MINISTRY OF NATIONAL EDUCATION
THE ANNALS OF THE
UNIVERSITY OF ORADEA
ECONOMIC SCIENCES
TOM XXII
2nd ISSUE / DECEMBER 2013
ISSN 1222-569X (p in ed o ma )
ISSN 1582-5450 (elec onic o ma )
451
THE COMPARATIVE RISK AND PERFORMANCE ANALYSIS OF HUNGARIAN
AND ROMANIAN EXCHANGE INDICES
Tibo Ta nóczi, Edina Kulcsá
Uni e si y o Deb ecen, Facul y o Applied Economics and Ru al De elopmen ,
Deb ecen, Hunga y
Uni e si y o O adea, Facul y o Economic Sciences, O adea, Romania
Uni e si y o Deb ecen, Facul y o Applied Economics and Ru al De elopmen ,
Deb ecen, Hunga y
a noc[email p o ec ed]
k[email p o ec ed]
Abs ac : Nowadays, he mos dominan cha ac e is ics o he inancial
en i onmen a e ins abili y, a iabili y, iskiness and unce ain y. I is di icul o ind
a ield whe e he decision making p ocess is isk- ee. This s a emen is especially
ue in case o inancial in es men s acco ding o which isk aking is ewa ded.
Bu i is also ue ha he inancial ma ke pa icipan s canno be comple ely
a oided isks, bu he e a e many op ions o managing and minimizing hem. One
o he mos well-known heo ies o inancial ins umen s' isk minimiza ion is he
mode n po olio heo y, which is he collec ion o ools and echniques by which a
isk-a e se in es o may cons uc an op imal po olio. In po olio heo y i is also
known he possibili y o isky asse s di e si ica ion o ob ain he op imal e u n/ isk
a io. Consequen ly, his pape aims o examine he e icien po olio al e na i es
by de e mina ion o pe o mance a ios based on CAPM model and mode n
po olio heo y, such as Sha pe a io, Jensen’s alpha and T eyno a io and isk
measu ing me hods, such as Value a Risk, o Expec ed Sho all. In p esen
esea ch we concen a e o a compa a i e analysis o po olios consis in main
s ock indices sha es o wo neighbo ing coun ies om Cen al and Eas e n
Eu ope: Hunga y and Romania. The analysis was pe o med on he Romanian
BET and Hunga ian BUX s ock ma ke indices using he six-mon h daily closing
p ices. Da a o he analysis we e downloaded om he o icial websi es o
Romanian and Hunga ian s ock exchanges. The s a is ical analysis was made in
R s a is ical sys em. Using such ools o unco e in o ma ion and ask be e
ques ions will suppo he in es o s o make be e and be e in es men
decisions. The esul s o p esen esea ch show a g ea e pe o mance le el o
Romanian po olio, bu also a highe le el o isk, wi h lowe ola ili y owa d
ma ke changes and majo speci ic isk. Fo he Hunga ian po olio, he
pe o mance is mo e empe a e, he le el o isk is also smalle and he ola ili y o
ma ke ac o s is mo e ele an , so he speci ic isk is mode a e in his case.
Keywo ds: di e si ica ion, po olio heo y, isk, e icien po olio, e u n,
pe o mance analysis
JEL classi ica ion: G10, G11, G12, G19
452
1. In oduc ion
In ou days, economic en i onmen is cha ac e ized by isk, ola ili y and
unce ain y. The mos o economic en i ies a e p o i o ien ed, he e o e du ing
hei ac i i y de eloping he isk aking is ine i able. In he case o company which
ca ies ou inancial in es men s, he isk aking has a special ole. Acco ding o
well-known p inciple “who doesn’ isk, doesn’ win”, in o de o achie e highe
e u ns, in es o s need o ake highe isk on capi al ma ke . The isk le el o
inancial asse s is di e en , while he easu y bills could be conside ed he low
isk o isk- ee asse s, he sha es e u n and also isk le el is highe . In
acco dance wi h mode n po olio heo y, he a ional in es o doesn’ in es i s
capi al exclusi ely in one ype o inancial asse . He es ablishes i s in es men
decision on he base o ela ionship be ween e u n and isk, so as o achie e
maximum e u n wi h minimum isk possible. Measu ing po olio pe o mance is
one o he mos impo an ools o po olio op imiza ion. The e o e, his a icle
aims o examine wo neighbo ing Cen al and Eas e n Eu ope si ua ed coun ies’,
majo indices sha es using h ee pe o mance-based indica o s and isk
measu ing me hods.
2. Re iew o li e a u e
In Hunga ian, Romanian and in e na ional li e a u e can be ound a ious heo ies
abou gene al isk concep . We wan o unde line he mos ele an o hem. The
one o he mos known de ini ion o gene al, o e all isk is he likelihood o an
ad e se e en occu s. Alas ai in his Mas e ing Risk Modelling book gi es mo e
de ini ion o isk. The mos equen ly men ioned a e he ollows: he p obabili y o
occu ing di e en ou comes; de ia ions om he expec ed esul s; he chance o
symme ic occu ence o p o i o loss (Alas ai , 2009: 59). Re o Galla i in his wo k,
which is called Risk managemen and capi al adequacy, de ines isk like a
“si ua ion in which he e is a possibili y ha he ecei ed esul s de ia e om he
expec ed esul s” (Galla i, 2003: 8). Acco ding o Galla i, he de iance om he
expec ed esul s mus be unde s ood in posi i e and also in nega i e way. We
conside ha in he case o inancial asse s, he second de ini ion is mos
cha ac e is ic, because he equency and he ampli ude o de iance om
expec ed ou comes a e la ge . I is clea ha in he case o isky asse s he ime
ac o plays a e y impo an ole, oo.
453
One o he mos well-known heo ies abou isk is he Knigh ’s heo y, acco ding o
which he e is a signi ican di e ence be ween he concep o isk and unce ain y.
Knigh ’s wo k (1921) especially is o ien ed by dis inc ion be ween isk and
unce ain y. Acco ding o him, he main di e ence be ween isk and unce ain y
lies in he possibili y o measu emen , so while he isk can be measu ed, he
unce ain y could no be. He also says, ha i he isk could be quan i ied i also
could be managed while in he case o unce ain y his is no speci ic, because i
couldn’ be measu ed and managed. Knigh ’s isk quan i ica ion heo y mos
s onges c i icism comes om Keynes (1937), who said “ he economic unce ain y
o u u e canno be sol ed by looking a s a is ical pa e ns o he pas ” and “ he
u u e human decisions (…) does no depend on s ic ly ma hema ical
expec a ions, because hese ypes o calcula ions ha e no basis.” Acco ding o
Keynes and his ollowe s, he de elopmen s o u u e decisions will no be a ec ed
by “s ic ly ma hema ical expec a ions” (Bélyácz, 2011: 380).
Nowadays economic en i onmen ’s essen ial ea u e is iskiness. The dis inc ion
be ween isk and unce ain y is especially impo an in decision making p ocess, so
in his poin o iew, he isk e e s o a si ua ion in which he decision-make could
assign p obabili ies o andom e en s, while in he case o unce ain y his is no
possible. In he case o unce ain y, can’ a ach p obabili y o a andom e en ,
because chance and odds cha ac e ize i be e (Szász, 2011). While some au ho s
deals wi h he dilemma be ween isk and unce ain y, ano he y o de ine he
componen s o he isk, namely he unce ain y and a iabili y (Molak, 1997;
Cullen–F ey, 1999). Wilson and Shlyakh e (Molak, 1997) conside ha he
a iabili y means he empo al and spa ial he e ogenei y o alues. Because
unce ain y is ela ed wi h he lack o in o ma ion, knowledge means ha wi h
in o ma ion and knowledge acquisi ion i could be educed. Howe e , he a iabili y
couldn’ be educed wi h u he in o ma ion and knowledge. A inancial asse s,
in o ma ion and knowledge plays an essen ial ole, because ce ain economic
news and in o ma ion eco ds sudden, unp edic able changes. In ou opinion, in
he case o inancial asse s, he in o ma ion se es no only he isk minimiza ion,
bu some imes hey e en inc ease he isk le el. I is clea , he iskiness and he
e u n o inancial asse s, highly depends on kind, quan i y and quali y o
in o ma ion. Vose (2008) also conside s isk consis s o wo pa s, bu he ega ds
ha a iabili y is he special case o unce ain y. This kind o unce ain y and
a iabili y oge he is called by Vose o al unce ain y. We can see he e o e, in he
o eign li e a u e becomes mo e and mo e in ol ed se ing he componen s o isk,
a he han he dis inc ion be ween isk and unce ain y in he ounda ion o
economic decisions (Ta nóczi-Feny es, 2010). Acco ding o Tapie o (2004), he
global inancial c isis is no he consequence o lack o in o ma ion, knowledge, bu
he in es o s and decision-make s’ “men al de iciency”, because hey
o e es ima ed ce ain in o ma ion and in he con ex o economic c isis, hey
o e eac ed i (Bélyácz, 2011). Fo in es o s who in es in isky asse s, he isk is
una oidable, and he mo e hey wan o gain, he mo e hey ha e o isk. Abou he
inancial in es men s’ isk, we conside he Molak and Cullen-F ey app oach is
mo e closely, because in he case o sha e p ices, e u ns, isk displays in o ms o
a iabili y and ola ili y. The isk, a iabili y can’ be comple ely elimina ed, bu
he e a e a ious isk minimiza ion echniques, among which he bes known is he
di e si ica ion which is p esen ed in amous wo k o Ha y Ma kowi z “Po olio
454
Selec ion” (Illés, 2007). In acco dance wi h mode n po olio heo y, a a ional
in es o would no in es his money in o a single inancial asse s, he sha es i
be ween a ious isk le els asse s. In ac , his is he cen al ole o po olio heo y.
The in es o can decide in acco dance o ela ionship be ween isk- e u n, on how
much is p o i able o him o buy om some isky asse s. The mode n po olio
heo y has a majo impac on Capi al Asse s P icing Model (CAPM) de eloping.
The CAPM model de eloped a new guidance o ela ionship be ween isk and
e u n. Based on Ma kowi z mode n po olio heo y, Sha pe, Lin ne and T eyno
h ough hei esea ch leads o he conclusion ha he e is a s ong co ela ion
be ween ma ke isk and asse s’ expec ed e u ns. In his con ex , i is essen ial
mapping and assessmen o gene al and ma ke isk. The one o he bes known
isk measu emen me hod is he a iance and s anda d de ia ion, which could be
also, calcula ed unc ion o p obabili y. The a iance, o squa ed de ia ion, could
be de ined like weigh ed a e age o he squa ed de ia ions be ween possible
alues, which in inance could be e u ns, losses and expec ed alue. Bu nei he
he a iance, nei he he s anda d de ia ion a e no a di ec me hod o isk
measu emen , because exp ess isk wi h de ia ion o e u n. Is canno pu equali y
be ween isk and de ia ion o e u n, so we can in e p e he de ia ion o e u n like
a p oxy o isk (Hol on, 2004). Bo h he high esul o a iance and s anda d
de ia ions shows a high isk le el, while low alue shows he con a y. The
s anda d de ia ion and a iance i is also used o de e mining he isk o inancial
asse s, bu hese me hods exp ess isk in absolu e alue, which is sui able only o
compa ing he iden ical e u ns’ asse s (Illés, 2002). The ela i e s anda d de ia ion
o coe icien o a iance is one o he quan i ying me hods, which is mo e
ecommended by expe s in isk measu emen . The coe icien o a iance is he
a io be ween asse s s anda d de ia ion and asse s e u n. A key ole in inancial
ins umen s’ isk quan i ica ion plays a be a coe icien (β). Be a has an especially
impo an signi icance in applica ion o Capi al Asse s P icing Model (CAPM),
because measu es he sys ema ic, non-di e si iable, ma ke isk le el, using only
one numbe . In ac , by knowing he sys ema ic isk, he e u n o po olio and he
isk- ee asse e u n, we could calcula e he expec ed e u n o po olio o asse .
So, he be a coe icien is an exp ession o ma ke isk le el and also shows he
sensi i i y o inancial asse o mo emen s o ma ke benchma k po olio. A highe
alue o be a ela es a highe le el o isk and e u n (Mun, 2006). Ma hema ically,
he alue o be a is calcula ed like “ a io o co a iance be ween an asse and
ma ke po olio and ma ke po olio a iance" (Illés, 2002: 141). When be a is
equal wi h 1, i means ha he asse e u n is nea o ma ke e u n. I be a alue is
less han 1 indica es a low sensi i i y, o he wise he change o ma ke ac o s has a
li le e ec on asse e u n. I be a is g ea e han 1, i means ha he asse is e y
sensi i e o ma ke changes, so changes o ma ke isk ac o s cause mo e
signi ican a ia ion in e u n e olu ion (A en, 2010: 45). The applica ion o CAPM
model was widely c i icized, because acco ding o some expe s i ’s impossible o
cha ac e ize he sys ema ic, mac oeconomic isk ac o s h ough one numbe .
Du ing he CAPM model applica ion, he model de elope assumed ha he
inancial ma ke s a e pe ec ly balanced, he in es o s ha e homogeneous
expec a ions, bu he cu en economic en i onmen and ecen ly de eloped
inancial u bulences has s ongly e u ed hese assumes. A e y se ious weakness

455
o model is ha ma ke and inhe en mac oeconomic isk ac o s a e comple ely
s a ic (Al ă , 2002: 70-71).
A key componen o inancial decisions ounda ion is he po olio pe o mance
measu emen . The pe o mance measu emen has an essen ial ole o in es men
decisions ounda ion and con ibu es o he adding alue o success ulness o
in es men and isk minimiza ion. Po olio pe o mance a ios answe s o h ee
e y impo an ques ions: wha is he e u n on asse , why has he po olio
pe o med ha way, how can be pe o mance imp o ed (Bacon, 2008: 1).
3. Resea ch me hodology
In he compa a i e analysis o wo neighbo ing coun ies sha es po olio we used
he sha es baske o Romanian (BET) and Hunga ian (BUX) main s ock exchange
indices. The da a included in p esen s udy a e hese wo coun ies main s ock
indices sha es daily closing p ices, o 6 mon hs back. The da a used we e
collec ed om he o icial da abases o Hunga y, Budapes S ock Exchange
websi e: www.be .hu and Romania, Bucha es S ock Exchange websi e:
www.b b. o. The s a is ical analysis was buil on he R s a is ical so wa e sys em.
In he R s a is ical sys em he e a e a ailable all he packages (modules) which is
necessa y o his analysis. The R s a is ical sys em is open sou ce so wa e, ha
ensu e many analyzing, modeling and isualiza ion acili ies and ano he
ad an age is ha i could be connec ed wi h Excel sp eadshee , which pe mi s he
usage o di e en da abases. In his s udy, we used he ‘Pe o manceAnaly ics’
module, because his package aims o aid us in using he la es esea ch o
analysis o e u n s eams, such as s ock e u ns and po olio pe o mance a ios.
In po olio’s inancial asse s selec ion, managing and es ablishing o e icien
inancial decisions, he isk, e u n and he ela ionship be ween isk- e u n
de e mina ions has an impo an unc ion. In addi ion, in decision-making and isk
minimiza ion, he po olio pe o mance has an impo an ole. Based on CAPM
model, hese wo closely ela ed concep s a e used in po olio pe o mance a ios
calcula ion. Fo eign li e a u e p esen s mo e pe o mance based indica o s, o
which he well-known a e Sha pe a io, T eyno a io and Jensen’s alpha.
William Sha pe’s (1966) indica o is based on mode n po olio heo y and he
essence o a io consis in showing how much is he ewa d o a iabili y, so his is
why in o eign li e a u e his a io is also called as “ ewa d- o- a iabili y a io”. The
Sha pe pe o mance a io is calcula ed acco ding o (1) o mula:
୔ൌ୉൫ୖ౦൯ିୖూ
஢ሺୖౌሻ (1)
whe e, E(RP) – he expec ed e u n o he po olio; RF – he e u n on he isk- ee
asse ; σ(RP) – s anda d de ia ion o he po olio e u ns.
As i can be seen om he o mula, he Sha pe a io compa es excess e u n abo e
isk- ee asse wi h o al isk o po olio (Amenc - Le Sou d, 2003: 109). The
indica o can also be unde s ood as he e u n pe uni o a iabili y. Acco ding o
his, he highe alue o Sha pe a io indica es a mo e a o able isk- e u n
combina ion (Bacon, 2008: 67).
While Sha pe a io is based on mode n po olio heo y, he Jensen’s a io o alpha
(1968) is based on Capi al Asse s P icing Model (CAPM) and can be desc ibed by
456
he ollowing (2) co ela ion:
Ƚ୔ൌ ሺ୔ሻെ୊െȾ୔ሺሺ୑ሻെ ୊ሻ (2)
whe e, E(RP) – he expec ed e u n o he po olio; RF – he e u n on he isk- ee
asse ; βP – he sys ema ic isk o po olio; E(RM) – he expec ed e u n o ma ke
po olio.
Jensen assumed ha he po olios a e no pe ec ly di e si ied and he e o e he e
is pa o po olio e u n which is missed om CAPM model, which in ac will be
explained by Jensen, h ough Jensen’s alpha. Essen ially, he Jensen’s
pe o mance a io compa es he po olio excess e u n abo e isk- ee a e wi h
e u n ecei ed by applica ion o ma ke model. I Jensen’s alpha has a posi i e
esul , means ha he po olio e u n is highe han he e u n ecei ed by using
he CAPM model. The majo weakness o his a io consis s in he ac ha pe mi s
only he compa ison o po olios wi h simila isk le els.
The T eyno ’s pe o mance a io (1965), o o he wise “ ewa d- o- ola ili y a io” is
also closely ela ed wi h CAPM model. The indica o is e y simila wi h Sha pe’s
a io, wi h he di e ence ha T eyno compa es he excess e u n abo e isk- ee
a e wi h he sys ema ic isk, and no wi h he o al isk o po olio, how i is
p esen ed in he (3) o mula:
୔ൌ୉൫ୖ౦൯ିୖూ
ஒౌ (3)
whe e, E(RP) – he expec ed e u n o he po olio; RF – he e u n on he isk- ee
asse ; βP – he sys ema ic isk o po olio;
The indica o can be also explained as he e u n pe uni o ola ili y. In case o
his a io, he po olio wi h highe alue will be p e e able (Amenc - Le Sou d,
2003: 108). The T eyno a io is a well-known indica o , bu in p ac ice i is a ely
used, because no ake in o accoun he speci ic isk. I he po olio is well
di e si ied he Sha pe a io and he T eyno a io shows simila esul s.
In his s udy, a compu a ion o las wo a ios we ha e used as benchma k
po olio he e u ns o Hunga ian s ock indices (BUX) e u n, o analyzed pe iod.
4. Resul s o he esea ch
In analyzing o Hunga ian and Romanian main indices sha es baske e u ns, we
s a wi h p esen a ion o po olios e u ns dis ibu ion o s udied pe iod, which is
illus a ed in he Figu e 1.
457
Figu e 1: The dis ibu ion o Romanian and Hunga ian po olios e u ns
Sou ce: Own compu a ion
A i s we can see, ha he Hunga ian po olio e u ns is much close o no mal
dis ibu ion hen he Romanian. 50% o Hunga ian po olio e u ns a e si ua ed
be ween -0.00630 and 0.00640, while 50% o Romania po olio e u ns a e
si ua ed be ween -0.0027 and 0.0050. We can also obse e in he case o
Romania, ha he dis ibu ion o po olio e u ns is much mo e igh skewed,
because he e a e some ou lie s e u ns nea o 0.003, which is indica ed by he
alue o skewness oo, uppe han 0. In he case o Hunga ian po olio his is no
speci ic; he e he alue o skewness is close o 0, and he his og am is mode a e
ailed. In e ms o ku osis, nei he in wo cases is no speci ic he no mal
dis ibu ion ku osis, which ep esen a ku osis alue a 3. A Romanian e u ns
dis ibu ion, his is uppe han 3, which illus a es a sligh ly lep oku ic dis ibu ion,
close o no mal dis ibu ion, while a Hunga ian da a ku osis we can obse e a
ku osis alue lowe han 3 and uppe han -3, which is also u he by
ecommended alue.
Table 1: Hunga ian and Romanian e u ns s a is ics
Hunga ian e u ns
Re u ns
Densi y
-0.02 -0.01 0.00 0.01 0.02
0 10 20 30 40
Romanian e u ns
Re u ns
Densi y
-0.01 0.00 0.01 0.02 0.03
0 10 20 30 40 50 60 70
458
Sou ce: Own compu a ion
In e ms o da a de ia ion be ween maximum and minimum alue o e u ns, we
can see he g ea e de ia ion in he case o Hunga ian po olio. S anda d de ia ion
illus a es he same ac , which means mo e signi ican a iabili y, unce ain y in
case o Hunga ian po olio e u ns. The LCL (Lowe Con idence Le el) and he
UCL (Uppe Con idence Le el) Mean compu e a con idence in e al mean based
on he S dDe (s anda d de ia ion) o analyzed da a and he z alue o 95%
con idence in e al. The lowe and uppe con idence le el es ima ion gi es an
indica ion o how much is he unce ain y in ue mean compu a ion. The LCL Mean
and he UCL Mean is mo e signi ican a Romanian po olio in compa ison wi h
Hunga ian po olio. The esul s show ha a Romanian sha es e u ns, he
unce ain y is g ea e han in he Hunga ian case, on his aspec .
Fo analyzing he po olio pe o mance and isk, i is impo an o in e p e he
indica o s om Table 2. Fi s h ee indica o s illus a e he Sha pe a ios which
measu e he e u n pe uni o isk by using di e en isk measu e indica o s as
denomina o : S dDe (s anda d de ia ion), VaR ( alue a isk) and ES (expec ed
sho all). By analyzing hese h ee indica o s, we can see ha “ he ewa d o
a iabili y” has g ea e alues in he case o Romanian po olio, wha means a
be e combina ion o isk and e u n. The nega i e esul s o Hunga ian Sha pe
a ios a e caused p ima ily by he nega i e alues o e u ns. Analyzing Jensen’s
alpha, we ha e see posi i e alue in bo h o si ua ions, which means ha he e is a
pa o e u n which isn’ i explained by using o CAPM model.
Table 2: Pe o mance and isk a ios o Hunga ian and Romanian e u ns
Hunga ian
po olio e u ns
Romanian
po olio e u ns
S dDe Sha pe
-0.03865
0.21857
VaR Sha pe
-0.02244
0.23021
ES Sha pe
-0.01842
0.15353
Jensen Alpha
0.02512
0.48000
T eyno Ra io
-0.09639
3.75783
Semi a iance
0.00965
0.00559
Hunga ian po olio
e u ns
Romanian po olio
e u ns
Minimum
-0.0231
-0.0114
Qua ile 1
-0.0063
-0.0027
Median
-0.0002
0.0004
A i hme ic Mean
-0.0004
0.0015
Qua ile 3
0.0064
0.0050
Maximum
0.0242
0.0307
LCL Mean (0.95)
-0.0021
0.0002
UCL Mean (0.95)
0.0014
0.0029
S dDe
0.0094
0.0071
Skewness
-0.1390
1.3089
Ku osis
-0.3682
3.3447