Folia Oeconomica Stetinensia DOI: /foli COMPARISON OF A MODIFIED AND CLASSIC FAMA-FRENCH MODEL FOR THE POLISH MARKET

Transcription

1 Folia Oeconomica Seinensia DOI:.55/foli-27-7 COMPARISON OF A MODIFIED AND CLASSIC FAMA-FRENCH MODEL FOR THE POLISH MARKET Sanisław Urbański, Ph.D. AGH Universiy of Science and Technology Faculy of Managemen Gramayka, 3-67 Kraków, Poland surbansk@zarz.agh.edu.pl Received November 26, Acceped 2 March 27 Absrac This paper shows a comparison of he resuls of reurn, risk, and risk price simulaion by a modified and classic Fama-French model. The modified model defines he new ICAPM sae variable as a funcion of he srucure of a company s pas financial resuls. The model ess are run on he basis of socks lised on he Warsaw Sock Exchange. In ligh of he classic model he risk price, on he esed marke, urned ou univariae due o HML, however, in ligh of he modified model, risk price urned ou o be hreedimensional due o he proposed facors, and marke porfolio. The facors of he modified model, compared wih he HML and SMB, are widely perceived by porfolio managers, and he simulaion resuls indicae a greaer possibiliy o use his pricing applicaion by large insiuional invesors. Keywords: ICAPM applicaions, Fama-French model, reurn simulaion, sysemaic risk, price of risk, marke porfolio JEL classificaion: G, G2

2 Comparison of a Modified and Classic Fama-French Model for he Polish Marke 8 Inroducion Mos of he exising pricing procedures of securiies are based on he capial pricing heory (CAPM) or arbirage pricing heory (APT). The APT developed by Ross (976) assumes ha reurns are generaed by an unknown number of unknown facors. Similarly, he ICAPM generalized by Meron (973) is based on a marke porfolio and k facors dependen on unknown sae variables. We can see considerable similariies beween boh heories; however, differences are due o mehodological reasons. The differences beween he heoreical assumpions have no impac on he pricing. The pracical implemenaions of boh heories come down o esing he models which assume a linear form of he sochasic discoun facor. Designing new applicaions of pricing is jusified because neiher ICAPM nor APT define he known pricing facors. On he oher hand, even he mos famous lieraure algorihms do no always generae he correc reurns on he esed markes. The Fama-French (993) model (FF hereafer) propose HML and SMB facors, as he funcions of sae variables: capializaion and book o marke value indicaor. Exensive research conduced since he mid-wenieh cenury has shown a significan relaionship beween hese variables and fuure reurns. Examples are offered by he works of Saman (98), Rosenberg, Reid and Lansein (985), Reinganum (98), Lakonishok and Shapiro (986) or Fama and French (992). However, only in 995, did Fama and French indicae ha direc facor generaing he fuure reurns is he srucure of earnings in he las five-year period, while he capializaion and book o marke values, dependen on earnings, indirecly affec pricing. Fama and French (996) underlined hose facors simulaneously generaing reurns and earnings are sill unknown, which should be invesigaed. This logic conclusively confirms he need for he building of new pricing procedures. A he urn of he 2h and 2s cenuries, various ess of CAPM and ICAPM applicaions were proposed. Also, CCAPM applicaions were invesigaed. Examples include he work of Carhar (995), Leau and Ludvigson (2), Yogo (26) or Pekova (26), which were esed on he US marke. The mos famous research sudy is probably ha of Carhar (995) in which he auhor modifies he classic FF hree facor model, proposing a fourh facor as a one-year momenum. Leau and Ludvigson (2) propose condiional applicaions of he CAPM and CCAPM models. They argue ha condiional applicaions beer describe reurns in comparison wih uncondiional applicaions. Yogo (26) proposes he facorial applicaion of CCAPM, using durable and nondurable consumpion. The auhor concludes ha durable consumpion well describes changes in business cycles, and should be he main facor explaining

3 82 Sanisław Urbański reurns. Pekova (26) shows ha he replacemen of HML and SMB by innovaions in he aggregae dividend yield, erm spread, defaul spread, and one-monh T-bill increase he model s explanaory power as compared wih he classic FF model. Research on he Polish marke focused on esing he classic CAPM. Examples esing he ICAPM applicaions are he works of Zarzecki e al. (24 25), Kowerski (28), Czapkiewicz and Wójowicz (24) or Urbański (2, 22). Kowerski esed he classic FF model on he basis of monhly observaions in he hisorical period of Czapkiewicz and Wójowicz (24) esed he Carhar (995) model in Urbański (2, 22) used he research resuls of FF (995) and proposes he aggregaed wo and hree facor models as he ICAPM applicaions. Urbański, in his previous works, esed he proposed model on 5 porfolios formed in one direcion, using Cochrane s (2, p. 435) advice. The ess performed on he Polish marke in show far lower pricing errors in he case of an aggregaed model as compared wih he FF hree facor model. However, he procedure of esing boh models (alhough complying wih Cochrane s recommendaions) differs from he FF (993) proposiion. The classic FF hree facor model is based on 25 porfolios formed in he wo direcions, which is refleced by sae variables of he ICAPM applicaion. Therefore, o make an unambiguous assessmen I have compared he resuls of pricing (in he ligh of heoreical assumpions and pracical possibiliies of he use by porfolio managers and invesors) by he classic FF model and hree facor aggregaed model (modified FF model hereafer) under he proposed 25 esing porfolios, formed in he wo direcions, reflecing he sae variables of he wo models. Secion 2 presens he pricing mehodology proposing new sae variables, in he ligh of FF (995) proposiions, and my own consideraions. Secion 3 presens daa used for calculaions. Secion 4 shows he resuls of calculaions and discusses differences in he resuls of he performed ess from he perspecive of pracical applicaions by porfolio managers. The final secion presens he conclusions.. Theoreical basis of he Fama and French model modificaions The basic pricing equaion of any asse can be presened by dependency () if and only if he law of one price is reasonable (see Cochrane, 2, pp ): p = E ( m x ) () i + i, + In he case of he classic FF model hese are he capializaion and book o marke indicaor.

4 Comparison of a Modified and Classic Fama-French Model for he Polish Marke 83 where: p i is he curren asse price i, m + is he sochasic discoun facor (SDF), x i,+ is a fuure pay-ou. xi, + Defining an asse reurn as: r i, +, equaion () can be wrien as follows: p i E( m+ ri, + ) = (2) In he case of he hree-facor ICAPM applicaion SDF is a linear funcion (3) of reurn of he marke porfolio RM, and wo facors which ake ino accoun he influence of wo hypoheical sae variables S i S 2. These variables should secure all fuure naure saes. m = a + brm + cs + ds (3) 2 If a risk free asse exiss, and is reurn is (see Cochrane, 2, p. 3): he pricing model (2) akes he following form: RF =, E( m + ) where: γ = RF var( brm ), M γ = RF var( S ), S γ = RF var( S ), S2 2 i, M var( brm ) cov( brm, ri ) β =, β = var( S ) cov( S, r ), i, S i i,s2 2 2 ri β = var(s ) cov(s, ), E( r ) E( RF) =γ β +γ β +γ β (4) i M im, S is, S2 is, 2 brm is rae of reurn of a marke porfolio approximaed by excess rae of he reurn of he sock index WIG over he risk-free rae, and S = cs, as well as S2 = ds are 2 facors of he assumed ICAPM applicaion. FF (993) claim ha heir proposed hree-facor model is he Meron ICAPM applicaion. In his model he size and book o marke value raio (BV/MV) are risk facors, while S = cs = HML and S2 = ds 2 = SMB are known funcions of he size and BV/MV. In he furher work FF (995, pp ) conclude: If he average-reurn relaions are due o raional pricing, hen (i) here mus be common risk facors in reurns associaed wih size and BE/ME, and (ii) he size and book-o-marke paerns in reurns mus be explained by he behaviour of earnings. The evidence presened here shows ha size and BE/ME are relaed

5 84 Sanisław Urbański o profiabiliy. A he end of he paper he auhors pose wo quesions which have no been answered ye: (i) Wha are he underlying economic sae variables ha produce variaion in earnings and reurns relaed o size and BE/ME? (ii) Do hese unnamed sae variables produce variaion in consumpion and wealh ha is no capured by an overall marke facor and so can explain he risk premiums in reurns associaed wih size and BE/ME? (see FF, 995, p. 54). The paper will aemp o answer o he firs quesion. On he basis of FF (995, pp. 34 4, Figures 2, and Table ) I modify an FF (993) hree facor model, expecing ha he following conjecure is rue: Conjecure The economic sae variable ha produces variaion in he fuure earnings and reurns relaed o size and BV/MV is a vecor of srucure of he pas long-erm differences in profiabiliy. The adoped general sae variable can be refleced by funcional FUN, defined by equaions (5), (6) and (7). where: NUM nor( ROE) nor( AS) nor( APO) nor( APN) FUN = = DEN nor( MV / E) nor( MV / BV ) S( Q) PO( Q) = = ROE = F; AS = F2 = ; APO = F3 = ; i i S( nq ) PO( nq ) i = = PN( Q ) APN = F = MV E = F MV BV = F PN( nq ) = 4 ; / 5; / i 6 = i i (5) (6) F j (j =,, 6) are ransformed o normalized areas <a j ; b j >, according o Eq. (7): min Fj cj F j nor( Fj) = a j + ( bj a j) max min d j Fj cj Fj + ej (7) In Equaions (6) and (7), he corresponding indicaions are as follows: ROE is a reurn on book equiy; i i i S( Q ), PO( Q ), PN( Q ) are values ha are accumulaed from he = = = beginning of he year as ne sales revenue (S), operaing profi (PO) and ne profi (PN) a he

6 Comparison of a Modified and Classic Fama-French Model for he Polish Marke 85 end of i quarer (Q i ); i i i S( nq ), PO( nq ), PN( nq ) are average values, accumulaed = = = from he beginning of he year as S, PO and PN a he end of Q i over he las n years (he presen research assumes ha n = 3 years); MV/E is he marke-o-earning value raio; E is he average earning for he las four quarers; MV/BV is he marke-o-book value raio; a j, b j, c j, d j, e j are variaion parameers. In equilibrium modelling F j (j =,, 6) can be ransformed ino he equal normalized area <; 2> (see Urbański, 2). The consruced funcional FUN represens an invesor consrucing a porfolio, using he srucure of he pas long-erm differences in profiabiliy, which consiss of he bes fundamenal and undervalued socks. FUN is dependen on company evaluaion indicaors, occurring in he numeraor and company marke pricing indicaors in he denominaor. As far as he classificaion of companies o he porfolio is concerned, I base his on he crierion ha I define as opimal he FUN value calculaed for all companies lised in a given marke. F j variables are funcions of company evaluaion indicaors (for j =,, 4) and funcions of pricing indicaors (for j = 5, 6). Given ha F j may change considerably, FUN value may be frequenly impaced in a major or minor way. For his reason, i is necessary o ransform all F j variables o mach he appropriaely defined sandardized areas, in accordance wih Equaion (7). I mus be noed ha parameers a j and b j define he border of he F j variable sandardized area, and have a varying impac on FUN value by given variables. The consruced porfolio conains N companies, for which FUN assumes N highes values (for long posiions). Funcional FUN is a gauge of securiies ha are assessed well by NUM and a he same ime priced lowly by DEN. NUM represens an invesor building a porfolio, comprising he bes fundamenal firms, while DEN represens an invesor who purchases undervalued socks. Invesors consruc he porfolios by maximizing FUN and NUM or minimizing DEN (if long invesmens are considered). FUN conains a clear economic inerpreaion and may consiue a crierion for selecing securiies for he porfolio. The invesmen is more aracive if he FUN value is greaer (Urbański, 2). A represenaive invesor can successively achieve above-average reurns on condiion of he correc predicions of economic saes ha deermine he fuure value of asses. If invesmens on he basis of FUN allow for achieving above-average reurns, hen he relaion beween FUN and he resulan of differen, boh known and unknown invesmen mehods, can be concluded. These invesmen mehods should predic fuure saes of naure. In oher words funcional FUN should deermine sae variables which will secure fuure invesmen paymens. Research conduced by Urbański (2) shows he possibiliy of an invesmen decision based on FUN, and achievemen of above-average reurns on WSE in Therefore,

7 86 Sanisław Urbański i is assumed ha he conjecure abou he relaion beween FUN and he resulan of invesmen mehods (ha should predic fuure saes of naure) is rue. Thus, pricing procedures designed on he basis of such sae variables are ICAPM applicaions. In he case of he proposed mulifacor model, as he modificaion of he FF hree facor model, parameers of equaion (4) are defined as follows: brm = RM RF (8a) S = cs = HMLN (8b) S = ds = LMHD (8c) 2 2 where HMLN (high minus low) is he difference beween he reurns from he porfolio wih he highes and lowes NUM values in period ; LMHD (low minus high) is he difference beween he reurns from he porfolio wih he lowes and highes DEN values in period ; RM RF is he marke facor, defined as he excess reurn of sock index WIG over he risk-free rae. Considering (8), i can be shown ha pricing model (2) and he following represenaion are equivalen (e.g. Balvers, 2, pp ): ri RF =β i, HMLN HMLN +β i, LMHD LMHD +βi, M ( RM RF ) (9) The proposed financial pricing model (9) can be esed in wo passes (a) and (b). r RF =α + β F + e ; =,..., T ; i =,, m (a) i i ik k i k = K r RF =γ + ˆ γ β +ε ; i =,..., m; =,..., T (b) i k ik i k = K where: F k is he vecor of facors (k = HMLN, LMHD, RM-RF), β i,k and γ k (k = HMLN, LMHD, M) are vecors of sysemaic risk and risk price componens due o he HMLN, LMHD and marke porfolio M. 2. Daa and range of research Pricing Model Simulaions are carried ou on he basis of all sock quoed on he Warsaw Sock Exchange (WSE) main marke in , characerized by posiive book value during he las reporing period. Daa referring o he fundamenal resuls of he esed socks is aken

8 Comparison of a Modified and Classic Fama-French Model for he Polish Marke 87 from he daabase creaed by he Nooria Service company, 2 while daa for reurns compuing is provided from he Warsaw Sock Exchange daabase. s and componens of sysemaic risk and risk premium are modelled by he classic, and modified FF models described by equaions (). In he case of he classic FF model F k is he vecor of FF facors HML, SMB and RM-RF, β i,k and γ k are vecors of sysemaic risk and risk price componens due o he HML, SMB and marke porfolio M. In he case of he modified FF model F k is he vecor of he FF facors HMLN, LMHD and RM-RF, β i,k and γ k are vecors of sysemaic risk and risk price componens due o he HMLN, LMHD and marke porfolio M. The analysis is carried ou on he quarerly reurns of formed porfolios. The quinile porfolios are formed in wo direcions on he values of sae variables ha are used by each model. In he case of he classic FF model he porfolios are formed on BV/MV and capializaion. Firsly, all esed companies are divided ino five porfolios due o BV/MV. Then, each so formed quinile porfolio is divided ino five porfolios due o capializaion. In he case of he modified FF model he porfolios are formed on NUM and DEN. Similarly, he esed companies are divided ino five porfolios due o NUM. Then each so formed quinile porfolio is divided ino five porfolios due o DEN. In oal, 25 porfolios are formed for each version of he FF model. 3. Resuls and analysis The dependen variable of regressions () consiues he excess of reurns of 25 es porfolios. Tables and 2 presen heir mean values for he porfolios esing he classic and modified FF model. Tables 3 and 4 show he mean values of capializaion and BV/MV for he porfolios esing he classic FF model. Tables 5 and 6 show he mean values of NUM and DEN for he porfolios esing he modified FF model. The disribuions of mean value of excess reurns on porfolios formed on BV/MV and NUM are similar. The highes values are observed for he s BV/MV quiniles, and he lowes for he 5h quiniles. However, in he classic FF model he all mean values are saisically equal o zero. The lowes values of capializaion are found for he highes BV/MV quiniles, while he values of BV/MV are similar for all capializaion quiniles and he firs four quiniles of BV/ MV. In he case of he highes BV/MV quinile he highes BV/MV value is for he s quinile of capializaion and monoonically decreases o he 5h quinile. 2 Nooria Service sells sock analysis ools and he provision of financial daa and quoaions, see hp://ir.nooria.pl.

9 88 Sanisław Urbański Table. Dependen variable of he classic FF model; excess reurns on 25 sock porfolios formed on capializaion and BV/MV Book-o-marke value (BV/MV) quiniles Size quiniles low high low high means sandard deviaions Small Big saisics for means Small Big Noes: The sample period is from 995 o 22, 64 Quarers. Size is he capializaion of he porfolio. Source: own calculaions. DEN quiniles Table 2. Dependen variable of he modified FF model; excess reurns on 25 sock porfolios formed on DEN and NUM low bad NUM value quiniles high good low bad high good means sandard deviaions Small cheap Big priced saisics for means Small cheap Big priced Noes: The sample period is from 995 o 22, 64 Quarers. Source: own calculaions.

10 Comparison of a Modified and Classic Fama-French Model for he Polish Marke 89 Table 3. Capializaion values of 25 sock porfolios formed on capializaion and BV/MV Size quinile Book-o-marke value (BV/MV) quiniles low 2 4 high low 2 4 high means sandard deviaions Small 85,442 64,957 29,974 7,37 56,483 4,95 3,44 9, ,993 89,298 69,43 34,9 2,83 92,3 32,393 2, , ,56 42,468 63,73 49,35 25,92 87,768 46,96 4,8,525,22,25 334,337 55,6 44,25 745,656 36,427 56,297 Big 6,938,272 8,86,226 2,999,759 2,87,82 4,346,26 5,688,788 3,66,362 4,22,733 Noes: The sample period is from 995 o 22, 64 Quarers. Size is he capializaion of he porfolio. Source: own calculaions. Table 4. BV/MV indicaors of 25 sock porfolios formed on capializaion and BV/MV Book-o-marke value (BV/MV) quiniles Size quinile low high low high means sandard deviaions Small Big Noes: The sample period is from 995 o 22, 64 Quarers. Size is he capializaion of he porfolio. Source: own calculaions. DEN quinile Table 5. NUM values of 25 sock porfolios formed on DEN and NUM low bad NUM value quiniles high good low bad high good means sandard deviaions Small cheap Big priced Noes: The sample period is from 995 o 22, 64 Quarers. The small DEN value porfolios are characerized by he small values of MV/BV and MV/E, herefore hey are called cheap. The big DEN value porfolios are characerized by he big values of MV/BV and MV/E, herefore hey are called priced. Source: own calculaions.

11 9 Sanisław Urbański DEN quinile Table 6. DEN values of 25 sock porfolios formed on DEN and NUM low bad NUM value quiniles high good low bad high good means sandard deviaions Small cheap Big priced Noes: The sample period is from 995 o 22, 64 Quarers. The small DEN value porfolios are characerized by he small values of MV/BV and MV/E, herefore hey are called cheap. The big DEN value porfolios are characerized by he big values of MV/BV and MV/E, herefore hey are called priced. Source: own calculaions. The values of NUM are similar for all DEN quiniles. However, DEN values decrease from he s o he 5h quinile of NUM. This means ha companies presening good financial resuls are characerized by smaller values of MV/BV and MV/E. The loadings of explanaory variables of regressions (a) and (b) are sysemaic risk componens, esimaed in he firs pass, and risk premium componens, esimaed in he second pass. The parameer values of regressions () are deermined by means of he GLS mehod wih he applicaion of he Prais-Winsen procedure wih firs-order auocorrelaion. The impac of model facor loadings on reurns is shown in Figures o 4. In ligh of he modified FF model, invesmens in companies showing good financial resuls (high NUM), boh cheap and priced companies, demonsrae growing reurns for growing HMLN (see Figures a, c, and 2a), while invesmens in companies showing bad financial resuls (low NUM), boh cheap and priced companies, demonsrae decreasing reurns for growing HMLN (see Figures a, c, and 2b). On he oher hand, invesmens in cheap companies, and showing boh good and bad financial resuls (small DEN), demonsrae growing reurns for growing LMHD (see Figures 3a, and 4a, 4c). Simulaneously, invesmens in priced companies, and showing boh good and bad financial resuls (big DEN), demonsrae decreasing reurns for growing LMHD (see Figures 3c, and 4a, 4c). In ligh of he classic FF model, invesmens in value companies (high BV/MV), boh small and big capializaion socks, demonsrae growing reurns for growing HML (see Figures b, d, and 2b), while invesmen in growh companies (low BV/MV), boh small and big capializaion socks, demonsraes decreasing reurns for growing HML (see Figures b, d, and 2d). On he

12 Comparison of a Modified and Classic Fama-French Model for he Polish Marke 9 a) Modified FF model b) Classic FF model.2. NUM = 4.5. NUM = Cheap socks (DEN small) Bad sock Good sock NUM = 2 HMLN.3 c) Modified FF model d) Classic FF model NUM = Priced socks (DEN big) Bad sock Good sock NUM = 4 NUM = 2 HMLN Small socks Value sock BV/MV = 4 BV/MV = 2 = 3..5 Growh sock, Big socks Value sock BV/MV high HML Growh sock BV/MV low.5 HML Figure. The impac of HMLN and HML loadings on reurns for porfolios formed on: a) and c) NUM, and b) and d) BV/MV Source: own elaboraion. a) Modified FF model b) Classic FF model Good financial resuls (NUM high) DEN = 4 Priced sock DEN = 3 Cheap sock.5 HMLN c) Modified FF model d) Classic FF model Value socks (BV/MV high) CAP big CAP = 3 CAP = 2 CAP small.5 HML Bad financial resuls (NUM low).2 DEN = 2.5 Cheap sock.2.4 DEN = 3.6 Priced sock.8 DEN = 4 HMLN Growh socks (BV/MV low). CAP = 3.5 CAP = CAP big.5.2 CAP small.25.3 HML Figure 2. The impac of HMLN and HML loadings on reurns for porfolios formed on: a) and c) DEN, and b) and d) Capializaion Source: own elaboraion.

13 92 Sanisław Urbański a) Modified FF model b) Classic FF model Cheap socks (DEN small) NUM = 3 Small socks BV/MV = 4.8 Good sock.8 BV/MV = Bad sock NUM = Value sock BV/MV = 2.2 NUM = 4.2 Growh sock.5 LMHD.5 SMB c) Modified FF model d) Classic FF model Priced socks (DEN big).5 NUM = 3 NUM = 4 NUM low NUM high NUM = 2 LMHD Big socks.5 Growh sock BV/MV = 2 BV/MV = 4 Value sock SMB Figure 3. The impac of LMHD and SMB loadings on reurns for porfolios formed on: a) and c) NUM, and b) and d) BV/MV Source: own elaboraion. a) Modified FF model b) Classic FF model Good financial resuls (NUM high).8 Cheap sock.6.4 DEN = DEN = 3 DEN = 4.6 Priced sock.8 LMHD Growh socks (BV/MV low).5 Small sock.4 CAP = CAP = 2. CAP = 4.5. Big sock.2 SMB c) Modified FF model d) Classic FF model Bad financial resuls (NUM low).6 Cheap sock.4 DEN = 3.2 DEN = DEN = 4.4 Priced sock.6 LMHD Value socks (BV/MV high).6.4 Small sock CAP = 2.2 CAP = Big sock.8 SMB Figure 4. The impac of LMHD and SMB loadings on reurns for porfolios formed on: a) and c) DEN, and b) and d) Capializaion Source: own elaboraion.

14 Comparison of a Modified and Classic Fama-French Model for he Polish Marke 93 oher hand, invesmens in small capializaion companies, boh value and growh companies (high and low BV/MV), demonsrae growing reurns for growing SMB (see Figures 3b, 4b, and 4d). However, invesmens in big capializaion companies, boh value and growh companies (high and low BV/MV), demonsrae decreasing reurns for growing SMB (see Figures 3d, 4b, and 4d). Table 7 presens he values of parameers of regressions (b), and saisics esing he mulifacor efficiency of generaed porfolios by he classic and modified FF models. Table 7. Regressions of excess reurns on he loadings of he classic and modified FF model facors r RF =γ +γ hˆ +γ sˆ +γ bˆ +ε ; i =,, 25; =,, 64 i i h i s i b i i Parameer Modified FF model Classic FF model γ (S) γ h(hmln/hml) (S) γ s(lmhd/smb) (S) γ b (S) GRS-F p-value, % Q A (F) p-value, % R 2 LL, % Noes: This able presens esimaion resuls assessing he classic and modified FF models. RF is he 9-day Treasury bill rae of reurn. h ˆi, s ˆi, b ˆi are he loadings on he model facors. The response variable is excess reurn on 25 sock porfolios formed in period. (S) corresponds o he saisic of Shanken (992) adjusing for errors-in-variables. GRS-F is he F-saisic of Gibbons e al. (989) ha he generaed porfolios are mulifacor efficien. Q A (F) repors F-saisic and is corresponding p-value indicaed below for he Shanken es (985) ha he pricing errors in he model are joinly zero. R 2 LL is a measure, follows Leau and Ludvigson (2), showing he fracion of he cross-secional variaion in average reurns ha is explained by each model and is calculaed as follows: RLL = [ σc( ri) σc( ei)]/ σ c( ri), where σ c denoes a cross-secional variance, and variables wih bars over hem denoe ime-series averages. The sample period is from 995 o 22, 64 Quarers. Source: own calculaions. In he case of he modified FF model he perceived risk price is mulidimensional due o HMLN, LMHD and marke porfolio facors, and amouns o 4, 3 and % per quarer,

15 94 Sanisław Urbański respecively. However, in he case of he classical FF model he risk is priced only due o he HML facor, and amouns o 5% per quarer. There is no basis o rejec he zero hypohesis which presumes ha boh models generae mulifacor efficien porfolios, which is confirmed by he values of he GRS-F and Q A (F) saisics. Conclusions This paper presens wo ICAPM applicaions of socks pricing on he Warsaw Sock Exchange modified vs. he classic hree facor Fama-French model. Boh pricing procedures are esed on he basis of 25 porfolios, formed in wo direcions, according o he algorihm proposed by FF (993). The adopion of exacly he same esing boundary condiions allows for comparing he informaion effeciveness of boh models. The resuls of research can be summarized as follows:. The sae variable, generaing fuure reurns, of he modified FF model is he srucure of pas financial resuls in relaion o he company value modelled by HMLN and LMHD facors. 2. The sae variable, generaing fuure reurns, of he classic FF model is a change of BV/ MV in relaion o he company value modelled by HML and SMB facors. 3. The srucure of pas financial resuls is more widely perceived by invesors and (according o he FF (995)) has a direc impac on reurns. 4. The resuls of pricing simulaions by he modified FF model (compared wih he classic FF model) are more widely perceived by invesors and financial managers, and hey are as follows: a) If he diversiy of financial resuls increases (HMLN increases): buy good financial companies (high NUM), he higher reurns are for priced companies (big DEN), sell bad financial companies (low NUM), he higher reurns are for priced companies (big DEN), b) If he diversiy of value increases (LMHD increases): buy cheap companies (small DEN), he higher reurns are for good financial companies (high NUM), sell priced companies (big DEN), he higher reurns are for bad financial companies (low NUM).

16 Comparison of a Modified and Classic Fama-French Model for he Polish Marke In ligh of he modified FF model he risk price is hree-dimensional due o HMLN, LMHD and marke porfolio facors, and amouns o 4, 3 and % per quarer, respecively. 6. In ligh of he classic FF model he risk price is univariae due o HML, amouning o 5% per quarer. 7. The resuls of Gibbons e al. (989), and Shanken s (985) ess are similar for boh models. Acknowledgemens Financial suppor for his paper from he Naional Science Cenre, Poland (Research Gran 25/9/B/HS4/294) is graefully acknowledged. References Balvers, R.J. (2). Foundaions of Asse Pricing. Wes Virginia Universiy. Carhar, M.M. (995). Survivor bias and persisence in muual fund performance. Thesis (Ph.D.), Graduae School of Business, Universiy of Chicago. Cochrane, J. (2). Asse Pricing. New Jersey: Princeon Universiy Press. Czapkiewicz, A., Wójowicz, T. (24). The four-facor asse pricing model on he Polish sock marke. Economic Research-Ekonomska Israživanja, 27 (), DOI:.8/33677X Fama, E.F., French, K.R. (992). The Cross-Secion of Expeced Sock s. Journal of Finance, 47 (2), DOI:./j b4398.x. Fama, E.F., French, K.R. (993). Common Risk Facors in he s on Sock and Bonds. Journal of Financial Economics, 33 (), DOI:.6/34-45X(93) Fama, E.F., French, K.R. (995). Size and Book-o-Marke Facors in Earnings and s. Journal of Finance, 5 (), DOI:./j b569.x. Fama, E.F., French, K.R. (996). Mulifacor Explanaions of Asse Pricing Anomalies. Journal of Finance, 5 (), DOI:./j b522.x. Gibbons, M.R., Ross, S.A., Shanken, J. (989). A Tes of he Efficiency of a Given Porfolio. Economerica, 57 (5), 2 52.

17 96 Sanisław Urbański Kowerski, M. (28). Trójczynnikowy model Famy i Frencha dla Giełdy Papierów Warościowych w Warszawie. Przegląd Saysyczny, 55 (4), Leau, M., Ludvigson, S. (2). Resurrecing he (C) CAPM: A Cross -Secional Tes when Risk Premia Are Time-Varying. Journal of Poliical Economy, 9 (6), Lakonishok, J., Shapiro, A.C. (986). Sysemaic Risk, Toal Risk, and Size as Deerminans of Sock Marke s. Journal of Banking and Finance, (), Meron, R.C. (973). An Ineremporal Capial Asse Pricing Model. Economerica, 4 (5), Pekova, R. (26). Do he Fama-French Facors Proxy for Innovaions in Predicive Variables? Journal of Finance, 6 (2), DOI:./j x. Reinganum, M.R. (98). A New Empirical Perspecive on he CAPM. Journal of Financial and Quaniaive Analysis, 6 (4), Rosenberg, B., Reid, K., Lansein R. (985). Persuasive Evidence of Marke Inefficiency. Journal of Porfolio Managemen, (3), 9 6. Ross, S.A. (976). The Arbirage Theory of Capial Asse Pricing. Journal of Economic Theory. 3 (3), Saman, D. (98). Book Values and Sock s, The Chicago MBA. A Journal of Seleced Papers, 4, Shanken, J. (985). Mulivariae Tess of he Zero-Bea CAPM. Journal of Financial Economics, 4, Shanken, J. (992). On he Esimaion of Bea-Pricing Models. The Review of Financial Sudies, 5 (), 33. Urbański, S. (2). Modelowanie równowagi na rynku kapiałowym weryfikacja empiryczna na przykładzie akcji noowanych na Giełdzie Papierów Warościowych w Warszawie. Kaowice: Wydawnicwo Uniwersyeu Ekonomicznego w Kaowicach. Urbański, S. (22). Mulifacor Explanaions of s on he Warsaw Sock Exchange in Ligh of he ICAPM. Economic Sysems, 36 (4), Yogo, M. (26). A Consumpion-Based Explanaion of Expeced Sock s. Journal of Finance, 6 (2), Zarzecki, D., Byrka-Kia, K., Wiśniewski, T., Kisielewska, M. (24 25). Tes of he Capial Asse Pricing Model: Polish and Developed Markes Experiences. Folia Oeconomica Saiiensa, 2 (3 4),