Asymmetric Conditional Volatility on the Romanian Stock Market - DISSERTATION PAPER-

Transcription

1 ACADEMY OF ECONOMIC STUDIES DOCTORAL SCHOOL OF FINANCE AND BANKING Asymmeric Condiional Volailiy on he Romanian Sock Marke - DISSERTATION PAPER- MSc Suden: STANCIU FLORIN AURELIAN Coordinaor: Professor MOISĂ ALTĂR Buchares, July

2 ABSTRACT Recen sudies show ha a negaive shock in sock prices will generae more volailiy han a posiive shock of similar magniude. The aim of his paper is o es he hypohesis under which he he condiional variance of sock reurns is an asymmeric funcion of pas informaion. This paper invesigaes he volailiy of he Romanian Sock Marke using daily observaions from Buchares Exchange Trading Composie Index (BET-C) for he period from April 16, 1998 (index launch dae) hrough June 1, 2008 and for a subsample period. Preliminary analysis of he daa shows significan deparure from normaliy. Moreover, reurns and squared residuals show a significan level of serial correlaion which is relaed o he condiional heeroskedasiciy due o he ime varying volailiy. These resuls sugges ha ARCH and GARCH models can provide good approximaion for capuring he characerisics of BET-C. The empirical analysis suppors he hypohesis of asymmeric volailiy; hence, good and bad news of he same magniude have differen impacs on he volailiy level. In order o assess asymmeric volailiy we use auoregressive condiional heeroskedasiciy specificaions known as TARCH and EGARCH. Our resuls show ha he condiional variance is an asymmeric funcion of pas innovaions raising proporionaely more during marke declines, a phenomenon known as he leverage effec. 2

3 CONTENTS I. Inroducion 4 II. Lieraure Review 6 III. Mehodology Models of Predicable Volailiy (he GARCH model, he EGARCH model and he TGARCH model) A Parially Non-Parameric ARCH Model Individual Socks Cross Secional Regression.. 16 IV. Empirical Daa and Resuls Preliminary Daa Analysis The GARCH, EGARCH and TGARCH Models The Parially Non-Parameric ARCH Model A Cross Secional Analysis of he Dependence beween he Degree of Asymmery and he Leverage Raio 27 V. Concluding Remarks Bibliography. 32 Appendix 34 3

4 I. INTRODUCTION Two of he mos common empirical findings in financial lieraure are ha he disribuions of high-frequency asse reurns display ails heavier han hose of normal disribuion and ha he squared reurns are highly serially correlaed. Furhermore, many empirical resuls indicae ha he sock index reurn presened asymmeric volailiy. The findings of Schwer (1990), Nelson (1991), Campbell and Henschel (1992), Rabemananjara and Zakoian (1993), Engle and Ng (1993), Henschel (1995), Bekaer and Wu (2000), Wu (2001), and Blair, Poon and Taylor (2002) provided he evidence. The purpose of my paper is o es wheher volailiy on he Romanian Sock Marke is also asymmeric, in he sense ha negaive shocks on reurns increase he nex period s condiional volailiy more han posiive shocks of equal magniude. In order o assess his sylized fac of financial marke volailiy, I have chosen he series of reurns for he Buchares Exchange Trading Composie Index (BET-C) for he period from April 16, 1998 (index launch dae) hrough June 1, 2008 and a subsample period from November 1, 2004 hrough June 1, BET-C is he composie index of BVB marke. I is a marke capializaion weighed index. BET-C reflecs he price movemen of all he companies lised on he BVB regulaed marke, Is and Iind Caegory, exceping he SIFs (Financial Invesmen Companies generaed from he romanian privaisaion process). The BET-C index is he mos comprising index on he Romanian sock marke, aking ino accoun he sock price evoluion of 55 lised companies 1. Using he BET-C Index reurn series, in secion IV, I compare he GARCH (1, 1) model wih hree oher volailiy models ha allow for asymmery in he impac of news on volailiy. In addiion, here is evidence ha individual sock also exhibis asymmeric volailiy. Black (1976) and Chrisie (1982) were among he firs o documen and explain a negaive relaionship beween curren individual sock reurn and fuure volailiy in he US equiy markes. The leverage effec is a phrase ha describes he asymmeric response of volailiy o shocks of differing signs. Black (1976) showed ha if he price on day fell hen he volailiy on day + 1 would, on average, be higher han if he price rose by he same amoun. Black's 1 The composiion of he index as of July 2008 is available in Figure 1 in Appendix 4

5 explanaion of his phenomenon saed ha a price fall reduces he value of equiy and hence increases he deb-o-equiy raio. This increase in leverage raises he riskiness of he firm and an increase in volailiy is observed. Chrisie (1982) esed Black's explanaion by looking a he relaionship beween he asymmery in equiy volailiy and he deb-o-equiy raio of firms. Chrisie demonsraes ha sock price changes and volailiy are inversely relaed, i.e. he elasiciy of volailiy wih respec o he value of equiy is negaive. He also finds ha volailiy is an increasing funcion of financial leverage suggesing ha his may be he cause of he negaive elasiciy of volailiy wih respec o he value of equiy. He found a srong relaionship beween he leverage effec and he deb-o-equiy raio, bu claimed ha he debo-equiy raio did no fully explain he effec. If such asymmeries exis in individual socks reurns i is naural o expec ha in a cross secional analysis he size of he asymmery will be posiively relaed o he degree of financial leverage (i.e, he higher he leverage he more asymmeric he response of volailiy o innovaions). Oherwise he asymmeric impac of innovaions on volailiy has o be explained by facors oher han he financial leverage. In Secion IV of my paper, I find welve individual socks from he Romanian sock marke ha exhibi asymmeric volailiy over he period saring June 1, 2004 o June For each of hese companies I calculae four over-he-sample-period mean leverage raios (wo of hem based on he book value of equiy and he oher wo on he marke value of equiy), hen employ he cross-secion regression mehod of Koumos and Saidi (1995) o deermine wheher he esimaed degree of asymmery, for each sock, is relaed o some measure of financial leverage. The res of he paper is organized as follows: Secion II presens a selecion of relevan lieraure on he issues concerning aasymmery in condiional variance and is deerminans. Secion III inroduces he conceps and models used in he empirical analysis. Secion IV describes he daa, he acual implemenaion of he models and discusses he resuls, while Secion V concludes. 5

6 II. LITERATURE REVIEW Recen empirical sudies of naional sock-index reurns have noed several empirical regulariies. Firs, daily sock reurns have been found o presen auocorrelaions. The exisence of an AR process has been aribued o nonsynchronous rading (Scholes and Williams, 1977; Lo and MacKinlay, 1990), ime-varying shor-erm expeced reurns (Fama and French, 1988; Senana and Wadhwani, 1992), and coss of price adjusmen (Amihud and Mendelson, 1987; Damodaran, 1993; Koumos, 1998). Second, in muli-counry analysis, cross correlaions of sock reurns have been repored in sudies by Hamao e al (1989), Koumos and Booh (1995), Kim and Rogers (1995), and Chiang (1998). Their findings indicae ha naional sock reurns are significanly correlaed and ha linkages among inernaional sock markes have grown more inerdependen over ime. Third, following he approaches by Engle (1982), Bollerslev (1986), French e al (1987), Schwer (1989), Pagan and Schwer (1990), Baillie and DeGennaro (1990), he cumulaive evidence indicaes ha sock volailiy exhibis a clusering phenomenon, i.e. large changes end o be followed by large changes and small changes end o be followed by small changes. In heir review of his marke phenomenon, Bollerslev e al (1992) repor ha he GARCH(1,1) model appears o be sufficien o describe he volailiy evoluion of sock-reurn series. A drawback of sandard ARCH-ype models is ha he esimaed coefficiens are assumed o be fixed hroughou he sample period and fail o ake ino accoun he asymmerical effec beween posiive and negaive shocks o sock reurns. This leads o he fourh regulariy - an asymmerical effec is found in sudying sock-reurn series. I has been shown ha a negaive shock o sock reurns will generae greaer volailiy han will a posiive shock of equal magniude. By exending he research mehods proposed by Nelson (1991), Glosen e al (1993), Engle and Ng (1993) and Koumos (1997, 1998, and 1999) find significan evidence o suppor he asymmerical hypohesis of sock-index reurns. More recenly, Bekaer and Wu (2000) and Wu (2001) highligh he leverage effec and volailiy feedback effec in explaining asymmerical volailiy in response o news and find supporive evidence in Nikkei 225 socks. 6

7 Noe ha in he specificaion of he asymmerical parial-adjusmen price model (Amihud and Mendelson, 1987; Damodaran, 1993; Koumous, 1998), where prices incorporae negaive reurns faser han posiive reurns, he news variable is implicily embedded in he auoregressive process of he mean equaion. These models are useful and appropriae if our ineres is o focus on examining wheher news of negaive reurns is incorporaed ino curren prices faser han news reflecing posiive reurns. On he oher hand, Bekaer and Wu s model (2000) provides a unified framework o examine asymmerical volailiy in response o news a he firm level and he marke level. The abiliy o forecas financial marke volailiy is imporan for porfolio selecion and asse managemen as well as for he pricing of primary and derivaive asses. While mos researchers agree ha volailiy is predicable in many asse markes, hey differ on how his volailiy predicabiliy should be modeled. In recen years he evidence for predicabiliy has led o a variey of approaches, some of which are heoreically moivaed, while ohers are simply empirical suggesions. The mos ineresing of hese approaches are he "asymmeric" or "leverage" volailiy models, in which good news and bad news have differen predicabiliy for fuure volailiy. These models are moivaed by he empirical work of Black (1976), Chrisie (1982), French, Schwer, and Sambaugh (1987), Nelson (1990), and Schwer (1990). Pagan and Schwer (1990) provide he firs sysemaic comparison of volailiy models. This paper builds on heir resuls, focusing on he asymmeric effec of news on volailiy. The imporance of a correcly specified volailiy model is clear from he range of applicaions requiring esimaes of condiional volailiies. In he valuaion of socks, Meron (1980) shows ha he expeced marke reurn is relaed o predicable sock marke volailiy. French, Schwer, and Sambaugh (1987) and Chou (1988) also find empirical evidence for his relaionship. Schwer and Seguin (1990) and Ng, Engle, and Rohschild (1992) show ha individual sock reurn volailiy is driven by marke volailiy, wih individual sock reurn premiums affeced by he predicable marke volailiy. In he valuaion of sock opions, Hull and Whie (1987) sugges ha sochasic sock reurn volailiy migh be he source of some documened pricing biases of he Black-Scholes opion-pricing formula. Furhermore, he research of Day and Lewis (1992) shows ha implied volailiy from he Black-Scholes model canno capure he enire predicable par of fuure volailiy relaive o some GARCH and 7

8 EGARCH models. Amin and Ng (1993) show ha opion valuaion under predicable volailiy is differen from opion valuaion under unpredicable volailiy. Finally, he predicabiliy of volailiy is imporan in designing opimal dynamic hedging sraegies for opions and fuures (Baillie and Myers (1991) and Engle). The predicabiliy of volailiy migh also affec he resuls of even sudies (for example, Connolly (1989)) There is a long radiion in finance [see, e.g., Cox and Ross (1976)] ha models sock reurn volailiy as negaively correlaed wih sock reurns. Influenial aricles by Black (1976) and Chrisie (1982) furher documen and aemp o explain he asymmeric volailiy propery of individual sock reurns in he Unied Saes. The explanaion pu forward in hese aricles is based on leverage. A drop in he value of he sock (negaive reurn) increases financial leverage, which makes he sock riskier and increases is volailiy. Alhough, o many, "leverage effecs" have become synonymous wih asymmeric volailiy, he asymmeric naure of he volailiy response o reurn shocks could simply reflec he exisence of ime-varying risk premiums [Pindyck (1984), French, Schwer, and Sambaugh, (1987), and Campbell and Henschel (1992)]. If volailiy is priced, an anicipaed increase in volailiy raises he required reurn on equiy, leading o an immediae sock price decline. Hence he causaliy is differen: he leverage hypohesis claims ha reurn shocks lead o changes in condi-ional volailiy, whereas he ime-varying risk premium heory conends ha reurn shocks are caused by changes in condiional volailiy. Which effec is he main deerminan of asymmeric volailiy re-mains an open quesion. Sudies focusing on he leverage hypohesis, such as Chrisie (1982) and Schwer (1989), ypically conclude ha i canno accoun for he full volailiy responses. Likewise, he ime-varying risk premium heory enjoys only parial success. The volailiy feedback sory relies firs of all on he well-documened fac ha volailiy is persisen. Tha is, a large realizaion of news, posiive or negaive, increases boh curren and fuure volailiy. The second basic ene of his heory is ha here exiss a posiive ineremporal relaion beween expeced reurn and condiional variance. The increased volailiy hen raises expeced reurns and lowers curren sock prices, dampening volailiy in he case of good news and increasing volailiy in he case of bad news. 8

9 A survey of he exising lieraure on asymmeric volailiy is offered by Bekaer and Wu (2000) 1 : Sudy Volailiy measure Presence of asymmery Explanaion Black (1976) Gross volailiy Socks, porfolios Leverage hypohesis Chrisie (1982) Gross volailiy Socks, porfolios Leverage hypohesis French, Schwer and Sambaugh (1987) Condiional volailiy Index Time-varying risk premium heory Schwer (1990) Condiional volailiy Index Leverage hypohesis Nelson (1991) Condiional volailiy Index Unspecified Campbell and Henschel (1992) Condiional volailiy Index Time-varying risk premium heory Cheung and Ng (1992) Condiional volailiy Socks Unspecified Engle and Ng (1993) Condiional volailiy Index (Japan Topix) Unspecified Glosen, Jagannahan and Condiional volailiy Index Unspecified Runkle (1993) Bae and Karolyi (1994) Condiional volailiy Index Unspecified Braun, Nelson and Sunier Condiional volailiy Index and socks Unspecified (1995) Duffee (1995) Gross volailiy Socks Leverage hypohesis Ng (1996) Condiional volailiy Index Unspecified Bekaer and Harvey (1997) Condiional volailiy Index (Emerging Markes) Unspecified In recen year, Cheung and Ng (1992), Duffee (1995), Koumos and Saidi (1995), Kiazawa (2000), and Blair, Poon and Taylor (2002) have also confirmed ha he volailiy of individual sock exhibis asymmery. In sudying 30 DJIA companies, Koumos and Saidi (1995) showed ha all sock reurns exhibi asymmeric volailiy in he sense ha negaive innovaions increase volailiy more han posiive innovaions of an equal magniude wih one excepion. 1 This able liss a sample of sudies on he relaionship beween reurns and condiional volailiy. Condiional volailiy sudies ypically use GARCH models o measure volailiy; gross volailiy ypically refers o he sandard deviaion of daily reurns compued over he course of a monh. The unspecified label in he explanaion column means ha asymmery was modeled bu he researchers did no specify he exac cause of he asymmery. 9

10 On he average, a negaive innovaion increases volailiy 2.13 imes more han a posiive innovaion. Yoshsugu Kiazawa (2000) esimaed he leverage effec using he EGARCH model for panel daa wih a large number of sock issues and a small number of daily observaions focusing on he Tokyo Sock Exchange. They indicaed ha he leverage effec is significan in he span from June 22 o 29 in Blair, Poon and Taylor (2002) esimaed he leverage effec of he S&P100 index and all is consiuen socks from an exension of he asymmeric volailiy of GJR model. They indicaed ha he index and he majoriy of socks have a greaer volailiy response o negaive reurns han o posiive reurns and he asymmery is high for he index han for mos socks. III. METHODOLOGY 1. Models of Predicable Volailiy (he GARCH model, he EGARCH model and he TGARCH model) The firs par of my analysis relies on he GARCH model developed by Bollerslev (1986), he Exponenial GARCH model inroduced by Nelson(1991) and he GJR Threshold GARCH model inroduced by Glosen, Jagannahan, and Runkle (1993). Following Engle and Ng(1993), I also fi o my series of reurns a parially non-parameric ARCH model. Le Y be he rae of reurn of a paricular sock or he marke porfolio from ime - 1 o ime. Also, le F - 1 be he pas informaion se conaining he realized values of all relevan variables up o ime - 1. Since invesors know he informaion in F -1 when hey make heir invesmen decision a ime - 1, he relevan expeced reurn and volailiy o he invesors are he condiional expeced value of Y, given F -1, and he condiional variance of Y, given F -1. We denoe hese by m and h respecively. Tha is, m = E(y / F - 1 ) and h = Var(y / F - 1 ). Given hese definiions, he unexpeced reurn a ime (he shock) is ε = y -m. Engle (1982) suggess ha he condiional variance h can be modeled as a funcion of he lagged ε 's. Tha is, he predicable volailiy is dependen on pas news. The mos deailed 10

11 model he develops is he ph order auoregressive condiional heeroskedasiciy model, he ARCH(p): p 2 h i i i 1 where α 1,..., α p, and ω o are consan parameers. The effec of a reurn shock i periods ago (i < p) on curren volailiy is governed by he parameer α i. We would expec ha α i < α j for i > j. Tha is, he older he shock, he less effec i has on curren volailiy. In an ARCH(p) model, an old shock which arrived a he marke more han p periods ago has no effec a all on curren volailiy. Bollerslev (1986) generalizes he ARCH(p) model o he GARCH(p, q) model, such ha : p q 2 i i i 1 i 1 h h where α 1,..., α p, β 1,..., β p, and ω o are consan parameers. i i The GARCH model is an infinie order ARCH model. Empirically, he family of GARCH models has been very successful. Of hese models, he GARCH (1, 1) is preferred in mos cases (survey by Bollerslev e al. (1992)). The (1,1) in GARCH (1,1) indicaes ha h is based on he mos recen observaions of ε 2, and he mos recen esimae of he variance rae. The more general GARCH (p,q) model calculaes 2 h from he mos recen p observaions on ε and he mos recen q esimaes of he variance rae. In he GARCH(1, 1) model, he effec of a reurn shock on curren volailiy declines geomerically over ime. Seing ω = γ*v L, where V L is he long-run average variance rae and, γ is he weigh we apply o i, he GARCH(1,1) model can be wrien as: h = γ* V L + α* ε β*h -1, Once ω, α and β have been esimaed, we can calculae γ as (1- α β). The long-erm variance V L can hen be calculaed as ω/ γ. For a sable GARCH(1,1) process, we require α + β < 1. Oherwise he weigh applied o he long-erm variance is negaive. The ARCH (or α ) effec 11

12 indicaes he shor run persisence of shocks, while he GARCH (or β ) effec indicaes he conribuion of shocks o long run persisence (namely, α + β ). Subsiuing γ = 1 α β in he above equaion, he variance rae esimaed a he end of day n- 1 for day n is : On day (n+k) in he fuure, we have : h h k h V V L 2 ( 1 ) VL 1 h 1 L 2 ( VL ) ( h 1 V 1 L 2 ( k VL ) ( h k 1 1 L The expeced value of ε 2 n+k-1 is h n+k-1. Hence : E ( h k VL ) ( ) E( h k 1 VL ), where E denoes he expeced value. Using his equaion repeaedly yields : k E ( h k ) VL ( ) ( h VL ) This equaion forecass he volailiy on day (n+k) using he informaion available a he end of day n-1. When α + β <1, he final erm in he equaion becomes progressively smaller as k increases. Our forecas of he fuure variance rae ends owards V L as we look furher and furher ahead. This analysis emphasizes he poin ha we mus have α + β <1 for a sable GARCH(1,1) process. When α + β >1, he weigh given o he long-erm variance is negaive and he process is mean fleeing raher han mean revering. Despie he apparen success of hese simple parameerizaions, he ARCH and GARCH models canno capure some imporan feaures of he daa. The mos ineresing feaure no addressed by hese models is he leverage or asymmeric effec. A reurn r i, displays asymmeric volailiy if : var [r i, +1 / I, ε i, < 0] - ζ 2 i, > var [r i, +1 / I, ε i, >0] - ζ 2 i,, where r i, is he reurn of he sock of firm i, and : r i, + 1 = E(r i, + 1 / I ) + ε i, +1 ζ 2 i,+1 = var(r i, +1 / I ) In oher words, negaive unanicipaed reurns resul in an upward revision of he condiional volailiy, whereas posiive unanicipaed reurns resul in a smaller upward or even a downward revision of he condiional volailiy. ) V ) 12

13 This effec suggess ha a symmery consrain on he condiional variance funcion in pas ε 's is inappropriae. Many volailiy models have been proposed o incorporae he leverage effec. The wo mos widely used are he EGARCH (Nelson (1991)) and he GJR (Glosen, Jagannahan and Runkle (1993)) models. The condiional variances in boh models depend upon boh he signs and magniudes of he reurns, and hence are asymmeric in heir response o posiive and negaive reurns. Nelson proposed he EGARCH model o overcome some weaknesses of he GARCH mode in handling financial ime series. The EGARCH model, unlike he linear GARCH models, uses logged condiional variance o relax he posiiveness consrain of model coefficiens and easily inerpres he persisence of shocks as condiional variance. Therefore, i has been exensively cied in lieraure as he asymmeric GARCH model. Exponenial GARCH (p,q) : log( h ) q p j log( h j ) j 1 i 1 i h i i k r 1 k h k k, where r is he asymmeric level. Exponenial GARCH (1,1) : log( h ) log( h 1 ) 1 h 1 1 h 1 2 /, where ω, β, γ, and α are consan parameers. Nelson's original specificaion for he log condiional variance is a resriced version of: log( h ) q p r i i j log( h j ) i E j 1 i 1 h i h i k 1 k h k k, which differs slighly from he specificaion above. Esimaing his model will yield idenical esimaes excep for he inercep erm ω, which will differ in a manner ha depends upon he disribuional assumpion and he asymmery order p. For example, in a p =1 model wih a normal disribuion, he difference will be α 1* 2 /. 13

14 The EGARCH (1,1) model is asymmeric because he level of ε - 1 / h 1 is included wih a coefficien γ. Since his coefficien is ypically negaive, posiive reurn shocks generae less volailiy hen negaive reurn shocks, all else being equal. The EGARCH model differs from he sandard GARCH model in hree main respecs: 1. The EGARCH model allows good news and bad news o have a differen impac on volailiy, while he sandard GARCH model does no 2. The EGARCH model allows big news o have a greaer impac on volailiy han he sandard GARCH model. 3. The EGARCH model imposes no consrains on he parameers o ensure non-negaiviy of he condiional variance. GJR (Threshold) GARCH : h h S, where S if 0, S 0 oherwise The variable S - 1 is a dummy variable equal o one if ε 1 > 0, and equal o zero oherwise, so in his case here are wo ypes of shocks. There is a squared reurn and here is a variable ha is he squared reurn when reurns are negaive, and zero oherwise. On average, his is half as big as he variance, so i mus be doubled implying ha he weighs are half as big. In his model, good news, ε 1 > 0, and bad news, ε 1 < 0, have differen effecs on he condiional variance; good news has an impac of α, while bad news has an impac of α + γ. If γ > 0, bad news increases volailiy, and we say ha here is a leverage effec. If, γ 0, he news impac is asymmeric. The ease of inerpreaion and applicaion has also made he GJR(p,q) model very popular among financial praciioners. The GARCH model is a special case of he TARCH model where he hreshold erm is se o zero. A comparison beween he GARCH(1, 1) model and he EGARCH(1, 1) suggess an ineresing meric by which o analyze he effec of news on condiional heeroskedasiciy. Holding consan he informaion daed 2 and earlier, we can examine he implied relaion beween ε -1 and h. Engle calls his curve, wih all lagged condiional variances evaluaed a he level of he uncondiional variance of he sock reurn, he news impac curve because i 14

15 relaes pas reurn shocks o curren volailiy. This curve measures how new informaion is incorporaed ino volailiy esimaes. In he GARCH model, his curve is a quadraic funcion cenered on ε -1 = 0. Tha is, posiive and negaive reurn shocks of he same magniude produce he same amoun of volailiy. Also, larger reurn shocks forecas more volailiy a a rae proporional o he square of he size of he reurn shock. If a negaive reurn shock causes more volailiy han a posiive reurn shock of he same size, he GARCH model underpredics he amoun of volailiy following bad news and overpredics he amoun of volailiy following good news. Furhermore, if large reurn shocks cause more volailiy han a quadraic funcion allows, hen he sandard GARCH model underpredics volailiy afer a large reurn shock and overpredics volailiy afer a small reurn shock. For he EGARCH, i has is minimum a ε -1 = 0, and is exponenially increasing in boh direcions bu wih differen parameers. The news impac curve of he GJR model of Glosen, Jagannahan, and Runkle (1990) is cenered a ε -1 = 0, bu has differen slopes for is posiive and negaive sides. 2. A Parially Non-Parameric ARCH Model An alernaive approach o esimaing he news impac curve is o implemen a nonparameric procedure which allows he daa o reveal he curve direcly. Several approaches are available in he lieraure, including noably, Pagan and Schwer (1990) and Gourieroux and Monfor (1992). Gourieroux and Monfor essenially specify a hisogram for he response of volailiy o lags of he news which hey esimae by maximum likelihood. In heir mos successful model however, hey inroduce a GARCH erm o capure he long memory aspecs. Parially Non-parameric ARCH : We divide he range of { ε } ino m inervals wih break poins η i. Le m - be he number of inervals in he range where ε -1 is negaive. Also, le m+ be he number of inervals in he range where ε -1 is posiive, so ha m = m + + m -. We denoe hese boundaries by he numbers { η -m,, η -1, η 0, η 1,. η m }. These inervals need no be equal size, nor do we need he same number on each side of η 0. For convenience and he abiliy o es symmery, we selec η 0 = 0. If we define 15

16 P i =1, if ε > η i = 0, oherwise, and N i =1, if ε < η -i = 0 oherwise, hen a piecewise linear specificaion of he heeroskedasiciy funcion is : h h m m 1 ipi 1( 1 i ) ini 1( 1 i ) i 0 i 0 This funcional form, which is really a linear spline wih knos a he η i 's, is guaraneed o be coninuous. Beween 0 and η 1 he slope is θ 0 while beween η 1 and η 2 i is θ 0 + θ 1, and so forh. Above η m, he slope is he sum of all he θ 's. If he parial sums a each poin are of he same sign, he shape of he curve is monoonic. To obain beer resoluion wih larger samples, we increase m. This is an example of he mehod of sieves approach o nonparameric esimaion. A larger value of m can be inerpreed as a smaller bandwidh, which will give lower bias and higher variance o each poin on he curve. 3. Individual Socks Cross Secional Regression In he second par of his paper, I invesigae wheher he absolue size of he asymmery for each of he individual socks in he seleced 12 sample is linked o he financial leverage. I adop he EGARCH (1,1) specificaion o es for asymmeric volailiy in individual sock reurns. Given he daa for he reurns R, esimaes for he parameer vecor θ = (ω, β, γ, α), for each sock are obained by maximizing he log-likelihood of he reurns over he sample period. The general specificaion for he mean equaion is : R = α 1 + β 1 *R -1 + ε The erm β 1 *R -1 is used o accoun for any auocorrelaion ha may arise due o nonsynchronous rading. I also augmen he mean equaion wih a number of AR erms in he cases where hey appear o be significan. While some auhors argue ha here is no need for more han one AR erm, we find ha in some cases higher-order AR erms are also significan. Then, following Koumos and Saidi (1995) I esimae he following cross secion regression : 16

17 γ i = a 1 + a 2 *(D/E) i + a 3 *(A) i + u i for i =1,.,n,where n is number of socks, γ i is he absolue value of he degree of asymmery discussed earlier, (D/E) i is some measure of financial leverage, (A) i is asse size, u i is an error erm and a 1, a 2 and a 3 are coefficiens o be esimaed. The variable (A) i is used o accoun for heeroskedasiciy in u i due o firm size. A posiive and saisically significan a 2 coefficien implies ha variaions in he asymmeric response of volailiy o shocks can be aribued o variaions in he deb o equiy raio across firms. I now urn o he descripion of he daa used and he analysis of he empirical findings. IV Empirical Daa and Resuls 1.Preliminary daa analysis The empirical par of his paper deals wih he daily reurn raes of he Buchares Exchange Trading Composie Index (BET-C) for he period saring from April 16, 1998 (index launch dae) hrough June 15, 2008 (2533 obs.) and a subsample period from November 1, 2004 hrough June 1, 2008 (895 obs.). The daa were obained from he Buchares Sock Exchange websie and he daabases of wo brokerage companies. The series of he daily sock index has been adjused for dividends and splis. Daily reurns for he index were calculaed as he percen logarihmic difference in he daily sock index, i.e., R = 100*(ln P - ln P -1 ). The series of coninuously compounded index reurns obained his way is saionary (he null of a uni roo is clearly rejeced) for boh daa samples, as we can see from he ADF es saisics presened in Table 1 and 2. A graphic represenaion of he wo series of daa is given in Figures 1 and 2. My firs analysis of he whole range of daa available on he index since is launch dae proved unsaisfacory in erms of deecing presence of asymmeric volailiy. This proved o be because of he beginning period of he index. A quick view of Figure 2 indicaes ha he period from 1998 o 2004 was aypicall from he poin of view of even an emerging marke. The index had very low flucuaions for mos of his period, saying mainly in he range of

18 poins, hen rose slowly owards is launch level of 1000 poins. Neverheless, he sandard deviaion of he reurn series was (see descripive saisics Table 3), higher even han he sandard deviaion of he reurn series sample beween (which is 1.485, as we can see in he descripive saisics Table 4), period in which he index level flucuaed beween a minimum of poins and a maximum of poins. Since our focus is on he condiional variance, raher han he condiional mean, I concenrae on he unpredicable par of he sock reurns, as obained hrough a procedure similar o he one in Engle and Ng (1993). The procedure involves an auoregressive regression which removes he predicable par of he reurn series. Engle and Ng regress heir series y of daily reurns of he Japanese Topix Index on a consan and y -1,..y -6. Auocorrelaions are correlaions calculaed beween he value of a random variable oday and is value some days in he pas. Predicabiliy may show up as significan auocorrelaions in reurns and volailiy clusering will show up as significan auocorrelaions in squared or absolue reurns. From sudying he correlogram of he BET-C daily reurn series, we see ha auocorrelaion definiely exiss, and here is a significan spike a lag 7. (Table 5). The auocorrelaion in index reurn has been aribued o nonsynchronous rading. An explanaion for his phenomenon is offered, for example, in Lo and McKinley (1990). Supposing ha he reurns o socks i and j are emporally independen, bu i rades less frequenly han j, if news affecing he aggregae sock marke arrives near he close of he marke on one day, i is more likely ha j's end-ofday price will reflec his informaion han i s simply because i may no rade afer he news arrives. Of course, i will respond o his informaion evenually bu he fac ha i responds wih a lag induces spurious cross-auocorrelaion beween he closing prices of i and j. As a resul, a porfolio consising of securiies i and j will exhibi serial dependence even hough he underlying daa-generaing process was assumed o be emporally independen So, o resume wih our analysis, denoing by y he rae of reurn of he BET-C index from day -1 o day, in order o ge he unpredicable par of he reurn series I regressed y on a consan and y -1,..y -7 : y = c + α 1 * y α 7 * y -7 + ε. 18

19 The resuls from his mean adjusmen regression are available in Table 6 and he correlogram of he residuals obained from his regression is available in Table 7. From he Ljung-Box es saisic for welfh-order serial correlaion for he levels, we find no significan serial correlaion lef in he sock reurns series afer our adjusmen procedure. The coefficiens of skewness and kurosis boh indicae ha he unpredicable sock reurns, he ε's, have a disribuion which is skewed o he lef and fla ailed. RESID01 Mean -7.59E-17 Median Maximum Minimum Sd. Dev Skewness Kurosis Furhermore, he Ljung-box es saisic for welfh-order serial correlaions in he squares srongly suggess he presence of ime-varying volailiy (see Table 8). 2. The GARCH model, he EGARCH model and he TGARCH model. Using he unpredicable sock index reurns series as he daa series, we esimae he sandard GARCH(1, 1) model, as well as wo oher parameric models which are capable of capuring he leverage and size effecs : he Exponenial-GARCH(1, 1) and he Threshold GARCH (1,1). In comparing five models ha allow for asymmeric impacs of shocks on volailiy, Engle and Ng(1993) find hese laer wo o have he bes parameerisaion. In his paper, I fi he above menioned models model for all daa series by maximizing he loglikelihood funcion for he model, assuming ha ε is condiionally normally disribued. The raionale for assuming condiional normaliy is predominanly ease of compuaion. However, as shown by Bollerslev and Wooldridge (1992), quasi-maximum likelihood esimaors using condiional normaliy of he error erms yield consisen and asympoically normal parameer esimaes as long as he condiional means and variances are correcly specified, even when he errors are no condiionally normal. All my inference is based on robus sandard errors from 19

20 he maximum likelihood esimaion, employing he procedures described in Bollerslev and Wooldridge (1992). All he models are implemened using he EViews economeric sofware. Firs we fi he EGARCH(1,1) model o he period of daily index reurn observaions saring April 16, The resul, presened in Table 9, is indicaive of he fac ha an asymmeric effec is no saisically significan (he coefficien γ corresponding o he ε -1 / h 1 erm isn saisically significan when compuing wih robus sandard errors or asympoically sandard errors), so here is no need o furher esimae he TGARCH model. The probable explanaion for he resul I have obained was presened in he firs par of his secion, and he conclusion may be ha a GARCH specificaion is beer suied for his daa series. The esimaion oupu from a GARCH(1,1) 1 model is : h = * ε * h -1 As we can see α + β = < 1, so he process is sable, he weigh applied o he long-run average variance rae γ = and he level of he long-run variance rae is V L = This corresponds o a volailiy of or 1.59% per day. We now move on modelling he condiional volailiy of he sample series of daily BET-C index reurns, from November 1, 2004 hrough June 1, As menioned preaviously, he model specificaion I use for he mean equaion is : Y = c + Y -1 +.Y -7 + ε, ε = η * h, where η is a sequence of normally, independenly and idenically disribued random variables wih zero mean and uni variance. (η ~ N(0,1)). The esimaion oupu(see Table 10) from he GARCH(1,1) model is : h = * ε * h -1 1 A GARCH(1,1) specificaion for his firs series of daa yielded higher log likelihood when compared o a GARCH(2,2) model. The (1,2) and (2,1) specificaions were also esimaed, bu he resuls were unsaisfacory. 20

21 (0.000) (0.000) (0.000) Again we have a sable process, α + β = < 1, and a long-run volailiy rae of 1,57% per day. The esimaed parameer for ε -1 2 in his equaion is lower compared o he one obained when we have fi he GARCH model o he longer series of daily reurns, meaning ha less weigh in he nex period s esimaion of volailiy is aribued o conemporaneous shocks on reurns, and more weigh is given o he mos recen esimaion of condiional sandard variance. The EGARCH (1,1) model and TGARCH(1,1) model are esimaed wih boh asympoic sandard errors and robus sandard errors. The esimaion resuls in Table indicae ha he parameers corresponding o he ε -1 / h 1 erm in he EGARCH is significan and negaive using boh sandard and robus sandard errors. The parameer corresponding o he S -1 2 ε -1 2 erm in he GJR is significan and posiive using boh sandard and robus sandard errors. All hese resuls are consisen wih he hypohesis ha negaive reurn shocks cause higher volailiy han posiive reurn shocks. We can also see ha he sandard GARCH(1, 1) has a lower log-likelihood han boh of hese leverage or asymmeric models. The GJR and he EGARCH yield similar log-likelihood. EGARCH : log( h ) log( h 1 ) h h 1 2 / TGARCH : h h S 1 1 In his laer model esimaion, he asymmeric effec, γ = , measures he conribuion of shocks o boh shor run persisence, α + 2, and long run persisence α + β + 2. The weighs now compued on he long-run average, he previous forecas, he symmeric news, and he negaive news are (0.0002, , , ) respecively. Since α + β + 2 < 1, he weigh applied o he long-run variance rae is no negaive and he process is sable. Clearly he asymmery is imporan since he las erm would be zero oherwise. In fac, negaive reurns in his model have more han wo imes he effec of posiive reurns on fuure variances. 21

22 The level of significance I obain for he coefficiens of he model erms governing asymmery is highly significan wih asympoic sandard errors (1% level of significance), and significan wih robus sandard errors (5% level of significance for he EGARCH and slighly over 5% for TGARCH 1 ). Robus -raios are designed o be insensiive o deparures from normaliy, especially exreme observaions. The effecs of significan spikes in volailiy on asympoic -raios and robus - raios are dramaically differen (McAleer and Ng (2002)). Each spike in volailiy increases he asympoic -raios bu decreases he robus -raios, wih he magniudes of he shifs being far greaer for he asympoic -raios. The conclusion I draw is ha here is asymmeric volailiy in he daily BET-C reurn series for he las 4 years, wih he noe ha i is probably parly deermined by he presence of exreme observaions. As we could see earlier in his paper, he kurosis of he unpredicable sock reurns series is quie high a 6.81 and ha is srong evidence ha he exremes are more subsanial han would be expeced from a normal random variable. In diagnosic checks, he Ljung-Box es saisic for 15 h order serial correlaions in he squared normalized residuals is no significan for neiher GARCH, EGARCH or TGARCH model specificaion. From his poin of view we can say ha all hree models appear o have done a good job in explaining he daa and largely removing auocorrelaion. However, he Ljung-Box es does no have much power in deecing misspecificaions relaed o he leverage or asymmeric effecs. In order o compare he models from his poin of view, I used diagnosic ess as suggesed by Engle and Ng : he Sign Bias Tes, he Negaive Size Bias Tes, and he Posiive Size Bias Tes. These ess examine wheher we can predic he squared normalized residual by some variables observed in he pas which are no included in he volailiy model being used. If hese variables can predic he squared normalized residual, hen - he variance model is misspecified. The sign bias es considers he variable S -1 a dummy 1 Asymmeric effecs in he daa are capured by γ, wih γ > 0. Since heory suggess ha he coefficien on S -1 2 ε -1 2 canno be negaive, hen a one-sided es will rejec he zero null hypohesis a he 5% level. 22

23 variable ha akes a value of one when ε 1-1 is negaive and zero oherwise. This es examines he impac of posiive and negaive reurn shocks on volailiy no prediced by he model under - consideraion. The negaive size bias es uilizes he variable S -1 * ε- 1. I focuses on he differen effecs ha large and small negaive reurn shocks have on volailiy which is no prediced by he volailiy model. The posiive size bias es uilizes he variable S -1 +* ε - 1, where S -1 + = 1 - S I focuses on he differen impacs ha large and small posiive reurn shocks may have on volailiy, which are no explained by he volailiy model. To conduc hese ess joinly, we can consider he regression : 2 v a b1s 1 b2s 1 1 b3s 1 1 e where, v = ε / h is he normalized residual, a, b 1, b 2, and b 3 are consan coefficiens and e is an i.i.d. error erm. The join es is he LM es for adding he hree variables in he variance equaion under he mainained specificaion. The es saisic is equal o T imes he R-squared from his regression. If he volailiy model being used is correc, hen b1 = b2= b3 = 0 and e is i.i.d. The join diagnosic es resul for he EGARCH(1,1) model we have fied earlier is : For he TGARCH(1,1) : For he GARCH (1,1) : v 2 = * S * S -1 - * ε * S -1 + * ε e (0.00) (0.67) (0.78) (0.91) v 2 = * S * S -1 - * ε * S -1 + * ε e (0.00) (0.83) (0.99) (0.72) v 2 = * S * S -1 - * ε * S -1 + * ε e robus p-values in paranheses. (0.00) (0.66) (0.56) (0.18), 2 ε -1 being in urn he series of sandardized residuals from he GARCH, EGARCH and TGARCH models 23

24 These resuls are also available in Table 15 in Annexes ogeher wih a join es saisic calculaed as T*R 2, which asympoically follows a χ2 disribuion wih 3 degrees of freedom under he null hypohesis of no asymmeric effecs (b1 = b2 = b3 = 0). Alhough he join diagnosic es for all hree predicable condiional volailiy models indicae ha he squared normalized residual canno be prediced by some variables observed in he pas which are no included in he volailiy model, he generally lower probabiliies (and especially much lower rejecion probabiliy of b 3 =0) in he join es for he GARCH model indicaes ha he asymmeric volailiy models are beer suied o our daa series and ha he GARCH may leave room for Posiive Sign Bias. Indeed compuing he Posiive Sign Bias Tes alone for he GARCH(1,1) model, in he following form : v 2 = a + b 3 * S + -1 * ε -1, yields To conclude, a he 5% level of significance, he GARCH(1,1) esimaed for he daily reurns series of he BET-C index allows he size of posiive shocks o influence volailiy more han he size of negaive shocks. Such a bias is no encounered when fiing EGARCH or TGARCH models o he daa series. 2 1 Summary Saisics of he Condiional Variance Esimaes Mean Sd. Dev Min. Max. Skewness Kurosis e h GARCH h EGARCH h TGARCH is he squared unpredicable reurn obained from he adjusmen regression in Par 1 of his secion. 24

25 As we can see he condiional variance produced by he EGARCH and TGARCH have he highes variaion over ime. The uncondiional variance of he condiional variance (he kurosis) is lower han he uncondiional variance of he squared residual for all hree models, a sign ha h is correcly specified in all cases. Neverheless he EGARCH and TGARCH models seem o capure he characerisics of he squared reurns ime series bes. 3. The Parially Non-Parameric ARCH Model. I now urn o he parially non-parameric model inroduced by Engle and Ng (1993) and presened earlier in he mehodology describing secion. I aemp o furher explain he volailiy process of he BET-C index for he period November 1, 2004 hrough June 1, 2008 using his mehod. Non-parameric models differ from parameric models in ha he model srucure is no specified a priori bu is insead deermined from daa. The erm nonparameric is no mean o imply ha such models compleely lack parameers bu ha he number and naure of he parameers are flexible and no fixed in advance. Nonparameric mehods are ofen referred o as disribuion free mehods as hey do no rely on assumpions ha he daa are drawn from a given probabiliy disribuion. As I have preaviously menioned in Secion II, I will work wih he unpredicable par of he reurn series, ε, as obained hrough an AR(7) mean adjusmen regression. The { ε } series is divided ino m inervals wih break poins η i. Since he purpose of my sudy is o invesigae he impac ha reurn shocks of differen signs and magniudes have on he nex period s BET-C index s condiional volailiy I sudy he order saisics of he daa series in order o choose he η i s. Neverheless, for purposes of symmery and abiliy o compare negaive wih posiive reurn shocks, we will choose η 0 = 0 1 and he same number of equally spaced inervals on each side of η 0. My series of unpredicable reurns has is maximum a (ha is 6.45% per day - highes reurn over he sample period) and is minimum a (ha is -9.28%). The sandard deviaion of he series is or 1.462% per day. Based on hese order saisics and 1 Also he median value of he series ( ) is quie close o 0, so we would roughly have he same number of observaions on each side of η 0 25

26 following Engle and Ng, I choose η i = i * ζ for i = 0, 4, 3, 2, 1, where ζ is he uncondiional sandard deviaion of ε. Hence he equaion o be esimaed for he parially nonparameric ARCH model is : h = ω + β * h i 0 θ i * P i-1 * (ε -1 i * ζ) + 4 i 0 δ i * N i-1 * (ε -1 + i * ζ), where P i-1 is a dummy variable ha akes he value of 1 if ε -1 > i*ζ and he value of 0 oherwise, and N i-1 is a dummy variable ha akes he value of 1 if ε -1 < -i*ζ and a value of 0 oherwise. The resul of he esimaion is (p-values in parenhesis below coefficien esimae) : h = * h * P 0-1 * ε * N 0-1 * ε -1 (0.6809) (0.0068) * P 1-1 * (ε -1 ζ) * N 1-1 * (ε -1 + ζ) (0.0052) (0.0003) * P 2-1 * (ε -1 2*ζ) * N 2-1 * (ε *ζ) (0.1391) (0.3136) * P 3-1 * (ε -1 3*ζ) * N 3-1 * (ε *ζ) (0.4421) (0.0653) * P 4-1 * (ε -1 4*ζ) * N 4-1 * (ε *ζ) (0.6831) (0.1654) As we can see from his esimaion oupu, if we compare he values of he coefficiens corresponding o he erms P i-1 * (ε -1 i * ζ) o heir counerpars N i-1 * (ε -1 + i * ζ), i is primarily he negaive shocks ha impac upon volailiy, as negaive ε -1 s cause more volailiy han posiive ε -1 s of equal absolue size. Moreover, only he coefficiens for posiive shocks greaer han he uncondiional sandard deviaion of he series, ζ, seem o inflic saisically significan upon volailiy, whereas negaive shocks of magniudes boh under and over ζ modify he nex period s condiional volailiy esimae. This finding suggess an asymmeric effec. The negaive coefficiens of he posiive shocks for i=2,4 and he posiive coefficien of he negaive shock for i=3 are somehow surprising, bu hey may be driven only by a few ouliers, since very few values of he series of daa lie beyond he 2 sandard deviaions border as shown in he hisogram figure below. 26

27 Thus he nonparameric esimaion resuls indicae ha he rue slope of he news impac curve as defined in mehodology secion of his paper is probably seeper on he negaive side. 3. A cross secional analysis of he dependence beween he degree of asmmery and he leverage raio For his par of my paper he purpose was o invesigae he presence of asymmeric volailiy a he level of reurns of individual socks lised on he Buchares Sock Exchange and, if a sufficien large sample would be found, o hen employ he cross-secion regression mehod of Koumos and Saidi (1995) o deermine wheher he esimaed degree of asymmery, for each sock, is relaed o some measure of financial leverage. This invesigaion was moivaed furhermore by he argumen of Blair, Poon and Taylor (2000). They sae ha if asymmery is absen or a weak effec in he socks and, furhermore, if he leverage effec canno explain he asymmery a he level of individual socks, han leverage canno explain he asymmery in he index, because he leverage level of he index is an aggregae of he leverage levels of individual firms 1. The dividend and splis adjused daily reurns were obained from he BSE websie and cover he period from June 1, 2004 o June In sudying he daily sock reurns for more han 30 companies ha are comprised in he BET- C index and for which daily rading volumes have been somewha significan for he las years, 1 Bekaer and Wu(2000) provide comparisons of volailiy asymmery beween he Nikkei 225 index and a few porofolios of Japanese socks, based upon mulivariae ARCH models. 27

28 I discovered only eleven for which esimaes for he parameer γ governing asymmery in an EGARCH(1,1) specificaion was saisically significan. Among hese here are wo banks (BRD and TLV), four indusrial companies (ALR, ART, ARS,TBM), wo pharmaceuical companies (BIO and SCD), wo oil indusry relaed companies (PEI and RRC) and one realesae developer, IMP. In order o enlarge he sample and o ge more saisical relevance from a cross-secional regression on his daa, I searched ouside he index for a few oher companies ha have been rading more inensively for he las years.there was jus one add-on o he sample, namely DUCL. So he final sample is made up of welve companies. Alhough he sandard period for which I analyze he daily reurns is June 1, 2004 o June for mos of he companies in he sample and is made roughly of 1010 observaions for each individual company, for hree of he companies he period is exended backwards up o 2002 due o significan periods of ime in which heir price didn flucuae due o emporary rading inerrupions and which affeced significanly a possible asymmeric condiional volailiy response o shocks. These companies are ALR and DUCL. As I menioned earlier he regression akes he following form : γ i = a 1 + a 2 *(D/E) i + a 3 *(A) i + u i, for i =1,.,n,where n is number of socks, γ i is he absolue value of he degree of asymmery discussed earlier, (D/E) i is some measure of financial leverage, (A) i is asse size, u i is an error erm and a 1, a 2 and a 3 are coefficiens o be esimaed. I acually esimae four measures of financial leverage, wo of hem based on he book value of equiy (sum of common sock, capial surplus, reained earnings) and he oher wo based on he marke value of equiy (calculaed as end-of-he period s price of common sock muliplied by he end-of-he-period s shares of common sock ousanding, where one period represens six monhs). The lengh of he period was deermined by he availabiliy of biannual financial saemens for he analyzed period. Accordingly, he leverage raios are : LR1 = long erm deb / book value of equiy LR2 = (long erm deb+shor erm deb) / book value of equiy LR3 = long erm deb / marke value of equiy LR4 = (long erm deb+shor erm deb) / marke value of equiy. So here are four regressions o be esimaed. I approximae he size of each company by he logarihm of is oal asses, denoed (A i ). 28

29 Again, since my focus is on he condiional variance, raher han he condiional mean, I concenrae on he unpredicable par of he sock reurns series for each sock as obained hrough an AR(p) auoregressive regression. The general specificaion for he mean equaion is R = α 1 + β 1 *R -1 + ε I also augmen he mean equaion wih a number of AR erms in he cases where hey appear o be significan. The exac AR specificaion is indened afer he symbol of each sock in he following able. The parameer vecors θ i = (ω i, β i, γ i, α i ) resuling from fiing an EGARCH (1,1) model o he series of unpredicable reurns for each sock are as follows : ω β γ α BRD AR(1) TLV AR(3) ALR AR(1) ART AR(0) TBM AR(5) BIO AR(1) SCD AR(1) PEI AR(5) RRC AR(0) IMP AR(0) ARS AR(6) DUCL AR(3) The resuls from he esimaed regressions are as follows : 29

30 The cross secion analysis reveals ha, unil now, differences in he degree of asymmery canno be aribued o differences in he degree of leverage in suppor of Chrisie s(1982) and Black s(1976) earlier findings. In his research for he 30 companies making up he DowJonesIndusrialAverage Index, Koumos (1995) finds a significan posiive relaionship beween he degree of asymmeric volailiy and he degree of leverage in only one of he regressions, which uses a leverage measure based on he book-value of equiy, wih an adjused R 2 of roughly 16%. Since he companies in he sample I used are probably he mos liquid and mos frequenly raded from he BET-C index, i can be said ha he leverage effec hypohesis was esed under he mos favorable circumsances. Furher research may es if ime-varying risk premiums can explain he asymmery. 30

31 V. Concluding Remarks The asymmeric response of condiional variance o shocks of differing signs and sizes is a sylized fac of volailiy which we mee in inernaional well developed sock markes boh a he marke index level and a individual sock reurn level. Recen sudies, which find evidence of asymmeric volailiy in emerging sock markes, have also been performed. In sudying he evoluion of he mos comprising index on he Romanian Sock Marke, he BET-C Index, I find proof of asymmeric response of he condiional variance of he index o negaive and posiive shocks, for he laer par of is hisory, November 1, 2004 hrough June 1, I aribue his finding o significan changes in erms of sock marke developmen from he preavious period of April 16, 1998 (index launch dae) hrough o December 2003, as esing for asymmeric volailiy for he whole hisorical period of he BET-C index proves unsaisfacory in erms of deecing asymmery In esing for asymmeric volailiy, I employ economeric models like he EGARCH, he TGARCH and a parially nonparameric ARCH model as inroduced by Engle and Ng (2003). These models seem o capure he characerisics of he unpredicable par of he index reurn series, as obained hrough an AR(7) regression, beer han a symmeric GARCH(1,1) specificaion, for he November 1, 2004 hrough June 1, 2008 period. On average, I find ha negaive shocks raise he nex period s condiional reurn variance by more han wo imes han posiive shocks. Using robus -raios as inroduced by Bollerslev and Woolridge, I find significance for he coefficiens of he erms governing asymmery in he EGARCH and TGARCH models a he 5% level of significance, whils using asympoic -raios significance is obained a he 1% level. This may be proof ha in par he asymmery is deermined by significan spikes in volailiy as shown by McAleer and Ng. The nonparameric approach which allows he daa series o unveil he news impac curve direcly also shows ha i is primarily negaive shocks ha raise he nex period s condiional variance. In he las par of my paper I es if variaions in he degree of financial leverage among a sample of welve individual socks from he BET-C index ha exhibi asymmeric volailiy can explain he variaions in he degree of asymmery. I find no proof of such a dependency so fuure research should concenrae on he ime-varying risk premium heory. 31

32 BIBLIOGRAPHY Baillie R. and De Gennaro R. (1990), Sock Reurns and Volailiy, Journal of Financial and Quaniaive Analysis, Vol. 25, No. 2, pp Bekaer Geer and C.R. Harvey (1997), Emerging Equiy Marke Volailiy, Journal of Financial Economics, Bekaer G. and Guojun W., (2000), Asymmeric Volailiy and Risk in Equiy Markes, The Review of Financial Sudies, vol 13, no. 1, 1-42 Bollerslev T. (1987), A Condiionally Heeroskedasic Time Series Model for Speculaive Prices and Raes of Reurn, The Review of Economics and Saisics, Vol. 69, No. 3, pp Bollerslev T., Livinova J., and Tauchen G. (2006), Leverage and Volailiy Feedback Effecs in High-Frequency Daa, Journal of Financial Economerics, vol. 4, no. 3, Campbell J.Y. and L. Henschel (1991), No News is Good News : An Asymmeric Model of Changing Volailiy in Sock Reurns, NBER Working Paper no Chiang C.T. and Doong S., (2001), Empirical Analysis of Sock Reurns and Volailiy: Evidence from Seven Asian Sock Markes Based on TAR-GARCH Model, Review of Quaniaive Finance and Accouning, 17, , Chrisie A.A.(1982), The Sochasic Behaviour of Common Sock Variances Value, Leverage and Ineres Rae Effecs, Journal of Financial Economics, 10, Engle R.., and V.K. Ng. (1993), Measuring and Tesing he Impac of News on Volailiy, The Journal of Finance, Vol. 48, No. 5, pp Engle R. (2004), Risk and Volailiy : Economeric Models and Financial Pracice, The American Economic Review, vol. 94, no. 3, Ercan Balaban (2006), Comparaive Forecasing Performance of Symmeric and Asymmeric Condiional Volailiy Models of an Exchange Rae, Universiy of Edinburgh Working Paper French K., Schwer G. and Sambaugh R. (1987), Expeced Sock reurns and Volailiy, Journal of Financial Economics, 19, 3-29 Glosen L., Jagannahan R. and Runkle D. (1993), On he Relaion beween he Expeced Value and he Volailiy of he Nominal Excess Reurn on Socks, Journal of Finance, Vol. 48, No. 5, pp

33 Guoujun W. (2001), The Deerminans of Asymmeric Volailiy, The Review of Financial Sudies, Vol. 14, No. 3, pp Koumos G. (1998), Asymmeries in he Condiional Mean and he Condiional Variance: Evidence From Nine Sock Markes, Journal of Economics and Business, 50, Henry, O. & Sharma, J., 1998., "Asymmeric Condiional Volailiy and Firm Size: Evidence from Ausralian Equiy Porfolios," Deparmen of Economics - Working Papers Series 617, The Universiy of Melbourne. Jinho B, Chang-Jin Kim, Nelson Charles, 2004, Why are Sock Reurns and Volailiy Negaively Correlaed?, Journal of Poliical Finance, vol. 14, 2007 McAleer M and Ng G. (2002), Recursive Modelling of Symmeric and Asymmeric Volailiy in he Presence of Exreme Observaions, Universiy of Wesern Ausralia, Working Paper Nelson B. Daniel (1991), Condiional Heeroskedasiciy in Asse Reurns: A New Approach, Economerica, Vol. 59, No. 2, (Mar., 1991), pp Pindyck S.R. (1984), Risk, Inflaion, and he Sock Marke, The American Economic Review, Vol. 74, No. 3, pp Rabemananjara R. and Zakoian J. M. (1993), Journal of Applied Economerics, Vol. 8, No. 1, (Jan. - Mar., 1993), pp Schwer W.G. (1989), Why Does Sock Marke Volailiy Change Over Time?, Journal of Finance, Vol. 44, No. 5, pp

34 Figure 1. BET-C Index Composiion as of July

35 Figure 2. BET-C Index Level and Reurn Evoluion April 16, June 15,

36 Figure 3 - BET-C Index Level and Reurn Evoluion November 1, June 15,

37 Table 1 37

38 Table 2 Table 3 Descripive Saisics for he daily index reurn series Dec Dec RD Mean Median Maximum Minimum Sd. Dev Skewness Kurosis

39 Table 4 - Descripive Saisics for he daily index reurn series Nov Jun RD Mean Median Maximum Minimum Sd. Dev Skewness Kurosis Table 5 Correlogram of daily index reurns Nov Jun

40 Table 6 Mean Adjusmen Regression for daily index reurns Nov Jun Table 7 Correlogram of residuals (unpredicable reurns series) 40

41 Table 8 Correlogram of squared residuals (unpredicable reurns series) 41

42 Table 9 EGARCH(1,1) esimaion oupu for April 16, June 15, 2008 Table 10 GARCH(1,1) esimaion oupu for Nov Jun

43 Table 11 - EGARCH(1,1) esimaion oupu (asympoic sandard errors) for Nov Jun Table 12 - EGARCH(1,1) esimaion oupu (robus sandard errors) for Nov Jun

44 Table 13 TGARCH (1,1) esimaion oupu (asympoic sandard errors) for Nov Jun Table 14 TGARCH (1,1) esimaion oupu (robus sandard errors) for Nov Jun

45 Table 15 - Join Diagnosic Tes Esimaion Oupu GARCH(1,1).. EGARCH(1,1) TARCH(1,1)... 45

46 Table 16 Parial Nonparameric ARCH esimaion oupu 46