Superiority of six factor model in Indian stock market

P asad, Sa oj S.; Ve ma, Ashu osh; Bakhshi, P i i; P asad, Shan anu
A icle
Supe io i y o six ac o model in Indian s ock ma ke
Cogen Economics & Finance
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Supe io i y o six ac o model in Indian s ock
ma ke
Sa oj S. P asad, Ashu osh Ve ma, P i i Bakhshi & Shan anu P asad
To ci e his a icle: Sa oj S. P asad, Ashu osh Ve ma, P i i Bakhshi & Shan anu P asad (2024)
Supe io i y o six ac o model in Indian s ock ma ke , Cogen Economics & Finance, 12:1,
2411567, DOI: 10.1080/23322039.2024.2411567
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FINANCIAL ECONOMICS | RESEARCH ARTICLE
Supe io i y o six ac o model in Indian s ock ma ke
Sa oj S. P asad
a
, Ashu osh Ve ma
b
, P i i Bakhshi
c
and Shan anu P asad
d
a
Depa men o Economics & Finance, Bi la Ins i u e o Technology & Science, Goa, India;
b
Indian Ins i u e o Fo es
Managemen (IIFM), Bhopal, India;
c
S P Jain School o Global Managemen , Mumbai, India;
d
Goa Ins i u e o Managemen
(GIM), Goa, India
ABSTRACT
This no el wo k is he i s s udy in India o inco po a e he Human capi al (HC) ac o
as a six- ac o asse -p icing model and p esen s a obus me hodology. The aim o
his wo k is o examine he abili y o he six- ac o model o cap u e excess e u ns
using a GMM amewo k wi h ime pe iods ha we e missing in p e ious s udies.
The e o e, da a o his s udy we e collec ed using he BSE 500 index. Building on his
insigh , his s udy a emp s o explain he inhe en isk ac o s ( i ms and ma ke s)
ha p edic e u ns o e a pe iod o ime, conside ing he dynamics o he Indian
ma ke . The GRS es also con i ms he supe io i y o he six- ac o model o he
Indian equi y ma ke . The s udy asse s ha he Ins umen al a iable- Gene alized
me hod o momen s (IVGMM) is a obus model o e OLS in explaining po olio
e u ns (single and bi a ia e), which implies ha OLS in he asse p icing model is
exagge a ed in he Indian con ex . Single po olios a e cons uc ed based on he ac-
o s o size, alue, ROE, INV and human capi al, while bi a ia e po olios a e con-
s uc ed based on he in e sec ion o any hese wo ac o s. This s udy con i ms he
signi ican ole o HC (weal h) in desc ibing he s ock e u ns o an economy. This
s udy con ibu es o he ongoing discou se on asse p icing models and o e s alu-
able implica ions o in es men decisions, isk managemen , and po olio cons uc-
ion in one o he mos a ac i e global inancial ma ke s.
IMPACT STATEMENT
This no el wo k is he i s s udy in India o inco po a e he Human capi al (HC) ac o
as a six- ac o asse -p icing model and p esen s a obus me hodology. The aim o
his wo k is o examine he abili y o he six- ac o model o cap u e excess e u ns
using a GMM amewo k wi h ime pe iods ha we e missing in p e ious s udies. The
s udy asse s ha he Ins umen al a iable- Gene alized me hod o momen s
(IVGMM) is a obus model o e OLS in explaining po olio e u ns (single and bi a i-
a e), which implies ha OLS in he asse p icing model is exagge a ed in he Indian
con ex . Single po olios a e cons uc ed based on he ac o s o size, alue, ROE, INV
and human capi al, while bi a ia e po olios a e cons uc ed based on he in e sec-
ion o any hese wo ac o s. This s udy con i ms he signi ican ole o HC (weal h) in
desc ibing he s ock e u ns o an economy. This s udy con ibu es o he ongoing
discou se on asse p icing models and o e s aluable implica ions o in es men
decisions, isk managemen , and po olio cons uc ion in one o he mos a ac i e
global inancial ma ke s.
ARTICLE HISTORY
Recei ed 17 Ap il 2024
Re ised 16 Sep embe 2024
Accep ed 27 Sep embe 2024
KEYWORDS
Asse p icing model; Human
capi al; Indian ma ke ;
GMM; GRS; Financial ma ke
SUBJECTS
In es men & Secu i ies;
Ma hema ical Finance;
Quan i a i e Finance;
S a is ics o Business,
Finance & Economics
JEL CLASSIFICATION
G120
1. In oduc ion
Subs an ial empi ical inance esea ch add esses he co ec alua ion o inancial asse s (San oni &
Sale no, 2023). While he CAPM (Sha pe, 1965; Lin ne , 1965) explains he linea isk- ewa d ela ionship,
he iden i ica ion o a ious ac o s ha signi ican ly con adic he model has called in o ques ion i s
global alidi y. Fabozzi and F ancis (1978) conclude ha he be a coe icien o he s ock a ies andomly
o e ime and con adic s he basic assump ions o he CAPM. The e o e, he abo e discussion sheds
CONTACT P i i Bakhshi [email p o ec ed] S P Jain School o Global Managemen , Mumbai, India
ß2024 The Au ho (s). Published by In o ma UK Limi ed, ading as Taylo & F ancis G oup
This is an Open Access a icle dis ibu ed unde he e ms o he C ea i e Commons A ibu ion License (h p://c ea i ecommons.o g/licenses/by/4.0/), which
pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal wo k is p ope ly ci ed. The e ms on which his a icle has been
published allow he pos ing o he Accep ed Manusc ip in a eposi o y by he au ho (s) o wi h hei consen .
COGENT ECONOMICS & FINANCE
2024, VOL. 12, NO. 1, 2411567
h ps://doi.o g/10.1080/23322039.2024.2411567
ligh on he limi a ion o CAPM be a in cap u ing o he inhe en ma ke isks, and i s s abili y has chal-
lenged he asse p icing amewo k globally (Sha pe, 1965). Acco ding o Bos and Newbold (1984),
mic oeconomic a iables such as he phase o he coun y’s business cycle, in la ion a e, and he com-
pany’s business en i onmen de e mine he be a o s ocks. Fama and F ench (1993) ex end CAPM by
adding alue (HML) and size (SMB) as key ac o s in explaining he excess e u ns o s ocks. Ca ha
(1997) ex ends he Fama-F ench h ee- ac o model by adding a momen um ac o o he model and
epo s ha his imp o es he explana o y powe o he model o mu ual und pe o mance. Following
he app oach o Mille and Modigliani (1961), Fama and F ench (2015) subsequen ly p oposed p o i abil-
i y (RMW) and in es men (CMA) as wo addi ional ac o s ha p o ide a be e R2 (71% and 94%) in
achie ing excess e u ns. Ch onologically, Chiah e al. (2016) also p oposed he FF i e- ac o model as a
be e asse p icing model in in e na ional s ock ma ke s. Howe e , bo h assump ions ha only he be a
ac o in luences asse p icing and ma ke is e icien a e con adic ed by ma ke anomalies epo ed in
he li e a u e, such as he size e ec (Banz, 1981), alue e ec (S a man, 1980), p ice-ea nings a io
(Basu, 1983), i m le e age (Bhanda i, 1988) and high di idend yield (Fama, 1998). As anomalies ha e no
heo e ical basis and canno be explained by economic heo ies, his has led o he de elopmen o
empi ical, esea ch-based ac o models. This shows ha he asse p icing model has always been
expanded in o a mul i ac o model wi h a new signi ican ac o , whe eby hese mul i ac o models
mimic he isk ac o di e en ly.
Fama and F ench (1992) bes -known h ee ac o s aim o p o ide a mo e comp ehensi e explana ion
o s ock e u ns ela i e o CAPM, pa icula ly in explaining he e u ns o small-cap and alue s ocks. The
model was hen ans o med in o a i e- ac o model by including p o i abili y and in es men ac o s o
cap u e he a ia ion in he a e age e u ns o di e si ied s ock po olios (Fama and F ench 2015).
Despi e hei popula i y, hese models ha e con lic ing esul s in ma ke s and limi a ions in s udies wo ld-
wide, which has always been a sou ce o explo ing a obus model. Looking a a b oade ma ke o en
coun ies, Lalwani and Chak abo y, (2020) ind ha he Fama-F ench i e- ac o model using GRS s a is-
ics and a e age absolu e in e cep s i s s ock p icing o ou coun ies well. Howe e , he s udy may
ha e elied on he c oss-sec ional da a. Khudoykulo (2020) poin ed ou he c ucial pe o mance o he
h ee- and i e- ac o models o e he CAPM be a model while explaining po olio e u ns in he Indian
ma ke om 2009 o 2018. In hei s udy, Bha i and Khan (2022) ake a la ge sample o 25 eme ging
economies co e ing a sample pe iod o 21 yea s, u he di ided in o p e-c isis, c isis and pos -c isis pe i-
ods, and ind ha he pe o mance o he h ee- ac o model in he Asian egion. The au ho s also in o-
duce he 10- ac o asse p icing model and con i m i s applicabili y o he Ame ican ma ke . Howe e ,
he s udy lacks consis ency in he p oxies used o p o i abili y, in es men s, liquidi y and le e age.
Recen ly, a new ac o p oposed by Pa k e al. (2024) es s he asse p icing model and simul aneously
in oduces COVID-19 as a p icing ac o in he asse p icing model. The s udy uses he wo-s ep GMM
model and examines he ela ionship be ween he COVID-19 ac o measu ed as pandemic isk and s ock
e u ns, indica ing ha i has a signi ican posi i e isk p emium. Al hough he s udy is he i s o p o-
pose COVID-19 as a ac o in asse p icing, i s applicabili y in di e en coun ies needs o be empi ically
es ed. Appa en ly, he Fama-F ench models in India also ha e di e en esul s and a e inconclusi e.
The e o e, a ious o he ac o s ha e been iden i ied o cons uc ing an op imal po olio. One o he
isk-mimicking ac o s igno ed by asse p icing models is human capi al (HC). Maye s (1972)poin sou
ha indi iduals may hold signi ican po ions o hei weal h in non-ma ke able asse s (HC), which canno
be easily aded in inancial ma ke s. Consequen ly, he exis ence o hese non-ma ke able asse s a ec s
indi iduals’po olio selec ion and in es men s a egies. Simila ly, Kim e al. (2011) sugges ed ha HC has
p edic i e alue in explaining asse e u ns. Howe e , HC is gaining popula i y (Campbell, 1996) and is ec-
ognized as an impo an ac o in he asse p icing model. This s udy measu es HC as an asse o he com-
pany and has an addi i e e ec wi h ega d o size and alue ac o s. Campbell (1996) emphasized ha
human capi al e lec s he ue weal h o he economy and should, he e o e, be pa o he asse p icing
amewo k. Jaganna han and Wang (1996) ind ha CAPM can be e explain mo e han 50% o he di e -
ences in c oss-sec ional e u ns when ma ke e u ns a e eplaced by human capi al. La e , Belo e al.
(2017), Kuehn e al. (2017) con i m ha human capi al is an impo an de e minan in measu ing c oss-sec-
ional s ock e u ns. The HC mul i ac o model is la e e e ed o as he six- ac o asse p icing model.
The e o e, he abo e s udies in a ious in e na ional ma ke s suppo he HC-based mul i ac o model and
2 S.S. PRASAD ET AL.
con i m i s supe io pe o mance in global ma ke s. Se e al s udies ha e demons a ed he p esence o
human capi al in he mul i ac o model in he in e na ional ma ke (Belo e al., 2017; Kim e al., 2011;
Kuehn e al., 2017; Le au, & e al., 2019). Simila ly, Maha ani and Na sa (2023) ound ha in ellec ual
capi al plays a ole in explaining asse e u ns in he Indonesian s ock ma ke o he pe iod 2012–2022.
Khan e al. (2023) highligh s he impo ance o human capi al in in es men decisions and ecommends
in es o s conside he size, alue and human capi al while aluing he i ms. The s udy ex ends he
Fama-F ench h ee- ac o by including human capi al as he ou h ac o and has shown i s alidi y o
Pakis ani i ms. Howe e , he s udy uses a smalle numbe o po olios o analysis. Anuno e al. (2023)
no e he applicabili y o he Fama-F ench i e- ac o model in Timo -Les e and emphasize ha he SMB
and HML ac o con ibu e nega i ely o he excess e u ns, while he p o i abili y ac o con ibu es
posi i ely o explaining he e u ns. Since Timo -Les e is a low-income coun y, he s udy can use human
capi al as a six h ac o in asse p icing as he coun y has he g ow h po en ial o human capi al.
Al hough he HC-based mul i ac o model is widely accep ed wo ldwide, i s alidi y mus be es ed in
eme ging ma ke s. Among he eme ging ma ke s, he Indian economy has wi nessed emendous
g ow h ac oss all sec o s o e he las decade. India anks i h among he op en coun ies in e ms o
g oss domes ic p oduc (GDP) in he wo ld, India
1
anks i h among he op 10 coun ies and is
expec ed o be he hi d
2
mos powe ul coun y by 2030. India’s exponen ial g ow h was he o iginal
mo i a ion o esea ch in he Indian ma ke . I onically, wo s udies on he six- ac o asse p icing model
also mo i a e us o in es iga e i s exis ence in he Indian ma ke . Some o he no able con ibu ions o
he six- ac o mul i ac o model a e om Shijin e al. (2012), who s a e ha he HC-based mul i ac o
model o e s mo e p edic i e e u ns han he single-index model o he Indian ma ke o 1996–2006.
The au ho s exclusi ely used G ange causali y es s, OLS eg ession, and impulse esponse unc ions o
he Ni y 50 index. Mai i and Balak ishnan (2018) also epo ha he six- ac o model e lec s e u n pa -
e ns be e han he h ee- and i e- ac o Fama-F ench models. This s udy uses GRS es s, 3D g aphs,
eg ession models, and esidual g aphs o BSE-500 index companies o he pe iod 2004–2016 o exam-
ine HC in cap u ing e u ns on asse s. I is pe inen o no e he e ha he human ac o as he six h
asse p icing model has ecei ed signi ican a en ion in he global ma ke bu has no ecei ed signi i-
can a en ion in he Indian ma ke in ecen imes a e 2017.
India, wi h i s ib an and apidly e ol ing s ock ma ke and di e se o e ings o s ocks om a ious
sec o s and indus ies, equi es an in es iga ion o he e ec i eness and supe io i y o he six- ac o
model. The e o e, ou s udy ex ends p e ious wo k in he con ex o a compe en asse -p icing ame-
wo k in he Indian ma ke . This no el wo k is he i s s udy in India o inco po a e he HC ac o as a
six- ac o asse -p icing model and p esen s a obus me hodology. The wo p e ious s udies in his a ea
a e e y limi ed and a e, he e o e, looking o me hods ha demons a e ag eemen be ween hem.
The a ailable li e a u e on he six- ac o model in India is limi ed o he s udy pe iod o 6–7 yea s ago.
The e is a need o a s udy o p opose a benchma k model o p icing asse s in he Indian s ock ma ke
while co e ing he pandemic (COVID-19) pe iod, as he e is no analysis in his a ea co e ing he pe iod
be o e, du ing and pos -COVID-19. The aim o his wo k is o examine he abili y o he six- ac o model
o cap u e excess e u ns using a GMM amewo k wi h ime pe iods ha we e missing in p e ious s ud-
ies. Since, GMM shows i s po en ial when he c oss-sec ional he e oscedas ici y o he da a exis s and
he collec ed ime se ies da a is small (Ki ie e al., 2017). Fu he mo e, GMM p o ides a amewo k o
add essing endogenei y issues by using ins umen al a iables o momen condi ions o iden i y and
es ima e causal ela ionships be ween a iables. Addi ionally, he con en ional s a ic app oach o
he Fama-F ench model may be mis-speci ied mis speci ied because i s pa ame e s ha e ime- a ying
p ope ies (Racico e al. (2019).
2. Da a
Fo he Indian ma ke , he BSE 500 is one o he bes choices o all equi y indices, as i has a s ong
ela ionship wi h all mac oeconomic a iables (Chaudha y & Bakhshi, 2021). The e o e, o his s udy,
da a was collec ed o companies lis ed in he BSE 500 index. The BSE 500 index co e s he op 20
sec o s o he Indian economy and ep esen s 93% o he o al BSE ma ke capi aliza ion
3
. O he 500
companies lis ed on he BSE 500 Index, he da a include only 280
4
companies o he 19-yea s udy
COGENT ECONOMICS & FINANCE 3

pe iod, ha is, om June 2002 o July 2021 (Mai i & Balak ishnan 2018), om he CMIE P owess
da abase. F om he ini ial sample o BSE 500 lis ed companies, we emo ed companies whose ma ke
capi aliza ion (MC) o size ac o da a o a pe iod o 19 yea s a e inadequa e o i egula . This p ocess is
epea ed o o he ac o s: BM a io (book alue o p ice a io) o alue, ROE ( e u n on equi y) o p o -
i abili y, INV (annual g ow h in o al asse s) o in es men s, and HC (sala ies and wages) o human cap-
i al o he s udy pe iod. As he lis o companies has changed due o u he inco po a ions and;
Me ge s and amalgama ions o companies. Likewise, companies wi h i egula i ies in hei closing p ices
a e emo ed om he sample. In he end, we le wi h 280 companies o which he da a is comple e
o all ac o s and o each yea . The da a is seconda y in na u e. Al hough he s udy uses a igo ous
da a collec ion me hodology, he analysis conduc ed in he s udy acknowledges he possibili y o su -
i al bias, which can be conside ed as one o he limi a ions. Selec ion bias, also known as su i o ship
bias, is he endency o include su i o s in an analysis and hose who ailed, d opped ou , o we e
o he wise emo ed a e omi ed. This is called ‘su i o ship bias,’a ype o selec ion bias. Failu e o con-
side all a ailable da a, pa icula ly hose los du ing he in es iga i e p ocess, could lead o o e ly op i-
mis ic conclusions. El akhani and Wei (2003) examined he su i o ship bias, he s ock p ice e ec , and
he small i m e ec in Canadian inancial ma ke s. The s udy ound e idence o su i al bias in
Canadian s ock e u ns, wi h he e u ns o su i ing companies being highe han he e u ns o he
en i e sample o companies. P e ious s udies by (B own & Goe zmann, 1995; G inbla & Ti man, 1993;
and Malkiel, 1995) emphasized he exis ence o su i o ship bias when examining he pe o mance o
mu ual unds. In he Indian con ex , Aga walla, e al. (2013) a gued ha he su i al bias ound in hei
s udy is negligible since he sample is om he Bombay S ock Exchange (BSE), which is simila o ou
sample. The e o e, he esul s o ou s udy may also be negligible o o e es ima e he p esence o su -
i al bias. Hence, o he obus ness o esul s, we ecommend ha subsequen s udies, when conduc ed
in he same a ea, should aim o include comp ehensi e da a om all subjec s, including hose who do
no su i e he s udy. Employing echniques such as su i al analysis o mul iple impu a ion o missing
da a can help mi iga e his bias and p o ide a mo e accu a e ep esen a ion.
The mo i a ion o he s udy is o ake a long pe iod o ime o he obus ness o he esul . Bo h he
ini ial and inal pe iods o he s udy show s abili y in he Indian s ock ma ke a e he global c isis,
which is conside ed a no mal pe iod o conduc ing he analysis. The Indian s ock ma ke seems o be
eco e ing since Ma ch 2002 a e a massi e e o is a ack (Sep embe 11) and is showing momen um
a e he global COVID-19 c isis. Howe e , his pe iod also includes a global ecession in 2008.
3. Me hodology
The p oxies o measu ing he six ac o s a e ma ke capi aliza ion (MC) o size, BM a io (book- o-p ice
a io) o alue, ROE ( e u n on equi y) o p o i abili y, INV (annual g ow h in o al asse s) o in es -
men s, and HC (sala ies and wages) o human capi al. Howe e , while ope a ing p o i measu es he
o e all p o i abili y o he company, analys s and in es o s c i ically examine ROE o es ima e he e u n
on he amoun o money hey ha e in es ed in he company. Addi ionally, people a e mo e likely o
buy sha es in a company wi h a high ROE a io. Fu he mo e, exis ing li e a u e also con i ms ha ROE is
a p oxy o p o i abili y (Haugen & Bake , 1996; Mai i & Balak ishnan, 2018). The sample companies we e
anked each yea in Ma ch based on he selec ed ac o s, o which mon hly log e u ns we e calcula ed
om July 2002 o June 2021. We main ained he s anda d p ac ice ollowed by (P asad & Ve ma, 2013;
Mai i & Balak ishnan, 2018), as i is he mos popula p ac ice. To cons uc i e po olios (P1, P2, P3, P4,
and P5), equally weigh ed po olios a e used o each ac o , wi h P1 ep esen ing he lowes ank and
P5 he highes ank. The ollowing po olios we e cons uc ed by con inuing he exis ing me hodology.
3.1. Single so ed po olios
Single-so ed po olios o each ac o eplica e i e equally weigh ed po olios consis ing o 56 s ocks
each. These a e e e ed o as P1 ( he smalles s ocks) and P5 ( he la ges s ocks) based on MC, P1 as
g ow h s ocks, P5 as alue s ocks based on he BM a io, P1 as weak s ocks, P5 as obus s ocks based
4 S.S. PRASAD ET AL.
on ROE, P1 as conse a i e s ocks, P5 as agg essi e s ocks based on in es men , P1 as low compensa-
ion s ocks, and P5 as high compensa ion s ocks based on sala ies and wages.
3.2. Bi a ia e po olios
Bi a ia e po olios a e cons uc ed om he in e sec ion o wo ac o s, keeping he size o each ac o
he same. To cons uc po olios based on he MC and BM a io, companies a e di ided in o wo small
and la ge companies based on MC, while companies a e di ided in o Low, Medium and High companies
based on he BM a io. Six po olios we e hen o med, e e ed o as SL, SM, SH, BL, BM, and BH.
The same p ocess was expanded o build six po olios a he in e sec ion o Small and La ge (MC) and
Robus , Neu al and Weak (ROE), e e ed o as SR, SN, SW, BR, BN, and BW. The o he six po olios a e
SC, SN, SA, BC, BN, and BA and a e o med by he in e sec ion o MC (Small and La ge) and INV
(Conse a i e, Neu al and Agg essi e). The inal se o six po olios o med by combining Small and Big
(MC) and lowe compensa ion and highe compensa ion (HC) a e SLc, SN, SHc, BLc, BN, and BHc. Fo
each po olio, excess e u ns we e calcula ed by sub ac ing he RBI’s 91-day T-bill isk- ee a e om
he po olios’mon hly mean e u ns. This s udy uses 91-day- T-bills as a p oxy o he isk- ee a e, and
BSE Sensex is selec ed as a ma ke p oxy.
This s udy examines he six- ac o model o which he po olios cons uc ed abo e a e eg essed
using he six independen a iables (SMB, HML, RMW, CMA, and LcMHc)
5
calcula ed as ollows:
SMB ¼1=3SLþSMþSH
ðÞ
−1=3BLþBMþBH
ðÞ (1)
Whe e SMB s ands o Small minus Big and ep esen s he size isk.
HML ¼1=2SHþBH
ðÞ
−1=2SLþBL
ðÞ (2)
Whe e HML s ands o High minus Low and ep esen s he alue isk.
RMW ¼1=2SRþBR
ðÞ
−1=2SWþBW
ðÞ (3)
Whe e RMW s ands o Robus minus Weak and ep esen s he p o i abili y isk.
CMA ¼1=2SCþBC
ðÞ
−1=2SAþBA
ðÞ (4)
Whe e CMA s ands o Conse a i e minus Agg essi e and ep esen s he in es men isk.
LcMHc ¼1=2 SLcþBLc
ðÞ
−1=2 SHc þBHc
ðÞ (5)
Whe e LcMHc s ands o lowe compensa ion minus highe compensa ion and ep esen s he human
capi al isk.
3.3. Empi ical es s
A ew ecen s udies in he ield o asse p icing models (Kesha i & Gau am, 2022) ha e used me hodolo-
gies ha s ill necessi a e a comp ehensi e asse p icing s udy in he Indian ma ke . The e o e, we used
wo di e en s a is ical me hods o ensu e he obus ness o he model and e eal i s applicabili y. Fi s ,
we use a join F- es o a se o po olios using GRS (Gibbons, Ross and Shanken, 1989). We assume
ha e u ns a e homoscedas ic and no au oco ela ed. The GRS es p o ides F-s a is ics o es whe he
he join absolu e alue o he in e cep is equal o ze o, which is based on he ollowing OLS equa ion:
Ri –RF ¼aiþb1i RM –RF
ðÞ
þb2iSMB þb3iHML þb4iRMW þb5iCMA þb6iLcMHc þei (6)
Howe e , s udies on he Indian ma ke by Mai i and Balak ishnan (2018) and Shijin e al. (2010)
equi e a obus me hodology, as he e is empi ical e idence ha he pa ame e es ima es o he six-
ac o amewo k using he IVGMM app oach ou pe o m adi ional OLS because o speci ica ion and
measu emen e o s (Roy, 2020). IVGMM is a s onge model o es ing he asse p icing model o e
Fama Macbe h’s wo-pass eg ession due o i s e iciency, obus ness, lexibili y and abili y o add ess
complex econome ic issues such as e iciency, endogenei y co ec ion, handling measu emen e o
and obus s a is ical in e ence. Mo eo e , in such complex issues wo-pass ime se ies leads o biased
esul s. (Ho 
a h & Wang, 2021; Jaganna han e al., 2002). In his s udy, we adop ed gene alized
COGENT ECONOMICS & FINANCE 5
me hods o momen s, a obus o m o he me hodology in he asse p icing amewo k ha assumes a
minimum s anda d e o and does no equi e s a iona y a iables. This can be exp essed by he ollow-
ing equa ion:
Ri –RF ¼aGMMi þbGMM1i RM –RF
ðÞ
þbGMM2iSMB þbGMM3iHML þbGMM4iRMW
þbGMM5iCMA þbGMM6iLcMHc þei (7)
The esul s o he es s ca ied ou using he S a a s a is ical so wa e a e u he explained.
4. Resul s
Table 1 shows ha he a e age excess e u ns o he P1 po olios a e highe han hose o he P5 po olios
o single-so ed po olios based on six ac o s (size, alue, RMW, CMA, and HC), and he isk associa ed
Table 1. Desc ip i e s a is ics o single-so ed po olios.
Po olios p1p2p3p4p5
MC
Re u ns 0.024 0.010 0.008 0.008 0.005
Risk 0.096 0.093 0.084 0.077 0.073
BV
Re u ns 0.018 0.013 0.011 0.006 0.006
Risk 0.091 0.083 0.081 0.086 0.080
ROE
Re u ns 0.010 0.010 0.012 0.012 0.011
Risk 0.099 0.086 0.082 0.075 0.076
INV
Re u ns 0.014 0.011 0.010 0.010 0.010
Risk 0.092 0.087 0.081 0.078 0.086
HC
Re u ns 0.016 0.013 0.010 0.009 0.006
Risk 0.094 0.085 0.082 0.080 0.078
No e. Re u n and isk a e he mean and s anda d de ia ion o he po olios.
Table 2. Co ela ion ma ix o independen a iables.
Sensex SMB HML RMW CMA LcMHc
Sensex 1
SMB −0.030 1.000
HML 0.036 −0.433 1.000
RMW 0.033 0.648 −0.142 1.000
CMA −0.018 0.206 0.447 0.073 1.000
LcMHc 0.020 0.147 −0.085 −0.010 −0.004 1
No e. Compu ed by au ho s.
Table 3. Desc ip i e s a is ics o double-so ed po olios.
MC/BV Po olios
SL SM SH BL BM BH
Re u ns 0.201 0.022 0.104 0.042 0.092 0.165
Risk 1.077 0.125 0.556 0.284 0.469 1.021
MC/ROE Po olios
SR SN SW BR BN BW
Re u ns 0.174 0.207 0.111 0.078 0.108 0.166
Risk 0.901 1.097 0.556 0.373 0.561 1.003
MC/INV Po olios
SC SN SA BC BN BA
Re u ns 0.097 0.128 0.104 0.103 0.085 0.097
Risk 0.571 0.736 0.523 0.546 0.515 0.537
MC/HC Po olios
SLc SN SHc BLc BN BHC
Re u ns 1.056 −0.577 0.737 −0.470 0.902 −0.385
Risk 6.177 3.005 4.281 3.383 6.014 2.426
No e. Re u n and isk a e he mean and s anda d de ia ion o he po olios.
6 S.S. PRASAD ET AL.
wi h he po olio is also highe . This implies his o ical ou pe o mance o (small-cap s ocks ela i e o
la ge-cap s ocks, alue s ocks ela i e o g ow h s ocks, high p o i abili y a io s ocks ela i e o low p o i -
abili y a io s ocks, and conse a i e in es men s ocks o e agg essi e in es men s ocks low compensa ion
s ocks o e high compensa ion s ocks). Based on ROE, he a e age e u n o he P5 po olio is sligh ly
highe han ha o he P1 po olio, indica ing ha in es o s p e e o in es in s ocks ha o e highe
e u ns on he in es men s hey make. Addi ionally, he isk associa ed wi h he P1 po olios is highe
ac oss all ac o s, indica ing highe ola ili y in ma ke mo emen s.
Be o e p oceeding wi h he GRS s a is ics, we de e mine he co ela ion be ween he independen
a iables o check o he p esence o mul icollinea i y. Table 2 shows ha he co ela ion be ween he
a iables is less han 0.50 in all cases, indica ing ha none o he independen a iables a e co ela ed
wi h each o he and he e o e he e is no mul icollinea i y be ween hem.
Table 3 p esen s ha he a e age excess e u ns o small po olios (SL, SR, SC and SLc) a e highe
han hose o la ge po olios (BH, BW, BA and BHc) o bi a ia e so ed po olios. The isk associa ed
wi h he po olios is also highe , which sugges ing a isk- ewa d a io.
Table 4 shows he esul s o he GRS es s o he six- ac o model o he single-so ed po olio based
on size, alue, RMW, CMA, and HC wi h he null hypo hesis ha he mean absolu e alpha is ze o. The
ejec ion o he null hypo hesis and he ac ha he mean absolu e alpha is close o ze o demons a e
he ine ec i eness o he ac o model in explaining e u ns. These esul s clea ly show ha all single
po olios so ed by size and alue a e ejec ed, while he RMW, CMA, and HC so ed po olios a e
accep ed by he GRS es , sugges ing he supe io i y o he six- ac o model. Table 5; on he con a y,
he six- ac o model was ound o be unde -speci ied in explaining he e u ns, showing ha he join
Table 4. GRS es esul s o single-so ed po olios.
Po olios GRS pValue Mean absolu e alpha AR
2
Size
P1-P5 7.474 0.0000.004 0.107
Value
P1-P5 3.793 0.0030.004 0.123
ROE
P1-P5 0.547 0.740 0.004 0.113
INV
P1-P5 0.547 0.740 0.004 0.113
HC
P1-P5 1.330 0.253 0.004 0.120
No e. GRS s a is ic wi h he co esponding p- alue a he 5% signi icance le el.
Table 5. GRS es esul s o bi a ia e po olios.
Po olios GRS pValue Mean absolu e alpha AR
2
MC/BV 0.380 0.891 0.005 0.840
MC/ROE 0.597 0.733 0.010 0.896
MC/INV 0.265 0.953 0.005 0.900
MC/HC 562.925 0.0000.317 0.265
No e. GRS s a is ic wi h he co esponding p- alue a he 5% signi icance le el.
Table 6. Rele ance es esul s o obus ins umen s.
Alpha Sensex SMB HML RMW CMA HC F-S a is ics
Sensex 0.007 –−0.028 0.007 0.016 −0.006 0.001 0.326
1.467 −0.636 0.293 0.931 −0.246 0.500
SMB −0.005 −0.062 –−0.334 0.272 0.291 0.012 94.660
−0.800 −0.640 −12.050 14.090 9.300 2.890
HML −0.007 −0.054 −1.181 –0.237 0.661 0.005 52.190
−0.590 0.290 −12.050 5.020 12.420 0.670
RMW 0.042 0.231 1.734 0.429 –−0.370 −0.024 43.730
2.390 0.930 14.090 5.020 −4.130 −2.280
CMA 0.011 −0.044 0.963 0.619 −0.192 –−0.007 34.870
0.890 −0.250 9.300 12.420 −4.130 −0.980
HC 0.325 0.755 2.914 0.368 −0.919 −0.549 –2.130
3.010 0.500 2.890 0.670 −2.280 −0.980
No e. Reg ession esul s o each explana o y a iable o all ins umen s wi h hei co esponding F-s a is ics.
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