IS THE CAPM DEAD OR ALIVE IN THE BRAZILIAN MARKET?

Transcription

1 RAE REVIEW OF APPLIED ECONOMICS Vol. 5, No. 1-2, (January-December 2009) IS THE CAPM DEAD OR ALIVE IN THE BRAZILIAN MARKET? Joe Akira Yoshino * & Edson Basos e Sanos * Absrac: The cenral purpose of his work is o es he Sharpe-Linner-Black Capial Asse Pricing Model in he Brazilian equiy marke. We have concluded ha he CAPM is dead in he Brazilian equiy marke because, besides using he marke premiums o explain he panel equiy premiums, here are also some anomalies, such as, he firm size, he equiy price-o-book value, he dividend yield, and he price-earnings raio. Furhermore, by using he recen panel coinegraion FMOLS (fully modified OLS) esimaor, his paper corroboraes he Fama & French hree-facor model (1992, 1993). This work finds also wo new hree-facor models o explain he local marke ha saisfy he non-arbirage condiion. These resuls are imporan for he purpose of asse pricing and hedging in he Brazilian equiy marke. JEL Classificaion: G12 Keywords: asse pricing, panel CAPM, Fama and French s hree-facor model, syle indexes INTRODUCTION The CAPM (Capial Asse Pricing Model) developed by Sharpe (1964), Linner (1965), and Black (1972) proposes: (i) he expeced reurn on equiy E( R i ) is a posiive linear funcion of is sysemaic risk β i ; and (ii) he marke risks β i s are enough o explain he cross-secion variaions of expeced reurns E( R i ). Consider he following regression where ER ˆ( R ) =γ +γ β +η (1) i f i 0 1 i i m (, ) m ( ) Cov R R i 2 β i =, η N( 0, σ i ) iid Var R, (2) i f ER ˆ( R ) i f m is an unbiased and consisen esimaor of ER ( R), R is he marke porfolio m reurn whose variance is given by Var ( R ), and i = 1,..., N, where N is he sock sample size. * School of Economics, Business Adminisraion and Accouning, Deparmen of Economic, Avenida Luciano Gualbero, 908, Sao Paulo, SP, Brazil, pyoshino@usp.br, edsonbasos@usp.br

2 128 Joe Akira Yoshino & Edson Basos e Sanos If we ake expecaions on boh sides of equaion (1) and verify he plausibiliy of γ 0 = 0 and m f γ 1 = ER ( R ), hen, we have a descripion of he capial securiy marke line, i.e., i f m f ER ( R) =βer ( R). (3) i The usual hypohesis es is characerized by he following consrucion m f H : γ = 0 and γ = E( R R ) (4) m f a 0 1 H : γ 0 or γ E( R R ). (5) To validae he CAPM, he inercep γ 0 mus be zero and he coefficien γ 1 has o be equal o m f he expeced marke porfolio reurn in excess of he risk-free rae ER ( R ). Despie is hisorical imporance, his hypohesis es presens wo obsacles ha weaken is saisical relevance. Firs, he esimaor is aained by a wo-sage esimaion using OLS (ordinary leas square). The firs sage of he esimaing procedure consiss of regressing he excess reurn of each individual sock R i R f m f on he marke excess reurn R R, i.e., i f m f i R R =α 0 +β( R R ) + u, (6) i where, α 0 is he inercep, u is he error erm saisfying he usual classical linear regression assumpions, and = 1,..., T i, where T i is he sample size for each individual sock ime series. In he second sage, we use he OLS mehod o esimae he parameers (γ 0, γ 1 ) of equaion (1), ha i f is, we regress he expeced excess reurn esimaor of each individual sock ER ˆ( R ) on he esimaor β ˆ i obained from he firs-sage regression, where he i f 1 esimaor ˆ( ) T i 1 ( i f ER R = Ti = R R ) i f is unbiased and consisen wih respec o ER ( R ). According o Miller and Scholes (1972), in he firs-sage, he measuremen error occurs for individual β i s. This problem causes a downward bias (oward zero) in he esimaor β ˆ i. As a consequence, in he second-sage, he securiy marke line is flaer han i should be, i.e., in equaion (1), ˆγ 1 is no an unbiased esimaor of γ 1, he rue value of expeced excess marke m f reurn ER ( R). Second, Fama and French (2004) call aenion for he posiive correlaion in he regression residuals. This problem produces he downward bias in he OLS esimaes of he sandard errors in he cross-secion regression slopes. This paper addresses hese issues for he Brazilian sock marke (BOVESPA Bolsa de Valores de São Paulo), where, in addiion o he esimaing difficulies jus presened, here is only a limied number of lised companies, causing he esimaion procedure o be more complex.

3 Is he CAPM Dead or Alive in he Brazilian Marke? 129 In heir seminal work, o aenuae he measuremen error problem, Black e al. (1972) and Fama and MacBeh (1973) aggregaed socks in porfolios sored by some crieria, such as, βi (marke risk), firm size, he book-marke value raio, ec. However, his mehodology is unfeasible o he Brazilian equiy marke because of he small-sample of equiy socks available for rading. For his reason, his work uses he fully modified OLS panel esimaor, or simply FMOLS [Im e al. (2003), Levin e al. (2002), Maddala and Wu (1999), and Pedroni (2000, 2001)], ha no only esimaes boh dimensions ogeher, i.e., he ime ( = 1,..., T) and cross-secion (i = 1,..., N), bu also deals wih he measuremen error problem, producing unbiased and consisen esimaors. Anoher advanage of using he FMOLS esimaor in our work is ha he FMOLS mehod is robus o he exisence of panel uni roos, ha is, ime-series reurns may be nonsaionary and coinegraed. We consider his approach new, since we are no aware of any work using he same economeric echnique for esing he panel CAPM. We also compare he FMOLS wih he usual OLS and check wheher ohers facors would be imporan o explain he panel equiy premium. The usual facor candidaes are firm size, equiy price-o-book value, price-earnings raio, equiy reurn, and dividend yield, variables ha have been commonly used in he lieraure. This paper is organized in he following way: Secion 2 describes he daa for composing he panel (cross-secion of socks over ime), Secion 3 presens he resuls for he panel CAPM ess, and Secion 4 resuls for alernaive models. Finally, Secion 5 conains he conclusions. THE DATA In comparison o he NYSE, he São Paulo Sock Marke (Bovespa) has a much more limied aciviy, wih around 300 lised companies and no more han 200 socks raded on a daily basis. The IBOVESPA is no only he mos widely used index in he Brazilian equiy marke bu also composed of around 52 socks. Is annual volume in 2006 was 3.1 billion of Brazilian Reais (approximaely 1.7 billion of American Dollars). Alhough here are 52 socks comprising he index, we consider only he mos represenaives ones, accouning for almos 70% of he index value, resuling in a sock sample size equal o N = Noneheless, i is imporan o remark ha he IBOVESPA mehodology is very differen from S&P500 and he Dow Jones Indusrial Average index, where marke capializaion and price level are, respecively, crucial facors for a sock o be represenaive in he index composie. Sock represenaiveness in he IBOVESPA is direcly linked o is liquidiy in erms of financial volume and number of orders placed. For example, even if a lised company has boh high marke capializaion and high sock price, bu if i is no frequenly raded in he sock exchange, han ha company will no be of grea imporance for he index. For a comprehensive discussion abou he IBOVESPA mehodology we refer o Bovespa (2008). Nowihsanding our sample consiss of only 24 socks, he IBOVESPA mehodology suggess ha i faihfully reflecs he sock exchange rading aciviy for he Brazilian equiy marke. 2 We have used monhly daa for all variables which are described below and have aemped o handle hree main issues, as follows: (A) Firs, he sample lengh of ime goes from Ocober, 1998 (1998:10) hrough Ocober, 2006 (2006:10), bu we have divided his sample in wo: one for esimaing purposes

4 130 Joe Akira Yoshino & Edson Basos e Sanos (1998:10 o 2002:12) and anoher, he forecasing period, o validae he esimaed model (2003:1 o 2006:10). The full sample does no consider boh he Asian and Russian crisis ha occurred in 1997 and 1998, bu includes boh he devaluaion of he Brazilian Real currency and he Argeninean conagion effec ha ook place in 1999 and (B) Second, we have consruced a balanced panel, i.e., for i = 1,..., T i and i = 1,..., N, represening he dimensions of he panel, where T i is he sample size of he observed reurns of each individual sock i, and N is number of socks, so ha T 1 = T 2 =... = T N. This propery enails he daa will range hroughou he enire lengh of ime and will be evenly disribued in equal ime periods. To mainain he panel balanced, when we find missing values on a specific monh in he ime-series of any of he explanaory variables, we simply eliminae ha monh from our sample; and (C) Third, we consider a 4-monh lag for hose explanaory variables involving accouning informaion, such as he companies earnings and equiy book values in order o eliminae any linear dependence ha migh exis beween hese explanaory variables and he error erm. I is imporan o remark ha CVM (Brazilian Securiies and Exchange Commission), he agency responsible for governing he capial marke in Brazil, requires ha financial repors comprising accouning informaion, such as balance shee and income saemen, are published quarerly by he companies used in our sample. When we ake hese issues ino consideraion, we obain a sample size for he esimaing period of N = 83 monhs, and a sample size for he forecasing period of N = 51 monhs. We have used he following variables o idenify poenial models, including he CAPM: i f R R : he individual equiy premium. The monhly nominal sock reurn R i minus he f nominal daily iner-bank cerificae of deposis (CD) rae R (compounded monhly). This is he dependen variable (LHS) in he panel regressions; m f R R : he marke excess reurn. The nominal IBOVESPA reurn R m minus he nominal f daily iner-bank CD rae R (compounded monhly). This variable is he usual candidae for he firs RHS variable in he regression when esing he CAPM; [ MkCap ]: he marke price of equiy or marke capializaion. To compue marke capializaion, we used he closing price for he las business day of he respecive monh muliplied by he oal number of shares obained from he las published quarerly financial repor; [ LnMk ]: firm size. This explanaory variable has been suggesed by Banz (1981) and, laer, used by Fama and French (1992). This variable may be expressed as LnMk = log( MkCap) ;

5 Is he CAPM Dead or Alive in he Brazilian Marke? 131 [BV]: [A]: [E]: [PE]: [DY]: book value of common equiy plus balance-shee deferred axes per share. Boh he book value and he number of common sock have been obained from he las published quarerly financial repor; oal book asses per share. This is a 12-monh railing variable, ha has been obained by he summaion of oal asses from he las 4 published quarerly financial repors and divided by he number of common shares obained from he las quarerly financial repor; earnings (income before exraordinary iems, plus income saemen deferred axes, minus preferred dividends) per ousanding common shares. This is a 12-monh railing variable, ha has been obained by he summaion of earnings from he las 4 published quarerly financial repors and divided by he number of common share obained from he las quarerly financial repor; Price-Earnings raio. The P/E raio is compued as sock price (P) divided by earnings (E) per share. We have used he closing price (P) for he las business day of he respecive monh and he earnings (E) jus as described above. When his raio is wo, i means ha if we pay P for he sock, hen we will recover our invesmen wih profis generaed by he company wihin wo periods; Dividend yield. Dividend/equiy price raio: dividend yield. I is he relaionship beween he accumulaed dividends paid in he period divided by he sock s price a he end of he period. This is a 12-monh railing variable, ha has been obained by summing dividends paid from he las 4 published quarerly financial repor; and, [LnMkBV]: sock profile. This variable may be expressed as LnMkBV = log ( MkCap / BV ) and represens he premium (or discoun) of he marke price relaive o is book value. When marke capializaion is small relaive o equiy book value, he sock is said o have value profile. Usually hese companies operae in maure indusries and invesors gains come primarily from dividends paid. On he oher hand, when marke capializaion is high relaive o equiy book value, hen he sock is said o have a growh profile. Growh socks operae in incipien indusries and reinves mos of is earnings, so ha invesors gains are obained mos from capial appreciaion. See Rosenberg e al. (1985) and Fama and French (1992). Boh marke capializaion (MkCap) and book value of common equiy (BV) have been obained as described above. Table 1 presens some basic saisics abou he variables o es he Brazilian CAPM. TESTING THE BRAZILIAN CAPM According o equaion (1), Linner (1965) ess wheher he inercep γ 0 is equal zero in he securiy marke line. Under he null hypohesis presened in (null), i is necessary ha he null hypohesis H 0 : γ 0 = 0 be also saisfied. Therefore, Linner (1965) has consruced a -es wih he following limiing disribuion:

6 132 Joe Akira Yoshino & Edson Basos e Sanos Table 1 Basic Saisics Poenial Variables for Tesing CAPM. Monhly Daa. Balanced Panel. Brazil: 1998: :10 Ticker Sock Risk Sock Equiy LnMk (size) LnMkBV price/ Dividend (sandard Sharpe Premium Log (sock s Log (sock s earnings Yield (DY) deviaion) raio E(R i -R cdi ) price* price/book- per share ousanding value of a (P/E) shares) share) TNLP PETR VALE USIM CSNA GGBR CMET ELET BBDC ITAU EBTP TSPP ITSA AMBV CSTB VCPA UBBR GOAU SDIA TCSL ACES ARCZ EMBR BRTP γ Var 0 ( γ ) 0 D N ( 0,1). (7) Insead, we prefer he equivalen χ 2 -es which has limiing disribuion equal o γ Var 2 0 ( γ ) 0 D χ 2 1. (8) I is worh noing ha Chan and Chen (1988) have proposed a differen approach for esing he null hypohesis in (4). Alhough, i seems ha heir es, when conrolling he effecs of firm size, has a beer power, hey relied on porfolio consrucion o esimae β i s, so ha hey could appropriaely miigae he measuremen error, following he same modus operandi inroduced by Black e al. (1972) and Fama and MacBeh (1973). As a consequence, his approach is no adequae when he number of socks is small, as i is he case of he Brazilian equiy marke.

7 Is he CAPM Dead or Alive in he Brazilian Marke? 133 Moreover, we prefer he Gibbons e al. (1989) and MacKinlay (1995) procedure, which has a more appealing inerpreaion of he above menioned chi-square saisic in erms of Sharpe Raios. 5 Considering he properies of minimum-variance fronier, Gibbons e al. (1989), and MacKinlay (1995) have showed ha he -es above is equivalen o γ SR 0 q SR m = N, 2 Var ( 0 ) 1 SR (9) γ + m where SR m is he Sharpe raio for he marke porfolio and SR q is he Sharpe raio for he angen porfolio (he bigges Sharpe raio among all socks in he panel). Using he informaion conained in column 3 of able 1 we have SR q = 1.069, which refers o he Sharpe Raio of Usiminas (icker: USIM5). 6 Figure SharpeRaio repors hese Sharpe raios for he Brazilian sock marke. Conemplaing only our sock sample (N = 24), our marke porfolio has a m f premium R R m = and sandard deviaion ( ) Var R =, resuling in a Sharpe 2 raio for he marke porfolio equal o SR m = Equaion (9) becomes Var( ) γ / γ = 1.816, 0 0 and, aking ino accoun he saisic disribuion in (8), we have a p -value of 0.18, herefore, considering a significance level of α = 0.05 or α = 0.10, we rejec he null hypohesis ha he inercep is zero for he securiy marke line of he Brazilian equiy marke in he period 1998: :10. Figure 1: Sharpe Raio. BOVESPA: 1998: :10

8 134 Joe Akira Yoshino & Edson Basos e Sanos Anoher concern is he exisence of coinegraion among he socks ime series. Table 5 shows several panel uni roo ess. These ess sugges ha we canno rejec he null hypohesis ha uni roos exis. Our approach for minimizing he occurrence of spurious regressions in a coinegraed panel is o use he FMOLS (fully modified OLS) esimaor. Table 2 repors he Brazilian CAPM regarding boh he OLS esimaor for individual equiies (esimaing mehod (1) and he FMOLS esimaor for he enire panel (esimaing mehod (2) Furhermore, he marke premium a significan facor o explain he sock premium for he panel (esimaing mehod 2). On one hand, his resul does no conradic he CAPM, however, on he oher hand, figure 2 shows a bad fi for he securiy marke line (SML). Figure 3 corroboraes his las asserion, showing ha he CAPM (esimaed by he OLS and FMOLS esimaors) is no a reasonable asse pricing model because i predics an equiy premium ha is much differen from he acual one. This problem may emerge from several reasons, such as, he failure of CAPM, he definiion of marke porfolio, he ex-pos daa, and he possible measuremen error for β i (he sysemaic risk). As a pracical maer, if hird paries use he CAPM o make buying and selling decisions of equiy in he Brazilian marke, and you are aware of his process, hen if you have a beer alernaive pricing model, as he ones ha we will propose in he nex secion, you will have a grea advanage over hese paries, so ha, you may profi a heir cos, jus like an arbirage. TESTING ALTERNATIVE MODELS The asse pricing models developed by Sharpe (1964), Linner (1965), and Black (1972) is valid jus when β i (he sysemaic risks) is enough o explain he equiy expeced excess reurns in a linear relaionship. All idiosyncraic risks are diversified and hese risks do no affec he equiy pricing. On he oher hand, several sudies find ha he cross-secional variaion in sock reurns can be explained by boh he marke risks β i s and oher facors, such as, he firm size (Banz, 1981), he book-o-marke value [Rosenberg e al. (1985); Chan e al. (1991)], he leverage (Bhandari, 1989), and he price-o-earnings raio (Basu, 1983). Fama and French (1995) proposed a hree-facor model. In addiion o β i, hey considered oher risks facors, such as SMB (he difference beween he reurn on a porfolio of small socks and he reurn on a porfolio of large socks) and HML (he difference beween he reurn on a porfolio of high-book-o-marke values and he reurn on a porfolio of low-book-omarke values). Noe ha Fama and French (1995) have inerpreed he variables SMB and HML, respecively, as firm size and sock profile. Alhough we have used he same variables (firm size and sock profile), we have calculaed hem in a disinguished manner, because Brazilian marke pracices are slighly differen from hose in he Unied Saes. As an example, he greaer a posiive SMB is he more represenaive of he group of small companies. On he oher hand, he greaer LnMk is he more depicing of he group of large companies. Hence, we need prudence while inerpreing he regression coefficiens for he models used in his paper and he one developed by Fama and French (1995). For insance, here is evidence ha small companies perform higher reurns han large companies, so one would expec a posiive regression coefficien for he firm size variable in Fama and French (1995), bu would expec a negaive coefficien in our model. In a similar fashion, he greaer a posiive HML is he more reflecing of he group of value socks, however, he greaer he LnMkBV is he more represenaive of he group of growh socks.

9 Is he CAPM Dead or Alive in he Brazilian Marke? 135 Table 2 The Brazilian CAPM Monhly Daa Esimaing Mehod 1 Esimaing Mehod 2 esimaor OLS esimaor FMOLS Socks y = a + bx y = a + bx a b R 2 a b R 2 Panel 0.74 ( 7.90 ) 1 TNLP ( 2.28) (10.01) (1.57) (11.04) 2 PETR (1.8) ( 9.50) ( 1.79) ( 11.49) 3 VALE (2.09) (2.43) ( 1.46) ( 1.99 ) 4 USIM ( 5.15) (2.61) (3.15) (5.01) 5 CSNA (4.41) (4.26) (2.51) (6.1) 6 GGBR (3.20) (4.62) (1.95) (6.78) 7 CMET ( 3.76) (1.95) (3.55) (2.30) 8 ELET ( 4.31) (4.32) (3.67) (5.09) 9 BBDC (2.49) (5.56) ( 3.72) (1.49) 10 ITAU ( 2.94) (4.81) (3.04) ( 4.65) 11 EBTP (4.20) (2.54) (5.66) ( -0.11) 12 TSPP (3.21) (7.16) (2.03) (8.81) 13 ITSA ( 2.18) (6.86) ( 3.62) (1.44 ) 14 AMBV ( 3.30) (2.28) (2.83) ( 5.13) 15 CSTB (3.19) ( 3.69) ( 1.45) (5.64) 16 VCPA (2.92) ( 2.21) ( 1.68) ( 4.25 ) 17 UBBR (3.48) (5.81) (3.85) (5.26 ) 18 GOAU (4.56) (2.32) (3.54) (3.50) 19 SDIA (4.72) (2.39) (4.86) (4.44) 20 TCSL (1.00) (5.21) ( 2.33) ( 3.1) 21 ACES (3.87) ( 4.24) (0.03) ( 5.7) 22 ARCZ (0.95) (2.26) (0.28) (3.67 ) 23 EMBR (3.6) (1.90) (3.18) (2.52) 24 BRTP ( 2.95) (5.54) (2.11) (6.86 ) Average Sd ( ): -suden. y: sock excess reurn over risk-free rae (daily inerbank CD); x: excess reurn of IBovespa over risk-free rae.

10 136 Joe Akira Yoshino & Edson Basos e Sanos Figure 2: The Brazilian Securiy Marke Line Figure 3: The CAPM model for Forecasing he Equiy Premium (ou-of-sample & cross-secion) Monhly Daa

11 Is he CAPM Dead or Alive in he Brazilian Marke? 137 This work does no es Fama and French (1995) model due o he limied number of socks in he Brazilian sock marke, bu he Fama and French (1992, 1993), which conradics he Sharpe-Linner-Black CAPM model. For he panel coinegraion regressions, wih hree facor models, he excess equiy reurn R i R f is esimaed as R R = a +β γ +β γ +β γ +η (10) i f i i i i i i i i where he panel has cross-secion dimension i = 1,..., N (number of equiies) and ime dimension = 1, 2,..., T, and esimaed parameers ˆi ˆi ˆi [ β1, β2, β 3] ha are called loading facors. Following he same reasoning of he las secion, he panel CAPM would be valid if we canno rejec he null hypohesis H : a = 0 and γ = E( R R ) and β =β = 0. (11) i m f i i 0 i i i The variables γ 2 and γ 3 are oher risk facors such as firm size, book-o-marke value, leverage ec. Under he following condiions: i m f i i γ 1 = R R, γ is he firm size; 2 γ is profile, 3 we have, as a paricular case of equaion (hree-facors), he panel version of he Fama-French hree-facor model (1992, 1993). Table 3 7 presens weny and one alernaive models in erms of panel coinegraion regarding he FMOLS (fully modified OLS) esimaor. All explanaory variables are significan. In his sense, he possible explanaory variables for he sock premium can be: (i) he marke premium; (ii) he square of marke premium (non-linear model); (iii) he firm size; (iv) he equiy profile; (v) he equiy price-earnings raio; and vi) he dividend yield. Neverheless, Fama and French (1992) poin ou ha he variables, such as, size, price-earnings raio, leverage and book-omarke (profile) are all scaled versions of he firm s sock price. As we have noed before, he coefficiens for firm size are negaive, and he coefficiens for he profile effec are posiive, ha is, large companies will underperform small companies reurns, and growh companies will overperform value companies, as we would expec. Neverheless, inerpreaion of he P/E coefficien is conroversial, since we have boh posiive and negaive regression coefficiens. A priori, we would expec a posiive coefficien, bu furher quesions should be addressed, such as he qualiy of earnings and he credibiliy of accouning pracices used o produce financial repors. If invesors have reasons o believe ha railing earnings are no imporan for predicing fuure earnings, hen he regression coefficiens could have a negaive effec on reurn. From able 3, we can verify ha when P/E is used alone or joinly wih he marke excess reurn, wheher or no squared, i has a negaive effec, bu when i is used joinly wih firm size or profile i has a posiive effec. One possible reason for he mixing sign for he coefficien of he P/E is ha firm size and profile may help invesors o idenify companies ha adop bes accouning pracices, urning P/E a more meaningful indicaor of fuure performance. Which model should be seleced? Wha would be an accepable crierion? We use he besfi crierion in erms of squared sum of forecasing errors for he cross-secion equiy premiums

12 138 Joe Akira Yoshino & Edson Basos e Sanos Table 3 Panel Coinegraion Explanaory Variables for he Equiy Premium. Monhly Daa Esimaor Explanaory variables: Financial variables only Bes-Fi Crieria FMOLS Dependen x: Marke x 2 : (Marke Size: Sock s price- P/E: sock s Dividend Sum Square Correlaion Variable: excess reurn excess LnMKT o- book value price/ Yield of differen Premiums Sock over risk- reurn over LnPVPA: Log earnings in Premiums (Acual vs. premium free rae risk-free rae) 2 (Sock s price/ per share (Acual vs. Fied) own capial Fied) per share) Model ( 3.90 ) Model (4.03 ) Model ( 4.55 ) (5.27) Model (-2.83) Model ( 3.30 ) (-2.90) Model (3.7) Model ( 5.46 ) (3.6) Model ( -293) Model E ( 3.37 ) (-3.13) Model (-5.48) Model (4.07 ) (- 5.31) Model ( -2.42) (2.3) Model (-2.86) (3.07) Model (4.64 ) ( 3.51 ) ( -2.95) Model E (3.83 ) (3.5) (-3.20) Model s-bes (4.57 ) ( 2.46) (3.4) Model E (3.84 ) (-294) (3.22) Model ( 3.92 ) (- 2.70) (-4.7) Model nd bes ( -2.47) ( 3.3) (3.07) Model rd. Bes (3.8) ( 2.90) (4.5) Model (3.47 ) (3.54 ) (4.6) (..): -suden; N = 24 (socks), T = 83 (number of monhs), max-lag = 4

13 Is he CAPM Dead or Alive in he Brazilian Marke? 139 (acual versus prediced). In oher words, according o equaion (hree-facors), for he enire panel (cross-secion of socks and esimaing period sample errors), he average of forecased equiy premiums is obained using he parameers ˆi ˆi ˆi [ β1, β2, β 3] esimaed for he esimaing period i i i sample (1998: :12) and he average of explanaory variables γ ˆ ˆ ˆ 1, γ2, γ 3 for he forecasing period sample (2003: :10). The resuls are presened in able 3, and he models are ranked boh by he forecasing error crierion and by he correlaions beween he fied and acual equiy premiums, as repored in he las wo columns of his able. Following hese crieria, we aained: (i) he model 16 in able 3 (he firs bes model due o is correlaion beween he acual premium and he prediced ones equals 1.00); (ii) he model 19 (second bes - correlaion 0.98); and; (iii) he model 20 (3rd bes- correlaion 0.97). These models are illusraed in figure 4, and, since acual equiy premiums lies almos exacly on he SML, hen if someone uses any oher differen model in heir invesmen decision process, one will be exposed o mispricing, which will evenually lead o wrong rading sraegies. As a consequence, we could denominae hese jus proposed hree-facor models as saisfying a non-arbirage condiion in he sense ha no one else in he equiy marke will have a beer price forecas han wha hese model can do. As a consequence, for he Brazilian equiy marke, hese new asse pricing models have beer performance han boh he usual CAPM and he Fama and French (1992) hreefacor model. This laer model allows is suscepible o arbirage for porfolios wih low β i s (he fied value is much differen from he acual daa). Figure 4: Three-Facor Models for Predicing he Equiy Premium (ou-of-sample & cross secion) Monhly Daa

14 140 Joe Akira Yoshino & Edson Basos e Sanos CONCLUSIONS This paper ess he CAPM for he Brazilian equiy marke using he recen panel coinegraion echnique, specifically, he FMOLS (fully modified OLS) esimaor. This approach is quie useful for emergen markes where here are a limied number of lised companies in he sock exchanges. Black-Jensen-Scholes or Fama-MacBeh approach of composing seleced porfolios is only possible for more developed markes where housands of equiies are raded. Our main conclusion is ha he Brazilian CAPM is dead for wo reasons. Firs, he inercep for he securiy marke line is no zero. Second, we find oher possible relevan explanaory variables for he panel sock premium: (i) he marke premium; (ii) he square of he marke premium (non-linear CAPM); (iii) he firm size; (iv) he equiy profile; (v) he equiy priceearnings raio; and vi) he dividend yield. Given hese candidaes, we may describe he nonarbirage condiion as he model having is square sum of forecasing errors of acual versus he prediced premium equals zero. The hree models ha approximae he non-arbirage condiion mos are: (i) The firs bes-model (correlaion 1.00 beween he acual and prediced premiums) has he following risk facors: a) bea; b) equiy profile, and c) firm size. Alhough his model reveals some similariies wih he model proposed by Fama and French (1992), heir model does no saisfy he non-arbirage condiion for he Brazilian equiy marke. The key difference beween Fama and French (1992) and his model is how o calculae he explanaory variables (firm size and sock profile) and how he model parameers were esimaed. We used he FMOLS esimaor whereas Fama and French (1992) used a wo-sage OLS procedure (ime series dimension in he firs-sage and cross-secion dimension for he securiy marke line in he secondsage); (ii) The second bes-model (correlaion 0.99 beween acual and fied premiums) is composed of: (a) sock profile; (b) firm size; and (c) equiy price-earnings raio; (iii) The hird bes model (correlaion 0.97) has he explanaory variables: (a) equiy profile; (b) equiy price-earnings raio; and (c) dividend yield. Noe ha, here is no marke premium as an explanaory variable in he las wo models. For furher developmens, we sugges o check he Fama and French (1992) hree-facor model for he NYSE, bu using he recen panel coinegraion echnique suggesed in his paper, insead of he usual wo-sage OLS procedure. In summary, besides he Fama and French (1992) hree-facor model, we found wo addiional hree-facor models wihou he marke premium as he firs facor. Furhermore, our hree-facor models are closes o absence of arbirage. As poined before, he non-arbirage condiion is violaed by Fama-French model for porfolios wih low β i s. Finally, he CAPM is also dead for he Brazilian equiy marke due o oher facors ha, in concurrence, explain beer he equiy premium. Therefore, he new alernaive facor models beer provide boh pricing and rading sraegies for he Brazilian sock marke.

15 Is he CAPM Dead or Alive in he Brazilian Marke? 141 Table 4 Number of socks Sock code Company Weigh in he Index (*) 1 TNLP4 Telemar PN PETR4 Perobrás PN VALE5 Vale do Rio Doce PNA USIM5 Usiminas PNA CSNA3 Sid. Nacional ON GGBR4 Gerdau PN CMET4 CAEMI PN ELET6 Elerobras PNb BBDC4 Bradesco PN ITAU4 Iaubanco PN EBTP4 Embrael PN TSPP4 Brasil Telec PN ITSA4 Iausa PN AMBV4 AMBEV PN CSTB4 Sid. Tubarão PN VCPA4 VCP PN UBBR11 Unibanco UNT GOAU4 Gerdau Me PN SDIA4 SADIA PN TCSL4 TIM Par PN ACES4 ACESITA PN ARCZ6 Aracruz PNB EMBR4 Embraer PN BRTP4 Brasil T Par PN 1.00 (*) Valid for Sep Table 5 Panel Uni Roo Tess. Brazil: 1998: Uni Roo Tess Equiy Marke LnMKT: Log PE: sock s Dividend premium premium [sock s price* price/earnings yield shares ousanding] per share Levin-Lin rho-saisic Levin-Lin -rho-saisic Levin-Lin ADF-saisic IPS ADF-saisic N = 24, T = 83, heero rends, subraced ime mean. ACKNOWLEDGMENT The auhor acknowledges he financial suppor provided by he Brazilian Cenral Bank, and assers ha he opinions in his aricle do no represen hose of he Brazilian Cenral Bank. References Ball, Ray (1978), Anomalies in Relaionships beween Securiies Yields and Yield-surrogaes. Journal of Financial Economics, 6(2-3), Banz, Rolf W. (1981), The Relaionship beween Reurn and Marke Value of Common Socks. Journal of Financial Economics, 9(1), 3 18.

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