Disponível em hp://www.anpad.org.br/rac RAC, Rio de Janeiro, v. 21, n. 6, ar. 6, pp. 851-874, Novembro/Dezembro, 2017 hp://dx.doi.org/10.1590/1982-7849rac2017170027 Applicabiliy of Invesmen and Profiabiliy Effecs in Asse Pricing Models Márcio André Veras Machado 1 Rober Faff 2 Suelle Cariele de Souza e Silva 1 Universidade Federal da Paraíba 1 Universiy of Queensland 2 Arigo recebido em 28.01.2017. Úlima versão recebida em 16.06.2017. Aprovado em 28.06.2017.
M. A. V. Machado, R. Faff, S. C. de S. e Silva 852 Resumo Ese esudo eve por objeivo invesigar se invesimeno e renabilidade são precificados e se explicam parcialmene as mudanças dos reornos das ações no mercado de capiais brasileiro, conforme o modelo de cinco faores de Fama e French (2015). Por meio de regressões em série emporal e em cross-secion, observou-se que B/M, momeno e liquidez, são associados com os reornos das ações, enquano que invesimeno e renabilidade não apresenaram significância. Observou-se, ambém, que não exise prêmio por invesimeno no Brasil. Porano, moivado pelo desempenho do B/M, do momeno e da liquidez para o mercado brasileiro, bem como pelo fraco desempenho da renabilidade e do invesimeno, pode-se consaar que o modelo de cinco faores de Keene e Peerson (2007) apresenou desempenho superior a odos os ouros modelos, especialmene quando comparado ao modelo de cinco faores de Fama e French (2015). Palavras-chave: modelos de precificação de aivos; renabilidade; invesimeno; liquidez. Absrac This sudy aims o invesigae wheher invesmen and profiabiliy are priced and if hey parially explain he variaions of sock reurns in he Brazilian sock marke, according o he Fama and French s (2015) five-facor model. By using ime series and cross-secion regression, we found ha book-o-marke, momenum and liquidiy are associaed wih sock reurns whereas invesmen and profiabiliy were no significan. We also found ha here is no invesmen premium in Brazil. Therefore, moivaed by he imporance of B/M, momenum and liquidiy o he Brazilian sock marke, as well as by he poor performance of profiabiliy and invesmen, we documen ha Keene and Peerson s (2007) five-facor model is superior o all oher models, especially he five-facor model by Fama and French (2015). Key words: asse pricing model; profiabiliy; invesmen; liquidiy. RAC, Rio de Janeiro, v. 21, n. 6, ar. 6, pp. 851-874, Novembro/Dezembro, 2017, www.anpad.org.br/rac
Applicabiliy of Invesmen and Profiabiliy Effecs 853 Inroducion Various models have been developed in search of facors ha could improve he explanaory power of he Capial Asse Pricing model (CAPM), as well as capure anomalies in asse pricing. Fama and French (1993) developed he hree-facor model, namely marke according o he CAPM firm size and book-o-marke raio (B/M). Carhar (1997) idenified he momenum facor and realised ha he hree-facor model and he CAPM were unable o explain i (Fama & French, 2004). So Carhar (1997) added momenum o Fama and French s (1993) hree-facor model, hus creaing he four-facor model, which produced superior empirical evidence. Keene and Peerson (2007) analysed he imporance of liquidiy as a risk facor in asse pricing models, and added i o Carhar s (1997) fourfacor model, hus concluding ha liquidiy is priced and explains par of sock reurn variaions, improving he model s explanaory power. Size, book-o-marke raio, momenum and liquidiy are some characerisics ha influence companies reurns. Oher characerisics also help explain reurns, such as facors associaed wih expeced profiabiliy and a company s expeced invesmen. Fama and French (2006, 2008, 2015), Hou, Xue and Zhang (2015) and Novy-Marx (2013) idenified ha profiabiliy is posiively relaed o average reurn. Fama and French (2006, 2008), Xing (2008) and Chen, Novy-Marx and Zhang (2010) documened he negaive relaion beween company invesmen and reurn. In addiion, Chen e al. (2010) proposed an alernaive hree-facor model composed by marke, profiabiliy and invesmen risk facors. According o Fama and French (2006), he exising lieraure idenifies differences in he average reurn of socks associaed wih book-o-marke, profiabiliy and invesmen risk facors, wihou simulaneously conrolling, however, for he said facors. Fama and French (2015) verified ha par of he variaion in sock reurns is lef unexplained by he hree-facor model hey developed in 1993. Then, moivaed by valuaion heory (Fama & French, 2006), as well as by empirical evidence documened in he lieraure abou he relaion beween reurn and profiabiliy (Novy-Marx, 2013) and reurn and invesmen (Cooper, Gulen, & Shill, 2008; Lam & Wei, 2011; Li, Becker, & Rosenfeld, 2012; Lipson, Moral, & Shill, 2011; Waanabe, Xu, Yao, & Yu, 2013; Xing, 2008), Fama and French (2015) and Hou e al. (2015) added profiabiliy and invesmen facors o he radiional asse pricing models. Fama and French (2015) added profiabiliy and invesmen facors o heir hree-facor model, hus creaing a five-facor model. As main resuls, hey found ha he five-facor model performed beer han he hree-facor model. In addiion, hey observed ha model performance was no sensiive o he way facors were consruced. Finally, jus like Xing (2008), Fama and French (2015) verified ha, by adding profiabiliy and invesmen facors, B/M facor urned ou o be redundan in explaining reurns. Hou e al. (2015) added profiabiliy and invesmen o marke and size facors, hus creaing an alernaive four-facor model. Aiming o assess he performance of he said model, hey compared he performance of he proposed model o ha of he hree-facor model by Fama and French (1993) as well as ha of he four-facor model by Carhar (1997), o explain 80 anomalies documened in he lieraure. Hou e al. (2015) found ha he proposed model performed beer han he hree-facor and four-facor models in explaining several of he significan anomalies. Given he above background, our paper aims o invesigae wheher invesmen and profiabiliy are priced and if hey parially explain he variaions of sock reurns in he Brazilian sock marke, according o Fama and French s (2015) five-facor model. To achieve his objecive we ook he following seps: inquire if invesmen and profiabiliy effecs exis in he Brazilian sock marke; invesigae if invesmen and profiabiliy mus be added o asse pricing models as predicive variables of sock reurns, afer conrolling he effec of oher risk facors presen in he lieraure; and, compare he performance of muli-facor models, as well as he impac of including profiabiliy and invesmen facors on he performance of said models. RAC, Rio de Janeiro, v. 21, n. 6, ar. 6, pp. 851-874, Novembro/Dezembro, 2017, www.anpad.org.br/rac
M. A. V. Machado, R. Faff, S. C. de S. e Silva 854 The analysis of he join performance of invesmen and profiabiliy in sock reurns as well as he use of such variables as risk facors in asse pricing models in developing counries has been rare. In addiion, he findings by Griffin (2002) do no suppor he noion ha i is beneficial o exend mulifacor models o a global conex; raher, he specific counry should be aken ino consideraion. This paper conribues o he lieraure on muli-facor models by offering inernaional evidence ouside he U.S. of he applicabiliy of invesmen and profiabiliy as risk facors in asse pricing models, especially in a developing counry, as is he case of Brazil, whose capial marke is he mos developed among Lain American counries. Moreover, he five-facor model expands he CAPM model which is a single-facor model commonly adoped o esimae sock reurns as i adds invesmen and profiabiliy risk facors, and i beer explains sock reurn variaions. This paper also conribues by providing suppor o researchers and capial marke professionals o choose he mos appropriae pricing model. By using a model ha beer explains sock reurn variaions, researchers and marke professionals will have a beer esimae of he firm s capial cos for capial budgeing and sock assessmen; i may also be used o esimae expeced reurns, o assess he performance of muual funds, and o analyse marke efficiency. Finally, more empirical researches ha demonsrae he applicabiliy and performance of alernaive models in markes oher han he U.S.A. allow proving ha alernaive models are superior (or, perhaps, ha hey are no superior) o he radiional ones, no only in he U.S. marke bu also in he inernaional specrum (Amman, Odoni, & Oesch, 2012). Empirical evidence of muli-facor models boh in he U.S. and in he inernaional marke suggess ha a grea par of reurns is sill lef unexplained (Fama & French, 2015; Hou, Xue, & Zhang, 2015; Walkshäusl & Lobe, 2014). Thus, new models ha add new facors and use new mehodological consrucions are welcome. Consequenly, his sudy also conribues o he lieraure by using a liquidiy facor, which was no aken ino consideraion in Fama and French (2015) or Hou e al. (2015), alhough i was found o be fundamenal in he Brazilian marke (Machado & Medeiros, 2011). Alhough he models by Fama and French (2015) and Hou e al. (2015) have a common focus, namely he inclusion of profiabiliy and invesmen facors, hey differ when i comes o implemenaion. They also reach inconclusive resuls, which jusifies he need for addiional empirical evidence, mainly ouside he U.S. marke, where said models were developed. Finally, his sudy inends o compare he performance of he five-facor model by Fama and French (2015) wih he five-facor model applied in Brazil by Machado and Medeiros (2011), which performed beer han he oher pricing models. There are five secions afer his inroducion. The nex secion presens daa, variables and summary saisics. Then, we addresses empirical analysis and resuls, as well as he oulines he model s performance. The nex secion presens a furher analysis and, finally, he conclusions. Daa, Variables and Summary Saisics Daa used in his sudy were colleced from Economaica, a daa base largely used in Brazil, which conains accouning and marke informaion of he companies lised a B3 (Brasil, Bolsa e Balcão). Daa includes companies ha are boh acive and inacive in he capial marke, in order o avoid survivor bias. The sampled period chosen was 1 June 1997 o 30 June 2014. The year 1997 was chosen since he operaionalisaion of some variables use daa relaed o wo previous years, which culminaes in using daa from 1995. Daa prior o 1995 in Brazil are affeced by high inflaion and lack of currency sandardisaion. This sudy used boh common socks and preferred socks, since in he Brazilian sock marke preferred socks ofen presen higher liquidiy han common socks. Thus, using only common socks as is he case of some inernaional sudies ha used daa on Brazil (Walkshäusl & Lobe, 2014; Waanabe e al., 2013) may lead o resuls ha are no necessarily dependable. The following companies were excluded from he analysis: (a) financial firms, because according o Fama and French (1992) a high book-o-marke raio does no mean he same for non-financial and financial companies; he raio for RAC, Rio de Janeiro, v. 21, n. 6, ar. 6, pp. 851-874, Novembro/Dezembro, 2017, www.anpad.org.br/rac
Applicabiliy of Invesmen and Profiabiliy Effecs 855 he laer is influenced by heir high degree of leverage; (b) firms ha did no presen marke value se on 31 December and 30 June of each year, for hese values serve o compue he book-o-marke raio and company size; (c) firms ha presened negaive equiy on 31 December of each year, as his affecs book-o-marke raio; (d) firms ha did no have monhly quoaions for 24 consecuive monhs, 12 monhs prior or 12 monhs afer porfolio formaion, considering ha his procedure reduces he influence of small-sized and young firms in he resuls (Anderson & Garcia-Feijó, 2006); and, (e) firms ha did no presen informaion concerning accouning daa. Daa of 188 socks (48% of he populaion), on average, were analysed per year. The year 2003 presened a minimum of 98 socks (27% of he populaion) and 2012 a maximum of 266 socks (69% of he populaion). The size of his sample is saisfacory, compared o oher sudies, mainly inernaional sudies ha used Brazilian sock daa. Machado and Medeiros (2011) and Walkshäusl and Lobe (2014) analysed, on average, 149 and 178 socks per year, respecively. As o marke capialisaions, in he 1997-2013 period, he sample corresponded o a minimum of 54% in 1998 and a maximum of 94% in 2010. In his sudy sample, 48% of he companies represen 85% of marke capialisaion in he analysed period. The explanaory variables analysed were size, B/M, momenum, liquidiy, invesmen and profiabiliy and he Table 1 shows he summary saisics. Specifically, size (ME) is he marke equiy (price imes shares ousanding) by he end of June of year. B/M is he book value of he Equiy in December of year -1 divided by he marke value of Equiy in December of year -1. Momenum (RET11) is he accumulaed reurn in he 11-monh period, saring July of year -1 and finishing May of year. Liquidiy (LIQ) is he negoiaed volume, represened by he annual average volume negoiaed, in Brazilian Reais, for he sock in he period from July of year -1 o June of year, according o he suggesion of Machado and Medeiros (2011). Profiabiliy (E/A) is calculaed as Earning Before Ineres and Taxes (EBIT) of year -1 divided by he operaional asse of year -1. Invesmen (INV) is he change in oal asse beween years -2 and -1 divided by he oal asse of year -2. Variables were measured a company level, following he orienaion by Aharoni, Grundy and Zeng (2013). Table 1 Summary Saisics for he Explanaory Variables Variable ME B/M RET11 LIQ E/A INV Average 4,123 1.24 0.11 205 0.10 1.98 SD 14,320 1.68 0.53 920 0.27 94.15 25 h 126 0.41-0.17 1 0.03 0.01 Median 645 0.80 0.12 9 0.09 0.09 75 h 3,054 1.43 0.38 93 0.17 0.21 CV 3.47 1.36 4.82 4.49 2.7 47.55 Noe. This able shows he summary saisics for he explanaory variables, including average, sandard deviaion, 25 h percenile, median, 75 h percenile and he coefficien of variaion (CV). Size (ME) is he marke equiy (price imes shares ousanding) by he end of June of year. B/M is he book value of Equiy in December of year -1 divided by he marke value of he Equiy in December of year -1. Momenum (RET11) is he accumulaed reurn in he 11-monh period saring July of year -1 and finishing May of year. Liquidiy (LIQ) is he negoiaed volume, represened by he annual average volume negoiaed, in Brazilian Reais, for he sock in he period from July of year -1 o June of year. Invesmen (INV) is he change in oal asse beween years -2 and -1 divided by he oal asse of year -2. Profiabiliy (E/A) is calculaed as Earning Before Ineres and Taxes (EBIT) of year -1 divided by he operaional asse of year -1. On average, he marke value of Brazilian companies is around 4 billion Reais (R$); sandard deviaion is R$14 billion (Table 1). The curren average volume negoiaed is around 205 million Reais; sandard deviaion is 920 million Reais. The median of he marke value and ha of he average volume negoiaed in he period analysed is around R$645 million and R$1 million, respecively. This indicaes ha he marke value and he negoiaed volume are no homogeneous among companies. Companies' B/M raio and he accumulaed reurn in he las 11 monhs are, on average, 1.24 and 11%, respecively. Profiabiliy and invesmen are, on average, 0.10 and 1.98, respecively. RAC, Rio de Janeiro, v. 21, n. 6, ar. 6, pp. 851-874, Novembro/Dezembro, 2017, www.anpad.org.br/rac
M. A. V. Machado, R. Faff, S. C. de S. e Silva 856 Empirical Analysis and Resuls Reurns o sored porfolios Aiming o know, iniially, how variables drive he variaion of reurns, socks were grouped according o a characerisic of ineres (explanaory variable). Table 2 shows he average monhly reurn for he quiniles formed on size, B/M, momenum, liquidiy, invesmen and profiabiliy variables. Specifically, by he end of June of each year, socks were arranged in ascending order according o he variable of ineres (size, B/M, momenum, liquidiy, invesmen and profiabiliy). They were sored ino five porfolios based on he quinile breakpoins. From July of year o June of year +1, he average monhly value-weighed reurn of each porfolio was calculaed. The porfolios were rebalanced annually, by he end of June of each year. Table 2 Average Monhly Reurn of Porfolios Formed on Size, Book-o-Marke, Momenum, Liquidiy, Invesmen and Profiabiliy Low 2 3 4 High H-L Panel A: Suden s -es Size-based porfolios 0.012** 0.019*** 0.014** 0.017*** 0.014** 0.002 B/M-based porfolios 0.023*** 0.017*** 0.009 0.005-0.002-0.025*** Momenum-based porfolios -0.006 0.010 0.015** 0.021*** 0.031*** 0.037*** Liquidiy-based porfolios 0.033*** 0.020*** 0.021*** 0.014** 0.012** -0.021** Profiabiliy-based porfolios 0.015** 0.009 0.015** 0.015** 0.018*** 0.003 Invesmen-based porfolios 0.017*** 0.007 0.010 0.017*** 0.014** -0.003 Panel C: Wilcoxon es Size-based porfolios 0.012*** 0.019*** 0.014*** 0.017*** 0.014*** 0.002 B/M-based porfolios 0.023*** 0.017*** 0.009** 0.005* -0.002-0.025*** Momenum-based porfolios -0.006 0.010** 0.015*** 0.021*** 0.031*** 0.037*** Liquidiy-based porfolios 0.033*** 0.020*** 0.021*** 0.014*** 0.012*** -0.021 Profiabiliy-based porfolios 0.015*** 0.009** 0.015*** 0.015*** 0.018*** 0.003 Invesmen-based porfolios 0.017*** 0.007** 0.010*** 0.017*** 0.014*** -0.003 Noe. By he end of June of each year, socks were arranged in ascending order according o he variable of ineres (size, B/M, momenum, liquidiy, invesmen and profiabiliy). They were sored ino five porfolios based on he quinile breakpoins. From July of year o June of year +1, he average monhly value-weighed reurn of each porfolio was calculaed. All variables are defined in secion Daa, Variables and Summary Saisics. *** p-value <0.01, ** p-value <0.05, * p-value<0.10. Table 2 shows ha he average monhly reurns of he spread porfolios are saisically significan for he porfolios consruced on B/M, momenum and liquidiy, according o he Suden s -es (excep for liquidiy, he resuls found by he Wilcoxon es raify he resuls obained by he Suden s -es). Based on B/M raio, companies wih high B/M should presen superior reurns o companies wih a low raio. Table 2 shows resuls conrary o wha was expeced, considering ha he average monhly reurn of he porfolio wih he highes B/M is inferior o ha of he porfolio wih he lowes B/M, generaing a premium of 2.5% per monh (p-value < 0.01), revealing evidence of he absence of B/M raio for he period sudied, and raifying previous resuls in Brazil (Machado & Medeiros, 2011, 2012). Companies wih he highes accumulaed reurns in he las 11 monhs reach average monhly reurns superior o RAC, Rio de Janeiro, v. 21, n. 6, ar. 6, pp. 851-874, Novembro/Dezembro, 2017, www.anpad.org.br/rac
Applicabiliy of Invesmen and Profiabiliy Effecs 857 companies wih he wors accumulaed reurns in he las 11 monhs, generaing a premium of 3.7% per monh (p-value < 0.01). Finally, porfolios formed by low-liquidiy companies reach superior reurns o he porfolios formed by high-liquidiy socks, generaing a premium of 2.1% per monh (p-value < 0.05). These resuls also raify previous resuls obained in Brazil for he aforemenioned variables (Machado & Medeiros, 2011, 2012). Table 2 also shows ha for size, profiabiliy and invesmen, he average monhly reurns of he spread porfolios are no saisically significan, according o parameric and non-parameric ess, alhough hey presen he expeced sign, excep for size, considering ha more profiable companies presen higher average monhly reurn han less profiable companies. Table 2 also evidences ha more conservaive companies, in erms of invesmens, showed a higher average monhly reurn han companies ha inves more, and ha bigger companies had superior reurn o smaller companies. Therefore, since he five-facor model of Fama and French (2015) includes profiabiliy and invesmen as risk facors, his can be inerpreed as he firs sign of he model's poor capaciy o explain sock reurns in he Brazilian marke. On he oher hand, i signals a possible superioriy of he model ha conains B/M, momenum and liquidiy risk facors. Anoher issue was observed: he behaviour of he average reurns of he porfolios formed on he combinaion of size, B/M, profiabiliy and invesmen, which served as a basis o analyse he performance of muli-facor models (secion Model Performance). Table 3, Panel A, shows he average value-weighed reurns of he 25 porfolios consruced on he combinaion of five groups of size and five groups of B/M raio (5 x 5). In each column of Panel A of Table 3 wha can be seen is he size effec while he value effec can be seen on each line. Only in he firs column (low B/M) can he size effec be seen; companies of lower marke value have higher average reurns when compared o companies of higher marke value. Therefore, growh companies (low B/M) of low marke value reach superior average reurn o growh companies of high marke value. There is no evidence of B/M effec, since all reurns relaed o he high column are lower han he reurns in he low column, which raifies he resuls of Table 3. Table 3 Average Monhly Reurns of Porfolios Formed on Size, Book-o-Marke, Invesmen and Profiabiliy Panel A: 5 x 5 porfolios formed on size and B/M Low 2 3 4 High Small 0.026 0.017 0.011 0.006-0.008 2 0.026 0.029 0.015 0.012-0.003 3 0.018 0.025 0.015 0.004-0.006 4 0.031 0.020 0.014 0.012 0.003 Big 0.020 0.022 0.011 0.011-0.001 Panel B: 2 x 4 x 4 porfolios formed on size, B/M and profiabiliy Small B/M Low 2 3 High B/M Low 2 3 High Low E/A 0.034 0.020 0.008-0.005 Low E/A 0.016 0.015 0.014-0.001 2 0.028 0.022 0.006-0.006 2 0.024 0.020 0.004-0.004 3 0.028 0.020 0.008 0.000 3 0.020 0.018 0.005 0.001 High E/A 0.026 0.017 0.001-0.003 High E/A 0.020 0.020 0.003 0.002 Big Coninues RAC, Rio de Janeiro, v. 21, n. 6, ar. 6, pp. 851-874, Novembro/Dezembro, 2017, www.anpad.org.br/rac
M. A. V. Machado, R. Faff, S. C. de S. e Silva 858 Table 3 (coninued) Panel C: 2 x 4 x 4 porfolios formed on size, B/M and invesmen Small B/M Low 2 3 High B/M Low 2 3 High Low Inv 0.028 0.016 0.000-0.002 Low Inv 0.026 0.023 0.015-0.001 2 0.028 0.028 0.013 0.001 2 0.019 0.026 0.006-0.003 3 0.030 0.017 0.012 0.001 3 0.021 0.016 0.012 0.000 High Inv 0.022 0.012 0.003-0.016 High Inv 0.025 0.009 0.004-0.003 Noe. Panel A shows he average value-weighed monhly reurns of he 25 porfolios consruced from he combinaion of five size groups and five B/M raio groups. Panel B shows he average value-weighed monhly reurns of he 32 porfolios consruced from he combinaion of wo size groups, four B/M raio groups and four profiabiliy-relaed groups. Panel C presens he average value-weighed monhly reurns of he 32 porfolios consruced from he combinaions of he wo size groups, four B/M raio groups and four invesmen-relaed groups. Panel B of Table 3 shows he average reurns of he 32 porfolios consruced on he combinaion of wo size groups, four B/M raio groups and four profiabiliy-relaed groups. Each column of Panel B of Table 3 shows profiabiliy effec and each line shows value effec. Regardless of he company size, he B/M effec is conrary o wha was expeced, since all reurns relaed o he high column are lower han he reurns in he low column, which raifies previous resuls. To companies of high marke value, excep for he hird quarile (in he column), he average reurns of more profiable companies is superior o hose of less profiable companies, which suggess evidence of a profiabiliy effec. Ye, for companies of low marke value, a profiabiliy effec can be observed only when he company has a high B/M raio. Panel C of Table 3 shows he average reurns of 32 porfolios consruced on he combinaion of size, B/M and invesmen variables. These porfolios were consruced he same way as he porfolios for Panel B; only he hird variable (profiabiliy) was subsiued for by he variable invesmen. Jus like Panel B, regardless of he company size, he B/M effec is conrary o wha was expeced. For companies of high marke value, in all quariles (in he column), he average reurns of companies ha inves less is superior o hose of companies ha inves more, which suggess evidence of invesmen effec. For companies of low marke value, however, invesmen effec is seen only in he firs wo quariles (in he column). Predicabiliy of reurns Variables ha produce grea spreads in porfolios average reurns are candidaes for common risk facors. However, hose variables ha are used o consruc porfolios and, consequenly, calculae spreads may no be associaed wih average reurns. Therefore, i is necessary o examine if he variables used in asse pricing models (Equaions 2 o 7) explain average reurns. For his reason, he approach by Fama and MacBeh (1973) was adoped o esimae he coefficiens of ineres in Equaion 1. RAC, Rio de Janeiro, v. 21, n. 6, ar. 6, pp. 851-874, Novembro/Dezembro, 2017, www.anpad.org.br/rac Big Re = + ME + BM RET11 LIQ + E/A INV (1) Where: 1 2 3 Re is he sock annual reurn from July of year o June of year +1; Size (ME) is he naural logarihm of he company s marke equiy (price imes ousanding shares) by he end of June of year. Book-o-marke (B/M) is he book value of he Equiy in December of year -1 divided by he marke value of he Equiy in December of year -1. Momenum (RET11) is he accumulaed reurn in he 11- monh period, beginning July of year -1 and finishing May of year. Liquidiy (LIQ) is he naural logarihm of he negoiaed volume, represened by he annual average volume negoiaed, in Reais, for he sock in he period of July of year -1 o June of year. Profiabiliy (E/A) is calculaed as Earning 4 5 6
Applicabiliy of Invesmen and Profiabiliy Effecs 859 Before Ineres and Taxes (EBIT) of year -1 divided by he operaional asse of year -1. Invesmen (INV) is he change in oal asse beween years -2 and -1 divided by he oal asse of year -2. The esimaion of Equaion 1 will provide evidence of he sign of he coefficien of he variables, which mus be negaive for size, liquidiy and invesmen and posiive for B/M, momenum and profiabiliy. In addiion, hrough he saed equaions, i is possible o see which variables explain sock average reurns. Table 4 shows he average slopes and he p-value for each variable examined in his sudy. The annual sock reurn is regressed on he variables of ineres. Regressions are conduced for all, small and big companies. Size groups are defined from he arrangemen of companies ino wo groups (Small and Big), based on he median of he company's marke value in June of year. Table 4 shows ha reurns are posiively associaed wih size, momenum and profiabiliy and negaively associaed wih B/M raio, liquidiy and invesmen. The sign of he relaion beween sock reurns and company size was no persisen among he models. Meanwhile, he sign of he B/M raio is persisen and significan in all models; however, i presens he opposie of he expeced sign, which raifies he findings of Tables 1 and 2 and previous empirical evidence (Machado & Medeiros, 2011, 2012). The coefficien associaed wih B/M raio ranges from -0.088 (p-value < 0.01) o -0.065 (p-value < 0.01). Table 4 Fama-MacBeh Regressions of Annual Reurns on Deerminan Reurn Variables Inercep ME B/M RET11 LIQ RENT INV F sa All 0.335 ** 0.002-0.065 *** 0.348 *** -0.021 ** 0.085-0.039 20.46 *** Small 0.579 *** -0.016-0.067 *** 0.368 *** -0.024 ** 0.101-0.074 16,48 *** Big 0.224 0.007-0.088 *** 0.345 *** -0.016-0.042-0.061 25,63 *** Noe. This able shows he average slopes and he coefficiens from cross-secion regressions. All variables are defined in secion Daa, Variables and Summary Saisics. Size groups are defined from he arrangemen of companies ino wo groups (Small and Big), based on he median of he company's marke value in June of year. *** p-value <0.01, ** p-value <0.05, * p-value<0.10. As o momenum and liquidiy, he coefficiens have he expeced sign, wih values of 0.345 (pvalue < 0.01) and 0.368 (p-value < 0.01) and -0.024 (p-value < 0.05) and -0.016 (p-value > 0.10), respecively, as well as saisical significance, in all analysed models. Meanwhile, invesmen and profiabiliy do no influence sock reurns, since, in all analysed models, heir coefficiens did no presen saisical significance, alhough he expeced sign was observed. We also verified wheher he resuls found were sensiive o company size, soring socks ino Small and Big, according o Table 4; he conclusion is ha resuls are qualiaively similar. Since invesmen and profiabiliy variables are included as risk facors in Fama and French s (2015) five-facor model, and i does no add explanaory power o reurns, his may be inerpreed as he second sign of he model s poor capaciy o explain sock reurns in he Brazilian marke. On he oher hand, raifying he resuls of Table 2, in all models, B/M, momenum and liquidiy were significan, which indicaes a possible superioriy of he model conaining he said variables as risk facors. Asse pricing models and facor consrucion To analyse asse pricing model performance, he hree ses of porfolios in Table 3 were regressed on he asse pricing models, according o Equaions 2 o 7. The firs se represens he sandard way of esing asse pricing models as saed in he lieraure, whereas he wo las ses are alernaive forms ha include profiabiliy and invesmen. RAC, Rio de Janeiro, v. 21, n. 6, ar. 6, pp. 851-874, Novembro/Dezembro, 2017, www.anpad.org.br/rac
M. A. V. Machado, R. Faff, S. C. de S. e Silva 860 E(R ) - R E(R c, ) - R f, = + b m, f, + s(smb) h( HML) (2) E(R ) - R E(R c, ) - R f, = + b m, f, + s(smb) h( HML) w( WML) (3) E(R ) - R E(R c, ) - R f, = + b m, f, + s(smb) h( HML) w( WML) l( LMH ) (4) E(R ) - R E(R c, ) - R f, = + b m, f, + r( RMW) c( CMA) (5) E(R ) - R E(R c, ) - R f, = + b m, f, + s(smb) r( RMW ) c( CMA) (6) E(R ) - R E(R c, ) - R f, = + b m, f, + s(smb) h( HML) r( RMW ) c( CMA) (7) Where: R p, is he porfolio reurn in monh ; R f, is he risk-free rae in monh, adoping he Selic rae as proxy; R p, R f, is he excess reurn of he porfolio; R m, is he marke reurn in monh ; R m, R f, is marke risk premium; SMB, HML, WML, LMH, RMW and CMA are, respecively, size, book-omarke, momenum, liquidiy, profiabiliy and invesmen facors, all in monh ;, b, s, h, w, l, r and c are he esimaed coefficiens in he regressions; and ε is he random error erm. Equaion 2 refers o he hree-facor model of Fama and French (1993), henceforh called model 1. Equaion 3 refers o he four-facor model of Carhar (1997), henceforh model 2. Equaion 4 refers o he five-facor model of Keene and Peerson (2007), henceforh model 3. Equaion 5 refers o he hree-facor model of Chen e al. (2010), henceforh model 4. Equaion 6 refers o he adaped fourfacor model of Hou e al. (2015), henceforh model 5. Equaion 7 refers o he five-facor model of Fama and French (2015), henceforh model 6. Apar from he models presened above, we analysed oher asse pricing models consruced from he combinaion of he facors in model 6. In addiion, we esed anoher five-facor model: i incorporaes liquidiy facor ino he adaped four-facor model by Hou e al. (2015), henceforh called model 7. Two oher models were esed: one model combines size wih profiabiliy and liquidiy, he oher model combines size wih invesmen and liquidiy. The choice for analysing sock liquidiy ogeher wih oher variables is due o he fac ha liquidiy premium exiss in Brazil (Machado & Medeiros, 2012); anoher jusificaion is he superior performance of Keene and Peerson s (2007) five-facor model in Brazil (Machado & Medeiros, 2011). Tables 1 and 3 raify he imporance of liquidiy in he Brazilian marke. For consrucing he facors of he pricing models, we carried ou a procedure o examine if he way facors are consruced was imporan in he asse pricing models es. The approach is similar o ha in Fama and French (2015). Therefore, hree ses of facors were used o capure reurn sandards verified in Table 2. In he firs approach (Table 5), facors were consruced independenly, and socks were classified in 2 x 3 ses of combinaions, where size ineraced wih he oher variables of ineres separaely. RAC, Rio de Janeiro, v. 21, n. 6, ar. 6, pp. 851-874, Novembro/Dezembro, 2017, www.anpad.org.br/rac
Applicabiliy of Invesmen and Profiabiliy Effecs 861 Table 5 Consrucion of Size, Book-o-Marke, Profiabiliy, Invesmen, Momenum and Liquidiy Facors Sor Breakpoins Facors and heir componens Consrucion of models 6, 5, 4 and 1 2 x 3 combinaion of ME and B/M, ME and E/A, ME and INV ME: median B/M: perceniles E/A: 30 h and 70 h perceniles INV: 30 h and 70 h perceniles SMB B/M = (SH + SN + SL)/3 (BH + BN + BL)/3 SMB E/A = (SR + SN + SW)/3 (BR + BN + BW)/3 SMB INV = (SC + SN + SA)/3 (BC + BN + BA)/3 SMB = (SMB B/M + SMB E/A + SMB INV )/3 HML = (SH + BH)/2 (SL+ BL)/2 RMW = (SR + BR)/2 (SW + BW)/2 CMA = (SC + BC)/2 (SA + BA)/2 Consrucion of models 3 and 2 2 x 3 combinaion of ME and B/M, ME and MOM, ME and LIQ ME: median B/M: 30 h and 70 h perceniles MOM: 30 h and 70 h perceniles LIQ: 30 h and 70 h perceniles SMB B/M = (SH + SN + SL)/3 (BH + BN + BL)/3 SMB Mom = (SW + SN + SL)/3 (BW + BN + BL)/3 SMB LIQ = (SH + SN + SL)/3 (BH + BN + BL)/3 SMB = (SMB B/M + SMB Mom+ SMB LIQ )/3 HML = (SH + BH)/2 (SL + BL)/2 WML = (SW + BW)/2 (SL + BL)/2 LMH = (SL + BL)/2 (SH + BH)/2 Consrucion of model 7 2 x 3 combinaion of ME and E/A, ME and INV, ME and LIQ ME: median E/A: 30h and 70h perceniles INV: 30h and 70h perceniles LIQ: 30h and 70h perceniles SMB E/A = (SR + SN + SW)/3 (BR + BN + BW)/3 SMB INV = (SC + SN + SA)/3 (BC + BN + BA)/3 SMB LIQ = (SH + SN + SL)/3 (BH + BN + BL)/3 SMB = (SMB E/A + SMB INV + SMB LIQ)/3 RMW = (SR + BR)/2 (SW + BW)/2 CMA = (SC + BC)/2 (SA + BA)/2 LMH = (SL + BL)/2 (SH + BH)/2 Noe. Variables were arranged independenly in 2 x 3 ses of combinaions, where size ineraced wih he oher variables of ineres separaely (B/M, E/A, INV, RET11, LIQ). Size breakpoin was he median of he marke values of he companies in he sample; for he oher variables breakpoins were he 30 h and 70 h perceniles corresponding o heir value. SMB facors (small minus big), HML (B/M-relaed high minus low), RMW (profiabiliy-relaed robus minus weak), CMA (invesmenrelaed conservaive minus aggressive), WML (momenum-relaed winner minus loser), LMH (liquidiy-relaed low minus high). Source: Adaped from Fama, E. F., & French, K. R. (2015). A five-facor asse pricing model. Journal of Financial Economics, 116(1), 1-22. hp://dx.doi.org/10.1016/j.jfineco.2014.10.010. The second and hird approaches of facor consrucion are similar o he firs approach; he only difference is he way variables are combined. In he second approach, facors are consruced independenly; socks were sored in 2 x 2 ses of combinaions. Size ineraced wih he oher variables of ineres separaely. Meanwhile, in he hird approach, all variables are joinly conrolled and socks are classified in 2 x 2 x 2 x 2 ses of combinaions, where all variables inerac wih one anoher. All facors were calculaed monhly. The marke facor for all models was obained by he difference beween he average monhly value-weighed reurn of all sample socks and he risk-free rae; Selic rae was adoped as proxy. Table 6 shows he summary saisics for he facors. The B/M, momenum and liquidiy risk facors were significan in all he analysed models, whereas invesmen was no significan in any of he analysed models, regardless of he form of facor consrucion. Profiabiliy was sensiive o he way RAC, Rio de Janeiro, v. 21, n. 6, ar. 6, pp. 851-874, Novembro/Dezembro, 2017, www.anpad.org.br/rac
M. A. V. Machado, R. Faff, S. C. de S. e Silva 862 facor was consruced; i was significan only when he facor was se in a 2 x 3 form (size and profiabiliy). Finally, he differen versions of he facors are highly correlaed, ranging from 0.896 o 0.995 for he SMB facor, from 0.722 o 0.862 for he profiabiliy facor, from 0.793 o 0.822 for he invesmen facor, from 0.734 o 0.880 for he liquidiy facor and from 0.887 o 0.918 for he momenum facor. These resuls raify hose obained from Tables 1 and 3, srenghening he evidence ha Fama and French s (2015) five-facor model has a poor capaciy o explain sock reurns in he Brazilian marke, as well as he possible superioriy of he model conaining B/M, momenum and liquidiy as risk facors. Table 6 Mean for he Monhly Reurns of he Facors Models 6, 5, 4 and 1 Models 3 and 2 2 x 3 Facors 2 x 2 Facors 2 x 2 x 2 x 2 Facors 2 x 3 Facors 2 x 2 Facors Rm - Rf 0.002 0.002 0.002 Rm - Rf 0.002 0.002 0.002 SMB 0.003 0.003 0.003 SMB 0.001 0.002 0.000 2 x 2 x 2 x 2 Facors HML -0.028 *** -0.020 *** -0.018 *** HML -0.028 *** -0.020 *** -0.019 *** RMW 0.007 ** 0.004-0.018 WML 0.029 *** 0.019 *** 0.015 *** CMA 0.000-0.003 0.001 LMH 0.010 ** 0.006 ** 0.005 * Model 7 2 x 3 Facors 2 x 2 Facors Rm - Rf 0.002 0.002 0.002 SMB 0.003 0.003 0.001 2 x 2 x 2 x 2 Facors RMW 0.007 ** 0.004 0.004 * CMA 0.000-0.003-0.001 LMH 0.010 ** 0.006 ** 0.005 * Noe. Rm Rf is he difference beween he average monhly value-weighed reurn of all socks of he sample and he risk-free rae (Selic); SMB is he size facor; HML is he B/M-based value facor; RMW is he profiabiliy facor; CMA is he invesmen facor, LMH is he liquidiy facor; and WML is he momenum facor. Since VIF values are below 5, here is no collineariy beween he variables, in any of he analysed models. *** p-value <0.01, ** p-value <0.05, * p-value<0.10. Model Performance This secion assesses how well asse pricing models explain he excess reurn of hree ses of porfolios. Thireen pricing models were analysed, six of which were proposed by oher auhors and were duly esed; he remaining models were consruced from he combinaion of he risk facors analysed in his sudy. In all, four hree-facor models, six four-facor models and hree five-facor models were analysed. If pricing models capure all he variaion of he expeced reurn, he inercep mus be zero for all porfolios. Thus we ran he GRS es proposed by Gibbons, Ross and Shanken (1989), which ess if all esimaed inerceps joinly equal zero. Based on he resuls of he GRS saisic, mos of he analysed models are incomplee descripions of he expeced reurn, since all inerceps of he analysed models are joinly saisically differen from zero. Due o his evidence, his sudy sough he less imperfec model, as suggesed by Fama and French RAC, Rio de Janeiro, v. 21, n. 6, ar. 6, pp. 851-874, Novembro/Dezembro, 2017, www.anpad.org.br/rac
Applicabiliy of Invesmen and Profiabiliy Effecs 863 (2015). The aim was o invesigae how profiabiliy, invesmen and liquidiy facors improved he descripion of he reurns. Table 7 shows he GRS es saisic, he average bsolue value of he inerceps ( α i ) and he cross-secion variaion of expeced reurns explained by he model (adjused R2). The Panel A, where he dependen variable of he regressions is he reurn of he porfolios consruced from size and B/M, shows ha he model ha conains marke, size, B/M, momenum and liquidiy risk facors (model 3) performed bes, according o he GRS saisic, average inercep and adjused R2. The subsiuion of momenum and liquidiy for profiabiliy and invesmen considerably worsens he GRS saisic and oher saisics, which shows ha model 3 is superior o model 6. Panel A of Table 7 shows ha, regardless of he way facors were consruced, he GRS saisic of he model consiued by marke, size and B/M (model 1) is very close o he GRS saisic of he model consiued by marke, size, B/M, profiabiliy and invesmen (model 6) as well as o varians of model 6, which excludes one of he facors (profiabiliy or invesmen). The models ha do no have he HML facor are he models ha have he highes GRS saisic and he highes absolue inerceps, on average, which suggess ha HML is imporan in he explanaion of reurns. Therefore, profiabiliy and invesmen do no aggregae value o mos of he models; also, such facors do no subsiue for HML. These findings diverge from he resul found by Fama and French (2015) in he US marke, which showed ha he five-facor model (marke, size, B/M, profiabiliy and invesmen) had he lowes GRS saisic, suggesing ha i was he leas imperfec model in explaining reurns, and ha i performed beer han he hree-facor model by Fama and French (1993) as well. The resuls shown in Panel A of Table 7 do no change when he reurns of he porfolios consruced from size, B/M and invesmen (2 x 4 x 4) are used as dependen variables, according o Panel C. Resuls from Panel C show ha model 3 capures all variaion of he reurns of he porfolios, when he facors are consruced as 2 x 2 x 2 x 2, no rejecing he null hypohesis ha he inerceps are joinly equal o zero. The excepion is Panel B of Table 7, in which facors are consruced as 2 x 3 and 2 x 2, where he five-facor model by Fama and French (2015), called model 6 in his sudy, performs beer han he oher models, especially he five-facor model by Keene and Peerson (2007), called model 3 in his paper. However, i is worh menioning ha profiabiliy and invesmen mus be observed joinly, herefore, as 2 x 2 x 2 x 2, since heir reurns are condiioned, according o he fundamenal analysis heory (Fama & French, 2006). In addiion, i is imporan o menion ha profiabiliy is one of he facors in Fama and French s (2015) model and his may explain is slighly beer performance. RAC, Rio de Janeiro, v. 21, n. 6, ar. 6, pp. 851-874, Novembro/Dezembro, 2017, www.anpad.org.br/rac
M. A. V. Machado, R. Faff, S. C. de S. e Silva 864 Table 7 Summary Saisics for Asse Pricing Models GRS Panel A: 25 porfolios consruced from Size and B/M RAC, Rio de Janeiro, v. 21, n. 6, ar. 6, pp. 851-874, Novembro/Dezembro, 2017, www.anpad.org.br/rac i R 2 GRS i R 2 GRS i R 2 2 x 3 Facors 2 x 2 Facors 2 x 2 x 2 x 2 Facors MKT SMB HML 2.144 *** 0.006 0.534 2.434 *** 0.007 0.538 2.599 *** 0.008 0.531 MKT SMB HML WML 2.092 *** 0.006 0.561 2.267 *** 0.006 0.561 1.799 0.005 0.539 MKT SMB HML WML LMH 1.969 *** 0.005 0.567 2.362 *** 0.006 0.574 1.797 0.005 0.553 MKT RMW CMA 3.741 *** 0.008 0.437 3.893 *** 0.008 0.445 4.072 *** 0.008 0.444 MKT SMB RMW CMA 3.726 *** 0.008 0.528 3.941 *** 0.008 0.540 4.202 *** 0.009 0.523 MKT SMB HML RMW CMA 2.139 *** 0.006 0.553 2.455 *** 0.007 0.567 2.503 *** 0.007 0.549 MKT SMB RMW 3.770 *** 0.008 0.514 3.959 *** 0.008 0.518 4.245 *** 0.009 0.497 MKT SMB CMA 3.978 *** 0.009 0.520 4.000 *** 0.009 0.533 4.168 *** 0.009 0.522 MKT SMB HML RMW 2.143 *** 0.006 0.540 2.544 *** 0.007 0.551 2.614 *** 0.008 0.534 MKT SMB HML CMA 2.150 *** 0.006 0.548 2.376 *** 0.007 0.562 2.497 *** 0.007 0.549 MKT SMB RMW CMA LMH 3.325 *** 0.008 0.530 3.865 *** 0.009 0.549 3.802 *** 0.008 0.522 MKT SMB RMW LMH 3.372 *** 0.008 0.516 3.949 *** 0.009 0.536 3.837 *** 0.008 0.511 MKT SMB CMA LMH 3.573 *** 0.009 0.522 3.851 *** 0.009 0.542 3.913 *** 0.009 0.517 Panel B: 32 porfolios consruced from Size, B/M and Profiabiliy MKT SMB HML 1.239 0.005 0.494 1.542 ** 0.006 0.501 1.438 * 0.006 0.503 MKT SMB HML WML 1.382 0.005 0.518 1.573 ** 0.005 0.514 1.032 0.005 0.494 MKT SMB HML WML LMH 1.603 *** 0.005 0.524 1.805 *** 0.005 0.523 1.146 0.005 0.503 MKT RMW CMA 2.483 *** 0.009 0.427 2.569 *** 0.010 0.437 2.657 *** 0.010 0.431 MKT SMB RMW CMA 2.446 *** 0.009 0.496 2.569 *** 0.010 0.506 2.633 *** 0.010 0.498 MKT SMB HML RMW CMA 1.217 0.005 0.522 1.477 * 0.005 0.532 1.361 0.005 0.528 Coninues
Applicabiliy of Invesmen and Profiabiliy Effecs 865 Table 7 (coninued) GRS RAC, Rio de Janeiro, v. 21, n. 6, ar. 6, pp. 851-874, Novembro/Dezembro, 2017, www.anpad.org.br/rac i R 2 GRS i R 2 GRS i R 2 MKT SMB RMW 2.477 *** 0.009 0.485 2.581 *** 0.010 0.485 2.663 *** 0.010 0.482 MKT SMB CMA 2.636 *** 0.010 0.477 2.652 *** 0.010 0.486 2.652 *** 0.010 0.485 MKT SMB HML RMW 1.226 0.005 0.511 1.539 ** 0.006 0.517 1.433 * 0.006 0.518 MKT SMB HML CMA 1.231 0.005 0.506 1.490 * 0.005 0.518 1.373 0.005 0.516 MKT SMB RMW CMA LMH 2.413 *** 0.009 0.500 2.476 *** 0.009 0.512 2.528 *** 0.009 0.491 MKT SMB RMW LMH 2.448 *** 0.009 0.489 2.536 *** 0.009 0.498 2.553 *** 0.009 0.480 MKT SMB CMA LMH 2.606 *** 0.010 0.481 2.539 *** 0.010 0.493 2.644 *** 0.009 0.474 Panel C: 32 porfolios consruced from Size, B/M and Invesmen MKT SMB HML 1.766 ** 0.007 0.474 2.018 *** 0.007 0.483 2.003 *** 0.008 0.485 MKT SMB HML WML 1.743 ** 0.006 0.501 1.905 *** 0.006 0.504 1.335 0.006 0.486 MKT SMB HML WML LMH 1.652 ** 0.006 0.503 1.838 *** 0.007 0.512 1.278 0.006 0.495 MKT RMW CMA 3.158 *** 0.009 0.409 3.290 *** 0.010 0.421 3.290 *** 0.010 0.415 MKT SMB RMW CMA 3.134 *** 0.009 0.482 3.322 *** 0.010 0.493 3.354 *** 0.010 0.484 MKT SMB HML RMW CMA 1.789 *** 0.006 0.507 2.034 *** 0.007 0.521 1.904 *** 0.007 0.515 MKT SMB RMW 3.147 *** 0.010 0.456 3.229 *** 0.010 0.460 3.394 *** 0.011 0.452 MKT SMB CMA 3.315 *** 0.010 0.470 3.405 *** 0.011 0.481 3.376 *** 0.010 0.480 MKT SMB HML RMW 1.778 *** 0.006 0.482 2.009 *** 0.007 0.495 1.993 *** 0.008 0.492 MKT SMB HML CMA 1.781 *** 0.007 0.499 2.034 *** 0.007 0.513 1.918 *** 0.007 0.511 MKT SMB RMW CMA LMH 2.748 *** 0.009 0.483 2.997 *** 0.010 0.498 3.034 *** 0.009 0.476 MKT SMB RMW LMH 2.776 *** 0.009 0.457 2.927 *** 0.009 0.473 3.049 *** 0.009 0.451 MKT SMB CMA LMH 2.922 *** 0.010 0.472 3.054 *** 0.010 0.487 3.163 *** 0.010 0.467 Noe. This able shows saisics of he GRS es, he probabiliy (p-value) of he GRS saisic, he average absolue value of he inerceps ( ) and he adjused R 2 for each esed asse pricing model and for each analysed se of porfolios. Panels A, B and C show, respecively, he summary saisics of he 25 porfolios based on Size and B/M, he 32 porfolios based on Size, B/M and Profiabiliy and he 32 porfolios based on Size, B/M and Invesmen. The residuals of he regressions are adjused for heeroscedasiciy and auocorrelaion (4-lag Newey-Wes). *** p-value <0.01, ** p-value <0.05, * p-value<0.10 i
M. A. V. Machado, R. Faff, S. C. de S. e Silva 866 All his considered, resuls obained from Table 7 confirm he preliminary resuls obained from Tables 2, 4 and 6, namely he poor abiliy of Fama and French s (2015) five-facor model o explain sock reurns in he Brazilian marke and he possible superioriy of Keene and Peerson s (2007) fivefacor model, which uses marke, size, B/M, momenum and liquidiy as risk facors. These resuls are due o he poor performance of profiabiliy and invesmen and o he good performance of B/M, momenum and liquidiy. Furher Analysis Are book-o-marke, momenum and liquidiy redundan facors in Brazil? Fama and French (2015) found ha HML is a redundan facor in describing average reurns in heir five-facor model. They recommend an invesigaion ino his behaviour, o examine if i can be observed in inernaional markes. Alhough he resuls of he models performance do no suppor he suspicion ha HML is a redundan facor in Brazil, we aimed o verify if HML is a redundan facor wih profiabiliy and invesmen, as suggesed by Fama and French (2015). To verify if his resul is common in Brazil, we regressed each of he facors in he five-facor model by Fama and French (2015) on he oher four remaining facors. Table 8 shows he esimaed parameers in he regressions. Table 8 Esimaed Parameers in he Regressions Where One of he Model Facors is Regressed on he Remaining Facors Inercep Rm-Rf SMB HML RMW CMA R 2 2 x 3 Facors Rm-Rf 0.008-0.601 *** 0.110-0.195-0.118 0.172 SMB 0.002-0.267 *** -0.066-0.068-0.153 0.170 HML -0.025 *** 0.063-0.085-0.316 ** -0.072 0.068 RMW 0.002-0.068-0.053-0.191 * -0.253 *** 0.126 CMA 0.001-0.048-0.139-0.051-0.295 *** 0.074 2 x 2 Facors Rm-Rf 0.003-0.621 *** -0.137-0.550 *** -0.267 0.239 SMB 0.004-0.299 *** 0.036-0.054-0.323 *** 0.260 HML -0.019 *** -0.051 0.028-0.404 *** -0.263 0.103 RMW -0.001-0.123 ** -0.025-0.242 *** -0.378 *** 0.310 CMA -0.004-0.094 * -0.235 ** -0.248-0.595 *** 0.301 2 x 2 x 2 x 2 Facors Rm-Rf 0.004-0.728 *** -0.009-0.843 *** -0.241 0.317 SMB 0.006-0.302 *** 0.078-0.135-0.372 *** 0.306 HML -0.018 *** -0.003 0.063-0.159-0.409 ** 0.143 RMW -0.001-0.151 *** -0.058-0.085-0.210 *** 0.177 CMA -0.004-0.061-0.225 ** -0.305 * -0.294 *** 0.252 Noe. Rm Rf is marke facor; SMB is size facor; HML is B/M-based value facor; RMW is profiabiliy facor; and CMA is invesmen facor. The residuals of he regressions are adjused for heeroscedasiciy and auocorrelaion (4-lag Newey-Wes). *** p-value <0.01, ** p-value <0.05, * p-value<0.10. RAC, Rio de Janeiro, v. 21, n. 6, ar. 6, pp. 851-874, Novembro/Dezembro, 2017, www.anpad.org.br/rac
Applicabiliy of Invesmen and Profiabiliy Effecs 867 Regardless of he way facors were consruced, Table 8 shows ha he reurn of HML is no absorbed by he oher four facors, since he inerceps of he models are saisically significan: -2.5% per monh (p-value < 0.01) for he 2 x 3 facors, -1.9% per monh (p-value < 0.01) for he 2 x 2 facors and -1.8% per monh (p-value < 0.01) for he 2 x 2 x 2 x 2 facors. This resul corroboraes previous evidence of his sudy, which shows ha HML is an imporan facor for he explanaion of reurns in he Brazilian sock marke. On he oher hand, in he regressions o explain RMW and CMA, inerceps are no significan and, herefore, do no improve he mean-variance-efficien porfolio, as hey are combined wih oher risk facors. These findings conradic hose obained by Fama and French (2015). Table 8 shows ha HML is no a redundan facor in relaion o profiabiliy and invesmen, and ha profiabiliy and invesmen do no aggregae value o he explanaion of reurns. In addiion, Table 7 shows he imporance of model 3, which uses marke, size, B/M, momenum, and liquidiy facors o explain reurns. Therefore, his sudy invesigaed if any of he facors in model 3 is redundan. So, we regressed each facor in model 3 on he remaining four facors. Table 9 shows he esimaed parameers in he regressions. Table 9 Esimaed Parameers in he Regressions Where One of he Facors of he Five-Facor Model is Regressed on he Remaining Four Facors Inercep Rm-Rf SMB HML WML LMH R 2 2 x 3 Facors Rm-Rf 0.014 *** -0.251 ** -0.018-0.143 * -0.814 *** 0.516 SMB -0.001-0.152 * -0.068-0.048 0.184 0.183 HML -0.023 *** -0.019-0.113-0.109-0.128 0.048 WML 0.023 ** -0.303-0.169-0.230 0.071 0.104 LMH 0.008 ** -0.462 *** 0.172-0.072 0.019 0.501 2 x 2 Facors Rm-Rf 0.011 ** -0.287 ** -0.244 ** -0.367 *** -1.023 *** 0.515 SMB 0.002-0.192 ** 0.105 0.016 0.235 0.200 HML -0.015 *** -0.148 * 0.095-0.131-0.349 * 0.068 WML 0.018 * -0.372 ** 0.024-0.220-0.361 0.145 LMH 0.005 * -0.341 *** 0.117-0.192 * -0.119 0.450 2 x 2 x 2 x 2 Facors Rm-Rf 0.012 ** -0.459 *** -0.106-0.446 *** -1.072 *** 0.503 SMB 0.000-0.207 *** 0.045 0.088 0.055 0.210 HML -0.020 *** -0.041 0.038 0.126 * -0.190 * 0.073 WML 0.023 *** -0.340 *** 0.148 0.251-0.484 * 0.249 LMH 0.005 ** -0.306 *** 0.035-0.142 ** -0.182 ** 0.385 Noe. Rm Rf is he marke facor; SMB is size facor; HML is B/M-based value facor; WML is momenum facor; and LMH is liquidiy facor. The residuals of he regressions are adjused for heeroscedasiciy and auocorrelaion (4-lag Newey-Wes). *** p-value <0.01, ** p-value <0.05, * p-value<0.10 Regardless of he way facors are consruced, Table 9 shows ha HML reurn is no absorbed by he oher facors, since he inerceps of he models are saisically significan: -0.023 (p-value < 0.01) for 2 x 3 facors, -0.015 (p-value < 0.01) for 2 x 2 facors and -0.020 (p-value < 0.01) for 2 x 2 x 2 x 2 facors. Apar from HML, neiher liquidiy, inerceps of 0.008 (p-value < 0.05), 0.005 (p-value < 0.10) RAC, Rio de Janeiro, v. 21, n. 6, ar. 6, pp. 851-874, Novembro/Dezembro, 2017, www.anpad.org.br/rac