Estimating Short Run and Long Run Coefficients of Fundamentals Factors with Growth and Momentum Factor: Evidence from Emerging Markets

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1 Australasan Accountng, Busness and Fnance Journal Volume 0 Issue Artcle 3 Estmatng Short Run and Long Run Coecents o Fundamentals Factors wh Growth and Momentum Factor: Evdence rom Emergng Markets Adnan Shoab Bahra Unversy, Pakstan, adnanshoab@gmal.com Muhammad Ayub Sddqu FASTNatonal Unversy o Computer and Emergng Scences, Pakstan Follow ths and addonal works at: Copyrght 07 Australasan Accountng Busness and Fnance Journal and Authors. Recommended Caton Shoab, Adnan and Sddqu, Muhammad Ayub, Estmatng Short Run and Long Run Coecents o Fundamentals Factors wh Growth and Momentum Factor: Evdence rom Emergng Markets, Australasan Accountng, Busness and Fnance Journal, 0, 06, 737. do:0.53/aabj.v0.3 Research Onlne s the open access nstutonal reposory or the Unversy o Wollongong. For urther normaton contact the UOW Lbrary: researchpubs@uow.edu.au

2 Estmatng Short Run and Long Run Coecents o Fundamentals Factors wh Growth and Momentum Factor: Evdence rom Emergng Markets Abstract Ths study examnes the long term relatonshp o rsk premum and undamental actors n emergng stock markets o Chna, Inda and Pakstan keepng n vew leadng contrbuton o Fama and French 99 and Carhart 997 models. Contrary to the macroeconomc multactor models, ths study ncorporates rmspecc rsk actors related to the market premum; sze SMB, value HML, momentum WML and growth UMD as determnants o rsk premum. The rmspecc growth actor s ncorporated based on evdence rom Ho, Strange, and Pesse 008 by employng UMD whch s based on assets to market equy o the rm. Sample o 98 companes rom the three emergng markets or the perod o 0003 depcts market rsk premum as the leadng actor aectng rsk premum n Indan and the Pakstan markets. Results reveal market momentum beng hgh enough to overestmate coecents n the short run. However, the relatonshp s stablzed and adjusted n the long run. Chnese markets, where all the rsk actors seem to play ther role to determne rsk premum, are relatvely much stable and grownup and clearly represent matury o the Chnese markets. Dstncton between the short run and long run mght be useul or the nvestors o the three emergng economes. Accordng to the prncple o hgh rsk assocated wh hgh returns, small value happens to delver hgher returns wh hgher volatly. The growth stocks outperorm value stocks n these economes. Keywords FamaFrench, HML, SMB, WML, Market Gearng, Global Fnancal Crses, Long term relatonshp, Partal Adjustment Model Erratum Update le to Short Run and long run Ths artcle s avalable n Australasan Accountng, Busness and Fnance Journal:

3 Estmatng Short run and Long run Coecents o Fundamentals Factors wh Growth and Momentum Factor: Evdence rom Emergng Markets Adnan Shoab and Muhammad Ayub Sddqu Abstract Ths study examnes the long term relatonshp o rsk premum and undamental actors n emergng stock markets o Chna, Inda and Pakstan keepng n vew leadng contrbuton o Fama and French 99 and Carhart 997 models. Contrary to the macroeconomc multactor models, ths study ncorporates rmspecc rsk actors related to the market premum; sze SMB, value HML, momentum WML and growth UMD as determnants o rsk premum. The rmspecc growth actor s ncorporated based on evdence rom Ho, Strange, and Pesse 008 by employng UMD whch s based on assets to market equy o the rm. Sample o 98 companes rom the three emergng markets or the perod o depcts market rsk premum as the leadng actor aectng rsk premum n Indan and the Pakstan markets. Results reveal market momentum beng hgh enough to overestmate coecents n the short run. However, the relatonshp s stablzed and adjusted n the long run. Chnese markets, where all the rsk actors seem to play ther role to determne rsk premum, are relatvely much stable and grownup and clearly represent matury o the Chnese markets. Dstncton between the short run and long run mght be useul or the nvestors o the three emergng economes. Accordng to the prncple o hgh rsk assocated wh hgh returns, small value happens to delver hgher returns wh hgher volatly. The growth stocks outperorm value stocks n these economes. JEL Classcaton: G0, G30 Keywords: FamaFrench; HML; SMB; WML; Market Gearng; Long term relatonshp; Partal Adjustment Model Bahra Unversy, Pakstan FASTNatonal Unversy o Computer and Emergng Scences, Pakstan 7

4 AABFJ Volume 0, no., 06. Introducton Perormance o stock markets usng stock returns has long been studed by researchers n the area o nance. The rst ever explanaton o varaton n stock returns was gven by Black, Jensen, and Scholes 97, Lntner 965, and Sharpe 96 n respect o derent versons o the Capal Asset Prcng Model CAPM. CAPM remaned core o dscusson among the nancal economsts or many decades untl anomales o ths model were dented. Applcably o sole CAPM n derent stock markets n order to measure ecency through estmaton o requred rate o return and rsk premum has not been a successul experence n varous economes. Ths nsucent explanaton o the ecency o capal markets compelled researchers to nclude other actors that explan the cross sectonal varatons n returns other than excess market returns or market rsk premum. Studes 3 have dented many other actors such as sze o rms SMB, book to market equy HML and leverage causng varaton n stock returns. Fama and French 993 dened the crosssectonal varaton n the average market return as the common rsk actor assocated wh the stock returns. They developed and employed varables such as Smallmnusbg SMB and HghmnusLow HML that explan the cross sectonal varaton n the stock returns and rsk premum o the ndvdual stocks. Over the several years, s observed that Fama and French model s unable to explan returns momentum actor occurs. Carhart 997 developed the momentum eect and extended the Fama and French Model by ncorporatng momentum actor that explans momentum eect n equy returns. These multactor models replaced the classcal CAPM model that used n the past. They are currently oten employed n developed markets n portolo management, nvestment perormance evaluaton and even n legal practce or assessng damages n lawsus Mchell & Netter, 99. There are consderable emprcal evdences dentyng sze and value eect n developed markets and emergng markets 5. However, long run adjustment pattern o sze, value and momentum eect n equy returns s stll dsputed terrory o multactor models, speccally n south Asan emergng markets. Moreover, Derent emprcal studes lke Hamada 97, Masuls 983, Bhandar 988, Dmrov and Jan 008 and Korteweg 00 provde dverse evdence on gearng and stock returns n developed markets, but ewer studes n emergng markets have ocused on gearng eect and s adjustment n equy returns as prce rsk actor. The concept o emergng markets emerged n 980s that descrbed the countres wh specc characterstcs lke, less ndustralzed, less developed equy markets, less lqud Schoeneld, 0; Slva & Chávez, 008, hgher transacton cost Bekaert, Harvey, & Lundblad, 007; Lesmond, 005 but havng sgncant growth potental and more ntended to economc lberalzaton Khanna & Palepu, 03. Fama and French 998 ndcated that emergng markets have value premum n ther stock returns. Addonally, emergng markets requre specal creron to deal wh ther market normaton because o derental behavor o the stakeholders. Ths led the researchers to study the emergng economes that have specc characterstcs. Ths study s also targeted towards those emergng markets where nvestors have had smlar behavor and have strong trade tes that are Pakstan, Inda and Chna. Pakstan and Inda are now tryng to catch up Chna n the race o economc growth and process o development. 3 Banz 98, Basu 977, Stattman 980, Rosenberg, Red, and Lansten 985 and Bhandar 988; Fama and French 99 combned the sze and book to market value to capture the crosssectonal varaton n the stock returns; Fama and MacBeth 973 employed smlar varables usng regresson analyss or crosssectonal varaton o the average returns; Fama and French 993 urther rened the three actor model. O'Bren, Bralsord, and Gaunt 008; Bartholdy, Peare, and Wllett 000; and Lam Cakc, Fabozz, & Tan, 03; Lschewsk & Voronkova, 0 8

5 Shoab & Sddqu Estmatng Short run and Long run Coecents Ths study attempts to explan the long run adjustment pattern o equy returns under multactor models. Moreover, ths study attempts to explan the mpact o gearng eect on equy returns adjustment as prce rsk actor n emergng markets. Ths study also ncorporates SMB, HML, and WML as the common rsk actors n the determnaton o stock returns. WML representng the trend and momentum 6 o the market bult on wnnng and losng rms s ncorporated or momentum rsk actor 7. UMD represents another rsk actor related to market gearng, whch also depcts the uture growth prospects o the rm based on assetmarketequyrato n ths study Strong & Xu, 997. Eort has been made to capture the sgncance o rmspecc rsk actors or rsk premum n the emergng markets contrary to the ndngs o Fama and French 998. Fama and French 996 model explans only the ratonal behavor o prcng 8. Incorporaton o rmspecc growth actors market gearng measured through market leverage UMD mght determne stock returns to an extent. Prevous studes provde evdence o lnkage o market leverage and stock returns 9 Strong & Xu, 997. Market leverage, as dened n the secton 3, as the prce rsk actor s ncorporated n ths study. Methodologcally ths study employs autoregressve models to compare the shortterm and longterm relatonshp o rsk premum and rmspecc actors such as market premum, SMB, HML, WML and UMD. The sample o 98 companes ncludes 3 companes o KSE, 53 companes o SSE n Shangha A share Index and 30 companes o BSE rom CNX 500 or the perod o The data has been collected orm Thomson Reuter DataStream Database or SSE, BSE, and a certan proporton rom KSE and publshed reports o State Bank o Pakstan0. Thus, scope o the current study s derent rom the multactor models employed by Merton 973 and Ross Lerature Revew Behavor o stock returns n relaton wh rsk actors has been major ocus o the researchers and academcans n the area o nancal economcs durng the last couple o years. The poneer work relatng stock return wh rsk s studed n terms o Asset Prcng Model o Sharpe 96, Lntner 965, and Black et al. 97. Sharpe, Lntner and Black SLB explan the stock return through market rsk premum. The capal asset prcng model CAPM developed the way or the practoners to thnk about the relatonshp between rsk and return. So ar CAPM has been tested emprcally by many studes whose ndngs are dverse. The rst study on the CAPM was conducted by Lntner 965 and Douglas 967. These studes revealed that the ntercept was much bgger than rsk ree rate and beta had lower value, though statstcally sgncant. Dverse results related to CAPM are attrbuted to measurement error and data related ssues Mller & Scholes, 97. Just ater one year Fama and MacBeth 973 perormed the standard test o CAPM on portolo or crosssectonal valdaton and ound out weak sgncant beta. Fndngs o these studes do not support CAPM and nor do they support the assumptons o CAPM. Prevous studes also reveal secury market lne whch s latter than the one estmated by the CAPM. 6 The market momentum s the rate o acceleraton o prces over tme. The dea behnd momentum s that prces are more lkely to move n same drecton due to acceleraton rather than changng the drecton that may be requred due to any crcumstances 7 Carhart 997 dented the momentum or the capturng the persstence o returns anomaly 8 Fama and French 996 explans that Fama and French model only explans the ratonal prcng o the stock 9 Bhandar 988; Dmrov and Jan 008; Gomes and Schmd 00; Hamada 97 provdes evdence o lnkage o market leverage and stock returns 0 For detals vs For detals see lerature o Black et al. 97; Fama and MacBeth 973 9

6 AABFJ Volume 0, no., 06 The alure o CAPM model leads to the development o multactor model lke ICAPM by Merton 973 and APT by Ross 976 based on macroeconomc actors, but the pattern o change n macroeconomc varables s much derent rom the varaton pattern o stock returns and capal marketspecc actors. On account o dverse results rom the estmaton o CAPM, nancal economsts ntroduced other actors. Banz 98 ntroduced rm sze as the actor aectng returns o secury. The rm wh small sze produces hgher returns Fama & French, 99. Smlarly, Bhandar 988 explans that the leverage eect s also assocated wh the rsk and return. Stattman 980, Rosenberg et al. 985 arm the posve relatonshp between average return and book to market equy rato. Basu 977 nds out sgncant mpact o earnng to prce rato E/P. The results show statstcally sgncant relatonshp o E/P wh returns ater controllng rm sze and beta. Ball 978 ntroduced the yeld surrogates proxes or dentyng underlyng rsk or explanng the average returns. Based on the surrogates dented n the lerature Fama and French 99 developed ther model. Sgncant varables o the model whch current study has also employed, nclude capably o sze and book to market equy n explanng the crosssectonal varaton o expected returns. Fama and French 99 also ncluded book leverage, and earnng to prce rato n explanng the cross sectonal varatons o the expected return and they ound that book to market equy and sze both explaned the crosssectonal varaton n the expected return. The leverage and E/P rato s by desgn ncorporated when sze and book to market equy are used to dene the crosssecton. The current study employed the two sgncant varables o the Fama and French 99 such as HML and SMB along wh two other actors or determnng stock returns and ther eectveness n the long run. The average stock returns are not posvely related to market beta when portolos are ormed based on sze and beta Fama & French, 99. Fama and French 993 nvestgated the explanatory power o the crosssectonal varaton through the varables employed by Fama and French whch revealed that maxmum varaton n stock returns were explaned by book to market equy and sze. The returns on small stocks are more sensve to the rsk captured by sze actor than the returns on bg stocks. Further, Fama and French 995 analyzed the consstency o the behavor o stockreturns n relaton to sze and BE/ME and behavor o earnngs n relaton to sze and BE/ME. The results show weak consstency especally concernng the value actor whch s attrbuted to the measurement error o the varables. Fama and French 996 explan the pattern o stockreturns whch are not explaned by the capal asset prcng models. The CAPM model s unable to explan long term reversal n stockreturns and short term stockreturns. However, the Fama and French three actor model explans much o the anomales o CAPM model except the contnuaton o short term returns. The results show that the three actor model explans reversal o long term returns. Yet there are other anomales whch are stll unaddressed. These anomales are beyond the scope o ths study. Many studes lke Connor and Sehgal 00 ; Fa 00; Drew, Naughton, and Veeraraghavan 003; Prajutasen 00 and Srmarksuk 007 generalzed Fama and French model n derent countres and dented lnear exposure o stock returns to market returns, sze and value actor. Addonally these studes explan crosssectonal varaton n stock returns by employng methodology o Fama and French 993 model. In contrast, several studes Clare, Prestley, & Thomas, 998; Ferson & Harvey, 999; Kothar, Shanken, & Sloan, 995; Pham & Long, 007 have come up wh results derent rom Fama and Connor and Sehgal 00 also shows weak explanatory power o these varables sze, value and market n explanng earnngs growth rate. 0

7 Shoab & Sddqu Estmatng Short run and Long run Coecents French model. Maln and Veeraraghavan 00 tested the robustness o Fama and French model n the developed countres and revealed growth stocks generatng hgher returns than the value stocks whch s contrary to the Fama and French model. Chang, Johnson, and Schll 00 revealed sgncance o SMB and HML n the hgherorder systematc comoments n the crosssectonal regressons or portolo returns but statstcally SMB and HML emerged as nsgncant. These studes tested the valdy o Fama and French model. However, long run adjustment patterns o rsk premum n equy returns need to be addressed. Moreover, these studes on Fama and French model are targeted towards developed markets. The emergng markets may depct derent results on sze and value eect valdy. Employng Fama and French model s not a common practce emergng markets speccally n south Asan regon due lqudy ssues Schoeneld, 0; Slva & Chávez, 008, transacton cost Bekaert et al., 007; Lesmond, 005, and uncertanty n applcably o sze and value eect Zaremba & Koneczka, 0. However, n late 000s, researchers have shted ther ocus on explorng emergng markets. Barry, Goldreyer, Lockwood, and Rodrguez 00 nvestgated,000 emergng markets stocks and ound robust value eect n emergng markets. Dmson et al., 05 also concluded the sgncance o value eect n emergng markets. These studes explaned the valdy o sze and value eect n emergng markets. However, the long run adjustment patterns o sze and value premum n equy returns need to evaluated n case o emergng markets. Applcaton o the Fama and French model n derent markets also reveal avorable results 3. However, Fama and French model s unable to explan actors nvolved n persstence o mutual unds perormance n the short run. Hendrcks, Patel, and Zeckhauser 993, Goetzmann and Ibbotson 99, Brown and Goetzmann 995, Grnblatt and Tman 99, and Wermers 997 clamed persstence o mutual unds perormance n the short run whch can be attrbuted to the hot hands or common nvestment strateges or asymmetrc normaton. The nably o the Fama and French model n explanng persstence o returns was also dented n the Fama and French 996. The anomaly o persstence o returns, whch s also known as momentum anomaly, motvated Carhart 997 to develop extenson o three actor Fama and French model by ntroducng the momentum actors. Evdence o testably o ths model s consstent wh sze, book to market and momentum actor n explanng the persstence o returns. The study recommended that the unds wh hgher past returns lead to hgher than average returns n the ollowng perod. The present study tests ths lagged eect o the rsk premum on the current rsk premum by employng autoregressve models. L Her, Masmoud, and Suret 00 explored mplcatons o our actor model o Carhart 997 n Canada and revealed results consstent wh the Carhart our actor model. Cakc et al. 03 explaned the behavor o sze, value and momentum n emergng markets. The results, based on 8 countres analyss through regresson, suggested the promnence o value eects and bg stock shows hgher premum than small stocks, whch s contrary to Fama and French 99. Ths study tested the Carhart Model, but doesn t denty the adjustment pattern o the stock returns towards changes n undamentals. The present study dentes the adjustment pattern o the stock returns towards market based actors changes. Rouwenhorst 999 also tested the momentum actor mplcaton n 0 emergng economes and dented smlar pattern as that o developed economes. However, ther results are based on qualatve analyss. The presents study not only quantes the mpact but dentes the adjustment pattern whch Rouwenhorst, 999 s unable to denty n ther study. The above studes dented that ample work s done on emergng economes but nsgncant work s 3 Maln and Veeraraghavan 00, Pham and Long 007

8 AABFJ Volume 0, no., 06 done on s adjustment pattern n the long run and ther eectveness n the market. Fnancal theorsts consder debt as the prmary source o nancal rsk. Prevous studes dented dverse ndngs related to the nluence o gearng on stock returns. Modglan and Mller 958 henceorth MM ponted n rst proposon that the returns rom real assets aect the value o a rm. Second proposon o MM depcts levered rm value remanng constant, but the cost o equy ncreasng wh ncreasng rsk. Derent emprcal studes lke Hamada 97, Masuls 983, Bhandar 988, Dmrov and Jan 008 and Korteweg 00 provde dverse evdence on gearng and stock returns. Strong and Xu 997 examned market gearng as drectly assocated wh returns and book gearng as nversely assocated wh stock returns. Ho et al. 008 ponted out market gearng revealng condonal prcng relaton wh returns. Gomes and Schmd 00 examned posve relaton o returns wh market gearng but statstcally nsgncant relaton o stock returns wh book gearng. Fama and French 99 explan posve relatonshp o market gearng wh returns, but assocaton becomes negatve wh adopton o book gearng. George and Hwang 00 reveal negatve relaton o gearng wh returns because o sensvy o hgh levered rms to nancal dstress rsk. Garlapp and Yan 0 adopts dynamc model to denty the lnk between dstressrsk and asset returns by ncorporatng gearng and nd out gearng explanng stock returns partcularly or the rms wh hgh probables o deault. However, none o these studes dented the market gearng as a prcersk actor. Most o the studes dented relatonshp between market gearng and stock returns. The market gearng actually depcts the market lqudy o the rm that sgnals or the uture growth o the rm due to growth actor s calculated through market lqudy. These studes are mostly based on developed market so s requred to test the relatonshp n emergng markets as prce rsk actor. The tendency o market gearng to explans stock returns as the prcersk actor s stll unaddressed. In the context o prevous studes related to the sze, value, momentum premums o multactor models, the man gap have been dented n term o how equy returns wll be adjusted to rsk premum n long run long run adjustment o rsk premum n equy returns. As the emergng market as less lqud, so studyng the adjustment pattern o rsk premums n equy returns has major mplcaton to exstng body o knowledge. Pror studes also explaned the market gearng mpact on stock returns n developed market but market gearng mpact as prce rsk actor on stock returns o emergng markets need to be addressed. Furthermore, adjustment o equy returns to market gearng eect s also captured n ths study. The present study ncorporates market value o leverage as the proxy or market gearng. These eects may explan rratonal behavor as prce rsk actor. The longterm relatonshp reveals consstency o rsk premum as response varable to the market premum, SMB, HML, WML and UMD. The present study estmates both the shortterm and longterm relatonshps n order to sngle out the adjustment process n the long run 5 whch urther provdes ecency content o the markets. Prevous Studes 6 on emergng economes, sngle out the gap towards studyng long term adjustment pattern. O'Bren et al. 008,. Bundoo 008., 008,. Pham and Long 007, Prajutasen 00, Lam 005, Connor and Sehgal 00, Javd and Ahmed 008. All have eher lmed samples and / or employed GMM Generalzed Method o moments model and most o these studes are based on the GRS test. 5 Prevous studes based the long run consstency analyss on the employment o longer tme seres n the model. However, ths s not case as the long run adjustment dentes the long run consstency and adjustments 6 Iqbal, Brooks, and Galagedera 008 Testng Condonal Asset Prcng Model: An Emergng Market Perspectve. Monash Unversy, Australa Workng Paper 3/08..

9 Shoab & Sddqu Estmatng Short run and Long run Coecents 3. Methodology Expected return and rsk premum are sgncantly mportant or the nvestors and ther estmaton has been done by some o the leadng studes o undamental actor models 7 n nance. CAPM, Fama and French 99 models, and Carhart 997 our actor models are a ew to menton. Ths study employs the methodology o Fama and French 99 n denng the varables. The objectve o ths study s estmaton o longterm consstency o relatonshp between rsk premum and the undamental actors ollowng the ndngs o Carhart 997 wheren stockreturns take sgncant boost rom ther lagged values. Methodologcally present study employs one o the ecent models such as the concept o partal adjustment usng autoregressve dstrbuted lagged models and Quantle regresson method n order to descrbe longterm consstency and adjustment pattern o stock returns usng rsk premum. Fndngs o such models also provde some mportant mplcatons about ecency o the markets. The Quantle regresson s an attempt to compare varaton across varous quartles o the companes through medan eect o ndependent varables on the dependent varable such as rsk premum. Partal adjustment model has been constructed or estmaton keepng n vew nably o Fama and French 996 model n explanng persstence o returns known as momentum anomaly and ntroducton o momentum actors by Carhart 997. Ther ndngs that the unds wh hgher past returns lead to hgher than average returns n the ollowng perod justy applcaton o partal adjustment o rsk premum usng the autoregressve models. Addonally, Quantle regresson s employed to see medan eect o undamental actors on the rsk premum. 3. Partal Adjustment and Autoregressve Model * Consderng the adjustment o actual returns Y t to the desred returns Y t. Partal adjustment model assumes that actual changes are equal to proportonal optmal change. Mathematcally relatonshp o actual and desred returns can be wrten as * Y Y = λ Y Y. t t t t Where, λ s the adjustment coecent 8, whch can also be consdered as the speed o adjustment. The greater the speed o adjustment, the hgher the ecency and the hgher the value o λ. Though tradonally the value o λ cannot be greater than but ollowng ndngs o Carhart 997 that the unds wh hgher past returns lead to hgher than average returns, the value o adjustment coecent can be greater than. The desred stock returns can be plotted aganst ndependent varables the actors as shown n the equaton. * Y β X =... Where the X s the ndependent varables and Y * s desred value o the dependent varable. Beng nose or rcton as component o the market, the gap between actual and 7 The models that uses observable asset or rm specc varable such as rm sze, market value, dvdend yeld etc. or development o actors s known as Fundamental Factor Models "Factor Models or Asset Returns," 006; Zvot & Wang, 007. Ths study used establshed undamental actor models lke CAPM, Fama and French Model, Carhart Four Factor Models, ve Factor model based on growth actor 8 The adjustment coecent reers to the rate at whch the actor loadng adjust n short runs that cumulatvely leads to complete adjustment n long run 3

10 AABFJ Volume 0, no., 06 desred s bound to exst. Incorporatng such a marketorented realy o nose the equaton 3 s derved rom the rst two equatons. Y µ * = Y t + λ Y Y t +. 3 Where, µ s the nonadjusted gap n each perod. Puttng equaton n 3 that s Y µ = Y t + λ β X Y t + Y λβ + µ.. 5 = λx + λ Y t So, the operatonal expresson o the equaton can be wrten accordng to the varables under nvestgaton. R λβ + µ 6 = λ Rm + λ R t R + λ R = λβ λ R t + µ m λ SMB 3 λ HML 7 Based on the Carhart 997 model the momentum actor s ncorporated and based on prevous studes, the mmc rsk actor based on market leverage as proxy or gearng 9 s also ncorporated n the model R λ WML 5 = λβ λ R m + λ R t λ SMB 3 + µ λ HML 8 R λ WML 5 = λβ λ R m λ UMD 6 λ SMB + λ R 3 t λ HML + µ 9 The equatons 8 and 9 provde shortterm relatonshp between the dependent and the ndependent varables. The longterm relatonshp can be estmated by dvdng each coecent by the estmated value o λ. 3. Quantle Regresson Analyss Quantle regresson provdes estmates o the lnear relatonshp between regressors and a speced Quantle o the dependent varable Koenker & Bassett Jr, 978. Least absolute devatons LAD s one o the specal cases o Quantle regresson whch corresponds to tng the condonal medan o the response varable the rsk premum. Quantle regresson descrbes better condonal dstrbuton o the response varable than condonal mean n the OLS analyss. Researchers can analyze any selected proporton o the response varable aected by the regressors ncluded n the model. It s robust method o modelng because s not based on assumptons related to the normal dstrbuton..d. 9 For theoretcal consderatons see lerature o Garlapp and Yan 0; Ho et al. 008; Strong and Xu 997

11 Shoab & Sddqu Estmatng Short run and Long run Coecents Quantle regresson model 0 corresponds to lnear regresson model as descrbed n 0. R p 5 = β WML p p 6 p R m UMD + µ p p 3 SMB p HML 0 Where 0 < p < ndcates the proporton under Quantle at p. Expected value o the error terms s 0 n lnear regresson model. Correspondng Quantle regresson s shown n equaton. Q R β p HML R m p 5, SMB, HML = β WML p 6 UMD p p R m p 3 SMB + The derence n the error term o the derent Quantles can be wrten as shown n equaton P q p q p q p q p q µ µ = β β + β β R m + β 3 β 3 SMB + β β HML p q p q + β 5 β 5 WML + β 6 β 6 UMD Where R = Stock returns o the th company at tme t, R = Rsk ree rate, R m = Market return o the stock market usng KSE 00 Index as proxy, SMB = Small mnus bg n terms o sze, HML = Hgh mnus low n terms o value actor, WML= Wnner mnus Looser n terms o average stock returns at t, UMD= Up mnus Down n terms o market gearng rato Varables used n the model are descrbed n the paragraphs to ollow. 3.3 Small mnus Bg SMB Overall value o the rm denes sze actor. Fama and French 99 dened sze as the market value o a share at year end December 3st tmes outstandng shares. In ths study sze varable s represented by the market value o a share at year end December 3st tmes outstandng shares. The SMB means small mnus bg stock returns o the portolo. In other words, SMB s the derence between the stocks returns o the small rms portolo and stock returns o the bg rms portolo. The present study uses the approach o Fama and French 0 n whch the sze breakponts are 3rd, 7th, 3th, and 5th percentles o the regon s aggregate market capalzaton, whch corresponds to Fama and French Hgh mnus Low HML The book to market equy rato s calculated as book value o equy BE o the rm dvded by market value o equy ME o the rm. Fama and French 99 consdered common equy plus deerred taxes as the book value and market prce o share as on 30 June scal year end tmes the outstandng shares as market value. The HML varable s developed to ncorporate value actor that explans varatons n the stock returns. The HML means hgh mnus low, whch s, the derence between returns o 0 For detals see lerature o Koenker and Bassett Jr 978 5

12 AABFJ Volume 0, no., 06 the portolo wh hgh BE/ME and the returns o the portolo wh low BE/ME. The portolos are developed usng the approach o Fama and French 0 n 5 portolos are sorted through sze book to market equy rato. 3.5 Wnner Mnus Loser The wnner mnus loser s developed to ncorporate the momentum actor that explans the varatons n the stock returns. The WML s the wnner mnus looser that s the derence between portolo o top perormer stocks and portolos o lower perormer stocks. Fama & French, 0 approach s used to develop WML actor by developng 5 portolo sorted through sze and lagged momentum. Accordng to Carhart 997, the anomaly o the Fama and French 99 that s related to persstence o returns that s also known as momentum anomaly due to whch the Carhart 997 developed the momentum actor that leads to urther studes n momentum eect Lee & Cho, Up mnus Down The gearng rato depcts nancal rsk employed by the rm. The market leverage as proxy or gearng s beng calculated as total assets dvded by market prce o shares As on Year end December 3 st tmes outstandng shares as calculated n Strong and Xu 997 and many other studes. The up mnus down s developed to ncorporate the mpact o rm uture growth opportuny that can explan the varatons n current stock returns. The UMD s upmnusdown and s the derence between the returns o portolo o hgher market gearng and returns o the portolo o lower market gearng. The 5 portolos are developed sorted through sze and growth measure, whch s consstent to the approach o Fama and French 0. Accordng to Strong and Xu 997 and Gomes and Schmd 00 the market gearng has mpact on stock returns. However, ths study dentes whether the market gearng s the prce rsk actor or not. For ths purpose the portolo are developed on the bass o market gearng and prce rsk actor s developed n the same manner as n Fama and French 99. The market gearng actually depcts the market lqudy o the rm that sgnals or the uture growth o the rm due to growth actor s calculated through market gearng or lqudy. 3.7 DATA Ths study employs 3 year monthly stock prces o 3 companes lsted n Karach Stock Exchange KSE; 30 companes o BSE ncluded n CNX 500, and 53 companes o SSE ncluded n Shangha or the perod o January00 to December03. Annual and bannual reports o the companes were que handy n the constructon o SMB and HML. The source o data s Thomson Reuter DataStream Database or Inda and Chna, but or Pakstan Annual Reports o the Companes, State Bank o Pakstan, and Thomson Reuter DataStream database were accessed. Long span o the data set provdes an opportuny to crcally explore applcaton o undamental actor models under derent economc suatons. Ths s the rst study o s knd that not only explans the longterm applcably o Fama and French n emergng economes but also attempt to capture maxmum anomales o the model. The emergng countres selected n sample are Inda, Chna and Pakstan because o In analyss, the term lqudy and growth s used nterchangeably 6

13 Shoab & Sddqu Estmatng Short run and Long run Coecents smlar nvestment pattern n these countres at the start o ther journey o growth teen years ago. Ltle emprcal work s ound on the applcably o Fama and French model n these emergng economes whch motvated the selecton o these countres n the sample. Moreover, these countres are the major players o the South Asa and ther economc mportance cannot be gnored. Based on the descrbed crera, cumulatvely the sample o 98 companes are ncorporated n the sample over the perod o 0003 that leads to 85,690 observatons or data ponts on the bass o whch results are estmated.. Analyss o Results Fndngs rom the estmaton o the models dscussed n the prevous secton are presented n ths secton. Results o the estmated Quantle regresson usng medan as the creron are also analyzed n ths secton. Shortrun causal relatonshp o rsk premum and the actors such as SMB, HML, WML and UMD are explaned rom the results depcted n table. The longterm relatonshp o the same varables s descrbed rom the results presented n table. Table 3 ndcates results o the Quantle regresson. Fve determnants o rsk premum are addressed n ths study. These ve determnants represent ve derent stages o development o capal market theores. The market premum represents Sharpe 96, Lntner 965, and Mossn 966. The Fama and French 99 model s represented by addonal two actors such as sze actor SMB and value actor HML. The model o Carhart 997 ntroduces momentum actor WML and Ross 976 model adds one more actor known as rm specc growth actor UMD. The short run estmaton o requred rate o return has been shown rom CAPM through FF Model, our Factor model 3, and rm specc growth actor, or Chna, Inda and Pakstan. In all the three countres, CAPM stock returns are sgncantly explaned by the market rsk premum p < % but the value o beta s less than beta < 70% n Pakstan and Chna whereas s hgher than or Inda. Overall perormance o the secures n the markets o Chna and Pakstan s deensve nstead o aggressve. On the contrary perormance o secures n Inda looks aggressve based on value o CAPMbeta greater than on the average. The stock returns are explaned n Pakstan and Chna by the market rsk premum o almost 67% and 6% respectvely ndcatng less sensvy o excess returns towards market rsk premum n these two countres. Volatly o the rsk premum s relatvely hgher n Inda than the other two countres where premum has been comparatvely stable durng the perod rom 00 to 03. Regardng the Fama and French FF model, SMBbeta s sgncant p < % wh a negatve sgn n Pakstan only. The value o SMBbeta reveals bgger rms accrung better rsk premum than the smaller ones n Pakstan Fa, 00; Gustason & Mller, 999. Inda and Chna have receved posve and sgncant value o the SMBbeta representng results as per ndngs o the Fama and French Fama & French, 99, 993 that the smaller rms outperorm n terms o rsk premum than the larger ones. The HMLbeta s nsgncant wh negatve sgn n Inda relectng value actor o the bg rm havng nsgncant role n the determnaton o rsk premum. However, HMLbeta s sgncant wh negatve sgn or the stock market o Chna and Pakstan n all the models rom through. These results clearly represent growth o the Chnese markets to consderable matury level. Durng the growth o rms, rsk premum s negatvely aected. Inverse relatonshp o value and rsk premum s also reerated rom the models whch Wh the purpose to denty the other envronmental actor mpact, the data s dssected n to two porton and estmated ndvdually. The results remans the same under both segments. 7

14 AABFJ Volume 0, no., 06 nclude momentum actor WML and rm specc growth actor UMD Chen & Zhao, 009; Danel & Moskowz, 03; Ho et al., 008. The negatve UMD s consstent wh the noton that nvestors requre greater return on assets wh less market lqudy to remburse them or the substantal cost o tradng these assets Ibbotson, Chen, Km, & Hu, 03.The value o HMLbeta s posve and sgncant on the th model whch nclude rm specc growth UMD and momentum WML actors. It means Pakstan secury markets return posve premum to the nvestors rom the growth o ther busness n the event o momentum and the value actors. Sgncance o the HMLbeta n the presence o WML actor s supported rom the posve and sgncant values o WMLbeta and UMDbeta n the models 3 and or Pakstan secury markets where pvalue < % n the Carhart 997 model and multactor model Agarwal & Poshakwale, 00; Asness, Moskowz, & Pedersen, 03. It can be concluded that rsng leverage n act causes an ncrease n the rsk whereby expected returns are ncreased Ho et al., 008. In Model 3 and the WMLbeta s 0.0 and 0.0 wh pvalue < %. Momentum actor s also negatve and sgncant or Chna. Ths negatve and sgncant relatonshp s aganst the ndngs o Carhart 997. Ths suaton s possble under only two scenaro. Frst, eher market s llqud.e. ocusng on looser stock, the market llqudy has progressve eect on and vce versa s correct or wnner stocks. When the market s llqud the hgh tradng cost reduces nvestor emnence. Subsequently, the broaden llqudy gap among wnner and looser ntend the looser portolo to earn hgher return to recompense or llqudy Acharya & Pedersen, 005. The second condon s that the volatle bearsh market s depcted by negatve beta o WML, whch llustrates that WML ecently short volatly n panc perod e.g. Grundy and Martn 00. So, can apparently nerred that the sample perod under consderaton s panc perod n Indan market and behavor o WML n such case s lke short call opton but only n panc perods Danel & Moskowz, 03. Comparatve analyss o the three countres ndcates requred rate o return o Inda beng hghly sensve to market rsk and nelastc to value, sze, momentum, and growth beta 3. Ths may be attrbuted to attude o nvestors who delberately ollow market rsk rather than value, sze, momentum and rm specc growth or the estmaton o requred rate o return. In case o Chna the stock returns are aected by market rsk, sze, value, momentum and rm specc growth actors. Such a mature attude o the nvestors relects establshed stock markets o Chna whch s more ecent than the Indan and Pakstan markets. The dagnostcs such as standard error o regresson, values o AIC and SBC are on the lower sde whch s avorable relecton o the models n terms o ness. Sgncance o the Fstats shows justes the relatonshp among dependent and ndependent varables. The long run relatonshp o rsk premum and s determnants actors are explaned rom the results shown n Table. As dscussed n the secton related to the methodology, long run s the perod ndcatng adjustment whch takes place n many short runs. The value adjustment parameter λ n all the models s more than uny. Carhart 997 recommended that the unds wh hgher past returns lead to hgher than average returns n the ollowng perod. Ths justes the value o adjustment parameter λ greater than. Results presented n table reveal reduced value o the ntercepts n the long run. As the value o ntercept tends to zero the models are valdated n the three markets o Chna, Inda and Pakstan. Values o the short run rsk actors are also stablzed n the long run that s why ther absolute values are reduced n the long run. Sensvy o stock returns towards actors 3 Frm Specc growth Coecent s reer to as Growth beta 8

15 Shoab & Sddqu Estmatng Short run and Long run Coecents s normalzed n long run. The derence s short term and long term coecent seems to be small because the derence only shows adjustment n one month. However, the cumulatve adjustment over the year s que substantal. Long run results show that the nvestors gve consderable mportance to market rsk or the estmaton o stock returns n rather than sze, value, momentum, and growth beta n Pakstan. The betas o sze, value, momentum, and growth are urther reduced n long run depctng that value o stock s explaned by market rsk n the long run. Very hgh sensvy o Indan market beta n the short run s reduced rom an average value o.05 to n the long run. The Indan market rsk beta stll remans major actor explanng stock returns n the long run. Here agan relatvely less weght s assgned by the Indan nvestors to sze, value, momentum, and rm specc growth actors. The abnormal returns are also reduced n the long run n the Indan stock markets. The abnormal returns are also reduced n long run n the Chnese stock markets because results are normalzed n the long run. However, sgncance o all the actors aectng rsk premum remans the same. These ndngs unequvocally relect matury o nvestors n the Chnese markets whch have grown up durng the perod o study. Results o Quantle regresson wh condonal medan are presented n table 3. The resultng betas o the actors under consderaton MPREM, SMB, HML, WML, and UMD are derent rom the actor loadngs dscussed above n estmatng medan stock returns. In case o Pakstan, the estmate o SMBbeta s sgncant wh posve values o 0.0, 0.008, and 0.06 n the three models. These values ndcate posve rsk premum attached to small rm due to hgher rsk o deault. Smlarly, the HML remans sgncant at medan stock returns wh negatve sgn ndcatng growth stock outperormng the value stock n Pakstan. The UMD retans prce rsk actor or medan stock returns. The luctuaton n stock returns s generally explaned by market rsk beta despe the act that other actors are sgncant but wh lower values. The negatve and sgncant value o WMLbeta n Inda retans volatly and bearsh market attude. More or less results o the Quantle regresson are consstent wh the ndngs dscussed earler. The robustness o the coecents s tested through Wald Coecent restrcton test, whch dented that coecents depcts true eects o the actor on stock returns. The results are not reported due to space savng purpose 9

16 AABFJ Volume 0, no., 06 TABLE : SHORT RUN RELATIONSHIP Ths table presents the short run relatonshp o stock returns wh asset prcng actors based on undamentals. The undamental actor models that are estmated or studyng short run relatonshp are CAPM, FFModel, Carhart our Factor Model 3, and our actor model wh rm specc growth actor. These models are estmated or Inda, Pakstan and Chna. The MPREM s the market premum, SMB s sze actor, HML s value actor, WML s momentum actor, and UMD s rm specc growth actor. Varables Pakstan Inda Chna Constant ** ** ** ** ** ** ** ** ** ** ** MPREM ** ** ** **.05 3.** ** ** ** 0.6.8** ** ** ** SMB ** ** ** ** ** 0..** ** ** ** HML * * 0.07.* ** ** ** WML ** ** ** ** ** ** UMD ** ** ** S.E. Regresson AIC SBC DW Stat FStats 890.** ** 88.0** ** 893.8** 703.9** 3776.** 38.6** 60.** 58.8**.0** 368.** * Sgncance at 5% level ** Sgncance at % level The models that are estmated n above table are R = β R + µ R = β R SMB HML + µ m R = Rm 3 SMB HML R β WML + µ 3 m 3 R = Rm 3 SMB HML WML 30 R β UMD + µ

17 Shoab & Sddqu Estmatng Short run and Long run Coecents TABLE : LONG RUN RELATIONSHIP Ths table presents the long run relatonshp o excess returns and asset prcng actor based on undamentals. The short run results are adjusted through adjustment coecent λ or attanng long run relatonshps and patterns. The patterns o sgncance remans the same. However, the actor loadngs vares among short run and long run depctng val mplcaton to relatonshps. Where MPREM s the market premum, SMB s small mnus bg, HML s hgh mnus low, WML s wnner mnus looser, UMD s up mnus down. Varables Pakstan Inda Chna Constant ** ** ** ** ** ** ** ** ** ** ** MPREM ** ** ** ** ** ** ** ** ** ** ** ** SMB ** ** ** ** ** 0..** ** ** 0.37* 7.6** HML 0.0.5* * 0.0.* ** 0. 3.** 0.09* 6.** WML ** ** ** ** ** ** UMD ** ** ** S.E. Regresson AIC SBC DW Stat FStats 890.** ** 88.0** ** 893.8** 703.9** 3776.** 38.6** 60.** 58.8**.0** 368.** * Sgncance at 5% level ** Sgncance at % level The models that are estmated n above table are R = β R + µ R = β R SMB HML + µ m R = Rm 3 SMB HML R β WML + µ 3 m 3 R β UMD + µ R = Rm 3 SMB HML WML 3

18 AABFJ Volume 0, no., 06 TABLE 3: QUANTILE REGRESSION Medan Ths table presents Quantle regresson at medan that dentes the mpact o undamental prcng actors on the condonal medan o excess returns. Ths provde complete pcture o dstrbuton o excess returns over tme seres. The model characterstcs lke sparsy, standard error o regresson and sgncant Quas LR stat shows the goodness o o the model. Where MPREM s the market premum, SMB s small mnus bg, HML s hgh mnus low, WML s wnner mnus loser, UMD s up mnus down. Varables Pakstan Inda Chna Constant ** ** ** ** ** ** * ** ** ** ** MPREM ** ** ** ** ** ** ** ** ** ** ** ** SMB 0.0.0** ** ** ** ** ** ** ** ** HML ** ** ** ** ** ** WML ** ** ** ** ** ** UMD ** ** Sparsy S.E. Regresson Quas LR Stat 535.5** 53.8** ** 538.3** 669.0** ** 707.5** 737.9** 85.9** 530.5** 53.5** 509.5** * Sgncance at 5% level ** Sgncance at % level The models that are estmated n above table are R β R + µ R = m R = Rm 3 SMB HML R β WML + µ 3 R β HML + µ R = Rm 3 SMB R β UMD + µ R = Rm 3 SMB HML WML 3

19 5. Concluson Ths study examnes the longterm consstency o undamental actor models based on adjustment n the short run, n the emergng markets o Chna, Inda and Pakstan. Ths study also examnes the rm specc growth actor measured by market leverage as a prce rsk actor explanng stock returns. The emprcal ndngs o ths study denty that actor based on market leverage s the prce rsk actor due to sgncant growth beta. The longterm consstency suggests that market momentum, s hgh enough to overestmate the coecents n short run whch are later, stablzed or adjusted n the long run. The stock returns n the short run mght be overestmated whch are normalzed n the long run. The longterm rsk premum can be consdered as eectve requred rate o return. Results o the quantle regresson retan smlar relatonshp o the requred rate o return and the rsk actors dented by the classc contrbuton o Sharpe 96, Lntner 965, Mossn 966, Fama and French 99, Carhart 997, and Ross 976. Addonally, coecents o quantle analyss are slghtly derent rom the other models. The derence may be due to nonnormaly o the stock returns rom the selected tme seres. The study provdes unque behavor related to emergng economes n applcaton o Fama and French 99 and Carhart 997 and addon o rm specc growth actor. Ths study dentes sze beta beng posvely assocated wh excess returns n emergng economes. The premum s attached to small rms due to hgher deault rsk rather than poor earnng n the depresson as mentoned Fama and French 993. Moreover, the value beta s ound as eher nsgncant or negatvely assocated wh stock returns. Growth stocks outperorm value stocks n these markets. Emergng economes suer rom long bearsh trend that leads to negatve momentum beta depctng volatle and bearsh markets. The negatve growth beta also depcts longtme down market spans n emergng economes as characterzed by lerature related to the emergng economes. The study supports Fama and French 998 that clamed that the emergng economes has value premum and results are consstent wh O'Bren et al. 008 and Connor and Sehgal 00. These results are nconsstent wh the studes based on developed countres Chang et al., 00; Maln & Veeraraghavan, 00. Ths study provdes the new nsght to asset prcng models based on market specc and company specc actors, n the categores o undamental actor models. Ths study dentes rm specc growth actor as prce rsk actor that may lead nvestor rratonaly. However, there are also actors whch explan excess returns. The unusual behavor o HML actor also provdes dssecton o value actor n the emergng economes o Chna, Inda and Pakstan. Usng the concept o Fama and French hypothess, requred rate o return s to be compared wh market portolo returns. Accordng to the prncple o hgh rsk assocated wh hgh returns, small value happens to delver hgher returns wh hgher volatly and growth stocks outperorm value stock n emergng economes. Ths rskreturn relatonshp elucdated by Fama and French model mght be very useul or medum and long term nvestors. In sum, small cap stocks have hgher average returns than large cap stocks. Chna has been observed as one o the most stable market among all the three economes o Inda, Pakstan and Chna where all the rsk actors play ther role to determne rsk premum. Contrary to ths, rsk premum s mostly determned by the market rsk actor n Inda and Pakstan. Eectve polcy measures should be taken to brng matury and ecency n the Indan and the Pakstan markets. 33