Wei-Qi, Liu; Jingxing, Zhang
A icle
BM(book- o-ma ke a io) ac o : Medium- e m
momen um and long- e m e e sal
Financial Inno a ion
P o ided in Coope a ion wi h:
Sp inge Na u e
Sugges ed Ci a ion: Wei-Qi, Liu; Jingxing, Zhang (2018) : BM(book- o-ma ke a io) ac o : Medium-
e m momen um and long- e m e e sal, Financial Inno a ion, ISSN 2199-4730, Sp inge ,
Heidelbe g, Vol. 4, Iss. 1, pp. 1-29,
h ps://doi.o g/10.1186/s40854-017-0085-6
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RESEARCH Open Access
BM(book- o-ma ke a io) ac o : medium-
e m momen um and long- e m e e sal
Liu Wei-qi and Zhang Jingxing
*
* Co espondence:
[email p o ec ed]
Shanxi uni e si y, No.92, Wucheng
oad, Xiaodian dis ic , Taiyuan ci y,
Shanxi P o ince, China
Abs ac
To explain medium- e m momen um and long- e m e e sal, we use he di e ence
be ween he op ional model and he CAPM model o cons uc a winne -lose po olio.
Acco ding o he CAPM model’s ze o explana o y abili y wi h espec o s ock ma ke
anomalies, we ob ain an anomaly in e p e a i e model. This s udy shows ha his
anomaly in e p e a i e model can explain s ock ma ke pe cep ions and medium- e m
momen um. Mos impo an ly, BM is a c i ical ac o in he model’s explana o y abili y.
We p esen a obus ness es , which includes selec ing new sample da a, adding new
auxilia y a iables, changing sample yea s, and adding indus y ixed e ec s. In gene al,
he BM e ec does ha e conside able explana o y powe in medium- e m momen um
and long- e m e e sal.
Keywo ds: S ock ma ke ola ili y, medium- e m momen um, long- e m e e sal, holding
pe iod, o ma ion pe iod, book- o-ma ke a io, e u n on equi y
In oduc ion
In a comple ely e ec i e ma ke , s ock ma ke ola ili y is andom. Howe e , h ough
daily obse a ions, we ind ha he s ock ma ke o en shows egula luc ua ions,
which is coun e in ui i e. These cyclical luc ua ions o en occu du ing a ce ain
pe iod and a e known as s ock ma ke isions. These phenomena ha e a ac ed
academic a en ion because hey can no longe be in e p e ed by adi ional me hods.
The momen um and e e sal e ec , as wo ypical s ock ma ke isions, ha e caused
hea ed discussion in he academic communi y. Re ail in es o s and ins i u ional in es-
o s belie e ha g asping momen um o e e sal means ha a s ock's u u e e u ns
can be p edic ed o p o i . Some such cases do exis . Jegadeesh and Ti man (1993)
i s disco e ed and p oposed ha he US secu i ies ma ke momen um e ec exis s
o h ee o 12 mon hs and p o ided a sho - e m p o i abili y s a egy. The au ho s
also ound ha his s a egy can ob ain 1% o he excess e u n a e wi hin a ce ain
pe iod. Wang Yonghong and Zhao Xuejun (2001) used one mon h o he smalles so
pe iod and disco e ed ha China's s ock ma ke has a clea e e sal e ec . The au ho s
also p o ed ha he ine ial e ec o China's s ock ma ke is no ob ious. Howe e ,
schola s ha e no gi en a de ini i e answe as o how o g asp hese isions. Resea ch
is s ill ad ancing inc emen ally. This pape ocuses on he in e p e a ion o he abo e
wo isions, cons uc s a model, and iden i ies a new isions model ha can be applied
Financia
l
Inno a ion
© The Au ho (s). 2018 Open Access This a icle is dis ibu ed unde he e ms o he C ea i e Commons A ibu ion 4.0 In e na ional
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 you gi e app op ia e c edi o he o iginal au ho (s) and he sou ce, p o ide a link o he C ea i e Commons license, and
indica e i changes we e made.
Wei-qi and Jingxing Financial Inno a ion (2018) 4:1
DOI 10.1186/s40854-017-0085-6
o he explana ion o he wo anomalies a he same ime. Fi s , we explain se e al
impo an basic concep s and p e ious esea ch esul s.
Momen um e ec is also known as he ine ial e ec . I implies ha he s ock had a
highe e u n in he pas and will ha e a highe e u n in he u u e; lowe s ock yields in
he pas mean ha he u u e e u n will be lowe . Jegadeesh and Ti man (1993) we e he
i s academics o disco e ha he momen um e ec exis ed in he US secu i ies ma ke
in h ee o 12 mon hs. Soon a e wa d, hey o e ed a sho - e m p o i abili y s a egy
and ound ha he s a egy, wi hin a ce ain pe iod, ob ained 1% excess e u n.
Then, Kaul and Con ad (1993) used sha es o he s ock lis ed on he New Yo k
S ock Exchange and he US S ock Exchange du ing he pe iod 1926 o 1989 o
s udy he s ock e u ns du ing eigh di e en in es men pe iods. The esea ch
ound ha ou o he in es men s a egies achie ed signi ican p o i s, wo s a -
egies belong o he momen um s a egy, he o he wo a e e e se s a egy. Almos
a he same ime, Rouwenho s analyzed he momen um e ec s o 12 Eu opean
coun ies' s ock ma ke s and ound ha almos all o hem showed sho - e m mo-
men um e ec and o a g ea e ex en han he US ma ke . While Rouwenho s
con i med ha applying momen um s a egies o eme ging ma ke s could acqui e
signi ican p o i , some schola s disco e ed ha in es o s ended o adop momen-
um s a egy in hei decision making. Fo example, Chen ound ha US in es o s
ha e momen um endency when hey make medium- e m in es men decisions.
Gi en his, we ind ha he s ock ma ke and he in es o s a e a ec ed by mo-
men um e ec wi hin h ee o 12 mon hs, which indica es he exis ence o he
medium- e m momen um e ec . This e ec b ings angible bene i s o in es o s.
G i in (2003) used 40 coun ies o explain he momen um e ec o mac oeco-
nomic cycle isk. He ound ha momen um gains we e p esen and signi ican in
hese coun ies, and ega dless o whe he he economic cycle was in an upswing
o a declining phase, he momen um gains we e signi ican ly posi i e. Thus, he
momen um e ec and he mac oeconomic cycle do no ha e a signi ican ela ion-
ship. Lee and Swamina han (2000) i s s udied he ela ionship be ween he mo-
men um e ec and s ock ading olume om he pe spec i e o ading olume.
The au ho concluded ha he ading olume o he s ock can p edic he income o
he momen um s a egy and he du a ion o he momen um e ec . When using
momen um s a egies in high s ock e u ns, he e ec o he momen um e ec will
become less and will con inue o a sho e ime. In addi ion o he long- e m e e sal
e ec s ound in he US ma ke , schola s ound a e e sal e ec in o he coun ies. This
inding indica es ha he e ec is no he eason o da a mining. Chan e al. (1996)
and Chui e al. (2000) ound sho - e m e e sal e ec s in he Japanese ma ke . Bay as
and Cakici (1999) no e long- e m e e sal e ec s in he o he se en coun ies.
A e unde s anding he mid-momen um e ec , we ind ha he e e sal e ec becomes
easie o in e p e . In simple e ms, he e e sal e ec is ha he s ock ha pe o med
poo ly in he pas pe iod will show a be e esul in he u u e. De bond and Thale
(1985) ound ha he po olio o he wo s pe o ming 10% s ocks paid 10% o e he
s ocks ha we e winne s a e he h ee-yea o ma ion; he lose po olio showed a
highe han a e age ma ke e u n a 19.6% while he winne po olio was s ill lowe han
5%. This s udy con i med ha he e e sal e ec exis s o e a long pe iod, and e e sal
s a egies can be used o achie e subs an ial e u ns o e a longe pe iod.
Wei-qi and Jingxing Financial Inno a ion (2018) 4:1 Page 2 o 29
Much con o e sy su ounds he exis ence o he momen um e ec and he e e sal
e ec on de eloped coun ies’s ock ma ke s. Zhu (2003) is one o he ep esen a i e
schola s and has p o ed ha China does no ha e a e e sal e ec h ough he s udy o
he secu i ies ma ke . Chen Qiao and Wang Shi (2003) ound ha he ine ial s a egy
based on he indus y po olio showed signi ican excess e u ns. Hameed and Ting
(2000) ound a signi ican p ice e e sal e ec in he Malaysian s ock ma ke indica ing
ha he e is a e e sal e ec in de eloped coun y s ock ma ke s. Gaun ’s (2000) s udy
ound ha he Aus alian ma ke also shows a signi ican e e sal e ec . His sample
in e al was om 1974 o 1997, he o ma ion pe iod was i e yea s and, a e an 18-
mon h holding pe iod, he e e sal e ec appea ed. F om he heo e ical esul s o
hese schola s, we conclude ha he e a e di e gen iews on whe he he e a e
momen um and e e sal ends in he Chinese ma ke , and he conclusions a e o ally
di e en . The ocus o ou s udy is o cla i y medium- e m momen um and long- e m
e e sal e ec s a he han p o e hei exis ence. Based on he abo e li e a u e, we
know ha he e e sal e ec is a ubiqui ous phenomenon and is concen a ed in he
medium and long e m. Thus, ou decision will be mo e inclined o choose he ma u e
US inancial ma ke so ha he s a emen on he exis ence o medium- e m momen-
um and long- e m e e sal will be uni ied. The US s ock ma ke has become a be e
op ion o ou empi ical analysis.
Typically, schola s a e di ided in o wo ca ego ies: beha io al inance and adi ional
inance. Beha io al inance scien is s o en use he heo y o o e eac ion and unde -
eac ion o explain he e e sal and momen um e ec s. The iew o long- e m
o e eac ion was i s in oduced by De Bond and Thale (1985, 1987). Addi ionally,
he e a e se e al in e p e a i e models in beha io al inance. The BSV model (Ba be is,
Shlei e , & Vishny, 1998) assumes ha ma ke in es o s ha e wo de ia ions when hey
make pe sonal decisions. One is a ep esen a i e bias; because in es o s so easily o e -
look ecen da a, he esul is o e - eac ion. The o he is conse a i e bias; in es o s
a e insensi i e o new in o ma ion causing inadequa e esponse o he in o ma ion. The
DHS model (Daniel, Hi shlei e , & Sub amanyam, 1998) di ides in es o s in o
in o ma ion-based in es o s and non-in o ma ion in es o s and conside s whe he in-
es o s a e sensi i e o new in o ma ion. The HS model (Hong & S ein, 1999), based
on assump ions conce ning in es o s’sensi i i y and ype, in e p e s he unde - eac ion
om di e en pe spec i es. Fama and F ench (1996), who a e ep esen a i es o
adi ional inance schools, analyzed he e e sal and momen um o s ock e u ns and
con i med ha he bene i s o long- e m e e sal s a egies can be explained by hei
h ee- ac o model, bu he model canno explain he medium- e m momen um e ec .
Fama and F ench (1996) also belie ed ha he CAPM ision is due o he CAPM
model, which lacks he conside a ion o o he necessa y isk ac o s. Conside ing he
p oblem wi h he CAPM model, ou analysis is es ablished based on he adi ional
inancial school, which uses a model simila o he ac o model o explain he wo
isions.
As men ioned, he BETA alue in he CAPM model is no a eliable isk indica o .
Some schola s ound ha i he new isk ac o is added in o he ac o models, some
excess e u ns can be explained. Some ype o ision will disappea . Bu wha a iable
should be added o he ac o model o explain he medium- e m momen um and
long- e m e e sal? Schola s ailed o each a consensus on his poin . Following he
Wei-qi and Jingxing Financial Inno a ion (2018) 4:1 Page 3 o 29
adi ional inancial idea, we conside he ype o impac ha occu s om adding BM
and ROE in o he model.
Fi s , we alida e he ze o in e p e a ion abili y abou he medium- e m momen um
and long- e m e e sal o he CAPM model. Then, we use he bene i o ecas model
ob ained h ough he MC model (Lyle & Wang, 2015) o cons uc independen a i-
ables di e ence and ob ain he ision in e p e a ion model. This pape chooses he MC
model as he basic model. We need o p o e he ollowing: Fi s , his model has be e
abili y han he CAPM model o o ecas u u e s ock ea nings. Second, his model has
he same abili y as he h ee- ac o model and he ou ac o s in e u ning a p edic ion.
The empi ical es ound ha medium- e m momen um was la gely explained, and a
small pa o he long- e m e e sal was explained.
Addi ionally, h ough a se ies o s udies, we disco e ed he BM as he mos c i ical
ac o in explaining abili y. I s alue is o ally di e en unde he e icien ma ke hy-
po hesis. The long- e m e e sal explaining abili y is a mo e han ha o he
medium- e m momen um. We design a se ies o co ela ion expe imen s ha a e
deemed signi ican o p o e ha he BM ac o g adually becomes no iceable o e ime,
which is also consis en wi h he adi ional inance si ua ion whe eby he ma ke ends
o become an e ec i e ma ke , and he ision will g adually disappea .
Fo he BM e ec , Fama and F ench (1992) s udied all he s ocks lis ed on NYSE,
AMEX, and NASDAQ om 1963 o 1990 and ound ha he 1.53% combina ion o
BM’s highes alue ( he alue combina ion) had he lowes mon hly yield ( he combin-
a ion o cha m). Xiao Jun and Xu Xinzhong (2004) used Shanghai and Shenzhen s ock
ma ke sha es om June 1993 o June 2001 as a sample and calcula ed holding sha es’
ea nings in one yea , wo yea s, and h ee yea s o ind ha he BM e ec does exis .
Finally, i we lack igo in ou esea ch me hods, we hope ha o he schola s in his
a ea p o ide mo e in-dep h s udy and mo e p oo will eme ge in he u u e.
The emainde o his pape is o ganized as ollows: sec ion2 p esen s he MC model
and de e mines he pa ame e s. Chap e 3 analyzes he BETA coe icien s o he CAPM
model based on he empi ical analysis. In Chap e 4, he exis ence o he s ock ma ke ,
ision model, and empi ical explana ion a e p oposed. Chap e 5 analyzes he model’s
inhe en explaining mechanism. Chap e 6 gi es a obus ness es , and Chap e 7 sum-
ma izes he ull ex .
Model
The speci ic o mula o he MC model is shown in (Lyle & Wang, 2015), and o he
de ailed de i a ion s eps a e gi en in he li e a u e.
i; þ1¼μi1−ωi
α1
α2

|{z}
β0
þ 1−k1κi!
|{z}
β1
bmi; þ ωi
1−k1κi
1−k1ωi!
|{z}
β2
oei; þξi; þ1ð1Þ
among β1¼1
α2
;β2¼ωi
α1
α2
;ξi; þ1¼α1
α2
εi; −ωiνi;

þηi; þ1
We ob ain he indus y pa ame e s om he es ima ed coe icien s o (Chen &
Wang, 2017):
Wei-qi and Jingxing Financial Inno a ion (2018) 4:1 Page 4 o 29

κ¼1−β1

=k1ð2Þ
μ¼β0=1−β2
 ð3Þ
ω¼β2=β1
1þβ2=β1

k1ð4Þ
In de eloping he model, i s , indus y pa ame e s mus be de e mined. O e ime,
any company ends o become mo e like i s pee s. Any abno mal expec ed ROE (o
excess expec ed e u n) will be g adually weakened due o he p esence o indus y
compe i ion. Equa ion (1) is also he co e model o he anomaly in e p e a ion.
Sample selec ion and da a sou ces
A e ob aining he p edic ion model, he coe icien s and o he implied pa ame e s o
his model mus be con i med. The sample is selec ed om he qua e ly aining da a
( he sunken da a), which is made up o 100 qua e ly da a poin s. The pe iod was om
he i s qua e o 1980 o he ou h qua e o 1994 o all he US inancial ma ke s
in Da aS eam. We implemen he ou -o -sample p edic ion om he i s qua e o
2010 o he ou h qua e o 2015. A his ime, we no longe use a sample o all
indus ies bu selec i e, and hese i e indus ies will un h ough he anomaly in e -
p e a ion and obus ness es . The main eason we ga he da a in his way is ha col-
lec ing whole indus y in ol es ex ensi e wo k and he p obabili y o e o is g ea e .
Empi ical analysis
Sample eg ession analysis
Fi s , he model is es ima ed h ough qua e ly da a by o dina y leas squa es (OLS).
The model coe icien s and model implici pa ame e s a e calcula ed using Equ. (1).
Panel B o Table 1 shows he ime se ies mean o each indus y. Panel A gi es he
summa y esul . The mean alues (median) o log BM and log ROE a e 0.045638
(0.0461) and 0.339625 (0.265), espec i ely. The cons an coe icien s co esponding o
median and mean alues a e 0.032162 and 0.02985, espec i ely. By compa a i e
analysis, we ind ha he i s -o de au o eg essi e pe sis ence pa ame e s o mean
(median) alues a e 0.964003 and 0.962121, espec i ely, o a gi en indus y; pe sis-
ence alues a e high. The s anda d de ia ion o he indus y pe sis ence pa ame e is
low, only 0.017613, while he ROE con inuous pa ame e 's s anda d de ia ion is
0.181218, which is la ge han he log e u ns. O e all, he MC model has good pe sis-
ence o expec ed e u ns.
Table 1 shows ha he coe icien and implici pa ame e s be ween indus ies di e ,
which sugges s ha e e y indus y’s esponse o ex e nal change a ies because o i s
unique cha ac e is ics. Fo mos indus ies, he o ecas e u ns a e consis en wi h
ac ual ea nings; ha is, he k alue is la ge enough. Some indus ies, such as gas, wa e ,
and mul iple u ili ies; li e insu ance; inancial se ices; and equi y in es men ins u-
men s ha e sligh ly la ge coe icien s. The e o e, hei e u ns a e ulne able o ou side
in luences. Indus ies such as ood and d ug e ail a e di e en . ROE coe icien alues
a e close o one implying e u ns a e easily in luenced.
Wei-qi and Jingxing Financial Inno a ion (2018) 4:1 Page 5 o 29
Table 1 Summa y o model pa ame e s
Reg ession coe icien s Implied pa ame e s
cons bm oe k w μ
Panel A: Reg ession esul s summa y
5 h pe cen ile -0.0119 0.013 0.1106 0.93523 0.707112 0.02003
25 h pe cen ile 0.02114 0.0322 0.179 0.950202 0.817889 0.031925
Mean 0.032162 0.045638 0.339625 0.964003 0.878349 0.056226
Median 0.02985 0.0461 0.265 0.962121 0.893978 0.041286
75 h pe cen ile 0.03772 0.0584 0.461 0.976566 0.938257 0.05825
95 h pe cen ile 0.05589 0.07149 0.61 0.995 0.98653 0.12964
S anda d de ia ion 0.013273 0.017437 0.198346 0.017613 0.084486 0.181218
Panel B: Indus y Coe icien
Elec ici y 0.03705 0.0453 0.114 0.964343 0.731332 0.041817
Equi y in es men ins umen 0.04606 0.0153 0.108 0.994646 0.89955 0.051637
Financial se ice 0.04952 0.0423 0.46 0.967374 0.941658 0.091704
Fixed line elecommunica ions 0.03535 0.0461 0.136 0.963535 0.763959 0.040914
Food and d ug e ail 0.03188 0.057 0.97 0.952525 0.972041 1.062667
ood p oduce s 0.05658 0.0288 0.51 0.98101 0.974212 0.115469
Fo es y & pape 0.03507 0.0402 0.384 0.969495 0.930503 0.056932
Gas, wa e , & mul iple u ili ies 0.06409 0.0225 0.59 0.987374 0.99193 0.156317
Gene al indus ial 0.03798 0.0436 0.262 0.966061 0.879962 0.051463
Gene al e aile s -0.01148 0.0622 0.53 0.947273 0.91966 0.024426
Heal h ca e equipmen & se ices 0.02878 0.0475 0.188 0.962121 0.817889 0.035443
Household goods & home cons uc ion 0.03397 0.0512 0.117 0.958384 0.710426 0.038471
Indus ial enginee ing 0.02985 0.0554 0.277 0.954141 0.854701 0.041286
indus ial me als & mining 0.03686 0.0332 0.259 0.976566 0.910593 0.049744
Indus ial anspo a ion 0.02691 0.0499 0.26 0.959697 0.860642 0.036365
Leisu e goods 0.01774 0.0632 0.354 0.946263 0.870677 0.027461
Li e insu ance 0.04108 0.0187 0.461 0.991212 0.989546 0.076215
Media 0.01825 0.0584 0.233 0.951111 0.81924 0.023794
Mining 0.02114 0.0594 0.62 0.950101 0.938257 0.055632
Mobile elecommunica ions 0.01277 0.0709 0.6 0.938485 0.918977 0.031925
No li e insu ance 0.03772 0.0322 0.265 0.977576 0.916162 0.05132
Oil equipmen & se ices 0.02799 0.0433 0.192 0.966364 0.836456 0.034641
Oil & gas p oduce s 0.03311 0.0266 0.541 0.983232 0.981192 0.072135
Pe sonal goods 0.0288 0.0545 0.179 0.955051 0.78464 0.035079
Pha maceu icals & bio echnology -0.01425 0.072 0.38 0.937374 0.86246 0.022984
Real es a e in es men & se ices 0.05535 0.0129 0.174 0.997071 0.957728 0.06701
Real es a e in es men us s 0.04822 0.0132 0.269 0.996768 0.981286 0.065964
So wa e & compu e se ices 0.02563 0.0593 0.56 0.950202 0.929461 0.05825
Spo se ices -0.01356 0.0769 0.222 0.932424 0.75965 0.017429
Technology ha dwa e & equipmen 0.02293 0.0613 0.138 0.948182 0.707112 0.026601
Tobacco 0.02047 0.0529 0.356 0.956667 0.893978 0.031786
T a el & leisu e 0.02875 0.0442 0.159 0.965455 0.80129 0.034185
Wei-qi and Jingxing Financial Inno a ion (2018) 4:1 Page 6 o 29
Expec ed e u ns analysis
A e de e mining he coe icien , we calcula e he ou -o -sample e u n. Fi s , we need o
p edic in-sample e u n be o e in e p e ing ision. The eason is he ollowing: i s , he
anomaly excess e u n is also a pa o he ac ual bene i ; second, p edic ing abili y in 3,
12, 24, and 36 mon hs is mainly possible because long- e m e e sal ypically occu s be-
ween h ee o i e yea s o holdings, and he medium- e m momen um ypically occu s
be ween h ee o 12 mon hs. Thus, i he model can p edic e u ns wi hin h ee yea s o
less, i is likely ha he MC model can explain he abo e wo anomalies be e .
By es ima ing he coe icien s and he implici pa ame e s o he model, he expec ed
e u ns o he holding pe iod T a e ob ained:
XT
j¼1μ þj−1¼^
μTþ1−
^
κT
1−κ
^
β1bm þ
^
β2 oe −μðÞ
hi ð5Þ
Fo he cons uc ion o he holding pe iod unde 1, 4, 8, and 12 qua e ly
pe iods acco ding o (Chena e al., 2017) (see Table 2), we compa e he a e age ex-
pec ed e u n and he a e age known ea nings a di e en imes. Fo example, he
mean (median) expec ed e u n is 0.7808 (0.82983), 0.56554 (0.5757), 1.4438
(1.6883), and 1.3871 (0.78332), espec i ely. When he lead ime is 1, 4, 8, and 12
qua e s, he known e u ns we e 0.74912 (1.07651), 0.9445 (1.87121), 1.4047
(2.4969), and 1.6952 (2.00348), espec i ely. Table 2 shows ha mos sho - e m
gains can be p edic ed. This shows ha he model e lec s he ac ual alue o
u u e e u ns, pa icula ly in one and ou qua e s.
P edic i e abili y eg ession es s
By expec ing c oss-sec ional p ope y, we need o e i y he MC model’s es ima ed
eliabili y. We ocus on companies’c oss-sec ional p ope y in he h ee-yea pe iod.
Table 2 Summa y o expec ed e u ns
1Q
ahead
4Q
ahead
8Q
ahead
12Q
ahead
Long
e m
LT-1Q
di e ence
12Q-1Q
di e ence
Panel A: Expec ed log e u ns
5 h -0.4794 -0.5047 -0.83602 0.79245 0.3987 -0.80482 -0.5963
25 h -0.2079 -0.3625 1.0216 0.9635 0.7758 -0.02842 -0.0692
Mean 0.7808 0.56554 1.4438 1.3871 1.3511 1.58205 0.721
Median 0.82983 0.5757 1.6883 0.78332 1.0587 1.4608 0.503
75 h 0.89856 0.8399 1.7164 1.89945 2.0655 1.249 0.9803
95 h 0.9563 1.56075 1.952 2.90988 2.7431 2.0729 1.5028
S anda d de ia ion 0.633536 0.6896 1.0295 0.83071 0.868 0.7052 0.74976
Panel B: Realized log e u ns
5 h -0.41356 -0.1694 -0.17981 -0.97937 0.3842
25 h -0.17805 -0.0497 -1.044 0.20461 1.0284
Mean 0.74912 1.3646 1.1662 1.6952 1.2974
Median 1.07651 0.9445 1.4047 2.00348 1.3002
75 h 1.5181 1.87121 2.3969 3.2014 1.5355
95 h 1.8595 2.1495 3.86763 3.5383 2.4085
S anda d de ia ion 0.910017 0.967892 1.675042 1.7374 0.662228
Wei-qi and Jingxing Financial Inno a ion (2018) 4:1 Page 7 o 29
We use he eg ession es me hod o es ima e he mixed holding pe iod log e u n
wi hin he limi ime:
i; þT¼δ0þδ1E i; þT

þωi; þTð6Þ
Unde he condi ion o δ0=0,δ1 = 1, he e will be an absolu e ue es ima e o he
expec ed e u n o any holding pe iod. Thus, by mee ing such a benchma k as much
as possible, when δ1 is mo e impo an , he expec ed alue is close o he ue alue.
Table 3 lis s he es ima ed esul s abou (7) o he 3, 12, 24, and 36-ahead mon hs.
In he p esence o indus y (no indus y) ixed e ec , he p edic ing coe icien s a e
0.717 (0.65284), 0.643 (0.5972), 0.5828 (0.50284), and 0.438 (0.4028), espec i ely, and
he coe icien is signi ican ly no ze o a he 1% le el. Because he holding pe iod e-
u n p oxies condi ionally change acco ding o he change in T and he holding pe iod
inc eases, he measu emen e o becomes la ge, and he coe icien is likely o g ad-
ually dec ease. Howe e , he co espondence be ween he expec ed e u n and he
known e u n is be e wi hin wo yea s, he p edic ed coe icien is g ea e han 0.5,
and he slope coe icien unde he h ee-yea lead pe iod has been signi ican ly less
han 0.5. This indica es ha he MC model may lack he abili y o explain long- e m
e e sal, bu we canno exclude he human ac o ha could be in luen ial and lead o
such a esul .
CAPM model pa ame e s
A e de e mining he basic coe icien s o he MC model, we mus de e mine he coe -
icien s o he CAPM model. To ensu e he consis ency o he da a, be o e p edic ing
he CAPM model coe icien s, we s ill use he his o ical qua e ly da a in Da aS eam
as sample da a al hough he calcula ion me hod will sligh ly di e . The s ock e u ns
Table 3 Re enue e u n
Panel A: Reg ession pa ame e summa y
Da a Reg ession coe icien s Implied pa ame e s
cons bm oe F k w μ
5 h pe cen ile 0.014 0.045 0.259 70.62 0.904 0.620 0.014
25 h pe cen ile 0.018 0.048 0.325 145.24 0.952 0.647 0.017
Mean 0.022 0.050 0.430 359.70 0.910 0.657 0.023
Median 0.025 0.058 0.539 879.02 0.948 0.800 0.041
75 h pe cen ile 0.029 0.065 0.872 1426.60 0.963 0.889 0.059
95 h pe cen ile 0.035 0.094 0.890 1552.22 0.976 0.913 0.064
s anda d de ia ion 0.027 0.054 0.205 819.93 0.015 0.090 0.036
3M
(1)
12M
(2)
24M
(3)
36M
(4)
3M
(5)
12M
(6)
24M
(7)
36M
(8)
E[
(i, +1)
] 0.717
***
0.643
***
0.5828
***
0.438
***
0.65284
***
0.5972
***
0.50284
***
0.4028
***
(0.073) (0.0615) (0.0295) (0.0103) (0.0624) (0.040) (0.0105) (0.004)
Cons -0.0343 0.0368 0.0329
***
0.0319
**
0.0286 0.3058 0.2528
**
0.2485
**
(0.063) (0.0132) (0.0202) (0.2840) (0.0468) (0.008) (0.0120) (0.025)
Numbe o obse a ions 2851 2212 2105 1776 2851 2212 2105 1776
Fixed e ec s no no no no yes yes yes yes
Adj.R
2
0.032 0.031 0.025 0.030 0.0193 0.0284 0.5020 0.1598
Wei-qi and Jingxing Financial Inno a ion (2018) 4:1 Page 8 o 29
Table 5 One hund ed g oups o wp, lp, wl, alue summa y able (Con inued)
5.5660 5.7970 4.0500 -6.3380 -6.9130
6 mon hs wp 0.0690 0.0364 -0.0425 0.0217 0.0292
lp -0.0335 -0.0551 -0.0407 -0.1476 0.1022
wl 0.102505※0.091487※-0.001725※0.1693044※-0.0730656※
4.1339 8.3676 -3.3159 6.4333 2.4222
9 mon hs wp 0.0597 0.0467 -0.0421 0.0054 -0.0460
lp -0.0442 -0.0427 0.0397 0.1088 -0.0912
wl 0.103965※0.089413※-0.0818328※-0.1034639※0.0452
6.1218 10.2500 -3.3015 -2.3915 -1.9165
12 mon hs wp 0.0503 0.0450 -0.0387 -0.0693 -0.0594
lp -0.0404 0.0478 0.0383 0.0731 -0.0612
wl 0.090685※-0.0028797※-0.076932※-0.1423882※0.0018128※
5.1261 -6.2303 -3.9858 -4.9017 2.1925
18 mon hs wp 0.0487 0.0393 0.0322 -0.0609 0.0515
lp -0.0437 -0.0439 -0.0396 -0.0672 0.0517
wl 0.092433※0.0832855※0.0719 0.0063171※-0.00022※
2.3860 4.2167 1.2674 3.3433 -2.0865
24 mon hs wp 0.0477 0.0446 0.0385 -0.0723 -0.0552
lp -0.0200 -0.0398 -0.0326 0.0418 0.0564
wl 0.0676301※0.0844540※0.071153※-0.1141 -0.1116
3.0767 10.1525 7.2020 -1.2751 -1.9976
30 mon hs wp 0.0291 0.0330 0.0318 0.0527 -0.0463
lp -0.0245 -0.0399 -0.0343 0.0604 -0.0495
wl 0.0536 0.0729 0.0661 -0.0077 0.0032618※
1.0736 1.0897 1.1173 0.8520 5.9153
36 mon hs wp -0.0217 -0.0325 -0.0293 -0.0590 0.0477
lp 0.0241 0.0175 0.0158 0.0647 0.0484
wl -0.0457920※-0.0500914※-0.045144※-0.1237 -0.000688※
-5.0737 -8.0590 -5.0440 -1.1230 -4.5070
48 mon hs wp 0.0445 0.0504 0.0401 0.2460 0.1566
lp -0.0295 -0.0460 -0.0378 -0.0732 -0.0604
wl 0.0740122※0.0965 0.0778 0.3192 0.2169
-3.0458 1.0312 0.9965 1.0826 -0.6063
60 mon hs wp 0.0255 0.0267 0.0211 0.0041 0.0044
lp -0.0027 -0.0024 0.0264 0.0600 0.0465
wl 0.0282 0.0291 -0.0053 -0.0558800※-0.0421593※
1.0402 1.0100 -0.9474 -4.0311 -3.6525
No e: * is a signi ican esul a e he bila e al - es wi h = “wp”co esponding o he winne po olio. “lp”co esponds
o he a e age e u n o he s a egy po olio. We conduc he - es abou he “wl” alue
Wei-qi and Jingxing Financial Inno a ion (2018) 4:1 Page 15 o 29

Among hem, he esul s we e signi ican o 3, 6, and 24 mon hs. The lose and winne
po olios shown in Table 5 ha e ob ious pe o mance in he momen um e ec .
Th ough obse a ion, we ind ha he momen um e ec has signi ican pe o mance
h ough he h ee o nine mon hs’holding pe iod. Du ing he same pe iod, he wl po -
olio showed an inc easing end wi h an inc ease in he o ma ion pe iod. The e o e,
we conclude ha when he combina ion pe iod and holding pe iod become longe , he
e ec o he e e sal and he momen um become less signi ican .
CAPM model ze o in e p e a ion abili y
Chan (1988) a gued ha he isk o winne s and lose s is changing o e ime and, when
he isk ac o is con olled, he e e sal s a egy can only p oduce minimal e u ns. In
acco dance wi h he me hod o Chan (1988), he CAPM model can be used o analyze
whe he he isk was con olled in he p ocess o momen um o e e sal o he s a e-
gy's p o i abili y:
p − A¼αþβ m − A
ðÞþε p∈ω;ιðÞ ð16Þ
ι − ω ¼αcþβc m −
ðÞþε ð17Þ
The ime in e al is one mon h, m is he e u n o he equal ma ke index, and
he e u n o he lose and winne po olio is checked by (16). (17) is used o es he
W-L po olio ( he same as L-W). The es esul s show ha he BETA alue can
explain mos o he change in he winne and lose po olio ea nings (abo e 75%).
Howe e , he W-L (o L-W) po olio canno be explained by his BETA. In he case o
s a egy 3-36, which b ings ou momen um e u ns, he e is a posi i e e u n on he
winne po olio, a nega i e e u n on he lose po olio, and his W-L po olio’s
BETA alue is no signi ican a all. The e o e, he BETA, as a isk measu e alue, has
no abili y o explain he momen um and e e se p o i abili y. This is heo e ically
a i med by he CAPM model ha ing ze o in e p e a ion on he medium- e m momen-
um and long- e m e e sal.
Vision in e p e a ion
We de e mined all he coe icien s equi ed o he MC model and he CAPM model,
and we also used he MC model o make a e enue o ecas es o all da a om
Fig. 3 Shows he di e en a es o W-L combina ions in di e en holding pe iods
Wei-qi and Jingxing Financial Inno a ion (2018) 4:1 Page 16 o 29
Janua y 2010 o Decembe 2015. Then, ollowing he de elopmen o he pape , we
ocus on he in e p e a ion o medium- e m momen um and long- e m e e sal.
Building an explana o y model
Fi s , we compa e he CAPM model wi h he MC model, see (1) and (7). To acili a e
unde s anding, we summa ize wo models ha emo e he cons an e m as ollows:
MC model
i, + 1
=β
1
bm
i,
+β
2
oe
i,
+ξ
i, + 1
(1)
CAPM model E(
i,
)−
,
=β
i
(E(
m
)−
,
)+ε
i
(7)
E( i, ) is he expec ed e u n, and i, +1is he expec ed log e u n. The coe icien o
ROE e lec s he p o i abili y o di e en i ms in he same indus y, and he βi in he
CAPM model is also an indica o o p o i abili y.
Since he wo models a e no o he same magni ude, he expec ed log e u ns in he
MC model need o be ans o med o he same magni ude as hose in he CAPM
model:
n i; þ1¼Aeβ0þβ1bmi; þβ2 oei; −1þηn
i; þ1ð18Þ
The abo e o mula ela es he expec ed ne e u n (ηi, +1 n ), he expec ed log
e u ns (Aeβ0+β1bmi, +β2 oei, −1), and known ne e u ns (n i, +1). The expec ed log
e u ns a e ans o med in o he abo e unc ion o m so ha we can ob ain expec ed
ne e u n. In his case, he expec ed e u n is mul iplied by he expec ed logis ic e u n
index (by he condi ional logis ic a iance). Pa ame e A ep esen s his mul iplica ion.
Pa ame e A can be es ima ed using wo non-linea i ele an eg ession condi ion
equa ions, including (1) and (19):
bmi; ¼X∞
j¼1kj−1
1E i; þj

−E oei; þj
 ð19Þ
A e ob aining he alue o pa ame e A, he expec ed ne e u n can be exp essed
as:
0
i¼Ae i−1ð20Þ
A e ha , we in oduce a new pa ame e γ:
γ¼
‘
i−E
i
ðÞ ð21Þ
The meaning o γis easy o unde s and. I is he di e ence be ween he wo models'
p edic ions o u u e e u ns. Logically, i he model has a ce ain abili y o explain he
medium- e m momen um and long- e m e e sal, his pa o he in e p e a ion is also
ully included in he γpa ame e . Then, we place he ac ual e u ns sample da a
di ec ly om he da abase in o o mula (22), which is:
R0¼R−γð22Þ
Finally, acco ding o he se ies o R′da a calcula ed by (22), we cons uc a new winne
and lose po olio and use he same me hod o e i y he exis ence o he anomalies in
he p e ious chap e o ob ain he new e u ns alue. Examining whe he he mid-
momen um and he long- e m e e sal a e weakened, i γcon ains hese wo e u n
anomalies, hen, h ough he new empi ical analysis, he wo anomalies will be well ad-
d essed. We o e an empi ical es heo y as ollows. The sample da a a e expanded om
Decembe 2015 o June 2016.
Wei-qi and Jingxing Financial Inno a ion (2018) 4:1 Page 17 o 29
By compa ing he sunken sample da a in he Da aS eam da abase wi h he da a
calcula ed using he MC model and he CAPM model in o (20), (21), and (22), we
ob ain he e u ns o Fig. 4 in Fig. 5, which co esponds o he change in Fig. 1.
Bo h he mid-momen um and he long- e m e e sal ha e weakened in he g aphical
end in Figs. 1, 2, and 4, and he change in he mon hly e u n is mo e ob ious han
he p e ious change. We show powe ul g aphical e idence in Figs. 5 and 6 and p o ide
a mo e con incing empi ical es .
Empi ical es
In addi ion o he p ocessing o he sample, he in e p e a ion p ocess is consis en
wi h he anomalies exis ence es . Tha is, he winne and lose po olios a e con-
s uc ed based on he new e u n da a.
Table 6 shows ha he winne s’po olio a di e en s ages o o ma ion is explained
o a la ge ex en by he h ee o nine-mon h holding pe iod’s mid-momen um and he
h ee o i e-yea holding pe iod’s e e sal e ec (Fig. 6). Addi ionally, he di e en o -
ma ion pe iods o he lose po olio in he h ee o nine-mon hs holding pe iod o he
momen um e ec and he h ee o i e-yea holding pe iod o he e e sal e ec a e
also in e p e ed o a ce ain deg ee. Fo example, he (3, 3) winne s (lose s) po olios
in Tables 5 and 6 a e 0.0385 (-0.0255) and -0.1384 (0.0631), espec i ely. The (3, 48)
winne s (lose s) po olios in Tables 5 and 6 a e -0.0246 (0.0221) and 0.13942 (-0.0246),
espec i ely. The alues in Table 6 sa is y he s ochas ic luc ua ions in he e ec i e
ma ke e u ns. Thus, he model can explain he mid-momen um and long- e m e e -
sal o he wo anomalies o some ex en , and he mid-momen um explaining capabili y
is g ea e han he long- e m e e sal. We p esen he h ee-dimensional line g aph
co esponding o Table 6, which is mo e in ui i e e lec ing he change a e he
change.
F om he desc ibed empi ical s udy, we d aw wo conclusions: i s , he MC model
has a ce ain abili y o p edic income, which is excellen news o he u u e o he US
s ock ma ke . Second, based on he CAPM model, we ob ain a new model wi h ex-
plana o y abili y o medium- e m momen um and long- e m e e sal. Acco ding o
he empi ical esul s, his model can explain he medium- e m momen um and shows
weak abili y, bu no comple ely ze o, o long- e m e e sal. In he exis ing s udy o
Fig. 4 Mon hly change cha (adjus ed)
Wei-qi and Jingxing Financial Inno a ion (2018) 4:1 Page 18 o 29
he US ma ke , he e a e ew models ha can explain bo h mid- e m momen um and
long- e m e e sal.
Co ela ion analysis
Since we ha e e i ied ha he MC model does exhibi some explana o y powe o
mid-momen um and long- e m e e sal, an ensuing p oblem a ises: whe he he BM o
ROE is a ac o in he in e p e a ion o he model? Gi en his ques ion, we conduc ed
he ollowing es s.
Fi s , we emo e he BM ac o and ROE ac o . Second, we epea he same p ocess
as desc ibed abo e. The econs uc ed model wi h only he BM ac o o ROE ac o
can explain he wo s ock ma ke anomalies, bu he abili y o he ROE ac o is weake
han he model wi h only he BM ac o .
As he wo company basic indica o s ha e some explana o y powe conce ning he
ision, we need o de e mine whe he he e is a co ela ion be ween hem and be ween
ROE, BM and BETA.
Richa d and Jeong (1997) p oposed such a model:
P
B ¼1þX∞
τ¼11þ ðÞ
−τE
ROE þτ− ðÞB þτ−1
B
 ð23Þ
I has been p o en ha he e is a co ela ion be ween he cu en book alue ( he
ecip ocal o he book ma ke a io) and he cu en ROE, and he cu en book alue
also con ains mo e in o ma ion on he u u e ROE compa ed o he cu en ROE,
which will cause change in he ROE. Addi ionally, Richa d and Jeong (1997) es ed he
co ela ion be ween he ROE and BETA alues and ound ha he coe icien s we e
nega i e. This indica es ha he e is no co ela ion be ween he wo alues. Nex , we
mus e i y he ele ance o he BM ac o and he BETA and he hyb id co ela ion
be ween he h ee.
We use he mixed eg ession me hod p oposed by Newey and Wes (1987) o eg ess
Eqs. (24) and (25), in o de o weaken he e oscedas ici y and sequence dependency ha
mixed eg ession may cause.
BM ¼ 0
0þ 0
1BETA ð24Þ
BE ¼ 0þ 1BETA þ 2ROE ð25Þ
Fig. 5 Annual a e age ea nings g aph (adjus ed)
Wei-qi and Jingxing Financial Inno a ion (2018) 4:1 Page 19 o 29
Table 6 Exis en ial e i ica ion esul s
Hold pe iod q Fo ming pe iod p 3 mon hs 6 mon hs 9 mon hs 12 mon hs 18 mon hs
3 mon hs wp -0.1384 -0.0843 -0.2944 0.2095 -0.0283
lp 0.0631 0.0295 -0.0298 -0.3943 0.3943
wl -0.2015※-0.1138※-0.2646※0.6038※-0.4226※
-7.5469 -9.5765 -2.3137 -6.5177 -2.1533
6 mon hs wp -0.0103 -0.0384 0.0483 0.2048 0.1948
lp 0.0384 0.2940 -0.9387 0.2984 -0.0849
wl -0.0487※-0.3324※0.9870※-0.0936 0.2798※
-4.3401 -2.4090 -4.4905 -1.0605 -1.1958
9 mon hs wp -0.2934 -0.0206 0.0853 -0.4832 0.0519
lp 0.0238 -0.0394 0.3085 -0.5293 -0.2085
wl -0.3172※0.0188※-0.2232※0.0461※0.2604※
-4.7922 -8.5792 -5.5912 -3.7257 -7.9083
12 mon hs wp -0.7083 -0.3582 0.3849 0.2048 -0.3028
lp 0.2925 0.2490 -0.0294 0.2084 -0.0247
wl -1.0008※-0.6072※0.4143※-0.0036※-0.2781※
-5.0284 -9.3962 -7.2975 -7.3374 -9.8217
18 mon hs wp -0.9240 0.0108 0.1052 -0.4937 0.2806
lp 0.0284 -0.2420 0.1083 -0.0284 0.2874
wl -0.9524※0.25284※-0.0030※-0.4653※-0.0068※
-8.06059 -7.7146 -0.0415 -2.7705 -9.0339
24 mon hs wp -0.0183 -0.0083 0.0398 -0.0408 -0.2084
lp 0.0482 0.0029 0.0184 -0.1294 0.1083
wl -0.0665※-0.0112 0.0214※0.0886※-0.3167※
-5.1487 -0.5971 -2.6853 -8.9878 -9.2583
30 mon hs wp -0.2948 -0.1294 0.2948 0.0698 -0.2949
lp 0.0290 0.1084 0.0108 -0.0908 0.2844
wl -0.3238 -0.2378 0.2840 0.1606※-0.5793※
-0.9548 -0.7403 -0.0126 -5.6271 -8.7080
36 mon hs wp 0.2084 -0.2850 0.0203 -0.3985 0.5082
lp 0.0129 0.0940 0.2984 -0.2084 0.2952
wl 0.1955 -0.379※-0.2781※-0.1901※0.213※
-1.8446 -3.6409 -2.0442 -3.9977 -6.2831
48 mon hs wp -0.0024 0.2044 -0.2049 0.0385 -0.0108
lp 0.0597 0.1094 -0.2943 -0.0044 0.2044
wl -0.0621※0.095※0.0894※0.04285※-0.2152※
-8.873 -7.2558 -8.5790 -5.5865 -6.3009
60 mon hs wp -0.0070 0.1939 0.1033 -0.0188 0.4298
lp -0.2934 0.0139 -0.0210 -0.1944 0.0039
wl 0.2864※0.1800※0.1243※0.1756※0.4259※
-2.8769 -5.2485 -8.0858 -6.7919 -8.9324
Hold pe iod q Fo ming pe iod p 24 mon hs 30 mon hs 36 mon hs 48 mon hs 60 mon hs
3 mon hs wp 0.0428 0.2490 0.1932 0.3942 0.1038
lp -0.0208 -0.0283 -0.0286 -0.0246 -0.0612
wl 0.06364※0.27734※0.22180※0.4188※0.1650※
Wei-qi and Jingxing Financial Inno a ion (2018) 4:1 Page 20 o 29

Table 6 Exis en ial e i ica ion esul s (Con inued)
-9.5661 -6.4948 -4.5017 -4.3875 -6.5235
6 mon hs wp -0.0242 0.1084 -0.3942 0.0329 0.2494
lp 0.6092 0.0903 -0.3934 -0.2820 -0.3028
wl -0.6334※0.01812※-0.0087※0.31494※0.5522※
-4.7564 -2.3861 -5.7409 -9.4873 -9.6719
9 mon hs wp 0.2058 0.5038 0.4846 0.2045 0.5028
lp 0.4080 -0.0920 0.2058 0.0385 -0.3040
wl -0.2022※0.5958 0.2788※0.1660 0.8068※
-7.3042 -1.2111 -7.6711 -1.7727 -2.5962
12 mon hs wp 0.3856 -0.4941 0.3494 0.3842 -0.0794
lp -0.5927 0.3859 0.4928 -0.3842 -0.5938
wl 0.9783※-0.88※-0.1434※0.7684※0.5144※
-7.2787 -8.0722 -2.9770 -7.2284 -5.0118
18 mon hs wp 0.1958 -0.1858 -0.0184 0.1540 -0.1885
lp 0.0593 0.0284 -0.1084 -0.3749 0.0563
wl 0.13653※-0.2142※0.09※0.5289※-0.2448※
-9.0714 -9.6582 -3.3249 -8.1674 -4.2962
24 mon hs wp -0.0183 0.1098 0.1282 0.2853 0.0828
lp 0.2945 -0.2084 -0.0173 0.2943 -0.2084
wl -0.3128※0.3182※0.1455※-0.0090 0.2912※
-3.5671 -5.7649 -3.3872 -1.3965 -7.8998
30 mon hs wp 0.3930 -0.0109 -0.0014 0.0194 0.1854
lp -0.1050 0.0335 0.1042 -0.1988 -0.4851
wl 0.498※-0.0444 -0.1056※0.2182※0.6705※
-1.2578 -1.7227 -3.6256 -5.0381 -6.5537
36 mon hs wp 0.0189 -0.3940 -0.2840 -0.0018 -0.1030
lp -0.2848 0.0592 -0.2020 -0.0188 -0.0128
wl 0.3037※-0.4532※-0.0820※0.0170 -0.0902※
-5.7673 -8.9516 -4.3568 -0.61444 -8.8585
48 mon hs wp 0.3095 -0.0240 0.4085 0.2953 0.0044
lp -0.1084 0.3848 -0.0220 -0.0140 0.0199
wl 0.4179※-0.4088※0.4305※0.3093※-0.0155
-1.7304 -5.2197 -2.3661 -3.6702 -1.1061
60 mon hs wp 0.1088 -0.0053 -0.2420 -0.0110 -0.0399
lp 0.2842 -0.0910 0.2985 0.0503 0.0018
wl -0.1753※0.0857※-0.5405※-0.0613※-0.0417※
-2.5214 -2.6269 -5.2042 -9.6926 -4.9969
Wei-qi and Jingxing Financial Inno a ion (2018) 4:1 Page 21 o 29
Tables 7 and 8 show he esul s o he co ela ion eg ession. The esul s in Table 7
a e almos nega i e. Howe e , i BM can e u n he isk, i should be posi i e. The e-
o e, he eg ession o (24) indica es ha he BM alue canno be used o e u n he
isk bu can be used o cha ac e ize co po a e isk (Penman, 1991).
In he mixed eg ession in Table 8, he BETA coe icien is less signi ican , and he
luc ua ion a ies g ea ly compa ed o he eg ession esul s in Table 7. A e adding
he indus y dummy a iable, we ound ha he coe icien o BETA has no signi i-
cance. This shows ha company isk impac s he BM a io. Thus, he indus y's special
ac o s cap u e isk mo e e ec i ely han BETA.
O e all, ROE and BM do no co ela e wi h BETA, and BM is less ele an o BETA.
Bu BM and ROE a e ela ed, and BM will cause change in he ROE. This leads o he
ollowing conclusion: he BM ac o is he undamen al eason ha models can explain
he medium- e m momen um and long- e m e e sal. In o he wo ds, he BM e ec
does ha e an impac on medium- e m momen um and long- e m e e sal.
Tes conclusions
Th ough he p e ious in e p e a ion o he mid-momen um and he long- e m e e sal
o he wo anomalies, we con i m ha BM, as an in luencing ac o , does ha e some
explana o y powe o he wo isions in he US s ock ma ke . On he o he hand, he
in e p e a ion also explains ha he BM e ec does cause pa o he mid-momen um
and long- e m e e sal o gene a e excess e u ns. The BM e ec can only pa ially
Fig. 6 So ing pe iod W-L combina ions o di e en holdings mon hly a e o change (adjus ed)
Table 7 C oss-sec ional eg ession wi h BM as he dependen a iable and BETA as he
independen a iable yea by yea
Cons BETA Adj.R
2
2010 0.2554 -0.1546 0.0655
2011 0.4229 -0.2986 0.0055
2012 0.3500 -0.2014 0.0204
2013 0.4476 -0.1012 0.0253
2014 0.2759 -0.0281 0.0062
2015 0.3939 -0.2399 0.0772
Wei-qi and Jingxing Financial Inno a ion (2018) 4:1 Page 22 o 29
explain he wo isions. The e is no in-dep h s udy on his subjec , and i is no he
ocus o his pape . Howe e , we belie e ha his issue will c ea e a meaning ul e-
sea ch di ec ion. O cou se, i he e is change in he u u e, we would conside con-
duc ing mo e de ailed esea ch. Addi ionally, BM as a model impac ac o is one o
which he sample da a a e easy o ob ain and calcula e, which is a a e ad an age.
Fo he model capaci y’s di e ence wi h espec o mid-momen um and long- e m
e e sal, we specula e ha he eason may be ha he book alue and he ma ke alue
a e in ini ely close o he same mean when he ime leng hens.
O e all, he esea ch esul s a e o g ea impo ance. Fi s , he MC model has a good
abili y o p edic ea nings, bu company's basic da a is no easy o ob ain. The explain-
ing o s ock mid-momen um and long- e m e e sal is con enien .
Fo he model’s abili y o p edic and explain, i s , we iden i y whe he he model's
capabili ies a e limi ed o e u n o ecas s. Second, we iden i y whe he his conclusion
can be applied o o he inancial indica o o ecas s. In o he wo ds, we iden i y
whe he he p inciples used in MC model cons uc ion can be exploi ed in di e en as-
pec s o esea ch in he u u e. Thi d, does his new model only apply o he abo e wo
ypes o isions, o is i possible o ha e explana o y powe o o he s ock ma ke
anomalies? I he new model is applied o o he s ock ma ke isions, wha will be he
consequence? This s udy only p esen s ideas, and u u e p ac ical applica ion is
equi ed. Howe e , his new model will ha e deep signi icance o u u e esea ch.
Resea ch p ospec s
Ou s udy uses a newly cons uc ed model o p o e he exis ence o medium- e m mo-
men um and long- e m e e sal, bu i also ob ains he in insic ela ionship be ween
he BM ac o and hese wo isions. This is undoub edly a g ea imp o emen in he
ield o inancial ma ke ision esea ch. Based on his esea ch, he au ho sugges s
ha he ollowing poin s should be discussed in dep h.
Fi s , he US ma ke has signi ican mid- e m momen um and long- e m e e sal.
China, as a ep esen a i e de eloping coun y, may ha e he same cha ac e is ics, which
is con a y o he s a ed e ec i e ma ke hypo hesis. Second, he MC model is used o
p edic u u e ea nings and o explain inancial isions in his pape . Thus, we can in e
whe he his model has good abili y in o he inancial ma ke s and e en in o he
Table 8 A compa ison o he esul s o yea - ound mixed eg ession wi h accoun - o-ma ke a io
Panel A: No dummy a iables
Independen a iable 2010 2011 2012 2013 2014 2015
Cons 0.8302 1.2207 1.2830 0.7492 0.9298 1.0593
BETA -0.0824 -0.0240 -0.3023 -0.0427 -0.6222 -0.3812
ROE 1.1221 1.8324 0.8066 1.4899 1.0270 1.9774
Panel B: The e a e dummy a iables
Independen a iable 2010 2011 2012 2013 2014 2015
In e cep 0.7045 0.9152 0.6048 0.5362 0.5065 1.0709
BETA -0.0783 -0.0656 -0.1084 -0.0936 -0.0676 -0.0905
ROE 1.3985 1.7643 1.3274 1.5536 1.5359 1.7982
Wei-qi and Jingxing Financial Inno a ion (2018) 4:1 Page 23 o 29
non inancial sec o s. Fu u e discussion will be based on exis ing esea ch. Thi d, since
he BM ac o does ha e a conside able in e nal ela ionship wi h medium- e m mo-
men um and long- e m e e sal, he BM ac o also p esen s some explana o y powe
o o he isions in he inancial ma ke . This esea ch ques ion will become ou u u e
main esea ch di ec ion.
Robus ness es
Con ol he sample age
When he model is calcula ed o he model coe icien s and esul s, he sample used is
he ini ial aining sample om 1980 o 1994. When we use he comple e model o es
he pe o mance o qua e ly log e u ns, we use a sunken sample om June 2010 o
June 2016. Acco ding o he empi ical analysis conduc ed by Kelly and P a (2013), we
need o conside he es ima ed de ia ion o he expec ed e u n due o he di e en
sample. The e o e, o a oid his de ia ion, we choose he sample da a om Janua y
1996 o Decembe 2009, which is a se o sample da a a di e en ime in e als o es
he sample sensi i i y.
Figu es 7 and 8 show he g aphical ep esen a ion o he slope coe icien s a e he
same eg ession as ha shown in Table 3 unde di e en samples. Figu e 9 includes he
indus y ixed e ec . The wo igu es will ha e di e en es esul s conside ing he di e -
en unning ime. Howe e , in he ma hema ical sense, hese esul s a e s ill signi ican ,
and he eg ession slope coe icien is s able wi h a ce ain economic signi icance.
Use oei, −1 ins ead o oei,
The nex s ep conce ns he choice o an auxilia y a iable oei, , which may lead o
un eliabili y in he es esul s. Tha is, in he p ocess o using he log ROE( oei, ) o e-
place he expec ed log ROE(hi, )o he nex pe iod, i is likely ha he MC model will
no ag ee wi h he es ima ion o β2. I he inal es esul is mode a e, his indica es
ha he lag alue o ROE is a use ul auxilia y a iable, and his auxilia y a iable can be
used o weaken po en ial bias in he coe icien es ima ing p ocess.
Panel A o Table 9 shows he summa y s a is ics o he model es ima e pa ame e s
using he auxilia y a iable eg ession me hod. Addi ionally, he ou h column o he
able eco ds he s a is ical esul s o he F s a is ic.
The F s a is ic esul s o he i h qua ile we e 93.1769, and he a e age qua ile was
765.4844. The coe icien o oei, inc eased om he leas squa es es ima e 0.339625
(0.265) o he a e age sco e (median) o 0.494119 (0.3615). This esul indica es ha
he esul s o he leas squa es es ima ion may be a ec ed by he measu emen e o ,
esul ing in an inc ease in he ROE coe icien es ima ion. In con as , he coe icien
a iance changes om 0.198346 o 1.176139, almos 10 imes ha o he p e ious e-
sul . Thus, as p e iously p oposed, he e is a ade-o be ween he es ima es o bias
and e iciency. The cons an coe icien es ima es will inc ease mu a ions. The inc ease
in all es ima ed coe icien s’anomalies will ine i ably lead o anomalies in he implici
model pa ame e s. Howe e , his can be educed by adjus ing he implici pe sis ence
pa ame e (0.9999). The mean (median) o he model es ima ion pa ame e s indica es
ha he long- e m uncondi ional expec a ion dec eases om he OLS es ima es
0.056226 (0.041286) o 0.047367 (0.042206). The pe sis ence pa ame e alue
Wei-qi and Jingxing Financial Inno a ion (2018) 4:1 Page 24 o 29