The comparative risk and performance analysis of Hungarian and Romanian exchange indices

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