turn 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 ex-istence 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 be-cause 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 di-versi…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(Ri) Rf = iM[E(RM) Rf] 8i= 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
2One possible interpretation is that Beta coe¢ cient captures the risk that each dollar
invested in a particular asset contributes to the market portfolio.
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 ex-ogenous factors4. 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.
Ri =E[Ri] + i1[F1] + i2[F2] +:::+ iK[FK] + i 8i= 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 empiri-cal literature that searches which and how many factors a¤ect stock returns. Typically these factors are macroeconomic factors such as: innovations in in‡a-tion expectain‡a-tions, innovain‡a-tions in the Gross Nain‡a-tional Product or GDP estimates, unexpected changes in investor’s con…dence and unexpected shifts in the yield curve.
3Equation 1 is typically tested using the following linear econometric models: R
i+ i RM;t + i;tor Ri;t Rf;t = i RM;t Rf;t + i;t(depending on whether the risk free rate is assumed to be constant or not), where i and iare estimated using time series regressions for each individual stock.
4Economists can think about this di¤erence as a demand side and a supply side approach.
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 project5.
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 inter-est. 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 prag-matic 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 frame-work with the aim of making its assumptions more realistic. One of this ex-tensions 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 intertem-poral maximizer in selecting his portfolio will take into account the relationship between current and future returns6. In other words, if the available invest-ment 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 avail-able opportunity set changes over time. As a result, in equilibrium investors
5In 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.
6Quoting 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
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 assets7) that is supposed to
capture the shifts in the investment opportunity set.
E(Ri) Rf = iM[E(RM) Rf] + N[E(RN) Rf] 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 set-ting. 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 consump-tion is perfectly negatively correlated with the marginal utility of an addiconsump-tional 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 re-turn 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), RC 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 observable8.
7Merton 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.
8It 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
E(Ri) Rf = iC[E(RC) Rf] 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 ( sj0 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(Ri) r0=[E(RG) Rf] iG+E[s10+r r0] i1+ (5) :::+E[sn0+r r0] in
From a practitioner’s perspective, the question of whether these models pro-vide 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.
9As 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.”
1 0Notice 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.
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 Interna-tional CAPM. He analyzed the case of the Swiss multinaInterna-tional 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 Interna-tional CAPM adding multilateral currency risk to global market portfolio risk). Equation (6) shows the resultingnested model.
Ri;t= i+ iM[RM;t] + iG[RG;t] + iM N ER[RM N ER;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(RM;tandRG;t) and …nally RM N ER;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 France11.
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
1 1Another example is Mishra and O’Brien (2001) who provided more evidence on the
dif-ference 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 mar-kets sample of ADRs and di¤erences of 57 and 70 basis points respectively for a 48 emerging markets sample of ADRs.
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 esti-mates. Basu (1977) showed that stocks with high earnings-price ratios had higher future returns than predicted by regular CAPM. Banz (1981) demon-strated that the same happened with those stocks with lowermarket capitaliza-tion. Bhandari (1988) useddebt to equity ratiosand found that stocks associated with relatively high debt to equity ratios yielded higher returns than those es-timated 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 iden-tical results for returns on stocks with highbook 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 mar-ket portfolio as new factors together with the marmar-ket portfolio in the CAPM equation. Equation 7 illustrates the three factor model.
E(Ri) Rf = iM[E(RM) Rf] + iS[E(SM Bt)] + iH[E(HM Lt)] (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. HM L(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 samples12.
1 2Using a sample of stocks from the Tokyo Stock Exchange from 1971 to 1988, Chan, Hamao,
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 ulti-mately COE. The main questions raised by this literature are: why idiosyncrac-tic risk matters? how much risk not priced in stock markets is idiosyncraidiosyncrac-tic? 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 risk13 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 port-folio 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.
1 3We apply this measure to our sample in section 4.
for U.S. retirement saving plans also suggests naïve diversi…cation in investor’s strategies. People are found to spread their contributions evenly across invest-ment options (a n1 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 in-complete information problem that could lead to undiversi…ed portfolios. Levy, probably inspired by the role of transaction costs and taxes that restrict port-folio diversi…cation, assumed an imperfect market and imposed a constraint on the number of securities that an individual could hold in his portfolio14. The
empirical implications of these models support the role of idiosyncratic risk in stock pricing and consequently in COE estimation15.
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 Levy16.
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
1 4For 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.
1 5Levy´ 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:
Ri= 1 ^
1+ 2 2i . 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)): Ri RF = i[RM RF]+ i where the null hypothesis is i= 0andi= 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)
1 6Nontraded assets that have been studied extensively in the literature are private
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).
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 rel-evant 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 mul-tifactor 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 199517 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 authors18 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 styl-ized 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-1 7The sample period di¤er for some countries. See Fama and French (1998). 1 8See Bekaert and Harvey (1997a) among others.
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 coun-tries semi deviations are lower than standard deviations, for emerging councoun-tries semi deviations are generally higher than standard deviations (see for example Grootveld and Salomons (2002))
As mentioned earlier, one theoretical implication of …nancial market integra-tion is the enlargement of the diversi…caintegra-tion opportunities set. These addiintegra-tional 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 correla-tions within these markets are also generally low (Wong Dávila (2003)). Harvey (1991), for example, reports that the average cross-country correlation of de-veloped 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, Har-vey 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…ca-tion 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 1991-1993, 1995 and 2000-2002 show statistically insigni…cant cross country-correlations, the lat-ter became larger and statistically signi…cant during the sub-periods 1994-1996 (Mexican Crisis) and 1997-1999 (South East Asia, Russian and Brazilian Crises). Other authors have focused on the impact of …nancial liberalizations, oc-curred during the late 80’s and early 90’s, on emerging stock markets correla-tions. 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
for the choice of the reference portfolio (market portfolio) as well as on the spec-i…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 “investabil-ity” 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-ante19 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 1982-1997) he corroborates that the Fama and French three- factor model e¤ectively provides a signi…cant explanation of returns20: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 corre-lated 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).
Stylized Facts, Data and Methodology
In this Section, we present the stylized facts for Latin American stock markets over the period 1990-2004. Then we introduce the dataset and analyze some sta-tistical properties of our data, and lastly we explain and discuss the econometric estimation procedure conducive to CAPM COE estimates.
1 9“Ex-ante” valuation models such as Gordon (1997) incorporate investor’s expectations
data on of stock prices in pricing formulas.
2 0Fama 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 coun-tries) and 8.7% (equally weighted councoun-tries).
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 domes-tic 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 1990-2004.
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 macro-economic 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 reforms21 carried out from the early nineties
on-wards, 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 alterna-tive 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
2 1These included domestic …nancial liberalization, the opening of the capital account,
so-cial 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 frame-work, such as laws intended to protect minority shareholder rights.
0% 20% 40% 60% 80% 100% 120% 140% 160% 1990 1992 1994 1996 1998 2000 2002 2004
Latin America Emerging Asia Developed Markets
Figure 1: Aggregated Stock Market Capitalization as Share of Ag-gregated GDP by Selected Groups. Latin America is Argentina, Brazil, Chile, Colombia, Mexico . Emerging Asia is Korea, Malaysia, Singapore and Thai-land. Developed Markets are Canada, Germany, Italy, Japan, UK and US. Consid-ered 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.
0% 20% 40% 60% 80% 100% 120% 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
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 Ex-changes
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 interna-tionalization trend in Latin American …rms publicly traded in stock markets22.
By the year 2000, 18.2% of Latin American traded …rms had gone interna-tional 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 interna-tionalization 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 1990-2004. Market liquidity for the countries in our sample grew until 1995-1996 and
2 2According 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.
0 100 200 300 400 500 600 700 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
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 1990.
Further evidence supporting the illiquidity phenomena in Latin America is shown in Table 1. For a sample23 of more than 127000 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 trouble-some. 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 prob-lem is exacerbated by common buy and hold investment strategies pursued by institutional investors.
2 3An description of the data is presented in next section
2 4See …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.
0% 5% 10% 15% 20% 25% 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
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 1993 3.6 4.8 17.9 6.0 4.1 5.6 13.6 1994 4.2 8.6 16.8 16.0 4.9 3.9 32.0 1995 10.8 14.1 15.5 31.0 12.0 7.9 30.2 1996 4.5 13.8 15.6 23.8 8.4 12.2 25.6 1997 5.1 17.7 16.0 16.6 5.7 15.2 16.6 1998 12.5 26.1 20.6 21.4 8.4 24.1 20.3 1999 20.1 22.7 21.9 33.7 10.0 38.3 26.6 2000 26.1 20.4 20.8 33.9 12.5 33.4 28.3 2001 35.8 22.8 21.1 33.9 13.7 44.9 31.8 2002 28.1 24.9 22.8 28.7 15.0 40.4 36.9 2003 14.0 20.5 20.4 24.1 14.1 36.0 38.7 2004 8.4 14.1 15.0 13.9 6.5 25.9 26.8 TOTAL 15.6 18.3 18.8 24.7 10.4 26.7 27.3
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 1990-2004. 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
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.
-1 0 1 2 3 4 5 6 1990m1 1995m1 2000m1 2005m1 date
Dow Jones MERVAL Argentina IBC Venezuela IGBC Colombia
-1 0 1 2 3 4 5 6 1990m1 1995m1 2000m1 2005m1 date
IPSA Chile IPyC Mexico
IGBVL Peru BOVESPA Brazil
Figure 5: Across-country comparison of local market annualized total returns (12 month moving average, in USD). Source: Economatica.
Stock Market Index N Min Max Mean Median Std Mean/Std Skewness Kurt osis Norm. Pr Fir st O. A C MERVA L Argentina 170 -0.423 1.190 0.017 0.022 0.158 0.105 2.5 20.6 0.000 0.09 BOVE SPA Brazil 170 -0.411 0.741 0.029 0.014 0.157 0.188 0.7 5.5 0.000 0.06 IPSA Chile 170 -0.309 0.207 0.017 0.016 0.077 0.221 -0.2 4.1 0.038 0.21* IGBC C olombia 170 -0.223 0.379 0.017 0.011 0.096 0.180 0.8 5.0 0.000 0.40* IPyC Mexico 170 -0.402 0.241 0.015 0.024 0.099 0.155 -0.9 5.4 0.000 0.14* IGBVL P eru 170 -0.286 0.604 0.023 0.011 0.116 0.200 1.5 9.3 0.000 0.08 IBC Venezuela 170 -0.419 0.483 0.010 -0.006 0.128 0.075 0.5 4.4 0.003 -0.02 DOW JON ES U SA 170 -0.151 0.106 0.010 0.013 0.042 0.230 -0.5 4.1 0.003 -0.09 Table 2: Descriptive Sta tistics of USD Total Returns from US and selected Latin American Stock Markets (1990-2004). Note: * stands for si gnificant autocorr elation coe ffic ients at 0. 05. Source: E conomatica. 24
Our dataset is an unbalanced panel spanning monthly observations for 921 pub-licly traded …rms in 1986-2004 -127,000 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 (1997-2004) in order to come up with comparable …gures.
We gather data from Datastream, Economatica, Morgan Stanley, and re-gional 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-,
MSCI26total returns, local market total returns27 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 1993.
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.
2 5Because J.P. Morgan EMBI+ data are not available for the whole sample period, we
com-plement 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).
2 6As usual, the Morgan Stanley Capital International index is used as a proxy of the global
2 7For Argentina, Brazil, Chile, Colombia, Mexico, Peru and Venezuela local market total
re-turns are obtained using MERVAL, BOVESPA, IPSA, IGBC, IPyC, IGBVL and IBC indexes, respectively.
AR BR CL CO MX PE VE TOTAL
Agriculture & Fishing 5 1 16 3 10 1 36
Chemicals & Chemical Products 6 19 8 1 2 5 3 44
Construction 3 14 3 9 3 32
Electrical Equipment & Electronic Products 2 9 1 3 15
Electricity 4 36 19 2 6 2 69
Finance & Insurance 8 25 15 16 15 11 11 101
Food & Beverages 5 18 16 3 16 13 2 73
Machinery & Equipment 1 10 2 5 18
Mining 3 6 2 3 15 1 30
Motor Vehicles & Related 3 16 1 20
Non-Metallic Mineral Products 4 4 5 6 7 6 3 35
Non-specified 4 4
Oil & Gas 10 8 2 2 1 23
Others 13 44 36 6 18 16 5 138
Paper & Paper Products 4 9 2 2 3 2 22
Pension Funds 36 3 39
Software & Data 1 1 2
Steal & Metal Products 4 29 7 7 4 4 55
Telecommunications 3 21 7 2 7 2 2 44
Textiles 3 26 5 2 3 9 3 51
Transportation & Storage 1 5 7 3 1 17
Wholesale & Retail Trade 1 10 16 2 21 3 53
TOTAL 81 307 211 47 120 115 40 921
Table 3: Number of listed stocks included in the sample by country and sector (unbalanced database, 1986-2004)
Sector AR BR CL CO MX PE VE TOTAL
Agriculture & Fishing 682 67 2630 342 796 144 4661
Chemicals & Chemical Products 912 3284 1007 144 256 578 482 6663
Construction 426 2248 157 745 215 3791
Electrical Equipment & Electronic Products 296 1757 192 404 2649
Electricity 447 3742 3382 102 573 220 8466
Finance & Insurance 896 4129 1793 1597 1601 1457 1499 12972 Food & Beverages 653 3169 2676 334 1941 1439 312 10524
Machinery & Equipment 148 1907 314 648 3017
Mining 637 1051 261 390 1785 84 4208
Motor Vehicles & Related 434 3163 127 3724
Non specified 508
Non-Metallic Mineral Products 533 607 895 634 920 895 467 4951
Oil & Gas 1008 1416 372 288 3 3087
Others 1322 5784 5182 771 1779 1835 728 17401
Paper & Paper Products 598 1768 382 277 382 270 3677
Pension Funds 5413 288 5701
Software & Data 131 117 248
Steal & Metal Products 393 5473 1147 924 568 472 8977
Telecommunications 364 1928 1042 116 604 294 99 4447
Textiles 427 4828 575 228 261 1091 402 7812
Transportation & Storage 50 564 1244 312 150 2320
Wholesale & Retail Trade 148 1313 2173 217 2248 303 6402
TOTAL 9868 47784 31821 5086 13146 13172 5329 126206
Table 4: Number of non-missing observations by country and sector (unbalanced database, 1986-2004) Year AR BR CL CO MX PE VE TOTAL 1986 1097 1097 1987 1327 1327 1988 1579 1579 1989 1815 1108 2923 1990 1909 1399 46 3354 1991 1950 1513 21 48 3532 1992 335 2000 1661 344 419 309 5068 1993 527 2165 1820 233 388 514 352 5999 1994 648 2395 1933 306 587 726 372 6967 1995 696 2529 2037 336 733 845 368 7544 1996 726 2651 2097 332 824 984 387 8001 1997 743 2781 2231 385 986 1128 429 8683 1998 786 2984 2300 457 1210 1240 453 9430 1999 816 3256 2328 484 1286 1247 448 9865 2000 884 3429 2341 492 1301 1256 452 10155 2001 937 3510 2349 511 1332 1286 444 10369 2002 931 3524 2314 527 1376 1268 425 10365 2003 931 3489 2243 519 1385 1191 408 10166 2004 908 3394 2147 504 1373 1068 388 9782 TOTAL 9868 47784 31821 5086 13146 13172 5329 126206 Table 5: Number of observations by country and year
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.
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 228:
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.
3.3.1 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 obser-vations 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 covari-ances -between illiquid stock and local market excess returns- would come out.
2 8We suggest the non-dedicated reader to skip this section without any loss of generality
and move on to section 4
2 9In the case of developed-country stock returns, Daves et al. (2000) show that high
fre-quency 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. Further-more, 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)
Assuming that the lower the frequency the lower the expected number of ob-servations 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).
3.3.2 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
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.
3.3.3 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¤er-ently, 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 …nan-cially 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
As noted in the literature survey, Koedijket al. (2002) derive their nested equation from a generalization of Stultz (1995), combining the multifactor In-ternational CAPM equation of Solnik (1983) and Sercu (1980)
Ri;t= i+ iG[RG;t] + iM ER[RM ER;t] + i;t (8) (whereRi;t,RG;tandRM ER;tstand for asseti, global portfolio and multilateral nominal exchange rate returns, respectively) with the standard Sharpe-Lintner’s domestic CAPM equation
Ri;t= i+ iM[RM;t] + i;t (9)
(whereRM;tis the return of the local market portfolio). Using 8 to price the local market portfolio, we get:
RM;t= M + M G[RG;t] + M M ER[RM ER;t] +ei;t (10) Then, plugging 10 in 9 yields a modi…ed CAPM which takes into account the global factors set out in ICAPM:
Ri;t= i+ M iM+ M G iM[RG;t]+ iM ER iM[RM ER;t]+ iMei;t+ i;t (11) Equalizing 11 and 8 yields the testable hypothesis, namely: H0: M G iM= iG and iM ER iM = iM ER 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 toRG;tandRM ER;ti.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:
Ri;t= i+ iM[RM;t] + iG[RG;t] + iM N ER[RM N ER;t] + i;t (12) to test the null hypothesis H0 : iM RER = 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 H0 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 miss-pricing 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