Simplicity Vs Accuracy: The Case Of Capm And Fama And French Model

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1 Australan Journal o Basc and Aled Scences, 5(10): , 2011 ISSN Slcty Vs Accuracy: The Case O Ca And Faa And French Model 1 Attaullah Shah, 1 Fahad Abdullah, 1 Tausee Khan, 2 Sa Ullah Khan 1 Insttute o Manageent Scences, Peshawar. 2 Kohat Unversty o Scence and Technology, Peshawar. Abstract: Practtoners reer to use catal assets rcng odel (CAPM) owng to ts slcty and convenences to estate exected return on rsky nancal assets whereas acadecs lke to use Faa and French three actors odel due to ts ablty to accurately redct exected returns. The objectve ths aer s to test the redctve ower o both o these odels n accurately estatng the exected returns. Snce any revous studes have suggested the develoent o ortolos nstead o usng ndvdual stocks returns or coarng the erorance o assets rcng odels, ths aer develos ve ortolos ro the cobnatons o sze and value stocks over a ve years erod ro In te seres regressons, results o both the CAPM and the Faa and French odel ndcate that ntercet values are ether nsgncant or close to zero. However, the sloe coecents o SMB and HML (roxes or sze and value reus n Faa and French odel) are nsgncant n ajorty o ortolos. These results avor the use o the CAPM odel to estate exected returns. To check robustness o the results, excess returns o ndvdual stocks were also regressed on rsk actors. These set o regressons show alost slar results as results o the ortolo regressons. Fnally, all rs were ooled and a sngle regresson was estated both or CAPM and Faa and French. The results are alost unchanged. Key words: INTRODUCTION (Markowtz, 1952, 1958) lad the oundaton o the Modern Portolo Theory (MPT). He roved that ortolo return s equal to weghted average return o the assets n ortolo, but ortolo rsk s not the weghted average rsk o the assets. Rather the ortolo rsk s a uncton o weghts assgned to the assets, the varances n returns o the assets, and the covarance atrces aong the assets returns. The Markowtz Fraework was also called ean-varance raework because ratonal nvestor would choose only those ortolos that axze return or a gven level o varance or nze varance or a gven level o return. The Markowtz raework was consdered ractcally too dcult whle handlng a ortolo wth large nuber o assets because o the large nuber o covarance ters. To sly the rocess o choosng stocks, (Shar, 1964; Lntner, 1965) ntroduced sngle actor odel whch was very sle and ntutvely aealng. The odel was the Catal Asset Prcng Model or the CAPM. The odel reaned oular or alost 4 decades. Owng to ts slcty and attracton, t s stll the ost extensvely aled and taught asset rcng odel. The dea o CAPM s that all nvestors wll nvest n one ecent ortolo, called the arket ortolo or Portolo M. Portolo M ncludes all rsky assets and hence t s a coletely dversed ortolo. Investors would requre rsk reu on a gven assets based on the asset s contrbuton to the ortolo M rsk. The asset s nut to the ortolo rsk s easured by the rato o assets covarance wth the ortolo M to the varance o the ortolo M. In CAPM ternology, ths rato s called beta. The hgher the beta o an asset, the hgher s the requred rate o return on that asset. Wth ths sle aroach, nvestent decson s based on whether a gven asset oers as uch return as ts requred rate o return or not. Deste the aarent slcty and ntutvely aealng theory, CAPM has not stood r to ercal tests. Researchers lke (Douglas, 1968; Black, Jensen and Scholes, 1972; Mller and Scholes, 1972; Faa and MacBeth, 1973) nd that CAPM underestate the true rsk reu on securtes. In a ore recent study, Faa and French (1992) use a very large data set o US rs over a erod o to estate rsk reus on securtes. They ound that there are three coon rsk actors n stock returns. The lcaton o ther study s that CAPM understate rsk reu on sall rs and rs wth hgh book-to-arket rato n cross-secton returns. Ths ndng uts queston ark on the accuracy o exected returns calculated wth the CAPM. Tll date, CAPM s the ost wdely taught asset rcng odel n nance courses and wdely used odel aong racttoners because o ts slcty. Does the slcty o CAPM coe at the cost naccuracy? Does Faa and French odel gve consstently better results even outsde develoed econoes? These ercal questons need to be tested n derent te erods and n derent arkets lke eergng econoes. The objectve o ths aer s to nvestgate these questons n Pakstan catal arket. Corresondng Author: Attaullah Shah, Insttute o Manageent Scences, Peshawar. E-al: attaullah.shah@scences.edu.k 528

2 Aust. J. Basc & Al. Sc., 5(10): , 2011 The rest o the aer s organzed as ollows. In the next secton, theory and assutons o CAPM. Secton 3 dscusses the ethodology and data o the study. Secton 4 resents results o both CAPM and Faa and French odel. And the secton 5 concludes the aer. Lterature Revew: A. The Catal Asset Prcng Model: The oundaton o CAPM s based on the work done by (Harry Markowtz, 1959) where an nvestor s assued to be rsk averse. The nvestor ots or a ortolo based on the ean-varance crteron to choose ean-varance ecent ortolos. The CAPM converts the algebrac condton on asset weghts n eanvarance odel nto testable rohecy o relaton between exected return and rsk by recognzng an ecent ortolo asset rces are to clear the arket o all assets. Two ortant assutons are added to the Markowtz odel to recognze the ean-varance ecent ortolo by (Share, 1964; Lntner, 1965). One assuton s the borrowng and lendng at a rsk ree rate ndeendent o the aount borrowed and lent and the second assuton s the colete agreeent o nvestors about the assets returns ro revous erod to the current erod. Wth the colete agreeent about the dstrbuton o returns and rsk-ree borrowng or lendng, all nvestors see the sae nvestent oortunty set and nvest n avalable rsky ortolos. Investors choose ether to lend or borrow at rsk-ree rate (known as searaton theore o (Tobn, 1958)) and nvest n a ortolo that les at the ont o tangency o a lne ro rsk-ree rate to the rsky ortolo oortunty set. Snce all nvestors are n agreeent about the jont dstrbuton o returns and they nvest n the tangency ortolo (ortolo M), the rsk reu that an nvestor wll requre on a rsky assets deends on how uch an asset adds to the rsk o the ortolo. I return on an asset has saller covarance or zero covarance wth return o the ortolo M, the rsk-reu on that asset wll be saller even the asset s standard devaton ( a easure o total rsk o the asset) s greater. In ure atheatcal ters, rsk reu on the asset wll deend on the rato o the covarance o the asset s and the ortolo M s returns to the varance o the ortolo M s return. Ths rato s called beta (β); Cov( R, R ) Var( R ) CAPM assues lnear and ostve relatonsh between an asset s beta and the rsk reu on the asset. Beta s the sngle actor n estatng rsk-reu on rsky assets. Ths also suggests that beta catures all eleents o the asset s systeatc rsk. The rsky asset ust coensate nvestors or the oortunty cost o unds and the eleents o ts systeatc rsk. The oortunty cost o unds s equal to the return on rsk-ree assets or return on an asset that has zero covarance wth the ortolo M. the equaton o CAPM s derved n the ollowng anner. E R ) R [( E( R ) R ] (1) ( Where E(R) s the exected return based on rsk-ree rate and the assets systeatc rsk R s the rsk-ree nterest rate, E(R ) s the exected return on the arket ortolo, and β s the beta o asset, whch s also the sloe n regressng an asset s excess return on the arket's excess return. It was notced by Jensen (1968) that the Share-Lntner verson o CAPM whch relates the exected return and arket beta also les a te seres regresson test. As er Share and Lntner verson o CAPM, the exected rsk reu on M (ts beta tes the exected value o (R t - R t ) coletely exlans the exected value o the asset s excess return. In realty t s so, the ntercet ter n the te seres regresson Jenson s Alha ust be zero or each asset. In cross secton regressons, ercal studes suggest a ostve relaton between beta and average return but t s too lat where ntercet s the rsk ree rate and co-ecent on beta s the exected arket return n excess o the rsk ree rate (Jensen, 1968; Douglas, 1968; Black, et al., Slar ercal ndng were conred n the te seres studes by (Black, et al., 1972; Frend and Blue, 1970; Stanbaugh, 1982). The alure o CAPM to redct near-to-real world rsk reu on stocks ay be because o theoretcal alngs and any slyng assutons. (Ross, 1978) rghtly onted out that the theoretcal ortolo M, whch s central to the theory o CAPM, can never be observed n real world and hence (Ross, 1978) says that CAPM s unstable. In any ercal studes, CAPM understated rsk-reu on the stock o sall rs and rs wth hgh book-to-arket rato. These two eatures ght be roxes or addtonal systeatc rsk actors whch the CAPM als to cature. To hel redct rsk reus on such rs accurately, (Faa and French, 1993) 529

3 Aust. J. Basc & Al. Sc., 5(10): , 2011 suggested addton o two ore rsk reus to the CAPM equaton. Faa and French odel s dscussed next. B. The Faa and French Model: (Faa and French, 1993) suggested an alternatve to the CAPM that ncluded two addtonal actors whch heled exlan the excess returns on a stocks or a ortolo. In addton to the arket actor, or (R R ), Faa and French added SMB (Sall nus Bg) and HML (Hgh nus Low). The actor SMB reresented the average return on sall ortolos (sall ca ortolos), less the average return on bg ortolos (large ca ortolos). The HML actor reresented the average return on value ortolos less the average return on two growth ortolos. The value ortolos reresented stocks wth a hgh Book Equty (BE) to Market Equty (ME) rato and the growth ortolos reresented the colete ooste wth low BE/ME ratos. Faa and French ound that the addton o these two actors enabled a ore robust exlanaton o the varablty n ortolo returns. The three-actor odel s descrbed by equaton (3) where the exected excess return on ortolo s E( R ) R [ E( R ) R ] S E( SMB) h E( HML) (3) Where (E(R )-R ), E(SMB) and E(HML) are exected reus, and the actor senstvtes or loadngs β, S and H are the sloes n the te seres regresson, R R ( R R ) S SMB h HML (4) (Faa and French, 1992; 1995; 1996 and 2004) share one consstent thee, n that the CAPM wth ts sngle beta actor als to rce other rsks whch contrbute to the exlanaton o a ortolo's exected returns. Faa and French odel suers ro two robles whch are the absence o roer theory and the odels alure n soe ercal tests. The Faa and French three actor odel s ad hoc n nature. The odel haens to gve better results on a gven date set, but the theoretcal undernnngs are not strong as they are n case o CAPM. Though soe suortve theores are beng sought now n acadec lterature. Second roble s that estates based on Faa and French show serous consstency ssue when based on derent data sets or te horzons. Method: A. Data: The study tests the CAPM and Faa and French three actor odel usng onthly data o KSE stocks selected ro derent sectors over the erod o January 2003 to Deceber All KSE 100-ndex coanes were ntally selected ro whch 5-ortolo were to be ade at the ntersecton o Sze and B/M actors. Only those rs were ncluded or whch onthly share rce data were avalable n the sad erod. Frs wth negatve equty were excluded ro the analyss. Closng share rces o the selected rs were taken at the end o each onth. KSE 100 ndex was taken as the roxy or the arket ortolo. The roxy or rsk ree rate was the rate on Pakstan s t-blls n resectve erods. B. Portolo Develoent: Earler studes on CAPM used cross-sectonal regressons whch suered ro several estaton ssues o whch two wdely recognzed are () errors n the resduals because o ostve correlaton () betas o ndvdual assets n cross-sectonal regressons were recse. To overcoe these robles, (Blue, 1970; Frend and Blue, 1970; Black, et al., 1972) beleve that dversed ortolos gve better estates o betas as coared to ndvdual assets. Followng these researchers and (Faa and French, 1993), we work wth ortolos as wells as ndvdual stocks to test CAPM and Faa and French odel. Fro the sale, two grous o rs on the bass o sze were ade. The rst grou, called BIG ncluded twenty largest rs o KSE-100 Index and the second grou, called SMALL contaned twenty sallest rs. Usng B/M rato crteron, the rs were classed nto three grous. Hgh B/M grou had twenty rs wth hghest B/M rato; Medu B/M and Low B/M grous ncluded 20 rs each wth edu and low B/M ratos resectvely. To ensure varaton n the data set, all ossble ortolo sets at the ntersecton onts o the above 5 grous were ade. The ntersecton onts are 6, however, there was no ntersecton ont n one case whch let us wth only 5 ortolos. These ortolos are labeled as B/L (bg sze wth low B/M rato), B/M (Bg sze and ddle B/M), B/H (Bg sze and hgh B/M rato), S/L (Sall sze wth low B/M rato), S/M (Sall sze wth Mddle B/M rato), and S/H (Sall sze wth hgh B/M rato). Model Seccaton: For cross-sectonal regresson, the ollowng odel as s seced. 530

4 Aust. J. Basc & Al. Sc., 5(10): , 2011 E( R ) R [ E( R ) R ] Where E(R ) s the exected return on stock. R s the rsk-ree nterest rate, E(R ) s the exected return on the arket ortolo, β s beta o stock or the sloe coecent n the CAPM regresson equaton. The equaton or the te seres regresson suggested by Jensen (1958) s gven below. The excess return on asset the exlaned varable and the excess return on the arket varable s the exlanatory varable: R R [ R R ] Where d (R - R ) s the excessve return or the stock, o (R - R ) reresent arket reu, alha (α) value, derent ro zero, would ndcate addtonal rsk reu above or below what the CAPM suggest. In the CAPM odel β or beta s the sngle actor when t coes to rcng rsk. Faa and French three actor odel adds SMB and HML to account or sze and value reu. The Faa and French three actor odel equaton s: E( R ) R [ E( R ) R ] S E( SMB) h E( HML) Where E(R ) R ) reresent arket reu, E(SMB) s the sze reu, and E(HML) reresent value reu, and the actor senstvtes. β, S, H, reresent sloes n the te seres regresson, The te-seres equaton s gven as: R R ( R R ) S SMB h HML Lke n CAPM regressons, (R - R ) s the excessve return or the stock, (R - R ) reresent arket reu s the rsk reu on arket ortolo; Alha(α) s the ntercet o regresson equaton; and ε reresents unexlaned art o excess return o asset. Both o the odels, CAPM and Faa and French odel shows exected returns or ndvdual stocks. These odels can be transored to show exected returns or a ortolo by rearrangng as or CAPM, ER( ) ( ) R And or FF three actor odel. ER( ) ( R ) S ( SMB) h ( HML) Where ER( ) R P R and R = average return o ortolo. RESULTS AND DISCUSSION In ths secton, we rst resent descrtve statstcs o the selected ortolos and then resent results o the regressons. A. Descrtve statstcs: Monthly returns o the selected ve ortolos were calculated between January 2003 and Deceber 2007 as entoned n revous secton. descrtve statstcs o the selected ortolos are gven n Table 1. Table 1: Descrtve Statstcs o Selected Portolos. Portolos Paraeters A B C D E Mean 3% 4% 0% 5% 2% Medan 3% 4% -1% 5% 1% Maxu 16% 31% 35% 28% 22% Mnu -10% -26% -28% -15% -18% Std.Dev 6% 12% 11% 12% 9% Table 1 resents descrtve statstcs o ve selected ortolo. The letters A, B, C, D and E reresent varous ortolos. These ortolos are A= Bg sze wth low B/M ortolo, B= Bg sze wth Medu B/M ortolo, C= Sall Sze wth Low, B/M ortolo, D= Sall Sze wth Medu B/M ortolo, E= sall sze wth Hgh B/M Portolo. 531

5 Aust. J. Basc & Al. Sc., 5(10): , 2011 Aong the ve ortolos, ortolo D oered the hghest average onthly return o 5% ollowed by ortolo B oerng 4% onthly return. The axu onthly return was yelded by ortolo C havng sall sze wth edu book to arket rato (35%), and the nu onthly return was yelded by ortolo C agan. The standard devatons were on the hgher sde or both ortolos B and ortolo D havng a 12% standard devaton. The nu standard devaton was 6% or ortolo A. Table 2 shows the correlaton between the returns on ortolos. The hghest correlaton o 71% s between the stocks o ortolo E (sall sze wth Hgh B/M Portolo) and ortolo A (Bg sze wth low B/M ortolo), and between ortolo E (sall sze wth Hgh B/M Portolo) and ortolo D (Sall Sze wth Medu B/M ortolo). On the other hand the lowest level o correlaton (41%) was between ortolo B (Bg sze wth Medu B/M ortolo) and ortolo C (Sall Sze wth Low B/M ortolo). Table 2: Correlatons between Portolo Returns A B C D E A 100% B 45% 100% C 59% 41% 100% D 63% 54% 66% 100% E 71% 51% 60% 71% 100% Table 2 resents atrx o correlaton aong the returns o ve selected ortolo over the erod January 2003 to Deceber 2007 wth onthly requency. The letters A, B, C, D and E reresent varous ortolos. These ortolos are A= Bg sze wth low B/M ortolo, B= Bg sze wth Medu B/M ortolo, C= Sall Sze wth Low, B/M ortolo, D= Sall Sze wth Medu B/M ortolo, E= sall sze wth Hgh B/M Portolo. B. Regresson Result: The analyss was based on sngle varate regresson analyss or CAPM and ultvarate regresson analyss or Faa and French odel. The deendent varable or both o the analyss was the excess return on ve ortolos, whle ndeendent varable or CAPM was only arket rsk reu but or Faa and French odel there were two addtonal ndeendent varables whch were sze reu (SMB) and value reu (HML). Table 3 and 4 suarzes the results o CAPM regressons. To be accurate redctor o rsk reu, ntercet n the CAPM regresson should be ether zero or statstcally nsgncant or both. At a sgncance level o 5% all the ntercets o the ve ortolos were non-sgncant whle the rsk actors (β) were sgncant or the all ortolos. Table 3: CAPM Regresson on Portolos. Portolos α β1 t(α) t(β1) R-Square Bg Sze and Low B/M * * Bg Sze and Medu B/M * * Sall Sze and Low B/M * * Sall Sze and Medu B/M * * Sall Sze and Hgh B/M * * * Sgncant at 1% ** Sgncant at 5% Table 4: Sngle Regresson o all Portolos Stacked In One Colun CAPM Α β1 t(α) t(β1) R-square * * * Sgncant at 1% ** Sgncant at 5% Table 5: Faa and French Model Regressons o Portolos. Portolos α β1 β2 β3 t(α) t(β1) t(β2) t(β3) R-Square Bg sze and low B/M * * Bg sze and Medu B/M ** Sall Sze and Low B/M * 3.461* * * * * Sall Sze and Medu B/M * ** sall sze and Hgh B/M * * * * * Sgncant at 1% ** Sgncant at 5% The te seres regressons o Faa and French odel show that at a condence nterval o 99% n ve sze to value ortolos, the ntercets were nsgncant or all the ve ortolos (A, B, C, D and E). The arket rsk reu was sgncant n our ortolos (A, C, D and E) whle n ortolo B t was nsgncant. At a condence nterval o 99% ost o the ortolos ddn t show any sgns o sze and value reu. Only ortolo C (sall sze wth low B/M) showed value and sze reu. It should be noted n ortolo C that SMB coecent was ostve or sall ortolo conrng a sze reu. Slarly the HML actor was negatve or low B/M stocks deonstratng exstence o value reu. Excet ortolo C and E, no other 532

6 Aust. J. Basc & Al. Sc., 5(10): , 2011 ortolo showed any sgns o sze or value reu. Portolo C showed sze reu whereas ortolo E shows soe sgns o value reu. At a sgncance level o 5% alost sae result can be seen wth non-sgncant ntercet and wth a sgncant rsk reu but or the sze and value reu no conclusve evdence could be ound. Table 6: Faa and French Model sngle Regresson n all Portolos. α β1 β2 β3 t(α) t(β1) t(β2) t(β3) R-Square * * * * * Sgncant at 1% ** Sgncant at 5% Concluson: Assets rcng has hstorcally been a rghtenng task or the nvestors and the acadecans and a lot o eorts have been ade to nd out a unversal odel whch can ossbly redct the exected returns n an accurate anner. Assets rcng odels such as CAPM and FF three actor odels gve nconsstent results across arkets, data sets and te horzons. Recently, the Faa and French odel has erored relatvely better than the CAPM n ercal tests. CAPM stll antan ts char due to ts slcty and convenence whch s why racttoners want the CAPM dead or alve. The urose o ths study s to know whether slcty coes at the cost o accuracy n the case o CAPM and Faa and French Model. The sale or ths study was taken ro rs ncluded n the KSE 100 Index. Monthly returns were calculated or a erod o ve years ro 2003 to KSE 100 ndex was used as a benchark or the arket return whle Pakstan t-bll rates were used as a roxy or rsk ree rate. Fve ortolos were ade the ntersecton o sze and B/M rato. In searate regressons, the excessve returns o these ortolos were regressed on the relevant rsk actors o CAPM and Faa and French odel n te seres regressons. The result showed that ntercets were nsgncant or all the ortolos n both CAPM and Faa and French Model n the te seres regressons. In the case o CAPM, both the ntercet and beta coecents were as exected (.e the ntercet was nsgncant and the beta sgncant). However, Faa and French odel dd not gve conclusve results about the sze reu and B/M rato reu. Only one ortolo out o ve showed both sze and value reu whle another ortolo showed only value reu. The evdence n ths aer goes n avor o CAPM. REFERENCES Akgray, V., Condtonal Heteroscedastcty n Te Seres o Stock Returns: Evdence and Forecast. Journal o Busness, 62: Aleat, A., P. Gottardo, M. Murga, "The Prcng o Italan Equty Returns", Econoc Notes, 29(2): Bacheler, L., 1900, "Théore de la Séculaton", Annales de l'ecole Norale Suéreure de Pars. Baesel, B. Jeroe, "On the Assessent o Rsk: Soe Further Consderaton",Journal o Fnance, 29 (5): Barber, B. and J. Lyon, "Detectng long-horzon abnoral stock returns: the ercal ower and seccaton o test statstcs", Journal o Fnancal Econocs, 43(3): Beltratt, Andrea. and d Tra, Masso., "The Cross-secton o Rsk Prea n the Italan Stock Market", Econoc Notes, (31): Berk, J., A Crtque o Sze-Related Anoales, Revew o Fnancal Studes, 8: Black, Fscher, "Catal Market Equlbru wth Restrcted Borrowng", Journal o Busness, 45(3): Black, Fscher Beta and Returns, Journal o Portolo Manageent, 20(1): Blue, E., Marchall, On the Assessent o Rsk, Journal o Fnance, 6(1): Blue, M., "Portolo Theory; a Ste Towards Its Practcal Alcaton." Journal o Busness, 43(2): Breeden, T. Douglas, 1979, An Interteoral asset rcng odel wth stochastc consuton and nvestent oortuntes, Journal o Fnancal Econocs, 7: Chan, K. Lous, Narashan Jegadeesh and Jose Lakonshok, Evaluatng the erorance o value versus glaour stocks: The act o selecton bas, Journal o Fnancal Econocs, 38(3): Chan, K.C. Lous Yasush Haao and Jose Lakonshok., Fundaentals and Stock Returns n Jaan, Journal o Fnance, 46(5): Claessens, S., S. Dasguta and J. Glen., Return Behavor n Eergng Stock Markets, World Bank Econoc Revew, 9(1): Connor Gregory, Sehgal Sanjay, Tests o the Faa and French Model n Inda, Workng Paer, : Danel and Ttan, 1997, Evdence on the Characterstcs o Cross Sectonal Varaton n Stock Returns, Journal o Fnance, 52(1):

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