Ay, Bay am E kin; Yağcila , Gamze Göçmen
A icle
In es iga ing he de e minan s o he d beha io : An
applica ion o he Hwang-Salmon me hod o he Tu kish
banking sec o
Ekonomika
P o ided in Coope a ion wi h:
Vilnius Uni e si y P ess
Sugges ed Ci a ion: Ay, Bay am E kin; Yağcila , Gamze Göçmen (2024) : In es iga ing he
de e minan s o he d beha io : An applica ion o he Hwang-Salmon me hod o he Tu kish banking
sec o , Ekonomika, ISSN 2424-6166, Vilnius Uni e si y P ess, Vilnius, Vol. 103, Iss. 3, pp. 40-56,
h ps://doi.o g/10.15388/Ekon.2024.103.3.3
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Ekonomika ISSN 1392-1258 eISSN 2424-6166
2024, ol. 103(3), pp. 40–56 DOI: h ps://doi.o g/10.15388/Ekon.2024.103.3.3
In es iga ing he De e minan s
o He d Beha io : an Applica ion o
he Hwang–Salmon Me hod o
he Tu kish Banking Sec o
Bay am E kin Ay
Ispa a Uni e si y o Applied Sciences, Tü kiye
Email: [email p o ec ed]
ORCID: h ps://o cid.o g/0009-0002-4089-6254
Gamze Göçmen Yağcila
Süleyman Demi el Uni e si y, Tü kiye
Email: [email p o ec ed]
ORCID: h ps://o cid.o g/0000-0002-5009-4696
Abs ac . E icien inancial ma ke s a e impo an o p icing asse s a ai alue. In an e icien ma ke ,
in es o s a e a ional in he ace o as and accu a e in o ma ion low, e alua e he in o ma ion co ec ly,
and e lec i in hei p icing decisions. Howe e , pa icula ly in imes o c isis and unce ain y, i is obse ed
ha some ma ke pa icipan s hesi a e in hei decision-making p ocesses, imi a e he beha io o o he indi-
iduals whom hey conside epu able because hey canno ely on hei own knowledge and expe ience, and
y o ollow he end. This endency, which is called he d beha io , des oys ma ke e iciency and p e en s
co ec p ice o ma ion. The e o e, i is impo an o iden i y i s de e minan s. The pu pose o he s udy is
analyzing he p ecense and de e minan s o he ding beha io in he Tu kish banking sec o du ing he pe iod
17.10.2017–10.11.2023. He d beha io is iden i ied using he Hwang–Salmon me hod, and logis ic eg ession
analysis and he K uskal–Wallis es a e applied o iden i y i s de e minan s. The indings e eal ha he ding
beha io is associa ed wi h he ise in isks and e u ns as well as he all in in e es a es and exchange a es.
Keywo ds: Beha io al inance, He d beha io , Hwang–Salmon Me hod, Logis ic eg ession, Banking sec o .
In oduc ion
Financial decisions and ma ke dynamics a e impo an o economic sys ems and busi-
nesses o achie e sus ainable success. In pa icula , inancial decisions a e highly s a e-
gic p ocesses ha equi e indi iduals and o ganiza ions o make he igh in es men s,
alloca e hei esou ces e ec i ely and manage hei isks consciously, and depend on
an unde s anding o ma ke dynamics. Al hough in es o s some imes ac beha io ally in
Recei ed: 04/04/2024. Re ised: 13/06/2024. Accep ed: 07/07/2024
Copy igh © 2024 Bay am E kin Ay, Gamze Göçmen Yağcila . Published by Vilnius Uni e si y P ess
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, 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 au ho and sou ce a e c edi ed.
Con en s lis s a ailable a Vilnius Uni e si y P ess
Bay am E kin Ay, Gamze Göçmen Yağcila . In es iga ing he De e minan s o He d Beha io
41
acco dance wi h hese dynamics, some imes hey may change hei beha io , decisions
and ma ke pe cep ions.
Ra ional models such as he Expec ed U ili y Theo y o he E icien Ma ke s Hypo he-
sis ail o explain hese pe cep ions. Beha io al models ha e been de eloped o compensa e
o his gap (Ka an, 2013). Wi h hei P ospec Theo y, Kahneman and T e sky (1979)
a gued ha in es o s can no be a ional all he ime and some imes decide un easonably
in isky si ua ions. Acco ding o he Beha io al Finance iew, which gained s eng h in
he inance and economics pe spec i e ollowing he Expec a ion Theo y, i s a es ha
in es o s may exhibi beha io s di e en om he a ionali y de ined in adi ional inance
models, ha hese i a ional beha io s may lead o e oneous o ma ion o p ices in he
ma ke and ha he a bi age mechanism may no be able o p e en his si ua ion (Ka an,
2022). P ice anomalies in he ma ke s cause inancial asse p ices o de ia e om hei
ue alue and hus call adi ional heo ies in o ques ion. P ice anomalies also b ing o
he o e on he main ac o o inancial ma ke s, he inancial in es o and inancial in-
es o beha io . This is explained by some cogni i e biases in beha io al inance. In he
s udy on In es o Psychology and Asse P icing by Da id Hi shlei e (2001), ou main
g oupings we e iden i ied. These g oups a e named as Sel -Delusion, Sho cu In e ence,
Emo ions and Sel -Con ol, and Social In e ac ion. Cogni i e biases ha occu in he
o m o e o s and biases a e shown in Hi shlei e ’s (2001) g ouping and subheadings in
Figu e 1 (Başa ı , 2021).
Figu e 1. G ouping o cogni i e biases.
Sou ce: Inspi ed by Başa ı (2021) P epa ed.
Social in e ac ion means ha indi iduals lea n and a e in luenced by each o he h ough
mu ual in e ac ion/communica ion. Be o e making a decision abou hei in es men ,
in es o s discuss hese decisions and he opinions hey ecei e om hei en i onmen
a ec hei decisions (No singe , 2017). Social in e ac ion is examined unde wo g oups:
ISSN 1392-1258 eISSN 2424-6166 Ekonomika. 2024, ol. 103(3)
42
social con agion and he ding beha io . The e a e many s udies in he li e a u e ha in-
es iga e he d beha io wi h di e en me hods. Howe e , s udies on he de e minan s
o he d beha io a e ela i ely limi ed. Re ealing he ac o s ha cause his beha io
will con ibu e o managing he expec a ions o in es o s, po olio manage s and policy
make s. In his con ex , he s udy aims o in es iga e he p esence and de e minan s o
he ding beha io o banking s ocks, which ha e an impo an place in BIST 100, he mos
equen ly ollowed index o Bo sa Is anbul. Fo his pu pose in sec ion 1, he concep o
he d beha io is explained. In sec ion 2, ela ed li e a u e is p esen ed. In o ma ion abou
he me hodology and da a o he esea ch is gi en in sec ion 3. Findings a e p esen ed in
sec ion 4. The las sec ion includes concluding ema ks and discussions.
1. Concep ual F amewo k: He d Beha io
While he concep o he ding appea s in many ields such as neu ology, sociology and zo-
ology, in he ields o economics and inance, i is de ined as ac o s gene ally imi a ing each
o he and shaping hei decisions by de e mining he beha io o o he s as a basis (Spy ou,
2013). Acco ding o Raa a e al. (2009), he ding beha io is de ined as he alignmen o
ideas o beha io s o indi iduals wi hin an en i onmen h ough local in e ac ion wi hou
cen al coo dina ion, while acco ding o Bikhchandani and Sha ma (2000), he ding beha io
in inancial ma ke s is de ined as a phenomenon in which in es o s shape hei in es men s
wi h he in en ion o mimicking he ac ions o o he in es o s (Demi e and Ku an, 2006).
The o ma ion o a “he d” is igge ed when an in es o akes an ac ion ha he/she would
no ha e aken i he/she had no known abou he o he in es o s. When he he d is o med
and i s p esence is el in he ma ke , i is obse ed ha in es o beha io does no include
new in o ma ion abou ma ke undamen als and he social lea ning p ocess is in e up ed
(Decamps and Lo o, 2002). Measu ing he d beha io is impo an because he ding can
lead o ma ke -wide misp icing and end shaping ha al e s indi iduals’ pe cep ion o
he economic undamen als o asse s (Baddeley, 2013). Due o i s impo ance, a ious
measu emen me hods ha e been de eloped. Hachicha e al. (2007) s a ed ha s udies on
he d beha io a e di ided in o wo ca ego ies. In hei s udy, he LSV measu e de eloped
by Lakonishok, Shlei e and Vishny (1992) and he PCM measu e o We me s (1994)
cons i u e he i s ca ego y, which equi es de ailed in o ma ion abou in es o s’ ading
ac i i ies and changes in hei po olios. The second ca ego y conside s he phenomenon
o he ding beha io as he collec i e ading beha io o indi iduals in o de o ack he
ma ke and uses c oss-sec ional p ice mo emen s o measu emen . Ch is ie and Huang
(1995) (CSSD), Chang, Cheng, and Kho ana (2000) (CSAD) and Hwang and Salmon (2001,
2004) a e he con ibu o s o his ca ego y o measu emen (Hachicha e al., 2007). The
LSV measu emen me hod de ines he d beha io as he imi a ion o simul aneous buying
o selling by a g oup o und manage s. I uses subse s o measu e speci ic cha ac e is ics o
beha io s (Lakonishok e al., 1992) and he e o e equi es specialized in o ma ion (Hwang
and Salmon, 2004). The CH he d beha io measu emen me hod p oposed by Ch is ie and
Huang (1995) examines whe he indi idual e u ns concen a e a ound he ma ke in pe iods
Bay am E kin Ay, Gamze Göçmen Yağcila . In es iga ing he De e minan s o He d Beha io
43
o ma ke complexi y and s ess. This measu emen me hod was la e expanded by Chang,
Cheng, and Kho ana (2000). Using a nonlinea eg ession speci ica ion, hey measu ed he
ela ionship be ween he le el o s ock e u n dis ibu ion and he o e all ma ke e u n using
he c oss-sec ional absolu e de ia ion o e u ns (CSAD). They a gue ha he endency o
ma ke in es o s o con o m o he gene al ma ke sen imen du ing pe iods o high p ice
mo emen s is su icien o ans o m a linea ela ionship in o a nonlinea one. Addi ionally,
he impo ance o mac oeconomic in o ma ion o eme ging ma ke s is emphasized (Chang
e al., 2000). Hwang and Salmon (2001) de eloped a me hod o measu e he d beha io by
conside ing linea ac o models and obse ed condi ions in undamen al mo emen s. Simila
o he CH me hod in e ms o u ilizing in o ma ion p esen in he ho izon al c oss-sec ion
mo emen s o he ma ke , i di e s in ocusing on ho izon al c oss-sec ional changes in
ac o sensi i i ies ins ead o using e u n alues hemsel es. I u ilizes he c oss-sec ional
s anda d de ia ion o loadings in he linea ac o model o indi idual asse s and is calcu-
la ed wi h he help o indi idual be as. The me hod au oma ically akes in o accoun he
e ec s o changes in he ime se ies ola ili y included in he c oss-sec ional a iance. I
is also a gued ha he d beha io is a ma e o deg ee, insepa able om any ma ke aken
in o conside a ion, and he e o e, a he han he p esence o absence o he d beha io , i is
ad oca ed o use exp essions like less he d beha io o mo e he d beha io . Fu he mo e,
his me hod allows o a dis inc ion be ween in en ional and alse he d beha io and ocuses
on in en ional he d beha io (Capa elli e al., 2004). In es o s can be d i en owa ds he
same poin by in o ma i e con en abou he ma ke , economic expec a ions, and in es o
sensi i i ies. This indica es ha in es o s can also ac based on hei economic a ionales.
Fo example, adi ional/non adi ional mone a y policies can be gi en (K okida e al., 2020).
When indi iduals aim o maximize e u ns and a oid isks in hei in es men s (Kuzu and
Çelik, 2020), i is possible o hem o ollow p eceding signals. In his case, e en hough
an in es o may pe cei e i as mo e a ional o exhibi di e en beha io based on hei
unique in o ma ion, he p obabili y o con o ming o he beha io o he majo i y wi h he
suppo o p e ious signals is high (Bane jee, 1992). The o egoing discussion demons a es
he impo ance o iden i ying he d beha io in unde s anding in es o beha io . The e o e,
explaining he de e minan s o he d beha io as well as iden i ying he d beha io may help
o cla i y ma ke dynamics.
2. Li e a u e Re iew
The issue o he d beha io is among he opics ha ha e been widely co e ed in he
li e a u e. I is possible o classi y hese s udies acco ding o hei measu emen me h-
ods. Al hough LSV, PCM, CH, CCK, Hwang and Salmon (2004) (he ea e HS-2004)
measu emen me hods a e encoun e ed (Se yawan and Ramli, 2016; Pochea e al., 2017;
Medhioub and Cha ai, 2019; Qasim e al., 2019; Choi and Yoon, 2020; Fe ouhi, 2021;
Li e al., 2023; Hong e al., 2024), his s udy is limi ed wi hin he scope o he me hod o
be used he e and he s udies using he HS-2004 measu emen me hod ha a e included in
he li e a u e. The s udies using he HS-2004 he d beha io measu emen me hod ( elying
ISSN 1392-1258 eISSN 2424-6166 Ekonomika. 2024, ol. 103(3)
44
on s ock be a coe icien s) s a ed wi h he s udy conduc ed by Hwang and Salmon in
2001 esul ing ha mo e he d beha io is obse ed in de eloping coun ies (Sou h Ko ea)
han in de eloped coun ies (USA, UK). In he nex s udy in 2004, Hwang and Salmon
s a ed ha hey ound he ding beha io when he ma ke ises o alls, and ha hey ound
signi ican mo emen s and pe sis ence, independen o ma ke condi ions.
Capa elli e al. (2004) ound he exis ence o he ding beha io in capi al ma ke s o I aly.
Kallin e akis (2006) es s he ding beha io in s ock ma ke s o 8 coun ies. Resul s on he
impac o speci ic egula o y es ic ions on ma ke -wide he ding beha io a e p esen ed.
Kallin e akis e al. (2007) de ec ed he ding beha io in MERVAL index du ing and
a e he A gen ine inancial c isis. Wang (2008) obse ed highe le el o he ding beha io
in de eloping coun ies hen de eloped coun ies. Demi e e al. (2010), ano he s udy on
eme ging economies, obse ed he ding beha io . Ami a and Bou i (2009) and Hachicha
e al. (2010) in es iga ed he ding beha io in To on o s ock ma ke and in bo h s udies
he ding beha io is obse ed.
Al ay (2008) examined he ding beha io in he Is anbul S ock Exchange (ISE). As
a esul o he s udy, al hough he d beha io was no obse ed in some pe iods, i was
s a ed ha he gene al endency was in a o o he d beha io . Ano he s udy on ISE by
Mede oğlu and Saldanlı (2019) ound he ding beha io ea u es. Doğukanlı and E gün
(2015) in es iga ed he ding beha io on BIST by examining 15 di e en sec o s. While
hey obse ed he ding beha io in some pe iods, i was also s a ed ha mo e signi ican
obse a ions we e made a sho equencies. Akçaalan e al. (2019) a gued ha he ding
beha io inc eases as he ading olume o in e na ional in es o s inc eases and in eac-
ion o inc eased ola ili y.
Some s udies in es iga ed he he ding beha io in ma ke s o he han equi y ma ke s.
De Gama Sil a e al. (2019) e ealed nega i e he d beha io du ing ex eme pe iods in
c yp ocu ency ma ke . Júnio e al. (2020) examined i een commodi y ma ke s and
obse ed he ding beha io .
In he li e a u e, he e a e also s udies ha HS-2004 model did no ind he d beha io
in he ma ke . Fo example; Abd-Alla (2020) did no ind he d beha io in he Egyp ian
S ock Exchange a e he COVID-19 pandemic. The e a e also s udies conduc ed unde
inancial psychology, whe e in es o s’ emo ions should be aken in o accoun . Filip and
Pochea (2023) applied Hwang and Salmon’s (2004) app oach by con olling o changes
in in es o sen imen , and sugges ed ha he ding is a pe manen ea u e in he US and
Eu opean s ock ma ke s.
When he accessible li e a u e is e iewed i is obse ed ha he ding beha io was
measu ed in di e en coun ies and ma ke s. Howe e , s udies on in es iga ing i s de-
e minan s a e insu icien . This s udy di e s om o he s udies in he li e a u e in ha i
ocuses on he ela ing he ding beha io o inancial a iables iden i ying i s de e minan s.
Analizing he a iables (Re u n, CDS, Vola ili y, USD/TR, Liquidi y, Vix) o iden i ying
he de e minan s o he ding beha io is expec ed o con ibu e o he li e a u e.
Bay am E kin Ay, Gamze Göçmen Yağcila . In es iga ing he De e minan s o He d Beha io
45
3. Me hodology and Da a
3.1. Measu ing He d Beha io
In o de o measu e he d beha io , he linea ac o model de eloped by Hwang and
Salmon (2004) was used in he s udy. The p ocess s eps (1)–(10) o he Hwang and
Salmon (2004) model a e as ollows.
In ligh o his in o ma ion, i s ly, loga i hmic e u n is calcula ed using equa ion (1):
𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕
𝑷𝑷𝒕𝒕−𝟏𝟏)
𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄
(
𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏
√𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎
)
(𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕
𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊
𝛽𝛽2, 𝛽𝛽1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽2)
𝛽𝛽2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 )
∑( 𝑋𝑋İ − 𝑋𝑋 )2
𝛽𝛽1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋
𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽1 − 𝛽𝛽2𝑋𝑋𝑖𝑖
𝜎𝜎 = √∑𝑢𝑢
𝑖𝑖2
𝑛𝑛 −2
se(𝛽𝛽2)= 𝜎𝜎
√∑(𝑋𝑋İ −𝑋𝑋)2
= 𝛽𝛽
2
se(𝛽𝛽
2)
𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖)
1+exp (𝑦𝑦𝑖𝑖)=1
1+exp (−𝑦𝑦𝑖𝑖)
𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖
1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
(1)
In equa ion (1),
i, : e u n o s ock in ime ,
P : he closing p ice o he ele an s ock in pe iod “ ”,
P –1: he closing p ice o he ele an s ock in pe iod “ ”-1.
Following he calcula ion o e u ns, excess e u ns a e calcula ed using he “Two-
Yea Bond Yields” (de i ed om he Tu kish wo-yea bond yield (TR2YT)). The cal-
cula ion o HS-2004 o he d beha io is shown in equa ion (2):
𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕
𝑷𝑷𝒕𝒕−𝟏𝟏)
𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓
𝒄𝒄
(
𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏
√𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎
)
(𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕
𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊
𝛽𝛽2, 𝛽𝛽1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽2)
𝛽𝛽2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 )
∑( 𝑋𝑋İ − 𝑋𝑋 )2
𝛽𝛽1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋
𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽1 − 𝛽𝛽2𝑋𝑋𝑖𝑖
𝜎𝜎 = √∑𝑢𝑢
𝑖𝑖2
𝑛𝑛 −2
se(𝛽𝛽2)= 𝜎𝜎
√∑(𝑋𝑋İ −𝑋𝑋)2
= 𝛽𝛽
2
se(𝛽𝛽
2)
𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖)
1+exp (𝑦𝑦𝑖𝑖)=1
1+exp (−𝑦𝑦𝑖𝑖)
𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖
1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
(2)
In equa ion (2),
H (m, ): hidden he ding pa ame e ,
βim : he be a coe icien o s ock “i” a ime “ ”,
si
2 : he a iance o he s ock be a,
Sm: he a iance o he ma ke be a.
H(m, ) ( he hidden he ding pa ame e ) is used o measu e he ding beha io . While
calcula ing he be a alues o s ocks, es ima ion (3) om he Capi al Asse P icing Model
is used (Doğukanlı and E gün, 2015: 12).
𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕
𝑷𝑷𝒕𝒕−𝟏𝟏)
𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄(
𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏
√𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎)
(𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕
𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊
𝛽𝛽2, 𝛽𝛽1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽2)
𝛽𝛽2 = ∑( 𝑋𝑋
İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 )
∑( 𝑋𝑋İ − 𝑋𝑋 )2
𝛽𝛽1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋
𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽1 − 𝛽𝛽2𝑋𝑋𝑖𝑖
𝜎𝜎 = √∑𝑢𝑢
𝑖𝑖2
𝑛𝑛 −2
se(𝛽𝛽2)= 𝜎𝜎
√∑(𝑋𝑋
İ −𝑋𝑋)2
= 𝛽𝛽
2
se(𝛽𝛽
2)
𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦
𝑖𝑖)
1+exp (𝑦𝑦𝑖𝑖)
=1
1+exp (−𝑦𝑦
𝑖𝑖)
𝐿𝐿𝑖𝑖=ln( 𝑝𝑝
𝑖𝑖
1−𝑝𝑝𝑖𝑖
)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
(3)
i, – : he excess e u n in each pe iod “ ” o he s ock in he pe iod se as he bench-
ma k,
m, – : he excess ma ke e u n in each pe iod “ ” o e he benchma k pe iod.
Howe e , Capa elli e al. (2004) o e a di e en pe spec i e on he calcula ion o he
be a alue in he men ioned measu e. As Doğukanlı and E gün (2015) epo ed, Capa elli
e al. (2004) s a ed ha in o de o each he H(m, ) alue, he - es s a is ical alues o he
be a coe icien s should be calcula ed h ough he speci ied eg ession and hese alues
gi e he H(m, ) alue o he ho izon al c oss-sec ion a iance.
ISSN 1392-1258 eISSN 2424-6166 Ekonomika. 2024, ol. 103(3)
46
In o de o each he - es alues, he eg ession model p esen end in equa ion (4)
was used:
𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕
𝑷𝑷𝒕𝒕−𝟏𝟏)
𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄(
𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏
√𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎)
(𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕
𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊
𝛽𝛽2, 𝛽𝛽1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽2)
𝛽𝛽2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 )
∑( 𝑋𝑋İ − 𝑋𝑋 )2
𝛽𝛽1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋
𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽1 − 𝛽𝛽2𝑋𝑋𝑖𝑖
𝜎𝜎 = √∑𝑢𝑢
𝑖𝑖2
𝑛𝑛 −2
se(𝛽𝛽2)= 𝜎𝜎
√∑(𝑋𝑋İ −𝑋𝑋)2
= 𝛽𝛽
2
se(𝛽𝛽
2)
𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖)
1+exp (𝑦𝑦𝑖𝑖)=1
1+exp (−𝑦𝑦𝑖𝑖)
𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖
1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
(4)
Yi: ( i, – ) is he isk p emium o he s ock and is he dependen a iable,
Xi: ( m, – ) independen a iable alues by exp essing he ma ke isk p emium,
β1: cons an o he eg ession,
β2: coe icien o eg esso s,
ui: he e o e m.
In o de o each he speci ied eg ession equa ion, he ollowing s eps should be aken.
The me hods o ob aining he alues o
𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕
𝑷𝑷𝒕𝒕−𝟏𝟏)
𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄(
𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏
√𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎)
(𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕
𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊
𝛽𝛽2, 𝛽𝛽1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽2)
𝛽𝛽2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 )
∑( 𝑋𝑋İ − 𝑋𝑋 )2
𝛽𝛽1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋
𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽1 − 𝛽𝛽2𝑋𝑋𝑖𝑖
𝜎𝜎 = √∑𝑢𝑢
𝑖𝑖2
𝑛𝑛 −2
se(𝛽𝛽2)= 𝜎𝜎
√∑(𝑋𝑋İ −𝑋𝑋)2
= 𝛽𝛽
2
se(𝛽𝛽
2)
𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖)
1+exp (𝑦𝑦𝑖𝑖)=1
1+exp (−𝑦𝑦𝑖𝑖)
𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖
1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
, se(
𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕
𝑷𝑷𝒕𝒕−𝟏𝟏)
𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄(
𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏
√𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎)
(𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕
𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊
𝛽𝛽2, 𝛽𝛽1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽2)
𝛽𝛽2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 )
∑( 𝑋𝑋İ − 𝑋𝑋 )2
𝛽𝛽1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋
𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽1 − 𝛽𝛽2𝑋𝑋𝑖𝑖
𝜎𝜎 = √∑𝑢𝑢
𝑖𝑖2
𝑛𝑛 −2
se(𝛽𝛽2)= 𝜎𝜎
√∑(𝑋𝑋İ −𝑋𝑋)2
= 𝛽𝛽
2
se(𝛽𝛽
2)
𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖)
1+exp (𝑦𝑦𝑖𝑖)=1
1+exp (−𝑦𝑦𝑖𝑖)
𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖
1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
) and a e shown in equa ions
(5) o (10). (In he equa ions men ioned, “n” deno es he numbe o s ocks).
S ep 1
𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕
𝑷𝑷𝒕𝒕−𝟏𝟏)
𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄(
𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏
√𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎)
(𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕
𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊
𝛽𝛽2, 𝛽𝛽1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽2)
𝛽𝛽2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 )
∑( 𝑋𝑋İ − 𝑋𝑋 )2
𝛽𝛽1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋
𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽1 − 𝛽𝛽2𝑋𝑋𝑖𝑖
𝜎𝜎 = √∑𝑢𝑢
𝑖𝑖2
𝑛𝑛 −2
se(𝛽𝛽2)= 𝜎𝜎
√∑(𝑋𝑋İ −𝑋𝑋)2
= 𝛽𝛽
2
se(𝛽𝛽
2)
𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖)
1+exp (𝑦𝑦𝑖𝑖)=1
1+exp (−𝑦𝑦𝑖𝑖)
𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖
1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
: Es ima ed coe icien o he independen a iable.
𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕
𝑷𝑷𝒕𝒕−𝟏𝟏)
𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄(
𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏
√𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎)
(𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕
𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊
𝛽𝛽2, 𝛽𝛽1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽2)
𝛽𝛽2
=
∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 )
∑( 𝑋𝑋İ − 𝑋𝑋 )2
𝛽𝛽1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋
𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽1 − 𝛽𝛽2𝑋𝑋𝑖𝑖
𝜎𝜎 = √∑𝑢𝑢
𝑖𝑖2
𝑛𝑛 −2
se(𝛽𝛽2)= 𝜎𝜎
√∑(𝑋𝑋İ −𝑋𝑋)2
= 𝛽𝛽
2
se(𝛽𝛽
2)
𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖)
1+exp (𝑦𝑦𝑖𝑖)=1
1+exp (−𝑦𝑦𝑖𝑖)
𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖
1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
(5)
S ep 2
𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕
𝑷𝑷𝒕𝒕−𝟏𝟏)
𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄(
𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏
√𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎)
(𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕
𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊
𝛽𝛽2, 𝛽𝛽1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽2)
𝛽𝛽2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 )
∑( 𝑋𝑋İ − 𝑋𝑋 )2
𝛽𝛽1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋
𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽1 − 𝛽𝛽2𝑋𝑋𝑖𝑖
𝜎𝜎 = √∑𝑢𝑢
𝑖𝑖2
𝑛𝑛 −2
se(𝛽𝛽2)= 𝜎𝜎
√∑(𝑋𝑋İ −𝑋𝑋)2
= 𝛽𝛽
2
se(𝛽𝛽
2)
𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖)
1+exp (𝑦𝑦𝑖𝑖)=1
1+exp (−𝑦𝑦𝑖𝑖)
𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖
1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
: Es ima ed cons an e m.
𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕
𝑷𝑷𝒕𝒕−𝟏𝟏)
𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄(
𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏
√𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎)
(𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕
𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊
𝛽𝛽2, 𝛽𝛽1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽2)
𝛽𝛽2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 )
∑( 𝑋𝑋İ − 𝑋𝑋 )2
𝛽𝛽1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋
𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽1 − 𝛽𝛽2𝑋𝑋𝑖𝑖
𝜎𝜎 = √∑𝑢𝑢
𝑖𝑖2
𝑛𝑛 −2
se(𝛽𝛽2)= 𝜎𝜎
√∑(𝑋𝑋İ −𝑋𝑋)2
= 𝛽𝛽
2
se(𝛽𝛽
2)
𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖)
1+exp (𝑦𝑦𝑖𝑖)=1
1+exp (−𝑦𝑦𝑖𝑖)
𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖
1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
(6)
S ep 3
𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕
𝑷𝑷𝒕𝒕−𝟏𝟏)
𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄(
𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏
√𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎)
(𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕
𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊
𝛽𝛽2, 𝛽𝛽1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽2)
𝛽𝛽2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 )
∑( 𝑋𝑋İ − 𝑋𝑋 )2
𝛽𝛽1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋
𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽1 − 𝛽𝛽2𝑋𝑋𝑖𝑖
𝜎𝜎 = √∑𝑢𝑢
𝑖𝑖2
𝑛𝑛 −2
se(𝛽𝛽2)= 𝜎𝜎
√∑(𝑋𝑋İ −𝑋𝑋)2
= 𝛽𝛽
2
se(𝛽𝛽
2)
𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖)
1+exp (𝑦𝑦𝑖𝑖)=1
1+exp (−𝑦𝑦𝑖𝑖)
𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖
1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
: Es ima ed e o e m.
𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕
𝑷𝑷𝒕𝒕−𝟏𝟏)
𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄(
𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏
√𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎)
(𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕
𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊
𝛽𝛽2, 𝛽𝛽1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽2)
𝛽𝛽2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 )
∑( 𝑋𝑋İ − 𝑋𝑋 )2
𝛽𝛽1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋
𝑢𝑢𝑖𝑖
=
𝑌𝑌𝑖𝑖 − 𝛽𝛽1
− 𝛽𝛽2𝑋𝑋𝑖𝑖
𝜎𝜎 = √∑𝑢𝑢
𝑖𝑖2
𝑛𝑛 −2
se(𝛽𝛽2)= 𝜎𝜎
√∑(𝑋𝑋İ −𝑋𝑋)2
= 𝛽𝛽
2
se(𝛽𝛽
2)
𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖)
1+exp (𝑦𝑦𝑖𝑖)=1
1+exp (−𝑦𝑦𝑖𝑖)
𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖
1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
(7)
S ep 4
𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕
𝑷𝑷𝒕𝒕−𝟏𝟏)
𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄(
𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏
√𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎)
(𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕
𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊
𝛽𝛽2, 𝛽𝛽1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽2)
𝛽𝛽2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 )
∑( 𝑋𝑋İ − 𝑋𝑋 )2
𝛽𝛽1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋
𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽1 − 𝛽𝛽2𝑋𝑋𝑖𝑖
𝜎𝜎 = √∑𝑢𝑢
𝑖𝑖2
𝑛𝑛 −2
se(𝛽𝛽2)= 𝜎𝜎
√∑(𝑋𝑋İ −𝑋𝑋)2
= 𝛽𝛽
2
se(𝛽𝛽
2)
𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖)
1+exp (𝑦𝑦𝑖𝑖)=1
1+exp (−𝑦𝑦𝑖𝑖)
𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖
1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
: S anda d de ia ion o e o e ms.
𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕
𝑷𝑷𝒕𝒕−𝟏𝟏)
𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄(
𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏
√𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎)
(𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕
𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊
𝛽𝛽2, 𝛽𝛽1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽2)
𝛽𝛽2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 )
∑( 𝑋𝑋İ − 𝑋𝑋 )2
𝛽𝛽1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋
𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽1 − 𝛽𝛽2𝑋𝑋𝑖𝑖
𝜎𝜎
=
√∑𝑢𝑢
𝑖𝑖2
𝑛𝑛 −2
se(𝛽𝛽2)= 𝜎𝜎
√∑(𝑋𝑋İ −𝑋𝑋)2
= 𝛽𝛽
2
se(𝛽𝛽
2)
𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖)
1+exp (𝑦𝑦𝑖𝑖)=1
1+exp (−𝑦𝑦𝑖𝑖)
𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖
1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
(8)
S ep 5.
se(
𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕
𝑷𝑷𝒕𝒕−𝟏𝟏)
𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄(
𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏
√𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎)
(𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕
𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊
𝛽𝛽2, 𝛽𝛽1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽2)
𝛽𝛽2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 )
∑( 𝑋𝑋İ − 𝑋𝑋 )2
𝛽𝛽1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋
𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽1 − 𝛽𝛽2𝑋𝑋𝑖𝑖
𝜎𝜎 = √∑𝑢𝑢
𝑖𝑖2
𝑛𝑛 −2
se(𝛽𝛽2)= 𝜎𝜎
√∑(𝑋𝑋İ −𝑋𝑋)2
= 𝛽𝛽
2
se(𝛽𝛽
2)
𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖)
1+exp (𝑦𝑦𝑖𝑖)=1
1+exp (−𝑦𝑦𝑖𝑖)
𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖
1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
) S anda d e o .
𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕
𝑷𝑷𝒕𝒕−𝟏𝟏)
𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄(
𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏
√𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎)
(𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕
𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊
𝛽𝛽2, 𝛽𝛽1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽2)
𝛽𝛽2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 )
∑( 𝑋𝑋İ − 𝑋𝑋 )2
𝛽𝛽1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋
𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽1 − 𝛽𝛽2𝑋𝑋𝑖𝑖
𝜎𝜎 = √∑𝑢𝑢
𝑖𝑖2
𝑛𝑛 −2
se(
𝛽𝛽2)=
𝜎𝜎
√∑(𝑋𝑋İ −𝑋𝑋)2
= 𝛽𝛽
2
se(𝛽𝛽
2)
𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖)
1+exp (𝑦𝑦𝑖𝑖)=1
1+exp (−𝑦𝑦𝑖𝑖)
𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖
1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
(9)
S ep 6
: - es alue.
𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕
𝑷𝑷𝒕𝒕−𝟏𝟏)
𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄(
𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏
√𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎)
(𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕
𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊
𝛽𝛽2, 𝛽𝛽1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽2)
𝛽𝛽2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 )
∑( 𝑋𝑋İ − 𝑋𝑋 )2
𝛽𝛽1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋
𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽1 − 𝛽𝛽2𝑋𝑋𝑖𝑖
𝜎𝜎 = √∑𝑢𝑢
𝑖𝑖2
𝑛𝑛 −2
se(𝛽𝛽2)= 𝜎𝜎
√∑(𝑋𝑋İ −𝑋𝑋)2
=
𝛽𝛽
2
se(𝛽𝛽
2)
𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖)
1+exp (𝑦𝑦𝑖𝑖)=1
1+exp (−𝑦𝑦𝑖𝑖)
𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖
1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
(10)
3.2. In es iga ing he De e minan s o He d Beha io
In his s udy, i s he pe iods in which he ding beha io eme ges a e iden i ied wi h he
app oach o HS-2004 and hen he de e minan s o he ding beha io a e in es iga ed
using he logis ic eg ession me hod. The a iables hough o be likely o igge he d
beha io a e equi y e u ns, USD/TL exchange a e, isk- ee in e es a e, ola ili y o
equi y e u ns, VIX ea index and Tu key 5-yea CDS p emiums.
Bay am E kin Ay, Gamze Göçmen Yağcila . In es iga ing he De e minan s o He d Beha io
47
Logis ic eg ession analysis is used when he dependen a iable is a bina y a iable
(0-1). Following Guja a i (1999, as ci ed in Budak and E pola , 2012), he me hodology
o logis ic eg ession analysis is explained in equa ions (11) - (13):
Linea eg ession model o k independen a iables is shown in equa ion (11).
𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕
𝑷𝑷𝒕𝒕−𝟏𝟏)
𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄(
𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏
√𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎)
(𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕
𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊
𝛽𝛽2, 𝛽𝛽1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽2)
𝛽𝛽2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 )
∑( 𝑋𝑋İ − 𝑋𝑋 )2
𝛽𝛽1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋
𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽1 − 𝛽𝛽2𝑋𝑋𝑖𝑖
𝜎𝜎 = √∑𝑢𝑢
𝑖𝑖2
𝑛𝑛 −2
se(𝛽𝛽2)= 𝜎𝜎
√∑(𝑋𝑋İ −𝑋𝑋)2
= 𝛽𝛽
2
se(𝛽𝛽
2)
𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖)
1+exp (𝑦𝑦𝑖𝑖)=1
1+exp (−𝑦𝑦𝑖𝑖)
𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖
1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
(11)
Equa ion (12) exp esses he cu ilinea ela ionship es ablished be ween he eg esso s
and he esponse a iable. This calcula ion assu es he esponse a iable o ake alues
be ween 0 and 1
𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕
𝑷𝑷𝒕𝒕−𝟏𝟏)
𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄(
𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏
√𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎)
(𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕
𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊
𝛽𝛽2, 𝛽𝛽1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽2)
𝛽𝛽2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 )
∑( 𝑋𝑋İ − 𝑋𝑋 )2
𝛽𝛽1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋
𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽1 − 𝛽𝛽2𝑋𝑋𝑖𝑖
𝜎𝜎 = √∑𝑢𝑢
𝑖𝑖2
𝑛𝑛 −2
se(𝛽𝛽2)= 𝜎𝜎
√∑(𝑋𝑋İ −𝑋𝑋)2
= 𝛽𝛽
2
se(𝛽𝛽
2)
𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖)
1+exp (𝑦𝑦𝑖𝑖)=1
1+exp (−𝑦𝑦𝑖𝑖)
𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖
1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
(12)
Equa ion (12) mus be linea ized o ob ain a logi model as in equa ion (13):
𝒓𝒓𝒊𝒊,𝒕𝒕=𝑳𝑳𝒏𝒏(𝑷𝑷𝒕𝒕
𝑷𝑷𝒕𝒕−𝟏𝟏)
𝑯𝑯 (𝒎𝒎,𝒕𝒕)=𝒗𝒗𝒗𝒗𝒓𝒓𝒄𝒄(
𝜷𝜷𝒊𝒊𝒎𝒎𝒕𝒕−𝟏𝟏
√𝒔𝒔𝒊𝒊𝟐𝟐𝑺𝑺𝒎𝒎)
(𝒓𝒓𝒊𝒊,𝒕𝒕 − 𝒓𝒓𝒇𝒇)= 𝒗𝒗𝒊𝒊,𝒕𝒕+ 𝜷𝜷(𝒓𝒓𝒎𝒎,𝒕𝒕− 𝒓𝒓𝒇𝒇)+ 𝜺𝜺𝒊𝒊,𝒕𝒕
𝒀𝒀𝒊𝒊= 𝜷𝜷𝟏𝟏+ 𝜷𝜷𝟐𝟐𝑿𝑿𝒊𝒊+𝒖𝒖𝒊𝒊
𝛽𝛽2, 𝛽𝛽1, 𝑢𝑢𝑖𝑖, 𝜎𝜎, se(𝛽𝛽2)
𝛽𝛽2 = ∑( 𝑋𝑋İ − 𝑋𝑋 )( 𝑌𝑌İ – 𝑌𝑌 )
∑( 𝑋𝑋İ − 𝑋𝑋 )2
𝛽𝛽1= 𝑌𝑌− 𝛽𝛽2𝑋𝑋
𝑢𝑢𝑖𝑖 = 𝑌𝑌𝑖𝑖 − 𝛽𝛽1 − 𝛽𝛽2𝑋𝑋𝑖𝑖
𝜎𝜎 = √∑𝑢𝑢
𝑖𝑖2
𝑛𝑛 −2
se(𝛽𝛽2)= 𝜎𝜎
√∑(𝑋𝑋İ −𝑋𝑋)2
= 𝛽𝛽
2
se(𝛽𝛽
2)
𝑦𝑦𝑖𝑖=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
𝐸𝐸(𝑦𝑦𝑖𝑖)=𝑝𝑝𝑖𝑖=exp (𝑦𝑦𝑖𝑖)
1+exp (𝑦𝑦𝑖𝑖)=1
1+exp (−𝑦𝑦𝑖𝑖)
𝐿𝐿𝑖𝑖=ln( 𝑝𝑝𝑖𝑖
1−𝑝𝑝𝑖𝑖)=𝛽𝛽0+𝛽𝛽1𝑋𝑋1+𝛽𝛽2𝑋𝑋2+⋯+𝛽𝛽𝑘𝑘𝑋𝑋𝑘𝑘+𝜀𝜀
(13)
By sol ing he model, i is possible o es ima e pa ame e s.
3.3. Da a and Va iables
In he s udy, he d beha io is in es iga ed o he pe iod 17/10/2017–10/11/2023. In o de
o apply he Hwan–Salmon me hod, he da a se was s a ed om 03/01/2017 and daily da a
we e used. Non ansac ion days we e excluded om he analysis. The da ase s included in
he s udy we e bank s ocks lis ed in BIST Liquid Bank Index (BIST_Bank; as o No embe
2023). S ock Re u ns, Dolla /TL Exchange Ra e, Risk F ee In e es Ra e, Vola ili y o S ock
Re u ns, VIX ea index and CDS p emiums we e de e mined as a iables included in he
s udy o explain he dependen a iable. In es o s in he index a e conside ed wi hin he
scope o he s udy. The Bo sa Is anbul (BIST) Bank Index ypically encompasses s ocks o
en i ies engaged in he banking sec o . These en i ies o en consis o banks and inancial
ins i u ions. Consequen ly, he en i ies indexed unde he BIST Bank Index a e ypically
a o ed and moni o ed by ins i u ional in es o s. While indi idual in es o s can also ade
in he en i ies encompassed in his index, ins i u ional in es o s usually alloca e la ge sums
and possess he po en ial o sway he index. The adjus ed s ock p ices o banks we e ob ained
h ough Finne Elek onik Yayıncılık Da a İle işim L d. Ş i (Finne Analysis Excel Module).
The s ock lis ed in he BIST_Bank a e shown below.
Table 1. BIST_Bank sha es
Bileşen Kodu Bileşen Adı
*XLBNK BIST LIKIT BANKA
1AKBNK.E AKBANK
2YKBNK.E YAPI VE KREDİ BANK.
3ISCTR.E IS BANKASI (C)
4GARAN.E GARANTI BANKASI
Bileşen Kodu Bileşen Adı
5VAKBN.E VAKIFLAR BANKASI
6HALKB.E T. HALK BANKASI
7TSKB.E T.S.K.B.
8SKBNK.E SEKERBANK
9ALBRK.E ALBARAKA TURK
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