2. Literature Review Theory of Investment behavior

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1 Effec of Equy Rsk Facors on he Reurn of Sock Porfolos of Companes Lsed a he Narob Secures Exchange n Kenya Beween 2009 and 2014 Mchael.N. Njogo 1* Edde Smyu 2 Sephen. T. Wahaka 3 Deparmen of Accounng and Fnance, School of Busness, Kenyaa Unversy, Kenya *Posal Address: KCA Unversy, P.o. Box , Narob, Kenya Absrac Invesors and nvesmen advsors srve o make he bes nvesmen decsons when formng a sock porfolo. However, a he Narob secures exchange n Kenya, mos nvesors are no opmzng he reurn of her sock porfolos because hey do no consder relevan facors when nvesng n socks. In parcular, hey do no consder equy rsk facors when formng sock porfolos. In he Uned Saes of Amerca, Dmensonal fund advsors have shown ha f acve nvesors l her sock porfolo owards equy rsk facors such as value rsk and sze rsk, he reurn of he sock porfolo formed s beer han ha of he marke porfolo. Capal asse prcng model has been he generally acceped model for explanng he relaonshp beween rsk and sock porfolo reurn varaons. However, he resrcve assumpon of employng he marke rsk as he only source of rsk n capal asse prcng model led o he nroducon of mulple facors models ha aemp o denfy oher sources of rsks ha are dsregarded by he capal asse prcng model. Avalable emprcal evdence sugges ha much of he varaon n sock reurns relaed o sze rsk, value rsk, momenum rsk, profably rsk and nvesmen rsk s lef unexplaned by Capal asse prcng model. Ths movaed he researcher o examne a model ha adds he fve rsk facors o capal asse prcng model. As a resul, a sx facors model was developed and used o deermne he ably of he combned sx equy rsk facors n explanng he varaon of sock reurns a he Narob secures exchange n Kenya. The general objecve of hs sudy was o esablsh he effec of equy rsk facors on he reurn of sock porfolos of companes lsed a he Narob secures exchange n Kenya beween 2009 and The sudy adoped he explanaory research desgn and he arge populaon was 45 companes ha were lsed a he Narob secures exchange by January 2009 (afer excludng companes ha were no radng conssenly and hose ha were delsed). A census of 45 companes was used o consruc sock porfolos beween 2009 and Daa was analyzed usng a modfed Fama and French (1996) mulvarae me seres regresson mehodology. The sudy found ou ha marke rsk, sze rsk, value rsk and nvesmen rsk have a sgnfcan effec whle profably rsk and momenum rsk have a weak posve effec on he reurn of sock porfolos a he Narob secures exchange. Ths sudy recommends a framework for enhancng facor nvesng sraeges, nroducng exchange raded funds ndex and revewng polces on prce deermnaon of lsed socks. The sudy avaled o nvesors, nvesmen advsors and academa he equy rsks ha are worh consderng when consrucng a sock porfolo a he Narob secures exchange for opmal sock reurns. Keywords: Sock Porfolo, Equy rsk facors, Sock Porfolo Reurn, Narob Secures Exchange n Kenya. 1. Inroducon Raonal nvesors are neresed n fndng ou why reurn of a gven sock porfolo dffers from ha of anoher sock porfolo (Rro & Wambugu, 2015). Capal asse prcng model (CAPM) by Sharpe (1964) has been he generally acceped model for explanng why he reurn of a sock porfolo vares from one sock porfolo o anoher sock porfolo. I predcs a posve lnear relaonshp beween marke rsk and sock reurns (Fama & French, 1993). As such, CAPM s based on he assumpon ha sock reurn varaon s only explaned by he marke rsk (Carhar, 1997) and no oher facor should have he power n explanng sock reurn varaons. However, Fama and French (1992) es on CAPM usng Uned Saes of Amerca (US) sock marke daa found ou ha marke rsk alone could no fully explan he sock reurn varaons. Furher, Hebner (2014) sudy usng US sock marke daa found ou ha CAPM explaned abou 70% of sock reurn varaons whle Rro and Wambugu (2015) sudy usng Kenyan sock marke daa found ou ha marke rsk explaned abou 51% of sock reurn varaons. Ths means ha he explanaory power of CAPM dffers from one sock marke o anoher (Aron, 2011) and changes n sock reurn should be of neres o nvesors snce can be used o deermne approprae sock nvesmen sraeges o be adoped. The oucome of Fama and French (1992) es on CAPM led o search for oher facors ha could mprove he explanaory power of CAPM. In 1993, Fama and French developed a hree facor model for descrbng he relaonshp beween US socks reurn and rsk facors. They found ou ha exposure o marke rsk, sze rsk and value rsk explan much of he sources of rsk ha accoun for sock porfolo reurn varaons. Hebner (2014) dd a follow up emprcal es on he Fama and French hree facors model and found ou ha he 31

2 explanaory power of he hree facors model on he US sock reurn was abou 93%. Anoher sudy by Rro and Wambugu (2015) usng Kenyan sock marke daa found ou ha Fama and French hree facors model explaned abou 62% of sock reurn varaons. Clearly, ncorporaon of sze rsk and value rsk no CAPM boased he explanaory power on sock reurn varaons. Ths shows ha Fama-French (1993) hree facor model s an mprovemen of CAPM bu sll leaves some unexplaned sock reurn varaons. Avalable ndependen emprcal sudes sugges ha much of he varaon n sock reurns relaed o sze rsk (Hunsad, 2015), value rsk (Ameer, 2013), momenum rsk (Jegadeesh & Tman, 1993), profably rsk (Novy-Max, 2010) and nvesmen rsk (Aharon, Grundy & Zeng, 2013) s lef unexplaned by Capal asse prcng model. Thus, developng an elaborae asse prcng model by ncorporang oher sgnfcan equy rsk facors apar from marke rsk remans a grey area n fnance (Goyal, 2011). Ths movaed he researcher o examne a model ha adds he fve rsk facors o Capal asse prcng model. As a resul, a sx facors model was developed and used o deermne he ably of he combned sx equy rsk facors n explanng he varaon of sock reurns a he Narob Secures Exchange n Kenya. Invesors and nvesmen advsors srve o make he bes nvesmen decsons when formng a sock porfolo (NSE, 2011). However, a he Narob Secures Exchange n Kenya, mos nvesors are no opmzng he reurn of her sock porfolos because hey do no consder relevan facors when nvesng n socks (CMA, 2010). In parcular, hey do no consder equy rsk facors when formng sock porfolos (Hebner, 2014). In he Uned Saes of Amerca, Dmensonal fund advsors have shown ha f acve nvesors l her sock porfolo owards equy rsk facors such as value rsk and sze rsk, he reurn of he sock porfolo formed s beer han ha of he marke porfolo (Carson, 2013). Ths s due o he fac ha n he long run small cap socks generae hgher sock reurns han large Cap socks and value socks generae hgher reurns han growh socks (Fama & French, 1993). Whle many sudes on equy rsk facors and porfolo consrucon have been done elsewhere, n Kenya only a few known o he researcher have been done and documened. For example Kamanda (2001) sudy on he equy porfolos held by Kenyan nsurance companes concluded ha majory of nsurance companes mananed poorly dversfed porfolos. Murur (2014) sudy on he effec of sysemac rsk on sock reurn found ou ha marke rsk and sock reurn had a srong negave auocorrelaon. He concluded ha apar from marke rsk, sock reurn could be a funcon of many oher rsk facors. However, he faled o denfy he oher rsk facors. Rro and Wambugu (2015) sudy on asse prcng model ess concluded ha Fama and French hree facors model performs beer han capal asse prcng model bu dd no capure oher relevan equy rsk facors nfluencng he reurn of a sock porfolo formed a NSE. The sudy also faled o capure oher relevan equy rsk facors responsble for he varaon n sock reurn. The ndenfed conexual gaps movaed he researcher o develop a sx facors model for esablshng he ably of marke rsk, sze rsk, value rsk, momenum rsk, profably rsk and nvesmen rsk n explanng he varaon of he reurn of a sock porfolo a NSE. The general objecve of hs sudy was o esablsh he effec of equy rsk facors on he reurn of sock porfolos of companes lsed a he Narob secures exchange n Kenya beween 2009 and Ths sudy s srucured as follows: Chaper one provdes he background of he sudy, saemen of he problem and he general research objecve. Chaper wo presens relevan heorecal revews, emprcal revews and he concepual framework. Chaper hree provdes deals on he research desgn, arge populaon, emprcal modelng and daa analyss whle Chaper four covers daa analyss resuls, presenaons and dscussons. Fnally, Chaper fve provdes a summary of fndngs, concluson, recommendaons and suggesed areas of fuure sudes. 2. Leraure Revew Theory of Invesmen behavor Jorgenson (1963) heory of nvesmen behavor was presened n hs publcaon on capal heory and nvesmen behavor. Accordng o hs heory, demand for a sock s movaed by he nvesors desre o maxmze her ne worh. To es he heory of nvesmen behavor, Jorgenson (1963) fed a sochasc equaon usng quarerly daa from US manufacurng companes beween 1948 and The es concluded ha he level of nvesmen n socks s deermned by pas changes n he prce of he desred sock, he value of replacng he sock, he long erm response of he sock prce o he underlyng marke condons, ax srucure and fuure changes n he demand of he sock. In her conrbuon o nvesmen heory, Jegadeesh and Tman (1993) sudy on momenum sock radng sraeges usng US sock markes daa noed ha purchasng socks of pas wnners and sellng sock of pas losers realzed sgnfcan posve reurns over a holdng perod of beween 3 and 12 monhs. They arbued he realzed posve reurn o delayed sock prce reacons o frm specfc nformaon. However, Sharpe, Alexander and Baly (2006) arbued momenum effec o a marke anomaly where socks whch ouperform peer durng he las 12 monhs end o perform well also n fuure. Pure momenum porfolos are 32

3 creaed usng socks wh he sronges momenum and sellng socks wh he lowes momenum (sambaugh, Yu & Yuan, 2012). Theory of Invesmen behavor herefore, enables nvesors o undersand how marke condons, profably, momenum and nvesmen amoun nfluence nvesmen decsons. The heory of nvesmen behavor was mporan n hs sudy snce helped he researcher n explanng he effecs of marke, profably, momenum and nvesmen rsks on he reurn of a sock porfolo a NSE. Effcen Marke Hypohess Theory Fama (1970) formulaed he effcen marke hypohess and saes ha s mpossble o bea he marke snce marke effcency causes he exsng sock prces o always ncorporae and reflec all he avalable nformaon (Beechey, Gruen and Vckery, 2000). Ths means ha Socks wll always rade a her fundamenal or far values, makng mpossble for nvesors o sell hem a nflaed prces or purchase socks ha are undervalued (Fama, 1970). I s herefore no possble o ouperform he marke porfolo hrough echncal analyss, fundamenal analyss or marke mng (Beechey, Gruen and Vckery, 2000). The only way an nvesor can oban hgher reurns s by nvesng n rsker nvesmens (Malkel, 2003). Thus, here s a lnear posve relaonshp beween sock reurn and rsk. Njuguna (2015) sudy nvesgaed he sock marke effcency of he Narob secures exchange n Kenya. He used he NSE 20 share ndex daa from 2000 o Afer analyzng he daa usng run es and seral correlaon es, he concluded ha Narob secures exchange n Kenya s effcen n a weak form. He also noed a subsanal mprovemen n he effcency of he Narob secures exchange beween 2000 and Ths suggess ha he advancemen n echnology ha was wnessed a he Narob secures exchange beween 2000 and 2015 may have conrbued o he ncrease n s effcency. Malkel (2003) observed ha EMH has been challenged by economss who sress ha psychologcal and behavoral facors nfluence he deermnaon of sock prces and by economercans who argue ha sock reurns are predcable. Bergen (2011) also noed ha here are many sock nvesors who have conssenly beaen he sock marke. For example warren buffe s consdered as one of he greaes sock marke nvesor of all mes because he has beaen he sock marke for many years. The ne worh of warren buffe was $ 62 bllon as of EMH heory was mporan n hs sudy snce aded n explanng he relaonshp beween he reurn of a sock porfolo and porfolo rsk. I was also helpful n explanng how EMH anomales (such as sze effec and value effec) a NSE could be exploed o earn superor reurns. Modern Porfolo Theory Modern porfolo heory was proposed by Markowz (1952) n hs publcaon on porfolo selecon. I s a heory n fnance ha explans how o maxmze porfolo expeced reurn for a gven amoun of porfolo rsk or mnmze rsk for a gven level of expeced reurn, by carefully choosng he proporons of varous asses consung a porfolo. Accordng o Markowz (1952), a porfolo exhbs rsk and reurn characerscs based on s composon and he way hose componens correlae wh each oher. For each level of rsk, here s an opmal asse allocaon ha s desgned o produce he bes balance of rsk versus reurn. An opmal porfolo wll provde eher he hghes reurns or he lowes rsk of all possble porfolo combnaons. I wll aemp o balance he lowes rsk for a gven level of reurn and he greaes reurn for an accepable level of rsk. The meeng pon of each level of rsk and reurn was consdered by Markowz as he pon where an opmal porfolo resdes. Fabozz and Markowz (2002) publcaon on he legacy of modern porfolo heory (MPT) posulaed ha porfolo heory helps nvesors o fnd a balance beween maxmzng porfolo reurn and mnmzng porfolo rsk. They furher observed ha porfolo heory provdes a powerful ool o complemen acvely managed porfolos and also assumes ha nvesors expec a hgher reurn for a hgher level of rsk. Ths mples ha here s a posve lnear relaonshp beween expeced reurn and rsk (Mannng & Naper, 2012). Once an advsor esablshes nvesor s level of rsk, he can consruc a porfolo ha maxmzes expeced porfolo reurn for a gven level of rsk (Mannng & Naper, 2012). The heory was used o denfy he equy rsk facors componens and o provde a lnkage beween rsk dversfcaon and he selecon of socks. Capal Asse Prcng Model Capal asse prcng model (CAPM) was developed by Sharpe (1964) usng he foundaon ha was lad by Markowz (1952) n hs modern porfolo heory (Ksaka, Mbh & Kur, 2015). I was he frs model o quanfy a rade-off beween sock reurn and rsk and s based on he assumpon ha marke rsk s he only explanaory varable n he varaon of sock reurn (Fama & French, 2012). Accordng o Campbell (2000), CAPM has been he generally acceped prcng heory ha lnks sock reurn and rsk. However, emprcal sudes such as Fama and French (1993), Novy-Marx (2010), Rro and Wambugu (2015) among ohers, have shown ha he source of rsk nroduced by CAPM does no fully explan he sock reurn varaons. Therefore, oher rsk facors need o be denfed and ncorporaed n a more comprehensve asse prcng model. CAPM was mporan n hs sudy snce provded a lnk beween marke rsk and sock reurn. 33

4 I also helped n measurng marke rsk and explanng he proporon n he varaon of sock reurn ha s explaned by he varaon n marke rsk. Fama- French Three Facor Model In 1993, Fama and French dd a sudy on common rsk facors n he reurns on socks and bonds usng daa from US sock marke. Ther sudy proposed a hree facor model whch s an mprovemen of he CAPM. The model s expeced reurn of asse j s compued as follows: R j R f = α + β ( Rm Rf) + β SMB + β HML jm js wherer s he reurn of asse j for monh, R f s he rsk free rae, R m s reurn of he marke, SMB=small j mnus bg and s he dfference beween he reurns on a dversfed porfolos of small socks and bg socks, HML= Hgh mnus low and s he dfference beween he reurns on a dversfed porfolos of hgh book o marke (value) socks and low book o marke (growh) socks and he beas are he slopes n he mulple regresson measure of exposure of asse j o each of hese sources of rsk and l s he dosyncrac erm. Afer analyzng her daa usng mulvarae me seres regresson analyss, Fama and French (1993) found ou ha marke rsk, sze rsk and value rsk are sgnfcan deermnans of sock porfolo reurn. The resuls of he analyss also show ha Fama and French (1993) hree facors model has a beer explanaory power han CAPM (Fama & French, 2012). Laer, Eraslan (2013) carred ou a sudy o es he valdy of he Fama and French hree facor model usng daa from he Isanbul sock exchange. He consruced nne porfolos usng sze and book-o- marke rao of frms n order o explan varaons n excess porfolo reurns usng marke rsk, sze rsk and book- o- marke rao rsk facor. He found ou ha sze facor had no effec on porfolos wh bg-sze frms bu could explan excess reurn varaons of porfolos wh small and medum szed frms. He also found ou ha Book o marke rao has an effec on porfolos wh hgh book o marke rao frms. He concluded by observng ha he hree facor model has a power o explan varaons on excess porfolo reurns bu hs power flucuaed hroughou he es perod. These sudes have demonsraed ha he hree facors model has a beer explanaory power han CAPM. However, he model sll leaves some unexplaned sock reurn varaons. Ths sudy adoped he hree facors ogeher wh oher hree rsk facors o form a sx facor model. The proposed model was expeced o have a beer explanaory power on sock reurn han he hree facors model. Fama and French hree facor model s mporan n hs sudy snce provdes some of he prmary equy rsk facors (marke rsk, sze rsk and value rsk) ha drve sock reurn and also provdes a sraegy for usng equy rsk facors n he consrucon of sock porfolos for a poenally hgher expeced long erm sock reurn. Concepual Framework A concepual framework refers o a group of conceps ha are broadly defned and sysemacally organzed o provde a focus, a raonale, and a ool for he negraon, presenaon and nerpreaon of nformaon (Cooper & Schndler, 2006). The concepual framework depced n fgure 2.1 below shows he relaonshp beween equy rsk facors (Marke rsk, Sze rsk, Value rsk, Profably rsk, Momenum rsk and Invesmen rsk) and reurn of a sock porfolo. Equy rsk facors are he ndependen varables whle he reurn of a sock porfolo s he dependen varable. jh + l 34

5 Fgure 2.1: Concepual framework Auhor (2017) 3. Research Mehodology Ths sudy adoped he explanaory research desgn. The desgn s preferred n suaons where a researcher n carryng a causal effec nvesgaon (Cooper& Schndler, 2006) such as esablshng he effec of equy rsk facors on he reurn of sock porfolos of companes lsed a he Narob secures exchange n Kenya. The arge populaon was 45 companes ha were lsed a he Narob secures exchange by January 2009 (afer excludng companes ha were no radng conssenly and hose ha were delsed). A census of 45 companes was used o consruc sock porfolos beween 2009 and Desk revew research was used o collec secondary daa from he Narob Secures Exchange daa Bank and Cenral bank of Kenya (CBK) daa bank. Secondary daa on lsed companes, lsed companes monhly closng sock prces, number of shares raded, marke capalzaon, Book value, marke value, Treasury blls rae and NSE20-share ndex values were exraced from he NSE and CBK daa banks for sx years ( ). NSE 20-share ndex reurn was used as he proxy for marke reurn whle Kenya 91-day Treasury bll rae was used as he proxy for he rsk free rae. The daa colleced was hen used o measure sock reurns and equy rsk proxes for sock porfolos a NSE beween 2009 and Usng a modfed Fama and French (1996) procedure weny four porfolos of socks were consruced as follows: Sx sze and Value porfolos were consruced based on he nersecon of he wo marke capalzaon and hree Book/marke rao sors, Sx sze and momenum porfolos based on he nersecon of he wo marke capalzaon and hree las 12 monhs average reurn sors, Sx sze and profably porfolos based on he nersecon of he wo marke capalzaon and hree Gross prof rao sors, Sx sze and Invesmen porfolos based on he nersecon of he wo marke capalzaon and hree growh n oal asses sors. Ths s presened n appendx I. The sudy adoped a modfed Fama and French (1996) mulvarae me seres regresson mehodology whch nvolved runnng me seres regressons o oban he esmaes of he rsk facor loadngs. Excess reurns (R -R f ) of he 24 porfolos consruced were regressed agans he sx equy rsk facors and he coeffcens of he rsk facors esmaed. The mulvarae me seres regresson model was specfed as follows: R R f = α + β 1 MTR + β 2 SR + β 3 VR + β 4 PR + β 5 MR + β 6 IR + l, 35

6 Where R = Coeffcen s of VR IR = : R f R = Value = Excess Rsk = Invesmen 1,..., 72 = Re urn = Tme Re urn rsk a me, PR Rsk on perod sock on sock facors, MTR a me, l porfolo n monhs porfolo = Marke = Pr ofabl, = The a me, R y error a me, α Rsk Rsk f = Rsk a me, SR a me, MR erms, = 1,..., 24 free rae a me, = Inercep = = Frm = Momenum Number, β, β, β, β, β, β 1 sze of 2 Rsk 3 Rsk 4 a me, porfolos a me, 4. Resuls and Dscussons The Focus of hs sudy was o esablsh he effec of equy rsk facors on he reurn of sock porfolos of companes lsed a he Narob secures exchange n Kenya. A modfed Fama-French (1996) mulvarae me seres mehodology was employed o es he null hypohess ha equy rsk facors have no sgnfcan effec on he reurn of sock porfolos a NSE. Dagnosc Tess Dagnosc ess were done o assess he valdy of he regresson models and also o provde gudance for furher sages of he regresson analyss. Mul-collneary ess, Auocorrelaon ess, Heeroscedascy ess and saonary ess were done. The oupus of he dagnosc ess are presened n appendx II. Resuls of he correlaon analyss beween pars of he ndependen varables ndcaed ha he correlaon coeffcens were beween -0.7 and Ths mples ha here s no mul-collneary among he equy rsk facors used n he model. Thus, he sx equy rsk facors can be used n he same model whou causng problems of mulcollneary (Cooper & Schndler, 2006). Auocorrelaon es shows ha here was no auocorrelaon snce he values of he Durbn Wason d-sascs for all he 24 porfolo models ncorporang he sx equy rsk facors les beween 1 and 3. Ths means ha he error erms of 72 monhs were no correlaed. The effcency of he esmaors was herefore no affeced and he sandard errors were no dsored. Hence, he es-sascs compued and he conclusons made were relable (Gujara, 2003). Breusch pagan es for heeroscedascy shows ha majory of he P-values are greaer han 0.05 ndcang consan varance of he error erms. Ths mples ha he esmaed coeffcens of he 24 regresson models are farly unbased. Fnally Phllps Perron (1988) un roo es suggess ha we rejec he null hypohess of a un roo n he varables snce all he crcal values a 1%, 5%, and 10% levels of sgnfcance are greaer han he es sascs for all he varables. We herefore conclude ha he me seres of he varables was generaed by a saonary process. Resuls of he dagnosc ess gave he researcher an assurance ha he oupus of he 24 regresson models were no spurous, -raos compued were no dsored and he sgnfcance ess done were vald. Equy Rsk Facors and Excess Reurn of a sock Porfolo Usng secondary sock daa from NSE and CBK (beween 2009 and 2014) and he help of Mcrosof excel he researcher compued he reurns of all he 45 socks and hen consruced 24 sock porfolos usng he equy rsk facors. Thereafer he reurns of he 24 sock porfolos were compued as well as he equy rsk values. The resuls of he relaonshp beween equy rsk facors and excess reurn of sock porfolos were hen presened afer adopng he Fama-French (1996) mulvarae me seres regressons. The sascal sgnfcance on he naure of he relaonshp beween socks porfolo reurn and equy rsk facors was esablshed afer analyzng he modal values of he sascs n he summary of conclusons on he 24 socks porfolo regresson models. The resuls are presened n appendx III. Hypoheses Tess Ths sudy esed he sascal sgnfcance of he sx rsk facors used n he model a 5% level of sgnfcance. The -values of he coeffcens of he facors were used o es he followng null hypoheses: H 01 : Marke rsk has no sgnfcan effec on he reurn of sock porfolos a NSE Afer esng he null hypohess, was observed ha all he absolue -values of he coeffcens of marke rsk for he sx facors model were greaer han he able crcal -sasc value of These resuls lead he researcher o a concluson ha marke rsk s sascally sgnfcan n he proposed sx facors model. The mplcaon of hs concluson s ha marke rsk has a sgnfcan effec on he reurn of sock porfolos a he Narob secures exchange. Furher, he coeffcens of marke rsk n he sx facors model had a posve sgn. Ths mples ha here s a sgnfcan posve relaonshp beween marke rsk and he reurn of sock porfolos a he Narob secures exchange. The hgher he exposure of a sock porfolo o marke rsks, he hgher he reurn of he sock porfolo. Ths means ha he reurn of a sock porfolo moves n he same drecon wh ha of he marke porfolo. These fndngs concur wh hose of oher researchers. For example, Sharpe (1964) sudy found ou ha here s a srong lnear relaonshp beween marke rsk and he sock reurn of frms lsed n he Uned Saes,

7 of Amerca sock markes whle Heshma (2012) sudy found a weak posve lnear relaonshp beween Saud Araban sock reurns and marke rsk. In Kenya, Rro and Wambugu (2015) ess of asse prcng models found ou ha marke rsk was a sgnfcan predcor of sock reurn bu does no fully explan he reurn of a sock porfolo formed a Narob secures exchange. The concurrence of he fndngs n dfferen sock markes can be arbued o he fac ha reurn of a sock porfolo moves n he same drecon wh ha of he marke porfolo. H 02 : Sze rsk has no sgnfcan effec on he reurn of sock porfolos a NSE Afer esng he null hypohess, was observed ha egheen (18) of he sze rsk absolue -values were greaer han he able crcal -sasc value of Only sx (6) of he sze rsk absolue -values were less han he able crcal -sasc value of Thus, majory of he value rsks were sascally sgnfcan. Ths mples ha sze rsk s a sascally sgnfcan predcor of sock reurns. Therefore, sze rsk has a sgnfcan effec on he reurn of a socks porfolo a he Narob secures exchange. Furher, majory (13) of he coeffcens of sze rsk are negave. Ths s an ndcaon ha here s a sgnfcan nverse relaonshp beween sze rsk and he reurn of a socks porfolo a he Narob secures exchange. The hgher he exposure of a sock porfolo o small sze socks, he hgher he reurn of he sock porfolo. These fndngs concur wh hose of oher researchers. For example Banz (1981) sudy dscovered ha small sze frms have hgher reurns han large sze frms a he New-York sock exchange. In Kenya, Rro and Wambugu (2015) ess of asse prcng models found ou ha value rsk was a sgnfcan predcor of sock reurn a Narob secures exchange. The concurrence of he fndngs n dfferen sock markes can be arbued o he fac ha small sze companes are nherenly rsker han large sze companes and nvesors n small cap socks demand a correspondng hgher rae of reurn. H 03 : Value rsk has no sgnfcan effec on he reurn of sock porfolos a NSE Resuls of he null hypohess es show ha seveneen (17) of he value rsk absolue -values were greaer han he able crcal -sasc value of Only seven (7) of he value rsk absolue -values were less han he able crcal -sasc value of Ths mples ha value rsk s a sascally sgnfcan predcor of sock reurns. Ths lead he researcher o a concluson ha value rsk has a sgnfcan effec on he reurn of a socks porfolo a he Narob secures exchange. Furher, majory (13) of he coeffcens of value rsk were posve. Ths s an ndcaon ha here s a sgnfcan posve relaonshp beween value rsk and he reurn of a socks porfolo a he Narob secures exchange. The resuls are n concurrence wh Fama and French (1993) sudy on cross-secon of expeced sock reurns usng US sock daa whch found ou ha here s a posve relaonshp beween value rsk and he reurn of a sock porfolo. Furher, Ameer (2013) sudy concluded ha value rsk s a sgnfcan deermnan of Paksan sock reurn and ha value rsk s nernaonal n characer. The concurrence n he sudes could be arbued o he fac ha frms wh hgh book value o marke value rao are perceved o be more rsky and nvesors are compensaed wh hgher reurns. H04: Profably rsk has no sgnfcan effec on he reurn of sock porfolos a NSE A close analyss of he coeffcens of profably rsk shows ha majory (13) of hem had a posve sgn. Ths s an ndcaon ha here s a posve relaonshp beween profably rsk and sock reurn a he Narob secures exchange. I was also observed ha sx (6) of he profably rsk absolue -values were greaer han he able crcal -sasc value of On he oher hand, egheen (18) of he profably rsk absolue - values were less han he able crcal -sasc value of Ths mples ha profably rsk has an nsgnfcan posve effec on he reurn of a socks porfolo a he Narob secures exchange. Snce some of he profably rsk values were sascally sgnfcan, we can conclude ha profably rsk has a weak posve effec on he reurn of sock porfolos a he Narob secures exchange. Some of he sudes ha have found a srong and sascally sgnfcan relaonshp beween profably rsk and sock reurn nclude Novy-Marx (2013) sudy whch found ou ha profably has a sgnfcan power of predcng sock reurns of companes lsed n he Uned Saes of Amerca sock markes whle Ksser (2014) emprcal sudy concluded ha an nvesmen sraegy based on sorng socks on gross profably generaes subsanal excess sock reurns. Concurrence of a posve profably effec n dfferen sock exchanges s arbued o he fac ha profably shocks are posvely correlaed wh sock reurn. H 05 : Momenum rsk has no sgnfcan effec on he reurn of sock porfolos a NSE An analyss of he coeffcens of momenum rsk shows ha majory (16) of hem had a posve sgn. Ths s an ndcaon ha here s a posve relaonshp beween momenum rsk and sock reurn a he Narob secures exchange. Afer esng he null hypohess, was observed ha four (4) of he momenum rsk absolue -values were greaer han he able crcal -sasc value of On he oher hand, weny (20) of he momenum rsk absolue -values were less han he able crcal -sasc value of Ths mples ha momenum rsk has an nsgnfcan posve effec on he reurn of a socks porfolo a he Narob secures exchange. However, snce some of momenum rsk values were sascally sgnfcan, we can conclude ha momenum rsk has a weak posve effec on he reurn of sock porfolos a he Narob secures exchange. 37

8 Oher smlar sudes done n oher counres nclude Barbers, Shlefer and Vshny (1998) sudy whch arbued momenum profs n he US socks markes o nheren bases n he way nvesors nerpre nformaon whle Pan (2010) sudy argued ha profably of momenum sraeges for US socks s arbued o he fac ha shor-erm sock reurns are posvely correlaed over shor lags of me. In Kenya, Rro and Wambugu (2015) sudy observed ha momenum rsk and sock reurns were posvely relaed. The concurrence n he posve relaonshp beween momenum rsk and sock reurns n dfferen sock markes could be arbued o nvesors under reacon o sock marke nformaon. H06: Invesmen rsk has no sgnfcan effec on he reurn of sock porfolos a NSE An analyss of he coeffcens of nvesmen rsk shows ha majory (16) of hem had a negave sgn. Ths s an ndcaon ha here s a negave relaonshp beween nvesmen rsk and sock reurn a he Narob secures exchange. Afer esng he null hypohess, was observed ha en (10) of he nvesmen rsk absolue -values were greaer han he able crcal -sasc value of On he oher hand, foureen (14) of he nvesmen rsk absolue -values were less han he able crcal -sasc value of Ths mples ha nvesmen rsk has a sgnfcan negave effec on he reurn of a socks porfolo a he Narob secures exchange. These resuls are n concurrence wh hose of Cooper, Gulen and schll (2008) sudy ha concluded ha US frms wh low nvesmen n he curren perod measured by asse growh end o have hgher reurns n he nex perod han frms wh hgher asse growh whle Tman and Xe (2004) found ou ha fnancng choces for US frms ha are assocaed wh ncrease n capal nvesmens resuls n negave sock reurns. The concurrence n he negave relaonshp beween nvesmen rsk and sock reurns s arbued o he fac ha asse growh has a forecasng power on sock reurns. 5. Summary of fndngs, Concluson and recommendaons The relaonshp beween sock reurns and rsk facors n developed sock exchanges has been horoughly documened n fnance and nvesmen leraure. However, here s lmed research on hs opc n developng sock markes (Chawana, 2011).Esablshng he effec of pre-specfed equy rsk facors on he reurn of sock porfolos a he Narob secures exchange n Kenya s a move owards conrbung leraure on he relaonshp beween equy rsk facors and reurn of sock porfolos n developng sock exchange markes. Ths sudy hypoheszed ha here s no relaonshp beween equy rsk facors and he reurn of sock porfolos a he Narob secures exchange. From he Fama-French (1996) mehodology, he null hypohess was rejeced and was concluded ha equy rsk facors have an effec on he reurn of sock porfolos a he Narob secures exchange. Summary of Fndngs Marke Rsk and Reurn of Sock Porfolos a NSE Marke rsk has a sgnfcan posve effec on he reurn of sock porfolos a he Narob secures exchange. Ths ype of rsk capures he amoun of exposure of a socks porfolo o he overall marke flucuaons as a resul of facors ha affec he overall performance of he sock marke. Invesors should herefore consder sock marke facors such as day o day marke news, recessons n he economy, changes n neres rae, nflaon rae and currency rsk when makng nvesmen decsons a he Narob secures exchange. Furher, nvesors should esablsh he general performance of he marke ndex before makng nvesmen decsons. Ths s because here s a general posve relaonshp beween sock reurn and sock marke reurn. An upward rend n he value of he NSE 20 share ndex ndcaes ha here s a general ncrease n he prces of socks a NSE. Such an upward rend s a sgnal for a possble profable nvesmen n socks a he NSE. Sze Rsk and Reurn of Sock Porfolos a NSE The fndngs of hs sudy have shown ha sze rsk has a sgnfcan negave effec on he reurn of sock porfolos a he Narob secures exchange. Ths demonsraes he exsence of value effec a he Narob secures exchange. They also show a concurrence on he exsence of sze effec n developng as well as developed sock exchanges. Ths was arbued o he fac ha small sze frms n all sock markes are rsker han socks of bg companes and as such nvesors are compensaed wh hgher reurns for nvesng n small sze socks. Furher, he fndngs show ha average excess reurns of a socks porfolo formed usng marke capalzaon and Book/marke sors a he Narob secures exchange are hgher for small sze socks han ha of he bg sze socks. Ths s an ndcaon ha socks of small companes (small cap socks) perform beer han socks of bg companes (bg cap socks) a he Narob secures exchange. Therefore, company sze whch s measured usng sock marke capalzaon s a sgnfcan deermnan of sock reurns a NSE. Fnally, as an nvesmen sraegy, nvesors a NSE should allocae more nvesmen resources o small cap socks han on bg cap socks for reurn opmzaon. Value Rsk and Reurn of Sock Porfolos a NSE Value rsk has a sgnfcan posve effec on he reurn of sock porfolos a he Narob secures exchange. Ths ype of rsk capures he amoun of exposure of a sock porfolo o value socks (socks wh hgh book value o marke value rao) compared o growh socks (socks wh low book value o marke value rao). The 38

9 greaer he exposure o value socks he hgher he reurn. Frms wh hgh book value o marke value raos seem o ouperform hose wh low book value o marke value raos a he Narob secures exchange. Ths s arbued o he fac ha frms wh hgh book o marke value rao are perceved o be more rsky and should herefore compensae nvesors wh hgher reurns. These fndngs show ha Book value/ marke value rao s an mporan deermnan of sock reurns a he Narob secures exchange. They also demonsrae he exsence of value effec a he Narob secures exchange. Based on hs fndng, he sudy recommends a value sraegy of nvesmen ha nvolves buyng socks wh low prces (Hgh book value o marke value raos) and sellng socks wh hgh prces (low book value o marke value raos) n order o maxmze he reurn of a sock porfolo a he Narob secures exchange. Profably Rsk and Reurn of Sock Porfolos a NSE Profably rsk has a weak posve effec on he reurn of sock porfolos a he Narob secures exchange. A NSE, profably rsk capures he amoun of exposure of a sock porfolo o socks of companes wh robus profably compared o companes wh weak profably. Posve effec of profably on sock reurns sems from profable companes rewards for havng chosen rsker fnancng opons han less profable companes. These fndngs ndcaed ha socks porfolos wh robus profably were assocaed wh hgher average sock reurns han socks porfolos wh weak profably. Thus, an nvesmen sraegy based on sorng socks on gross profably could generae subsanal excess sock reurns n he long run a NSE. Momenum Rsk and Reurn of Sock porfolos a NSE Momenum rsk has a weak posve effec on he reurn of sock porfolos a he Narob secures exchange. A NSE, momenum rsk s arbued o a marke anomaly where socks whch ouperform peers durng he las 12 monhs end o connue performng well n he mmedae fuure. These fndngs ndcae ha momenum effec s evden a he Narob secures Exchange. As an nvesmen sraegy, buyng socks ha had performed well n he pas and sellng socks ha had performed poorly n he pas a he Narob secures exchange can generae posve sock reurns over a 12 monhs holdng perods. Invesmen Rsk and Reurn of an opmal sock porfolo a NSE Invesmen rsk has a srong negave effec on he reurn of sock porfolos a he Narob secures exchange. Ths ype of rsk capures he exposure of a sock porfolo o socks of companes wh low asse growh raes a NSE. A NSE, frms wh low nvesmens n asses n he curren perod measured by asse growh end o have hgher reurns n he nex perod han frms wh hgher asse growh. Ths s due o he fac ha much of he avalable cash flows are used n ordnary operaons ha would generae hgher reurns. The ably of asse growh rae o predc sock reurn s also arbued o he fac ha asse growh rae s able o capure common reurn effecs across componens of a frm s oal nvesmens and hese componens vary from one frm o anoher. As an nvesmen sraegy, nvesors a NSE should nves n frms whose fnancng choces are assocaed wh asse conracon (such as share repurchases, deb repaymens, dvdend paymens and so on) snce such choces are followed by perods of hgh sock reurns. Concluson Capal asse prcng model has been he mos appled model n porfolo and nvesmen analyss. However, s nadequacy n explanng he reurn of socks has gven rse o he populary of mulfacor models ha ams a capurng he unexplaned sock reurn varaons. In hs sudy, a sx facors model was developed usng ndependenly and emprcally esed equy rsk facors o explan he sock porfolo reurn varaons a NSE. The resuls of he hypoheses ess leads o a concluson ha marke rsk, sze rsk, value rsk and nvesmen rsk have a sgnfcan effec whle profably rsk and momenum rsk have a weak posve effec on he reurn of sock porfolos a he Narob secures exchange. The sx facors models have a hgh explanaory power and her F-sascs ndcaes ha s an adequae model for explanng sock porfolo reurn varaons a he Narob Secures Exchange n Kenya. Recommendaons of he Sudy Ths sudy recommends a polcy framework for enhancng facor nvesng sraeges a he Narob secures exchange. Facor nvesng polcy framework s based on equy rsk facors ha have been proven emprcally by researchers o earn a sock reurn premum n he long run. In adopng a facor nvesmen sraegy, real nvesors, sock brokers and nvesmen advsors a NSE should allocae more nvesmen resources o small cap socks han n bg cap socks, nves more n value socks han n growh socks, buy socks wh he sronges momenum and sell socks wh he lowes momenum, allocae more nvesmen resources o socks of frms wh robus profably han hose wh weak profably and fnally nves more n socks of frms wh low growh n asses n he curren perod han frms wh hgh growh n asses n he curren perod for sock reurn opmzaon. The resuls of he sudy can also be used o develop a polcy on he concep of exchange raded funds (ETFs) nvesmens a he Narob secures exchange. ETFs aemp o replcae he performance of a specfc 39

10 ndex such as socks, bonds, currences and commody ndces. Specfcally, he resuls of hs sudy can be used n srucurng a sock ETFs conssng of small cap socks, value socks, growh socks and momenum socks. Inroducon of ETFs nvesmens a he Narob secures exchange could help managers of he muual funds, rus funds, and penson funds o opmze her nvesmen n socks a he Narob secures exchange n Kenya. Fnally, Capal markes Auhory could use he sudy fndngs o revew and srenghen he legal and regulaory framework of sock nvesmen polces. Some of he polces ha could be revewed nclude prce deermnaon of lsed socks usng fundamenal facors and marke forces of demand and supply, polcy on emporary hals n he radng of a secury as a resul of unusual movemens n he prce of a secury and regulaons n he growh enerprse marke segmen. Areas for Furher Research Ths sudy wll ac as a reference pon for fuure research sudes on porfolo consrucon, rsk dversfcaon and prcng of socks. Based on he resuls obaned, he followng are he suggesed areas for furher sudy: Usng he same mehodology, a smlar sudy should be exended o oher developng and developed counres o esablsh wheher he resuls are conssen. Oher mehodologes (such as GARCH, Panel daa, Quanle regresson, and ohers) could be used on he same sudy. Researchers could also explore he ncluson of oher facors no capured by he sx facors model. References Aharon, G., Grundy, B., & Zeng, Q. (2013). Sock reurns and he Mller Modglan valuaon formula: Revsng he Fama French analyss. Journal of Fnancal Economcs, 110(2), Ameer, D. (2013). A Tes of Fama and French Three Facor Model n Paksan Equy Marke. Global Journal of Managemen and Busness Research, 13(7). Aron, J.M. (2011). Facors nfluencng sock prces for frms lsed Narob Secures Exchange. Inernaonal Journal of Busness and Socal Scence. Vol 2 No. 20 Banz, R. W. (1981). The relaonshp beween reurn and marke value of common socks. Journal of fnancal economcs, 9(1), Barbers, N., Shlefer, A., & Vshny, R. (1998). A model of nvesor senmen. Journal of fnancal economcs, 49(3), Beechey, M., Gruen, D. W., & Vckery, J. (2000). The effcen marke hypohess: a survey. Sydney: Reserve Bank of Ausrala, Economc Research Deparmen. Campbell,J.Y (2000). Growh or glamour? Fundamenals and sysemac rsk n sock reurns. Journal of fnance, 56, pp Capal Markes Auhory (CMA). (2010). Annual repor and fnancal saemens Carhar, M. M. (1997). On perssence n muual fund performance. The Journal of fnance, 52(1), Carson, J. (2013). Three Rsk Facors ha nfluence your porfolo. Dmensonal Fund advsors Chawana, M. (2011). The effec of sysemac rsk facors on sock reurns n a developng counry: he case of Souh Afrca. Unversy of Souh Afrca, PhD hess. Cooper, D. & Schndler, P. (2006). Busness Research Mehod, McGraw Hll Cooper, M. J., Gulen, H., & Schll, M. J. (2008). Asse growh and he cross secon of sock reurns. The Journal of Fnance, 63(4), Eraslan, V. (2013). Fama and French hree-facor model: evdence from Isanbul sock exchange. Busness and Economcs Research Journal, 4(2), Fabozz, F. J., Gupa, F., & Markowz, H. M. (2002). The legacy of modern porfolo heory. The Journal of Invesng, 11(3), Fama, E. F. (1970). Effcen capal markes: A revew of heory and emprcal work. The journal of Fnance, 25(2), Fama, E. F., & French, K. R. (1992). The cross secon of expeced sock reurns. he Journal of Fnance, 47(2), Fama, E. F., & French, K. R. (1993). Common rsk facors n he reurns on socks and bonds. Journal of fnancal economcs, 33(1), Fama, E. F., & French, K. R. (1996). Mulfacor explanaons of asse prcng anomales. The journal of fnance, 51(1), Fama, E. F., & French, K. R. (2012). Sze, value, and momenum n nernaonal sock reurns. Journal of fnancal economcs, 105(3), Goyal, A. (2011). A survey of Emprcal cross- seconal Asse Prcng. Journal of porfolo Managemen 20(2) 26: Gujara, D. N. (2003). Basc Economercs. 4h ed. New York: McGraw Hll, Hebner, M. (2014). The dmensons of sock and Bond reurns. Index Fund Advsors, Inc 40

11 Heshma, N. A. (2012). Analyss of he Capal Asse Prcng Model n he Saud Sock Marke. Inernaonal Journal of Managemen, 29(2), 504. Hunsad,M. (2015). Combnng equy rsk facors. Implemenaon maers.index Fund Advsors, Inc Jegadeesh, N., & Tman, S. (1993). Reurns o buyng wnners and sellng losers: Implcaons for sock marke effcency. The Journal of Fnance, 48(1), Jorgen, D. (1963). Capal heory and Invesmen behavor, Amercan Economc Revew, Vol.53, No.2, Kamanda, N. S. (2001). An emprcal evaluaon of equy porfolos held by nsurance companes n Kenya (Docoral dsseraon). Ksaka, S. E., Mbh, J. A., & Kur, H. (2015). Deermnng he Opmal Porfolo Sze on he Narob Secures Exchange., 6(6), Ksser, M. (2014). Wha explans he gross profably premum?. Avalable a SSRN Malkel, B. G. (2003). The effcen marke hypohess and s crcs. The Journal of Economc Perspecves, 17(1), Mannng & Naper (2012). Modern Porfolo Theory: Expecaon vs. Realy: Whe Paper. Mannng & Naper publcaons. New York. Markowz, H. (1952). Porfolo selecon. The journal of fnance, 7(1), Murur, P. M. (2014). Effecs of Esmang Sysemac Rsk n Equy Socks n he Narob Secures Exchange (NSE)(An Emprcal Revew of Sysemac Rsks Esmaon). Inernaonal Journal of Academc Research n Accounng, Fnance and Managemen Scences, 4(4), Narob Sock Exchange (NSE), (2012). Hsory of organsaon, marke sascs. hp:// /markesascs/equysascs. hml. Njuguna, J.M. (2015). An nvesgaon of he marke effcency of he Narob secures exchange. School of economcs and fnancal scences. Unversy of Souh Afrca. Novy-Marx, R. (2010). The oher sde of value: good growh and he gross profably premum (No. w15940). Naonal Bureau of Economc Research. Novy-Marx, R. (2012). Is momenum really momenum?. Journal of Fnancal Economcs, 103(3), Rro, G. K., Wambugu, J. M., & Nyer, K. (2015). A Tes of Asse-Prcng Models a he Narob Secures Exchange., 6, Sharpe, W. F. (1964). Capal asse prces: A heory of marke equlbrum under condons of rsk. The journal of fnance, 19(3), Sharpe, W. F., Alexander, G. J., & Baley, J. V. (2006).Invesmens,6h Edon. Prn pack lmed, New Delh. Sambaugh, R. F., Yu, J., & Yuan, Y. (2012). The shor of : Invesor senmen and anomales. Journal of Fnancal Economcs, 104(2), Tman, S., We, K. C., & Xe, F. (2004). Capal nvesmens and sock reurns. Journal of fnancal and Quanave Analyss, 39(04), Appendces Appendx I: Porfolo Formaon Value (Book/Marke rao) Momenum (Las 12 monhs average reurn) Hgh (H) Medum(M) Low(L) Wnners (W) Neural (N) Losers (L) Bg (B) (1) B/H (2) B/M (3) B/L (7) B/W (8) B/N (9) B/L Sze Small(S) (4) S/H (5) S/M (6) S/L (10) S/W (11) S/N (12) S/L Profably (Gross prof rao) Invesmen (Growh n oal asses) Robus (R) Medum(M) Weak(W) Hgh (H I ) Medum(M I ) Low(L I ) Bg (B) (13) B/R (14) B/M (15) B/W (19) B/H I (20) B/M I (21) B/L I Sze (Marke capalzaon) Small(S) (16) S/R (17) S/M (18) S/W (22) S/H I (23) S/M I (24) S/L I Auhor (2017) 41

12 Appendx II: Dagnosc Tess Correlaon Marx for he sx Equy Rsk Facors Marke Rsk Sze Rsk Value Rsk Momenum Rsk Profably Rsk Invesmen Rsk Marke Rsk 1 Sze Rsk Value Rsk Momenum Rsk Profably Rsk Invesmen Rsk Auhor (2017) Durbn Wason d-sasc es for auocorrelaon (or Seral Correlaon) (For he sx Equy Rsk Facors ) Model d- Sasc Model d-sasc Model d-sasc Auhor (2017) Breusch pagan es for heeroscedascy (For he sx Equy Rsk Facors) Model P-Value Model P-Value Model P-Value Auhor (2017) Phllps Perron (1988) un roo es (For he sx Equy Rsk Facors ) Varable Tes Sasc 1% Crcal Value 5% Crcal Value 10% Crcal Value P -Value BH BM BL SH SM SL BW BN BL SW SN SL BR BM BW SR SM SW BH BM BL SH SM SL Marke Rsk Sze Rsk Value Rsk Momenum Rsk Profably Invesmen Rsk Auhor (2017) 42

13 Appendx III: Mulvarae Tme Seres Regressons Resuls (sx Equy Rsk Facors ) Fs row α β 1 β 2 β 3 β 4 β 5 β R 2 F- Sa 6 Second α β 1 β 2 β 3 β 4 β 5 β Adj. R 2 P-value 6 row 1- B/H a 2-B/M a 3-B/L a 4-S/H a 5-S/M a 6-S/L a 7-B/W a 8-B/N a 9-B/L a 10-S/W a 11-S/N a 12-S/L a 13-B/R a 14-B/M a 15-B/W a 16-S/R a 17-S/M a 18-S/W a 19-B/H a 20-B/M a 21-B/L a 22-S/H a 23-S/M a 24-S/L a Auhor (2017) 43