RELATION BETWEEN EXPECTED RETURN AND VOLATILITY AT BUCHAREST STOCK EXCHANGE, ON BUSINESS CYCLE STAGES

Transcription

1 RELATION BETWEEN EXPECTED RETURN AND VOLATILITY AT BUCHAREST STOCK EXCHANGE, ON BUSINESS CYCLE STAGES Viorica Chirilă Ciprian Chirilă 2 ABSTRACT: The sudy of he relaion beween risk and reurn is an imporan opic for invesors in financial asses, which is he reason why many researchers have ackled i. I is only naural for an invesor wih aversion for risk, who underakes a higher risk invesmen, mare o expec be rewarded accordingly, ha is o achieve higher reurn raes. The research conduced on various sock markes had conradicory resuls, which means ha he exisence of such a connecion is no cerain on all sock markes. According o a new hypohesis, ackled by he laes sudies, he aversion for risk of raional invesors may be relaed o he sages of he business cycles. This paper deals wih he connecion beween expeced reurn and volailiy a Buchares Sock Exchange, by analyzing he reurn and volailiy of he BET index porfolio. In order o assess his relaion, we employed heeroskedasic auoregressive models. The sudy was conduced beween January 2000 and April 20, as well as during wo sub-periods deermined by differen business cycle phases: economic growh and recession. The resuls revealed significan differences beween he whole analyzed period and he economic growh and recession sub-periods. By sudying BSE reurn hroughou he analyzed period, we conclude ha here is no relaionship beween expeced reurn and risk, whereas volailiy is asymmeric. Acually, one may winess a relaion beween reurn and risk, as well as a non-asymmeric response of volailiy o shocks during economic growh, and no risk-reurn relaionship and asymmeric volailiy during economic recession. Also, resuls have shown a posiive relaionship beween reurn and volailiy during economic growh, and a negaive relaionship beween he same during economic recession. Keywords: business cycle, reurn, volailiy, reurn-volailiy relaion JEL Classificaion: G, C 58 Inroducion In 990 William Sharpe was awarded he Nobel Prize for he Capial Asse Pricing Model ha he developed in 964 which marked he beginning of he asse pricing heory. This prize poined ou he imporance of sudying he connecion beween risk and reurn, o which researchers have given special consideraion since. Somewha laer, Linner (965) and Mossin (966) succeeded in reaching he same model independenly of he Nobel Prize winner. According o he heoreical asse pricing models, a risk-averse invesor who makes riskier invesmens should expec o be rewarded accordingly, i.e. o achieve higher raes of reurn. These models promoe a posiive relaionship beween expeced reurn and volailiy. Empirical research conduced on sock markes concerning he relaionship beween expeced reurn and volailiy led o conradicory resuls. Some sudies revealed a posiive relaion beween reurn and volailiy, whereas oher sudies demonsrae a negaive relaionship. For example Baillie and DeGennarro (990) found only a weak and almos non-exisen relaionship on he US sock marke. Koulakiois, Papasyriopoulos and Universiy Alexandru Ioan Cuza from Iaşi, Romania, Faculy of Economics and Business Adminisraion, Deparmen of Economics, Quaniaive Analysis and Informaion Sysems, chviorica@yahoo.com 2 Universiy Alexandru Ioan Cuza from Iaşi, Romania, Faculy of Economics and Business Adminisraion, Deparmen of Economics, Quaniaive Analysis and Informaion Sysems, chcipis@yahoo.com 49

2 Molyneux (2006), Theodossiou and Lee (995) discovered no significan relaionship. In conras, Glosen, Jagannahan and Runkle (993) on he US marke, and Dimiriou and Simos (20) in almos all welve EMU counries as well as five of he major EMU inernaional sock markes documened a negaive and significan relaionship. According o a new hypohesis, ackled by he laes sudies on he relaion beween reurn and volailiy, he aversion for risk of raional invesors may be relaed o he sages of he business cycles (Kim and Lee, 2008). The sudy of he reurn and risk relaed o socks, o sock porfolios and o sock index porfolios has led o he idenificaion of specific empirical characerisics (also known by he name of sylized facs). As for financial asses reurn raes, hey are srongly lepokuric (which feaure is also known by he name of fa ails ). Given he excessively curved disribuions, he reurn raes fail o observe a normal disribuion law. The feaure of reurn disribuions called fa ails shows ha he exreme values of he variables concerned occur more frequenly han in normal disribuion. This dependence reveals ha high (posiive or negaive) reurn raes are followed by oher exreme reurn raes, regardless of heir sign (Berdo, 2003). The exisence of his reurn dependence suggess ha reurn raes may be modeled using ARCH (Auoregressive Condiional Heeroskedasiciy) models. Sock reurn volailiy is characerized by saionariy, asymmery and clusering. Volailiy saionariy means ha volailiy is no divergen a infinium, bu ha i varies wihou fixed boundaries. Volailiy asymmery refers o he fac ha volailiy is higher on an asses/sock marke whose prices end o decrease han on a sock marke whose prices end o increase. The exisence of such a characerisic plays an imporan role in risk managemen, in hedging sraegies and also when seing he opion prices. Some of he idenified facors, which are crucial for his feaure, are he marke leverage effec, volailiy feedback and psychological invesmen facors, which are deermined by he percepion of he risk/profi balance a various marke levels. Volailiy clusering is a reurn volailiy characerisic according o which big variaions are followed by big variaions and small variaions are followed by small variaions (Mandelbro, 963). This characerisic shows ha a chock (which akes he form of new informaion) occurring on a sock marke is long lasing. The purpose of our paper is: - o deermine he characerisics of he reurn raes and volailiy of Buchares Sock Exchange during he above-menioned period, as well as during he economic growh and recession periods; - o sudy he relaion beween he expeced reurn and volailiy during he above-menioned period, as well as during he economic growh and recession periods, considering he previously deermined empirical characerisics of reurn and volailiy. In order o achieve hese goals, he second par of he paper is devoed o a shor descripion of he mehods employed o deermine he business cycle sages and o examine he relaion beween reurn and volailiy. In he hird par, we will describe he main resuls obained furher o he analysis of he connecion beween reurn and volailiy a Buchares Sock Exchange. The fourh par, which ends he paper, will include he conclusions of he empirical analyses performed. The resuls reveal ha he connecion beween reurn and volailiy a Buchares Sock Exchange should be analyzed on business cycle sages. The resuls obained during he economic growh periods are considerably differen from hose relaing o economic recession periods. Therefore, invesors, especially hose who has aversion for risk, should develop sraegies based on he sock exchange reurn and volailiy characerisics, depending on he business cycle sages. 50

3 Mehods Employed In order o analyze he reurn and risk characerisics a Buchares Sock Exchange, on business cycle sages, we will begin by deermining he business cycle sages and hen by examining he reurn and risk characerisics, depending on he business cycle sages we idenified. Therefore, we will describe hereunder he mehods ha we will employ. Real gross domesic produc and especially indusrial producion index are ofen used o esimae business cycles. However, since he Romanian gross domesic produc is available only on quarerly basis, we will use he indusrial producion index, which is available on monhly basis. The idenificaion of he exac imes of business cycle phase changing is known as cycle daing. One of he mos frequen and simple mehods of cycle daing was proposed by Bry and Boschan (97). Bry s and Boschan s daing algorihm (97) enables one o idenify he local rough or peak in a Y ime series ransformed by logarihm processing. A possible peak is idenified when a value y of he ime series is higher han k values of he Y variable in boh direcions [-k, +k], whereas a possible rough is idenified when a value y of he ime series is lower han k values of he Y variable in boh direcions [-k, +k]. The possible peak or rough changing imes ha were idenified should ake ino accoun he following iems of wha is commonly called censuring rules, in order o be validaed: - he business cycle changing imes should alernae, meaning ha a peak should be followed by a rough, hen by anoher peak and so on. For example, whenever wo successive peaks are idenified, one of hem should be removed, namely he one wih he lowes indusrial producion index; - as concerns parameer k, Bry and Boschan (Bry and Boschan, 97) sugges k=5 for monhly daa; - he minimum duraion of a complee cycle (i.e. from peak o peak and/or rough o rough) should be fifeen monhs; - according o Harding and Pagan (Harding and Pagan, 200), he minimum duraion of a business cycle sage should be six monhs; - he changing imes (peak and/or rough) deermined a he beginning and a he end of he indusrial producion index series should be removed, as hey are obained by comparing hem wih he firs and las series value, respecively. In our opinion, afer having idenified and validaed he business cycle changing imes, economic growh occurs during he periods beween a rough and a peak, whereas recession onses during he periods beween a peak and rough. Since asses reurn raes are dependen, hey may be modeled using auo regressive condiional models (Mills, 999; Nelson, 99; Boolerslev, 986;). Each of he auoregressive condiional models ried o ake ino consideraion as many empirical reurn and volailiy characerisics as possible. Auoregressive condiional models include wo equaions: condiional moving-average equaion and condiional volailiy equaion. The condiional moving-average equaion is generally a ARMA model. Neverheless, his equaion may also include oher reurn influence facors (such as macroeconomic variables). We will specify hereunder he condiional volailiy equaion of each model. The ARCH (Auoregressive Condiional Heeroskedasiciy) model was proposed by Engle in 982. When he developed his model, Engle considered he lepokuric naure of reurn raes, also called fa ails, and reurn volailiy variaion wih ime (Engle a al. 987; Engle and Bollerselv, 986). An ARCH(2) model based on an ARMA(,) model akes he form of he following equaion: - ARMA(,) reurn model: r a0 ar m () 5

4 (2) where: r - reurn of he index porfolio under survey; 2 - condiional error variance; condiional error variance is an error forecas for he day, considering he informaion available a he - ime; The following requiremens should be me in order for condiional variance o be null or posiive: 0 0,, 2,..., p 0. Since he analysis revealed a very high ARCH model order, he GARCH model was considered an improvemen of he former. The GARCH model manages o consider, in addiion o he characerisics aken ino accoun by he ARCH model, volailiy clusering. The GARCH (Generalized Auoregressive Condiional Heeroskedasiciy) model enables one o predic condiional volailiy, depending on he previous errors of he model, as well as on he previous volailiy predicions. Condiional volailiy in he GARCH model is an auoregressive process. The GARCH(p,q) model akes he form of he following equaions: - ARMA(,) reurn model: r a0 ar m (3) p p... q q (4) The following requiremens mus be me in order for he 2 condiional variance o be posiive: 0 0, i 0, i 0. Also, he saionariy requiremen is me if i i. The GARCH-M (GARCH in Mean) model allows considering he connecion beween risk and reurn. According o hese models, here is a direcion connecion beween he risk ha is underaken and he reurn ha is expeced: he higher he risk underaken by invesors, he higher heir award should be. Therefore, he moving-average equaion will include expeced volailiy, as explanaory variable, which may be measured by boh sandard deviaion and variance. The GARCH(p,q)-M() model is as follows: - reurn model r a0 ar m b (5) p p... p q (6) The following requiremens mus be me in order for he 2 condiional volailiy o be posiive: 0 0, i 0, i 0 and i i. EGARCH, PARCH, GJR-GARCH are models ha have been developed o consider he asymmeric shock impac on reurn. The EGARCH model manages o consider he asymmeric impac of new evens on reurn: a negaive piece of informaion having he same inensiy as a posiive piece of informaion deermines a higher volailiy increase. The EGARCH(,) model includes he following equaions: - ARMA reurn model: Y a0 ar m (7) ln ln (8) The asymmery is revealed by parameer. If his parameer is saisically significan, here is an asymmeric volailiy reacion, depending on he new informaion on he marke. As we also wan o consider he informaion asymmery effec when esimaing he relaion beween expeced reurn and condiional volailiy, he EGACH-M model provides his opion. EGARCH-M model: 52

5 r a ar m b (9) 0 ln ln (0) Since he EGARCH and EGARCH-M models have condiional volailiy in logarihmic form as a dependen variable, no more requiremens should be me in order o provide a posiive value of his parameer. If, when esimaing his model, we ge a saisically significan b we may say ha here is a relaion beween reurn and volailiy. Also, if is saisically significan, we may consider volailiy as asymmeric. Ding e al. (993) propose he Asymmeric Power ARCH (APARCH). Condiional variance for a APARCH(,,) is modeled by he equaion: 0 () The recorded parameers mus mee he following requiremens 0, 0 0, 0, 0 and. If 0, condiional volailiy is asymmeric. GJR-GARCH is anoher asymmeric model inroduced by Glosen e al. (993). A GJR(,) model has he following condiional variance equaion: S (2) where S is a dummy variable, which is when <0 and 0 in all he oher siuaions. The model requires ha, 0 0, 0, 0, 0. When 0, 2 condiional variance will be higher afer a negaive shock a momen ( <0). In order o esimae condiional volailiy, Engle (983) used normal disribuion, Bollerslev (987) proposed sandardized Suden disribuion, and Nelson (99) poposed Generalized Error (GED). Our sudy esimaes heeroscedasic models relying on hese hree disribuions. Once he heeroscedasic models have been esimaed, we esed specific regression model esimaion assumpions. Then we chose he bes model depending on Adjused R 2 and he Akaike, Schwarz, Hannan-Quinn informaion crieria. Main Empirical Resuls The daa used in his sudy is gahered from wo sources: Eurosa daabase for indusrial producion and Daasream for index BET. Our research firs ackled business cycle daing in Romania based on he Bry and Boschan daing algorihm (Bry and Boschan, 97) and hen reurn-volailiy relaion modeling by means of he heeroskedasic EGARCH-M model. As concerns Romanian business cycle daing, we employed he monhly indusrial producion index. The daa were found in he Eurosa daabase and hey refer o he January 200 April 20 period. As shown in figure a), he indusrial producion index has a monhly seasonaliy, and ha is he reason why we used he deseasonalized series provided by Eurosa. 53

6 50 IPI_RO 4.90 LIPI_RO_AJ a) indusrial producion index b) indusrial producion index adjused on seasonal and logarihmic basis Figure no.. - Evoluion of he indusrial producion index in Romania, beween January 2000 and April 20 The mehods provided by Bry and Boschan (97) enabled us o calculae he business cycle sage changing imes, which are shown in he able below: Business cycle changing imes in Romania peak rough 5/200 5/2002 5/2003 5/2005 3/2007 2/2008 Table no. According o he resuls obained, we achieved, in addiion o he iniial ime series, wo ime series, which include he BET index price values, markeable on Buchares Sock Exchange, during boh economic growh and recession. We calculaed he daily reurn raes beginning wih January, 2000 unil April 27, 20, based on he daily prices of he BET index a Buchares Sock Exchange. Coninuously compounded reurn, also called logarihmic reurn, is calculaed as follows: r ln P ln P 00 where: r - coninuously compounded reurn P, P - index porfolio price a ime and -, respecively The BET index porfolio reurn hroughou he whole analyzed period coninues o be known under he name of LRBET, he BET index porfolio reurn during he economic growh periods is called CLRBET, whereas he same reurn during he economic recession periods is called SLRBET. The firs reurn analysis sage is he idenificaion of is characerisics. Therefore, we analyzed he descripive saisics of he hree raes of reurn under survey, namely LRBET, CLRBET and SLRBET. The resuls are shown in he able below. 54

7 Table no. 2 Descripive saisics of he BET index porfolio reurn raes hroughou he whole analyzed period, as well as during he economic growh and recession periods LRBET CLRBET SLRBET Mean Median Max Min Sd. Dev Skewness Kurosis Jarque-Bera Prob Sum Sum Sq. Dev Obs During he analyzed period, he BET index porfolio has a low, ye posiive ( %), mean reurn rae. If we bear in mind ha hese reurn raes are daily, hey may increase considerably hroughou a monh. Therefore, when he reurn raes are saionary, invesors who own a porfolio similar o he BET index porfolio expec o have profi. The BET index porfolio reurn raes during he economic growh periods, called CLRBET, and during he economic recession periods, called SLRBET, are also posiive. However, invesors expec o aain higher reurn raes during economic growh han during economic recession periods. The BET index porfolio risk, measured by sandard deviaion, is much higher during economic recession periods ( ) han during economic growh periods (.67744). As he reurn rae medians are posiive, more han 50% of he reurn raes are posiive, which means ha i is more likely for invesors o have profi han o suffer losses. The disribuions of all he reurn raes under survey, namely LRBET, CLRBET and SLRBET, are all characerized by negaive asymmery (he asymmery indicaors are , and , respecively), which means ha hese disribuions lenghen owards he low, negaive values of he reurn raes. Also, as i is he case wih mos of financial series, heir disribuions are characerized by excess lepokurosis (he disribuion curving indicaors are much higher han 3, which is specific o mesokuric disribuions: , and , respecively).this means ha invesors may eiher have very high profi, or suffer grea losses. According o he graphic represenaion of he BET index porfolio reurn raes shown below, here are periods when he reurn raes have low, boh posiive and negaive, values and, also, periods when he reurn raes have high, boh posiive and negaive, values. Thus, he graphic represenaions show index porfolio reurn raes show volailiy clusering. 55

8 5 LRBET Figure no Evoluion of he BET index porfolio reurn rae beween January 2000 and April 20 In order o es he volailiy clusering hypohesis, which would acually mean ha reurn raes are dependen, we should begin by examining wheher he squares of he reurn raes are auocorrelaed. The Ljung-Box es enables us o do ha. According o he null hypohesis of he Ljung-Box es, he squares of he reurn raes are no auocorrelaed, whereas according o he alernaive hypohesis he squares of he reurn raes are auocorrelaed. Since he probabiliies associaed o he Ljung-Box (Q) es are lower han he risk underaken for esing hese hypoheses of 0.05, he null hypohesis is rejeced, and he alernaive reurn rae dependence hypohesis is acceped. Table no. 3 Toal and parial auocorrelaion funcions, he Ljung-Box es and probabiliies associaed o he Ljung-Box es LRBET2 LRBET_C2 LRBET_FI2 AC PAC Q-Sa Prob. AC PAC Q-Sa Prob. AC PAC Q-Sa Prob Remark: Resuls obained by means of he Eviews sofware The presence of he reurn rae dependence suggess ha he reurn raes may be modeled using ARCH (Auo Regressive Condiional Heeroskedasiciy) models. This is possible since he analyzed reurn raes, namely LRBET, CLRBET and SLRBET, are auocorrelaed. 56

9 The firs reurn modeling sage consiss of esing heir saionariy. As he Akaike and Schwaz crieria provide conradicory resuls for all he reurn raes wih Augmened Dickey-Fuller and Philips-Perron ess we used he KPSS es for he saionariy esing (Appendix ). For he KPSS es, he Akaike and Schwarz crieria provide he same resuls. CLRBET is saionary, whereas SLRBET and LRBET are no saionary and have a descending rend. These non-saionary reurn raes will become saionary if he rend is excluded. The descending rend of SLRBET and LRBET shows us ha he reurn raes diminished hroughou he analyzed period, as well as during economic recession. Afer he reurn raes have become saionary, we esed saionary reurn rae auocorrelaion. The oal and parial reurn rae auocorrelaion funcions are infinie and end o zero, which shows us ha hey may undergo ARMA modeling. The orders of hese models were deermined by ess based on he Schwarz crierion. The resuls obained confirm ha he lowes Schwarz crierion value is achieved for he AR() model. Hence, he heeroskedasic model mean equaion is a AR() model. In order o deermine he relaion beween reurn and volailiy, and also in order o consider a possible volailiy asymmery, we esimaed he GARCH, GARCH-M, EGARCH, EGARCH-M, A-PARCH, A-PARCH-M, GJR, GJR-M models for each of he hree reurn series analyzed, namely LRBET, CLRBET and SLRBET, relying on he hree disribuions described above, i.e. normal, suden and GED. Appendices 3, 4 and 5 show he informaion crieria for some of hese models. As concerns CLRBET, only wo of he esimaed models mee he specific regression model assumpions and he resricions imposed by each model. These models are: EGARCH(,)- M (Suden) and APARCH(,)-M (normal disribuion). From he informaion crieria sandpoin, EGARCH(,)-M (Suden disribuion) is he bes model. The resuls are shown in able 4. According o appendix 4, for SLRBET, only he esimaed GJR(,)-M models fail o mee he specific regression model assumpions. From he informaion crieria viewpoin, EGARCH- M(,) (GED) is he bes model. As for LRBET modeling, we idenified a single model which mees he specific regression model assumpions, namely APARCH-M(,) (Normal ). Table 4 shows he final resuls. Table no. 4 Resuls for esimaion of heeroscedasic models Variables CLRBET SLRBET LRBET Parameers EGARCH(,)-M EGARCH(,) -M A-PARCH(,) -M (Suden ) (Suden ). (Normal ) b (0.004) (0.9762) (0.648) â (0.838) (0.4846) â (0.079) (0.0000) (0.0000) ˆ (0.0000) (0.0000) (0.0000) ˆ (0.0000) (0.0000) (0.0000) ˆ (0.390) (0.023) (0.006) ˆ (0.0000) (0.0000) (0.0000) ˆ (0.0000) Remark: Resuls obained by means of he Eviews sofware The able above shows ineresing ye predicable resuls on he reurn and risk of he BET index porfolio and implicily of Buchares Sock Exchange. If we analyze he resuls of he enire period considered, we may say ha here is no connecion beween reurn and risk a Buchares Sock Exchange. Therefore, invesors wih aversion for risk should ake ino accoun ha if hey 57

10 underake a higher risk by making invesmens on he BSE his does no necessarily mean a higher rae of reurn. If we analyze he resuls separaely, he siuaion is differen beween he economic growh and recession periods. The economic growh periods reveal a connecion beween reurn and volailiy, whereas his is no he case in he economic recession periods. An invesor wih aversion for risk would be moivaed o inves or speculae on he BSE during he economic growh periods, when he had higher reurn raes for bigger risks. As for he volailiy of he enire analyzed period, he esimaed model shows us ha i is asymmeric. Therefore, volailiy is higher when mos of he prices decrease, as compared o he general sock exchange price increase periods. Also, he analysis of he economic growh period reveals a differen siuaion from he economic recession periods. Volailiy raes are no asymmeric during he economic growh periods, ye, during he economic recession periods, hey are asymmeric. Conclusions The laes sudies on he relaion beween reurn and volailiy dwell on he separae analysis of his connecion during economic growh and recession, respecively. The resuls obained suppor he exisence of a series of significan differences. For his reason, he purpose of our paper was o discover wheher hese ypes of differences occur in Buchares Sock Exchange, as well. In order o characerize Buchares Sock Exchange, we considered he BET index porfolio, whose daily reurn rae was deermined using he BET index prices. Hence, we analyzed hree raes of reurn, namely hroughou he analyzed period, during he economic growh periods and during he economic recession periods. The analyzed reurn raes are lepokuric, jus as all he reurn raes of financial asses, which means ha a BSE invesor may eiher have very high profis, or incur considerable losses. Volailiy clusering proves ha reurn raes are dependen and may be modeled using heeroskedasic models. The descripive reurn rae analysis beween January and April 27, 20, as compared o he reurn raes in he economic growh and recession periods, reveals differences as concerns he expeced raes of reurns and volailiies. Also, hey have a descending rend during economic recession periods. Our research reveals no relaion beween reurn rae and volailiy hroughou he analyzed period. However, furher o a separae analysis of he economic growh and recession, respecively, one may noice he exisence of a connecion beween reurn rae and volailiy, bu only during he economic growh period. Also, volailiy is asymmeric during economic recession periods, which riggers higher volailiy when a general BSE price decrease occurs. The resuls obained suppor our assumpion according o which here is a direc posiive relaion beween expeced reurn and volailiy during economic growh, which urns ino a negaive connecion during economic recession. The resuls obained have major implicaions for sock porfolio managers who are supposed o manage hose porfolios in close connecion wih he business cycle sages Acknowledgemen This work was cofinanced from he European Social Fund hrough Secoral Operaional Programme Human Resources Developmen , projec number POSDRU/.5/S/5984 Performance and excellence in posdocoral research in Romanian economics science domain References. Baillie R. T., DeGennarro R. P., 990. Sock Reurn and Volailiy, Journal of Fnancial and Quaniaive Analysis, Vol. 25, No. 2, June, pp

11 2. Berdo J.-P., Renabilié e volailiés des indices boursiers. Une analyse comparaive du BET, du Dow-Jones indusrials se du CAC 40, Conférences, Iasi 3. Boollerslev T., 986. Generalized Auoregressive Condiional Heerosckedasiciy, Journal of Economerics, 3, Bry G, Boschan C., 97. Cyclical Analysis of Time Series: Seleced Procedures and Compuer Programs, NBER, New York 5. Ding Z., Granger C.W.J., Engle R.F., 993. A long memory propery of sock marke reurns and a new model. Journal of Empirical Finance, Engle R.F., Lilien, D. M., Robbins, R.P., 987. Esimaing Time Varying Risk Premium in he Term Srucure: The ARCH-M Model', Economerica, 55, Engle R. F., 982. Auoregressive condiional heeroskedasiciy wih esimaes of he variance of he Unied Kingdom inflaion, Economerica, 50, Engle R.F., Bollerselv T.,986. Modeling he persisence of condiional variances, Economeric Reviews, 5, Glosen L., Jagannahan R., Runkle D., 993. On he relaionship beween he expeced value and he volailiy of he nominal excess reurn on socks, Journal of Finance 46, Harding D., Pagan A., 200. Exracing, Analysing and Using Cyclical Informaion, Mimeo, Universiy of Melbourne.. Kim S.-W., Lee B.-S., Sock Reurns, Asymmeric Volailiy, Risc Aversion, and Business Cycle: Some New Evidence, Economic Inquiry, Vol. 46 (2), Koulakiois A., Papasyriopoulos N., Molyneux P., More Evidence on he Relaionship beween Sock Price Reurns and Volailiy: A Noe, Inernaional Research Journal of Finance and Economics, no., Linner J., 965. The Valuaion of Risk Asses and he Selecion of Risky Invesmens in Sock Porfolios and Capial Budges. Review of Economics and Saisics. 47:, Mandelbro B. B., 963. The variaion of cerain speculaive prices, Journal of Business, XXXVI (963), Mills T. C., 999. The Economeric Modeling of Financial Time Series, Cambridge Universiy Press. 6. Mossin J., 966. Equilibrium in a capial asse marke. Economerica 4, Nelson D. B., 99. Condiional heeroskedasiciy in asse reurns: A new approach, Economerica. 59, Sharpe William F., 964. Capial Asse Prices:A Theory of Marke Equilibrium under Condiionsof Risk. Journal of Finance. 9:3, Theodossiou P., Lee U., 995. Relaionship beween volailiy and expeced reurns across inernaional sock markes. Journal of Business Finance and Accouning 22, EUROSTAT DATABASE hp://epp.eurosa.ec.europa.eu/poral/page/poral/saisics/search_daabase 59

12 APPENDIX The resuls of esing saionariy for BET index porfolio reurn during economic growh, economic recession and hroughou he analyzed period Characerisics Model wih inercep Model wih inercep and rend Model wihou inercep and rend CLRBET ADF es Criical value(5%) Akaike Schwarz PP es Criical value (5%) Akaike Schwarz KPSS es Criical value(5%) Akaike Schwarz SLRBET ADF es Criical value(5%) Akaike Schwarz PP es Criical value(5%) Akaike Schwarz KPSS es Criical value(5%) Akaike Schwarz LRBET ADF es Criical value(5%) Akaike Schwarz PP es Criical value(5%) Akaike Schwarz KPSS es Criical value(5%) Akaike Schwarz

13 APPENDIX 2 Toal and parial auocorrelaion funcions of saionary BET index porfolio reurns hroughou he analyzed period, during economic growh and economic recession Table no. Values of parial and oal auocorrelaion funcions and Ljung Box es for LRBET and CLRBET LRBET CLRBET AC PAC Q-Sa Prob AC PAC Q-Sa Prob Table no 2. Values of parial and oal auocorrelaion funcions and Ljung Box es for SLRBET SLRBET AC PAC Q-Sa Prob APPENDIX 3. Esimaion of heeroscedasic models for CLRBET Schwarz crierion values for various ARMA(p,q) models for CLRBET AR/MA Table no. 6

14 Table no. 2. Informaion crieria values of he esimaed heeroscedasic models for CLRBET EGARCH(,)-M EGARCH(,2)-M Informaion crieria Normal Suden GED Normal Suden GED Akaike 3, , , , , , Schwarz 3, , , , , , Hannan-Quinn 3, , , , , , Adjused R 2 0, , , Regres.hypo. no me were me. no me no me no me no me Table no. 2 (coninuaion) Informaion crieria values of he esimaed heeroscedasic models for CLRBET APARCH(,)-M GJR(,)-M Informaion crieria Normal Suden GED Normal Suden GED Akaike 3, , , , , Schwarz 3, , , , ,47065 Hannan-Quinn 3, , , , , Adjused R 2 0, , , , ,00623 Regres.hypo. were me. no me no me no me no me APPENDIX 4 Esimaion of heeroscedasic models for SLRBET Schwarz crierion values for various ARMA(p,q) models for SLRBET AR / MA Table no.. Table no. 2 Informaion crieria values of he esimaed heeroscedasic models for SLRBET GARCH(,)-M EGARCH(,) M Informaion Normal Suden GED Normal Suden GED crieria Akaike 3, , , , , , Schwarz 3, , ,8366 3, ,8023 3,8860 Hannan-Quinn 3, , , ,8804 3, , Adjused R 2 0, , , , , , Regres.hypo. were me were me were me were me were me were me Table no. 2 (coninuaion) Informaion crieria values of he esimaed heeroscedasic models for SLRBET APARCH(,)-M GJR(,)-M Informaion crieria Normal Suden GED Normal Suden GED Akaike 3, , , , , , Schwarz 3, , , , , ,8943 Hannan-Quinn 3, , , , , ,7832 Adjused R 2 0, , , , , , Regres.hypo. were me were me were me no me no me no me 62

15 ANEXA 5 Esimaion of heeroscedasic models for LRBET Schwarz crierion values for various ARMA(p,q) models for LRBET AR / MA Table no.. Table no. 2. Informaion crieria values of he esimaed heeroscedasic models for LRBET GARCH(,)-M GARCH(,2)-M Informaion Normal Suden GED Normal Suden GED crieria Akaike Schwarz Hannan-Quinn Adjused R Regres.hypo. no me no me no me no me no me no me Table no. 2 (coninuaion) Informaion crieria values of he esimaed heeroscedasic models for LRBET EGARCH(,)-M EGARCH(,2)-M Informaion crieria Normal Suden GED Normal Suden GED Akaike Schwarz Hannan-Quinn Adjused R Regres.hypo. no me no me no me no me no me no me Table no. 2 (coninuaion) Informaion crieria values of he esimaed heeroscedasic models for LRBET APARCH(,)-M GJR(,)-M Informaion crieria Normal Suden GED Normal Suden GED Akaike Schwarz Hannan-Quinn Adjused R Regres.hypo. were me no me no me no me no me no me 63