Measuring dynamics of risk and performance of sector indices on Zagreb Stock Exchange

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1 Measuring dynamics of risk and performance of secor indices on Zagreb Sock Exchange Tihana Škrinjarić Faculy of Economics and Business, Universiy of Zagreb, Zagreb, Croaia Absrac Invesors are ineresed in secor diversificaion on sock markes among oher imporan porfolio opics. This paper looks a five secor indices on Croaian capial marke as an example of a small, relaively illiquid marke. Secor indices have been consruced a he beginning of 2013 and since hen here is a lack of sudies, which focus on secor diversificaion on Zagreb Sock Exchange (ZSE). Thus, he purpose of his paper is o evaluae he recen dynamics of risk and performance of five secor indices on ZSE by employing MGARCH (Mulivariae Generalized Auoregressive Condiional Heeroskedasiciy) models empirically. Oupu from he analysis is used o form guidance for invesors on Croaian capial marke. The resuls indicae ha in he observed period from February 4h 2013 o Ocober 13h 2015 porfolios based on MGARCH mehodology ouperform oher porfolios in erms reurn and risk. Thus, i is advisable o use his mehodology when making porfolio selecion. Keywords: MGARCH, Croaian capial marke, ime varying risk, bea, performance measuremen. JEL classificaion: G11, C58, C32. DOI: /crebss Received: Ocober 12, 2015 Acceped: December 3, 2015 Inroducion There exis many differen models and mehods in quaniaive finance oday in order o give answers o differen invesors quesions. Many of hem are developed in order o explain differen financial marke special feaures, which differeniae hem from oher markes. Invesors deal wih porfolio rebalancing and risks on a daily basis and ha is why hey need high qualiy informaion on financial asses movemens regarding reurn and risk. In he las hree decades, here has been a rise of special class of financial economerics models, which are found o capure financial marke co-movemens of reurns and volailiies MGARCH (Mulivariae Generalized Auoregressive Condiional Heeroskedasiciy) models successfully. These models have become very popular in modeling because of heir abiliies o capure financial marke dynamics beer compared o oher (mosly linear) models (see Aielli 2013, Alexander 2008, Lükepohl 2006). Moreover, hey have been used exensively in he pas decade for financial and oher asses such as socks, bonds, 27

2 exchange raes, commodiies, ec. Developed markes were he firs ones explored, which is no surprising due o he grea number of asses, which could be analyzed on hem. In he las couple of years, markes in developmen are in he spoligh as well. However, by looking a he previous lieraure, i can be seen ha he majoriy of he papers eiher es for presence of co-movemens of reurns and volailiies in one counry by using MGARCH models or hey focus on volailiy spillovers beween counries (Baumöhl, Liócsa, 2014, Longin, Solnik, 2001, Gelos, Sahay, 2001, Horvah, Perovski, 2013, Kenaurgios, Samias, 2011, Syallignakis, Koureas, 2011, Wang, Moore, 2008). Baumöhl and Liócsa (2014) looked a 8 European emerging markes and MSCI World marke index for he period from 2000 o They focused on asymmery and he resuls indicaed ha here exiss asymmery in volailiy on few markes, bu he asymmery in correlaions is exised only on one marke. Longin and Solnik (2001) focused on 7 counries in he period The main resul in heir analysis was ha reurn correlaions were no consan over ime. As volailiy ges bigger on markes, he correlaion rises. Gelos and Sahay (2001) examined financial comovemens of European ransiion economies and found srucural breaks on exchange markes. Horvah and Perovski (2013) also focused on similar counries (Czech Republic, Hungary, Poland, Croaia, Macedonia and Serbia). The period hey looked was 2006 o 2011, and found ha CEE counries were more correlaed han Souh Easern European counries. Kenaurgios and Samias (2011) were ineresed in five Balkan emerging markes and European developed markes, along wih he US marke. I was found ha long run coinegraion beween Balkan and developed markes, as well as among Balkan markes hemselves. Syallignakis and Koureas (2011) have examined 7 CEE counries, US, German and Russian marke in he period from 1997 o Main resuls indicaed ha marke correlaions rise in crisis. Moreover, CEE markes are exposed o exernal shocks from developed markes. Wang and Moore (2008) also focused on hree CEE markes. In he period from 1994 o 2006, i was found ha correlaions rise in crisis periods. There is a lack of sudies, which ry o uilize he resuls from hese models in order o give guidance o (poenial) invesors on how o ac on financial markes. This guidance is very imporan in porfolio managemen because invesors are focused on achieving reurns, as well as on managing risks. If hey are able o model and financial asse risks and reurns, i will enable hem o form rading sraegies which could bea he marke. Any possibiliy which could provide achieving above average reurns and (or) minimize risks is more han welcome on financial markes. This is especially rue in imes when financial crisis occurs. MGARCH mehodology could be very helpful in giving some answers o such quesions. In ha way, his sudy is going o uilize aforemenioned mehodology in order o analyze financial asse risk and reurn in a more deailed way compared o sandard GARCH mehodology when analyzing financial asses. More informaion on financial asses is always welcomed in porfolio analysis when making invesmen decisions. Every ime a financial crisis his he markes, he focus of academics and invesors is shifed again more owards risks and performances of financial asses. The las crisis in 2008 has affeced many markes and invesors became more pruden afer i. This is especially rue for he Croaian capial marke (Škrinjarić, Besek, 2014). Analysis in his sudy is going o look a he Croaian marke as an example of a small illiquid marke and ry o fill he gap in exising research. Up unil now, he majoriy of research on Croaian capial marke has implicily assumed ha performance measures, reurn and risk co-movemens were no dynamic over ime. This can be seen by observing models in which only averages over he enire period have been used in he analysis (see Škrinjarć, Besek, 2014, for an overview of previous lieraure). 28

3 Only wo papers up unil now have used MGARCH models in order o give answers o some of he menioned issues. Škrinjarić (2015) focused on ime varying beas on Croaian capial marke, whils Škrinjarić and Šego (2015) focused only on wo asses: socks and bonds. Thus, he purpose of his paper is o use advanages of dynamics in MGARCH models in order o esimae changing performance and risk measures on Zagreb Sock Exchange in a more deailed way. In ha way, recommendaions can be made regarding opimal porfolio invesing and managing risks. Previous foreign lieraure, which uilizes his mehodology, mosly focuses on invesors as inernaional invesors. However, secor diversificaion is imporan o invesors as well, bu here exiss a scarciy of papers, which observe secor diversificaion (Hassan, Malik, 2007, Ho, Tsui, 2004, Kazke, 2013, Righia, Cerea, 2012). Hassan and Malik (2007) looked ad US secors in he period from 1992 o They found significan ransmissions of volailiies in six secors. The mehodology hey used was found useful for forecasing and improving he accuracy of asse pricing models. Ho and Tsui (2004) focused on secor indices in Japan and found asymmeric effecs in volailiies, volailiy persisence in he period from 1983 o Kazke (2013) analyzed economic secors in Souh Africa in he period He found ha domesic and global uncerainy influence shor run dynamics of comovemens beween he secors. Righia and Cerea (2012) examined financial and consumer secor on Brazilian sock marke from 2008 o The resuls indicaed ha here exiss bilaeral ransmission of volailiy. All of hese papers concluded ha MGARCH mehodology is useful in porfolio selecion. However, hey do no provide concree guidance on how, when and in which financial asse o inves in order o conduc successful porfolio managemen. This sudy is going o focus on secor diversificaion in order o explore opimal porfolio possibiliies on Croaian capial marke in a dynamic conex. Moreover, i will ry o give useful guidance on how o successfully manage porfolios on Zagreb Sock Exchange. The paper is srucured as follows. Second secion explains he mehodology used in he sudy. Secion hree repors he resuls from he empirical analysis, and final, fourh secion concludes he paper wih recommendaions based upon previous resuls. Mehodology Models wihin MGARCH mehodology assume ha volailiies of financial asse reurns have affec one on anoher, which is based upon he previous experience of researchers on financial markes. Thus, i is assumed ha financial reurns and heir volailiies move ogeher and MGARCH models capure hese dynamics over ime (Longin, Solnik, 1995, 2001). There exis a grea number of differen models wihin his mehodology, bu his paper is uilizing he Dynamic and Consan Condiional Correlaion models (DCC, CCC) because previous research on hese opics has found hem o be successful in capuring financial markes movemens. Moreover, firs wo generaions of MGARCH models require esimaion of a greaer number of parameers, which could make he esimaion procedure infeasible. DCC and CCC models are more parsimonious and ha is why hey are popular. Bollerslev (1990) developed he CCC model in which i is assumed ha he correlaions beween financial asse reurns are consan: r x 1 2 u, (1) D RD 29

4 in which r is he (m,1) vecor of reurns, Θ (m,k) marix of parameers, x (k,1) vecor of independen variables, ε (m,1) vecor of innovaion processes. 1/2 is he Cholesky facor (m,m) marix of he condiional covariance marix Ω (m,m), u is (m,1) vecor of normal i.i.d. innovaions, D (m,m) diagonal marix of condiional variances and R is (m,m) posiive definie uncondiional correlaion marix. Usually, he assumpion of mulivariae normal disribuion of u are made, because correcly specifying he condiional mean and variances resuls wih consisen esimaes (Engle, 2009). Variances in marix D are modeled by univariae GARCH (1,1) models: In order for condiional variances o be posiive, i mus hold i, 0, i 1, i i, 1 1, i i, 1 ha: α0,i>0, α1,i 0 and β1,i 0; and in order for hem o be finie, i mus hold ha α1,i+β1,i<1. Since i is ofen no reasonable o assume ha correlaions beween financial asse reurns are consan, Engle (2002) developed he DCC model: r x 1 2 u D R D, (2) 1 1 R diag 2 diag 2 Q Q Q Q 11 2 R Q 1 where R is (m,m) marix of condiional correlaions. Q is (m,m) variance and covariance marix of sandardized innovaions, (m,1) vecor of sandardized innovaions, D-1 ε, and R (m,m) posiive definie uncondiional correlaion marix. The dynamics of condiional correlaions is defined by nonnegaive scalars θ1 and θ2. I mus hold θ1+θ2<1 for he model o be saionary (Engle, 2002, 2009). Ding and Engle (2004) add ha sandardized innovaions saisfy E( )=Im, where Im is he ideniy marix, Cov( 2 2 )=0 i j, and Cov( 2 2 )=0, k>0. I can easily be seen ha, i, j,, i, j, k if θ1=θ2=0 holds, DCC model becomes CCC model. Models are esimaed in wo seps: in he firs sep, univariae GARCH models are esimaed wih respec o alphas and beas. In he second sep, he res of he model is esimaed wih esimaed parameers from he firs sep, wih respec o θ1 and θ2. For more deails see Aielli (2013), Alexander (2008), Ang, Chen (2005), Bollerslev (1990), Bollerslev, Wooldridge (1992), Lükepohl (2006). Resuls from hese models can be used in a number of ways. This paper is focused on performance measures of indices on Croaian sock marke. Tha is why we are focusing on bea, Sharpe raio, RAPA measure, Treynor raio, Jensen s alpha and Value a Risk. Bea is a well known concep from CAPM model (Sharpe, 1964, Linner, 1965). Here, we assume ha i is ime varying, defined as he following raio: cov i, ri,, rm, i,, 2 (3) M, where βi, is ime varying bea of i-h sock, ri, excess reurn on he i-h sock and rm, excess marke reurn in ime. Jensen s alpha (1967) is also a concep from CAPM model in which i is defined as abnormal reurn of financial asse (or porfolio) over heoreical expeced reurn. I is calculaed as follows: r r. (4) i, i, i, M, Sharpe raio (1966) is anoher measure of performance, in which he excess reurn is sandardized by reurn s sandard deviaion: 30

5 Sharpe i, ri,. (5) I gives informaion on how much individual sock (or index) achieves reurn by given one percen level of risk. RAPA raio (Modigliani, 1997) is a modificaion of he Sharpe raio, by using sandard deviaion of sock marke reurn as a modificaion facor: RAPA Sharpe. (6) i, i, i, M, I also measures risk-adjused performance, bu here we also adjus for sock marke risk as well. Treynor raio (Treynor, 1965) is a risk adjused measure as well, similar o he Sharpe raio. This raio sandardizes reurns by using bea as a measure of risk (sysemaic risk only): ri, Treynori,. (7) Finally, Value a Risk measure will be considered as a concep of measuring maximal loss invesors can face in cerain ime period wih level of cerainy γ: 1 VaR (1 ) E( r ), (8) i, i, i, i, 1 where is he inverse disribuion funcion of sandardized normally disribued random variable (see Alexander, 2008, for he derivaion of expression (8)). All of he menioned measures are ofen used as guidance on how o inves funds ino differen financial asses. However, in he pas lieraure, hey were used as saic measures in he majoriy cases. Nex secion is going o look a all of hese measures on a daily basis because of financial marke dynamics. Empirical research For he purpose of he empirical research, daily daa on five secor indices and sock marke index CROBEX has been colleced from ZSE (2015) for he period from February 4 h 2013 o Ocober 13 h Daa on 91 day Treasury bill ineres raes has been colleced from GFD (Global Financial Daa, 2015) and excess reurns have been calculaed by exracing he 91 day Treasury bill ineres rae from he original reurn series. Broad indices were considered as guidance for wha is happening in each secor on he marke, as previous research uses such indices as well. Moreover, a shor ime span is used because hese indices are calculaed since he beginning of 2013 and no oher daa on hem is available before ha dae. Table 1 Descripive saisics of each secor Secor / Sandard Mean Median Max. Min. saisics deviaion Skewness Kurosis Crobex Indusry Consrucion Food Transporaion Tourism Firs of all, descripive saisics was calculaed for each reurn series and he resuls are given in Table 1. If we observe he descripive saisics for he enire period for each reurn series, several conclusions can be made. On average, consrucion secor had he bigges loss and ourism was he only secor wih he average posiive reurn. Only hree secors performed beer han he sock marke (indusry and 31

6 ransporaion, besides ourism). Mos volaile secor was consrucion by comparing sandard deviaions, and he marke as a whole was safer compared o individual secors. Coefficiens of skewness and kurosis give informaion on he occurrence of exreme posiive and negaive reurns: ourism was once again beer compared o oher secors and he marke because invesors could have achieved greaer above average reurns compared o exreme below average ones. However, he informaion given in Table 1 is only averaged. Before esimaing models described in he previous secion, uni roo ess were performed on all reurn series and all reurns were found o be saionary on usual levels of significance. DCC GARCH (1,1) has been esimaed for each secor and index CROBEX. However, parameers ˆ 1 and ˆ 2 were found o be saisically no significan for indusry, consrucion and ransporaion secor. Tha is why CCC GARCH (1,1) has been esimaed for hose hree secors. Moreover, parameer ˆ in 1 univariae GARCH (1,1) specificaion of ransporaion reurn was found o be negaive so GARCH (0,1) has been esimaed in ha case. Deailed resuls from esimaion are given in Table 2. As i can be seen, secor reurns, which reac mosly o marke innovaion shocks, are indusry and food secor (alphas 1, ). Mos persisen volailiies are hose of ransporaion and ourism. These conclusions can be seen on Figures 1-5, which show condiional variances of each reurn series from esimaed models in Table 2. This is useful informaion for porfolio risk managing when a shock occurs on he marke. Those secors wih persisen volailiy could be avoided when exernal shock his he marke. Table 2 MGARCH esimaion resuls for each secor CROBEX Indusry Consrucion Food Transporaion Tourism ˆi * * *** ˆ 0, i ** *** *** ** ˆ 1, i *** *** *** *** ** ˆ 1, i *** *** *** *** ** *** ˆi, crobex *** *** *** - ˆ 1, i ** *** ˆ 2, i *** *** Log L SIC HQIC AIC Noe: ˆi is he esimaed value of average reurn, ˆ 0, i, ˆ 1, i and ˆ 1, i parameers in univariae GARCH specificaions, ˆi, crobex esimaed correlaion coefficien for each secor and CROBEX and ˆ 1, i and ˆ 2, i are esimaed parameers in DCC GARCH (1,1) models. Log L sands for log likelihood, SIC, HQIC and AIC sand for Schwarz, Hannan-Quinn and Akaike informaion crieria respecively. *, ** and *** sand for saisical significance on 10%, 5% and 1% level respecively. Tess for mulivariae auocorrelaion of sandardized reurns and mulivariae heeroskedasiciy of sandardized reurns up o lag 30 have shown ha here is no auocorrelaion and no heeroskedasiciy on usual levels of significance. Correlaion coefficiens of sandardized residuals, covariances and covariances beween squared residuals up o lag 30 of sandardized residuals are no saisically significan. Sric posiiviy of variances is ensured by posiive values of esimaed parameers in univariae GARCH equaions. Condiional variances are finie which is ensured by he condiion ˆ ˆ 1, i 1, i 1 in each univariae GARCH equaion. ˆ i 32

7 Figure 1 Condiional variance of consrucion reurn series Figure 2 Condiional variance of food reurn series Figure 3 Condiional variance of indusry reurn series 33

8 Figure 4 Condiional variance of ourism reurn series Figure 5 Condiional variance of ransporaion reurn series Esimaed resuls can now be used o calculae ime-varying performance measures for each secor reurn. Firs of all, CAPM beas have been calculaed as raios given in (3) and are shown on Figures I can be seen ha indusry and consrucion beas are mos volaile in he observed period, which could arac aggressive invesors. On he oher hand, ransporaion and food beas show ha hese secors were more aracive for conservaive invesors. 34

9 Figure 6 Time varying CAPM bea for consrucion secor Figure 7 Time varying CAPM bea for food secor Figure 8 Time varying CAPM bea for indusry secor 35

10 Figure 9 Time varying CAPM bea for ourism secor Figure 10 Time varying CAPM bea for ourism secor Nex, oher performance measures given in (4)-(8) have been calculaed in order o compare five secors and descripive saisics for each measure is summarized in Table 2. Firs of all, he Sharpe raio indicaes ha on average, ourism secor had he bigges sandardized reurn, which means ha his secor achieved he bigges reurn on equal level or risk compared o ohers. Greaes sandardized reurn could have been achieved in consrucion secor (which is no surprising due o is aggressiveness) and ransporaion secor provided minimal loss (again, no surprising because i was found o be conservaive). RAPA measure gives us similar conclusions, since i is calculaed by using he Sharpe raio. However, i considers secor's relaive riskiness o sock marke risk and in ha way, i is more comparable among secors. By observing secor alphas, ourism is again he bes performing secor, whils he mos of benefis could have been achieved in consrucion secor in good imes (posiive alpha) and food secor in bad imes (realizing smaller losses wih leas negaive alpha). The Treynor raio akes ino accoun sysemaic risk compared o Sharpe raio. Tha is why conclusions for bes and wors secor differ. 36

11 Since food secor was found o be conservaive, i is no surprising ha looking a Value a Risk, i provided he leas loss for poenial invesors. Overall, looking a secors, which performed wors, consrucion and indusry, had such performance ha alhough invesors could benefi from hem in good imes, hey could achieve grea losses as well. This is no surprising due o he resuls from MGARCH models in which i was found ha hese secors are mos aggressive ones. Ones ha are more conservaive were food, ourism and ransporaion. This is in accordance wih conclusions given in Škrinjarić (2015). Inclusive, he analysis based upon Table 3 can provide useful guidance on a daily basis in order o minimize risks and o achieve above average reurns. Table 3 Descripive saisics of performance measures Measure Saisics Consrucion Food Indusry Tourism Transporaion Mean Sharpe Maximum raio Minimum Mean Alpha Maximum Minimum Mean Rapa Maximum Minimum Mean Treynor Maximum Minimum VaR Mean Maximal loss Noe: bolded numbers indicae he bes secor and ialic ones indicae he wors secor. Furhermore, a couple of porfolios have been simulaed in order o compare heir performances based upon he resuls from MGARCH mehodology. Reurn on CROBEX is used as a represenaive of marke reurn in order o have a benchmark o compare MGARCH porfolios. Average porfolio is used as a benchmark as well as a simple rading sraegy. In ha way, CROBEX and average porfolio represen rading sraegies in which invesors do no ake ino accoun he dynamics in reurn and volailiies. Three porfolios have been simulaed based upon he resuls in Table 1: aggressive one, in which invesor holds wo aggressive indices: indusry and consrucion, conservaive one, in which invesor holds ourism, food and ransporaion secors; and he bea based porfolio in which invesor holds he index wih he greaes bea when he marke is bullish and when he marke is bearish, he holds he index wih he smalles bea. All performance measures, which have been calculaed for each secor reurn, have been calculaed for porfolios as well, and are given in Table 4. By looking a he resuls, i seems ha he conservaive porfolio ouperformed ohers based upon almos all measures (bea and VaR are excepions). The wors porfolio was he aggressive one. Moreover, majoriy of he porfolios ouperform he sock marke reurn as well. However, hese resuls are only averaged, so anoher comparison has been made, by making a disincion of he marke on bearish and bullish. The resuls are given in Table 5 and Table 6. 37

12 Table 4 Average performance of simulaed porfolios Porfolio Average Aggressive Conservaive Bea based CROBEX Reurn Bea Sharpe RAPA Treynor VaR Alpha Noe: bolded numbers indicae he bes secor and ialic ones indicae he wors secor. Table 5 Performance of simulaed porfolios in bear marke Porfolio Average Aggressive Conservaive Bea based CROBEX Reurn Bea Sharpe RAPA Treynor VaR Alpha Noe: bolded numbers indicae he bes secor and ialic ones indicae he wors secor. Table 6 Performance of simulaed porfolios in bull marke Porfolio Average Aggressive Conservaive Bea based CROBEX Reurn Bea Sharpe RAPA Treynor VaR Alpha Noe: bolded numbers indicae he bes secor and ialic ones indicae he wors secor. Bear marke is in line when sock marke reurns are negaive, and opposie is valid for he bull marke. If we wan o know if a porfolio is superior o ohers on he marke, we should look a is performance when he marke is falling or rising. As i can be seen in Table 5 and Table 6, conservaive porfolio ouperforms ohers when he marke is bearish, while bea based porfolio is bes when he marke is bullish. Overall, aggressive porfolio is showing he wors resuls. This means ha in he observed period, on he Croaian capial marke when he marke was falling, i was beer o be conservaive in order o lose less compared o ohers. Moreover, i was favorable o base he porfolio upon ime varying beas in order o gain he mos. These sraegies ouperformed he marke reurn and he average porfolio reurn in he whole observed period. Thus, resuls indicae ha using oupu from MGARCH mehodology is very helpful and useful when forming rading sraegies on sock markes. In ha way, (poenial) invesors could benefi by achieving greaer reurns compared o he marke reurn and oher rading sraegies, which do no ake ime 38

13 varying performance measures ino accoun. Moreover, hey could manage risks more efficienly by using informaion from ime varying risk measures. Invesors are advised o use reurn and risk measures on a daily basis, by applying MGARCH mehodology. In ha way, hey could achieve beer reurns compared o he marke reurn and oher rading sraegies. Moreover, hey could manage porfolio risk in a beer way compared o rading sraegies, which do no consider MGARCH mehodology. Conclusions This paper deals wih quesions regarding successful porfolio formaion in erms of good reurns and managing risks. Previous lieraure showed ha financial asse s reurns and volailiies could be successfully modeled by using MGARCH mehodology. However, here exiss scarciy of papers, which uilize he resuls from his mehodology in order o form rading sraegies wih porfolios, which could bea he marke. This paper is an aemp o do such analysis. In ha way, performance and risk measures have been calculaed on a daily basis in order o rank secor indices on Zagreb Sock Exchange. Based upon he resuls from dynamic reurns and volailiies, indices were classified as aggressive or conservaive. Moreover, a couple of porfolios have been consruced and rading sraegies have been simulaed in order o compare heir performances. The resuls indicae ha using informaion from dynamics of MGARCH models is useful when forming rading sraegies. Porfolios formed based upon he oupu from his mehodology have ouperformed he marke as a whole, as well as average porfolios, in erms of reurn and risk. Thus, using his mehodology could enhance porfolio selecion and enable invesor o achieve beer resuls compared o rading sraegies, which do no ake ino accoun menioned dynamics. However, here were some pifalls in his sudy. A relaively shor ime span was considered because secor indices are measured since 2013 in Croaia. Moreover, only broad indices have been observed. Invesors are ineresed in specific socks and fuure research is going o include asses ha are more specific. Furhermore, analysis was performed wih he assumpion of no ransacion coss, which could be very high on illiquid markes. Tha is why fuure work is going o include his problem as well. However, he preliminary analysis done in his paper is in accordance wih previous lieraure on his opic, which provides us a good saring poin for furher research. References 1. Aielli, G. P. (2013). Dynamic Condiional Correlaions: On Properies and Esimaion. Journal of Business & Economic Saisics, Vol. 31, No. 3, pp Alexander, C. (2008). Marke Risk Analysis, Volume II: Pracical Financial Economerics. John Wiley & Sons, Chicheser. 3. Ang. A., Chen, J. (2005). CAPM over he long run: NBER Working Paper Series, Naional Bureau of Economic Research. 4. Baumöhl, E., Lyócsa, Š. (2014). Volailiy and dynamic condiional correlaions of worldwide emerging and fronier markes. Economic Modelling, Vol. 38, pp Bollerslev, T. (1990). Modelling he coherence in shor-run nominal exchange raes: A mulivariae generalized ARCH model. Review of Economics and Saisics, Vol. 72, pp Bollerslev, T., Wooldridge J.M. (1992). Quasi-maximum likelihood esimaion and inference in dynamic models wih ime-varying covariances. Economeric Reviews, Vol. 11, pp

14 7. Engle, R. F. (2002). Dynamic condiional correlaion: A simple class of mulivariae generalized auoregressive condiional heeroskedasiciy models. Journal of Business & Economic Saisics, Vol. 20, pp Engle, R. F. (2009). Anicipaing Correlaions: A New Paradigm for Risk Managemen. Princeon Universiy Press, New York. 9. Gelos, R.G., Sahay, R. (2001). Financial marke spillovers in ransiion economies. Economics of Transiion, Vol. 9, No.1, pp Global Financial Daa (2015). GFD Daabase, Fixed Income Daabase. Available a hps:// [15 Ocober 2015]. 11. Hassan, S. A., Malik, F. (2007). Mulivariae GARCH modelling of secor volailiy ransmission. The Quarerly Review of Economics and Finance, Vol. 47, pp Ho, K-Y., Tsui, A. K. C. (2004). An Analysis of he Secoral Indices of Tokyo Sock Exchange: A Mulivariae GARCH Approach wih Time Varying Correlaions. Sochasic Finance, Auumn School and Inernaional Conference. 13. Horvah, R., Perovski, D. (2013). Inernaional sock marke inegraion: Cenral and Souh Easer Europe compared. Economic Sysems, Vol. 37, pp Jensen, M. C. (1967). The Performance of Muual Funds in he Period Journal of Finance, Vol. 23, No. 2, pp Kazke, N. (2013). Souh African Secor Reurn Correlaions: using DCC and ADCC Mulivariae GARCH echniques o uncover he underlying dynamics. Sellenbosch Economic Working Papers: 17/13, Universiei Sellenbosch Universiy. 16. Kenourgios, D., Samias, A. (2011). Equiy marke inegraion in emerging Balkan markes. Research in Inernaional Business and Finance, Vol. 25, pp Linner, J. (1965). The valuaion of risk asses and he selecion of risky invesmens in sock porfolios and capial budges. Review of Economics and Saisics, Vol. 47, No. 1, pp Longin F., Solnik B. (1995). Is he correlaion in inernaional equiy reurns consan: ?. Journal of Inernaional Money and Finance, Vol. 14, pp Longin F., Solnik B. (2001). Exreme correlaion in inernaional equiy markes. Journal of Finance, Vol. 56, pp Lükepohl, H. (2006). New Inroducion o Muliple Time Series Analysis. Springer, Berlin. 21. Modigliani, F. (1997). Risk-Adjused Performance. Journal of Porfolio Managemen, 1997, pp Righia, M. B., Cerea, P. S. (2012). Mulivariae generalized auoregressive condiional heeroscedasiciy (GARCH) modeling of secor volailiy ransmission: A dynamic condiional correlaion (DCC) model approach. African Journal of Business Managemen, Vol. 6, pp Sharpe, W. F. (1964). Capial asse prices: A heory of marke equilibrium under condiions of risk. Journal of Finance, Vol. 19, pp Sharpe, W. F. (1966). Muual Fund Performance. Journal of Business, Vol. 39, pp Syllignakis, M. N., Koureas, G.P. (2011). Dynamic correlaion analysis of financial conagion: Evidence from he Cenral and Easern European markes, Inernaional Review of Economics and Finance, Vol. 20, pp Škrinjarić, T. (2015). Time varying CAPM beas on Zagreb Sock Exchange, In Proceedings of he 13h Inernaional Symposium on Operaional Research, Zadnik Sirn, L., Žerovnik, J., Kljajić Boršnar, M., Drobne, S., Eds., Bled, Slovenia, Sepember 23-25, 2015, pp Škrinjarić, T., Besek, B. (2014). Pre and Pos Crisis Performance Measuremen of Croaian Sock Marke. Zagreb Inernaional Review of Economics and Business, Vol. 17, pp Škrinjarić, T., Šego, B. (2015) Dynamic modeling of sock and bond reurn correlaion in Croaia. In Proceedings of he 13h Inernaional Symposium on Operaional Research, Zadnik Sirn, L., Žerovnik, J., Kljajić Boršnar, M., Drobne, S., Eds., Bled, Slovenia, Sepember 23-25, 2015, pp Treynor J. (1965). How o Rae Managemen of Invesmen Funds. Harvard Business Review, January-February 1965, pp

15 30. Wang, P., Moore, T. (2008). Sock marke inegraion for he ransiion economies: imevarying condiional correlaion approach. The Mancheser School, Supplemen 2008, pp Zagreb Sock Exchange (2015). Trading daa and saisics, Indices. Available a hp:// [15 Ocober 2015]. Abou he auhor Tihana Škrinjarić graduaed a he major Economics and pos-graduaed Saisical Mehods for Economic Analysis and Forecasing a Faculy of Economics and Business, Universiy of Zagreb. Currenly, she is a PhD suden a he same Faculy, where she works as a research and eaching assisan a he Deparmen of Mahemaics eaching he courses Mahemaics, Economerics, Mahemaical Economics and Mahemaical Mehods for Managing Financial Asses. She won Mijo Mirković Prize and CRORS Bes Young Researcher Paper Award in 2014, Recor s Award in 2010 and Dean s Award in 2009 and Up unil now, lis of her publicaions includes 36 publicaions (universiy exbooks, scienific and professional papers, ec.) of which she presened some on six inernaional conferences. She was a Visiing Academic a Mancheser Business School, Universiy of Mancheser for five monhs in 2015, a Cenre for Analysis of Invesmen Risk and Division of Accouning and Finance. Her field of ineress includes applied financial economerics, wih focus on sock markes, nonlinear economeric models in finance and risk modeling. Auhor can be conaced a skrinjaric@efzg.hr. 41