Joanna Olbryś * Asymmetric Impact of Innovations on Volatility in the Case of the US and CEEC 3 Markets: EGARCH Based Approach

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1 D YNAMIC E CONOMETRIC M ODELS DOI: hp://dx.do.org/ /dem Vol. 13 (2013) Submed July 27, 2012 ISSN Acceped Aprl 3, Joanna Olbryś * Asymmerc Impac of Innovaons on Volaly n he Case of he US and CEEC 3 Markes: EGARCH Based Approach A b s r a c. The man goal of hs sudy s o nvesgae he asymmerc mpac of nnovaons on volaly n he case of he US and hree bgges emergng CEEC 3 markes, usng unvarae EGARCH approach. We compare emprcal resuls for boh he whole sample from Jan 3, 2007 o Dec 30, 2011, and wo equal subsamples: he down marke perod, and he up marke perod. Pronounced negave asymmery effecs are presened n he case of all markes, and are especally srong n he down marke perod, whch s closely conneced wh he 2007 US subprme crss perod. K e y w o r d s: volaly, asymmery effec, down and up marke, overlappng nformaon se, unvarae EGARCH model. J E L Classfcaon: C32, C58, G15. Inroducon The US sock marke s found o be he mos nfluenal marke n he world. The resuls of many sudes suppor he evdence for US domnance n he nernaonal sock markes, and herefore he S&P 500, he man ndex of he New York Sock Exchange, s unversally acceped as a benchmark ndex, boh n he case of developed and emergng markes research (e.g. Eun, Shm, 1989; Hamao e al., 1990; Koumos, Booh, 1995; Tse e al., 2003; Syropoulos, 2007; Lee, Sewar, 2010; Baumöhl, Výros, 2010; * Correspondence o: Joanna Olbryś, Faculy of Compuer Scence, Balysok Unversy of Technology, Wejska 45A, Balysok, Poland, e-mal: j.olbrys@pb.edu.pl Ncolaus Coperncus Unversy. All rghs reserved. hp://

2 34 Joanna Olbryś Olbryś, 2013). The recen research evaluaes he ransmsson of he US subprme crss o boh developed and emergng markes. However, he emergng markes responded very srongly o he deerorang suaon n he US fnancal sysem and real economy. For example, Dooley s and Huchson s (2009) regresson even sudy focusng on 15 ypes of news, ndcaes ha a range of fnancal and real economc news emanang from he US had sascally and economcally large mpacs on 14 emergng markes and several news evens unformly moved markes. As a maer of course, here are exremely more bad han good news durng he crss perod. Nelson (1991) pons ou ha researchers begnnng wh Black (1976) found evdence ha sock reurns are negavely correlaed wh changes n reurns volaly,.e. volaly ends o rse n response o bad news (excess reurns lower han expeced) and o fall n response o good news (excess reurns hgher han expeced). The purpose of hs paper s o nvesgae he asymmerc mpac of nnovaons on volaly n he case of hree bgges emergng CEEC 3 1 markes, and (for comparson) for he US sock marke, usng unvarae EGARCH approach (Nelson, 1991). We ry o deal wh he nonsynchronous radng effec II by usng a common radng wndow procedure and esmang suable EGARCH models based on daly open o close logarhmc reurns for he four major sock marke ndexes: S&P 500 (New York), WIG (Warsaw), PX (Prague), and BUX (Budapes). The man goal s o oban an overlappng nformaon se n he case of he CEEC 3 markes, as we es he mpac of common bad and good news. We compare emprcal resuls for boh he whole sample from Jan 3, 2007 o Dec 30, 2011 and wo equal subsamples: Feb 12, 2007 o Mar 9, 2009 as he down marke perod and Mar 10, 2009 o Mar 10, 2011 as he up marke perod. We observe pronounced negave asymmery effecs n he case of all markes, especally n he down marke perod, whch s closely conneced wh he 2007 US subprme crss perod. To he bes of auhor s knowledge, no such comparave nvesgaon has been underaken for he US and CEEC 3 sock markes. As menoned above, he mpac of bad and good news s descrbed n erms of unvarae EGARCH models whle e.g. Büner and Hayo (2012) advocae o ake no consderaon acual news n economc sense (e.g. EMU relaed news, news from he ECB, and he lke) 2. They analyze he 1 Three bgges emergng Cenral and Easern European Counres (CEEC-3), n order of larges populaon sze are: Poland, he Czech Republc, and Hungary (Büner, Hayo, 2012). 2 EMU European Economc and Moneary Unon; ECB European Cenral Bank.

3 Asymmerc Impac of Innovaons on Volaly 35 mpac of news on hree fnancal markes n Poland, he Czech Republc, and Hungary. The remander of he paper s organzed as follows. Secon 1 specfes a mehodologcal background and a bref leraure revew. Frs, we sress he valdy of he nonsynchronous radng problem. Nex, we presen he movaon for he choce of down marke and up marke subperods. A bref heorecal framework concernng he EGARCH(p, q) models s also presened. In Secon 2, we presen he daa and an emprcal analyss of he asymmerc mpac of nnovaons on volaly n he case of he US developed sock marke (as a benchmark marke) and he hree bgges emergng CEEC 3 markes. Then we dscuss he resuls obaned. Concluson recalls he man fndngs and sums hem up. 1. Mehodologcal Background 1.1. The Non-Tradng Problem Some sudes dsngush beween wo nonsynchronous radng effec problems. The frs problem, called nonsynchronous radng effec I, occurs when we analyze one seleced domesc sock marke. Sock radngs do no occur n a synchronous manner. Dfferen socks have dfferen radng frequences, and even for a sngle sock he radng nensy vares from hour o hour and from day o day. The acual me of las ransacon of he sock vares from day o day. As such we ncorrecly assume daly reurns as an equally spaced me seres wh a 24-hour nerval (Tsay, 2010, p. 232). The non radng effec nduces poenally serous bases n he momens and comomens of asse reurns such as her means, varances, covarances, beas, and auocorrelaon and cross-auocorrelaon coeffcens (e.g. Campbell e al., 1997; Doman, 2011). The second and poenally serous problem, called nonsynchronous radng effec II, occurs when we examne he relaons beween sock markes n varous counres. The naonal sock markes are operang n dverse me zones wh dfferen openng and closng mes, hereby makng reurn observaons nonsynchronous (Eun, Shm, 1989). These dfferences arse naurally from he fac ha radng days n dfferen counres are subjec o dfferen naonal and relgous holdays, unexpeced evens, and so forh (Baumöhl, Výros, 2010). Ths paper nvesgaes he asymmerc mpac of nnovaons on volaly n he case of he hree bgges emergng CEEC 3 sock markes, and (for comparson) for he US marke. For hs reason, we have o deal wh he nonsynchronous radng effec II. Many sudes aemped varous mehods

4 36 Joanna Olbryś o deal wh he nonsynchronous radng effec II. Some researchers use weekly or monhly daa o avod he non radng problem. Such soluons, however, may lead o small sample szes and canno capure he nformaon ransmsson n shorer (daly) meframes (Baumöhl, Výros, 2010). Oher papers presen varous daly daa machng procedures. For example, Hamao e al. (1990) dvde daly close o close reurns no her close o open and open o close componens. To examne how a nonsynchronous problem would affec he relaonshps beween seleced markes, some researchers esmae suable GARCH ype models (e.g. mulvarae EGARCH models) based on he open o close reurns (cf. Koumos, Booh, 1995; Tse e al., 2003; Olbrys, 2013). Syropoulos (2007, p. 46) says: ( ) would have been deal o use boh he open and close sock marke prces, n order o reduce poenal non synchronous radng bas beween he US and he European sock markes. In many sudes he followng approach, also called a common radng wndow, s very popular: he daa are colleced for he same daes across he sock markes, removng he daa for hose daes when any seres has a mssng value due o no radng (e.g. Eun, Shm, 1989; Booh e al., 1997; Olbrys, 2013) Movaon for The Choce of Subperods In our research, we compare emprcal resuls of asymmerc effecs of nnovaons on volaly n he case of he US and CEEC 3 markes for boh he whole sample from Jan 3, 2007 o Dec 30, 2011 and wo equal subsamples: Feb 27, 2007 o Mar 9, 2009 as he down marke perod and Mar 10, 2009 o Mar 10, 2011 as he up marke perod (each consss of 476 observaons). Syczewska (2010) proposed somewha dfferen subsamples as crss ( down marke ) and pos-crss ( up marke ) perods, bu we advocae Feb 27, 2007 as he begnnng of he down marke perod followng Dooley and Huchson (2009), and March 9, 2009 as he end of he down marke perod because of he global mnmum of he S&P 500 ndex value n he whole sample acheved on hs day. The overall S&P 500 ndex fell from (Feb 27, 2007) o (March 9, 2009). I los 51.64% of prevous value durng he down marke perod, whch s closely conneced wh he 2007 US subprme crss perod. Dooley and Huchson (2009) focus her analyss on he lnks beween he US and a broad range of emergng equy markes over a subprme crss sample perod from Feb 2007 o March 2009, ncludng Poland, Hungary, and he Czech Republc amongs ohers. Mun and Brooks (2012) exend he Dooley s and Huchson s analyss o a broader se of ndvdual developed and emergng markes, and also

5 Asymmerc Impac of Innovaons on Volaly 37 exend he whole sample perod o Feb 2010 (full 3 years). Frank and Hesse (2009) fnd ha end-february 2007 was a perod when early sgns of sress began o emerge n global markes pror o he me when he subprme crss was revealed n md The Exponenal GARCH Model Many researchers documened ha sock reurn volaly ends o rse followng good and bad news. Ths phenomenon was noed boh for ndvdual socks and for marke ndexes (Braun e al., 1995). Snce Nelson (1991) nroduced he unvarae Exponenal Generalzed Auoregressve Condonally Heeroskedasc (EGARCH) model, some papers employ hs model o capure he asymmerc effec of nnovaons on volaly. Several sudes presen varous applcaons of unvarae and mulvarae EGARCH models. In (Koumos, Booh, 1995) he ransmsson mechansm of prce and volaly spllovers across he New York, Tokyo and London sock markes from hree dfferen me zones s nvesgaed, usng he EGARCH approach. Jane and Dng (2009) propose he mulvarae exenson of Nelson s unvarae EGARCH model and compare her model wh he exsng one gven by Koumos and Booh (1995). Booh e al. (1997) provde he evdence on prce and volaly spllovers among four Scandnavan (Nordc) sock markes. Bhar (2001) apples an exended bvarae EGARCH model o provde evdence of lnkages beween he equy marke and he ndex fuures marke n Ausrala. Reyes (2001) examnes volaly ransfers beween sze based ndexes from he Tokyo Sock Exchange, usng a bvarae EGARCH model. Tse e al. (2003) employ a bvarae EGARCH model ha allows for boh mean and varance spllovers beween he US and Polsh sock markes. Balaban and Bayar (2005) es he relaonshp beween sock marke reurns and her forecas volaly derved from he symmerc and asymmerc GARCH ype models n 14 counres. Lee and Sewar (2010) examne asymmerc effecs on volaly n he case of he Balc and Nordc major sock ndexes, usng boh unvarae and mulvarae EGARCH models. Olbrys (2013) nvesgaes he nerdependence of prce volaly across he US developed sock marke and wo emergng Cenral and Easern European (CEE) markes n Warsaw and Budapes usng a mulvarae modfed EGARCH model. As a maer of fac, he asymmerc effecs of nnovaons on volaly for one seleced domesc sock marke could be well descrbed by he unvarae EGARCH model, alhough s now wdely acceped ha a mulvarae modelng framework (n he case of he group of markes) leads o

6 38 Joanna Olbryś more relevan emprcal models han workng wh separae unvarae models (Bauwens e al., 2006). Bu s worh sressng ha he mulvarae EGARCH model esmaon s parcularly dffcul due o he large number of esmaed parameers. The unvarae me seres R } can be expressed as: { R = μ + ε, (1) where: μ = E( R F 1) s he condonal expecaon of R gven he pas nformaon F 1, ε s he nnovaon of he seres a me. Nelson s unvarae EGARCH(p, q) model can be represened as follows (Tsay, 2010): q 1 1+ β 2 1B + + βq 1B ln (σ ) = α0 + g(z 1, p ) 1 α1b α pb ε = σ z, (2) ε F ~ N(0, σ ), z ~ N(0,1), 1 g(z ) = θ z + γ [ z E( z )], (3) where: σ = Var( R F 1) s he condonal varance of R gven he pas nformaon F 1, α s a consan, 0 B s he back-shf (or lag) operaor such ha Bg(z ) = g(z 1 ), q 1 p 1+ β1b + + β q 1B and 1 α 1 B α p B are polynomals wh zeros ousde he un crcle and have no common facors. The value of g(z ) depends on several elemens. Nelson (1991) pons ou ha o accommodae he asymmerc relaon beween sock reurns and volaly changes, he value of g(z ) mus be a funcon of boh he magnude and he sgn of z. In Eq. (3), g(z ) s a lnear combnaon of z and [ z E( z )] wh coeffcens θ and γ. The erm n he bracke measures he magnude effecs and he coeffcen γ relaes lagged sandardzed nnovaons o volaly n a symmerc way. The erm θ z measures he sgn

7 Asymmerc Impac of Innovaons on Volaly 39 effecs and he coeffcen θ relaes sandardzed shocks o volaly n an asymmerc syle. { g(z ) } =, s an..d. random sequence wh mean zero (Jane, Dng, 2009). For θ < 0 he fuure condonal varances wll ncrease proporonally more as a resul of a negave shock han for a posve shock of he same absolue magnude (Bollerslev, Mkkelsen, 1996). Boh z and [ z E( z )] are zero mean..d. random sequences wh connuous dsrbuons. The asymmery of g(z ) can be easly seen by rewrng as: ( θ + γ ) z γ E( z ) f z 0, g(z ) = (4) ( θ γ ) z γ E( z ) f z < 0. Snce EGARCH(p, q) = EGARCH(1, 1) s a smple case, Eq. (2) becomes: 2 ( ) α B) ln(σ ) = ( 1 α B) α + g(z, (5) Eq. (5) can be rewren (subscrp of α1 s omed) and hen: 2 * 2 ln(σ ) = α0 + α ln(σ 1 ) + g(z 1 ), (6) where α * 0 = cons. The parameer α n Eq. (6) deermnes he nfluence of he pas condonal volaly on he curren condonal volaly. For he condonal volaly process o be saonary, α < 1 s requred. The perssence of volaly may be also quanfed by examnaon of he half lfe ( HL ) defned by: ln( 0. 5 ) HL = (7) ln α whch measures he me perod requred for he nnovaons o be reduced o one half of her orgnal sze. An addonal advanage of he EGARCH model s ha no parameer resrcons are requred o nsure posve varances a all mes (Fszeder, 2009). C, Le R, = 100 ln be he open o close percenage logarhmc reurn a me for marke ( =1,2,3, 4, where 1 = New York, 2 = O, Warsaw,

8 40 Joanna Olbryś 3 = Prague, and 4 = Budapes). Then, he unvarae AR(1) EGARCH(1, 1) model for marke may be wren as follows: R, ln(σ = ϕ 2,, 0 ) = α + ϕ R *, 0, 1 2. Emprcal Resuls + ε + α ln(σ,, 2, 1 ) + θ z + γ [ z E( z 2.1. Daa Descrpon and Prelmnary Sascs The raw daa consss of daly openng and closng prces of major sock marke ndexes for New York (S&P 500 ndex), Warsaw (WIG ndex), Prague (PX ndex), and Budapes (BUX ndex). As menoned n Inroducon, he man goal was o oban he overlappng nformaon se n he case of he CEEC 3 markes, as we esed he mpac of common bad and good news. We used he common radng wndow procedure and removed he daa for hose daes when any seres has a mssng value due o no radng. Thus all he daa are colleced for he same daes across he four markes and fnally here are 1181 observaons for each seres for he perod begnnng Jan 3, 2007 and endng Dec 30, Snce CEEC 3 counres are geographcally close, he radng hours for he markes are abou he same. Tradng a he WSE (WIG ndex) sars a 9:00 a.m. and fnshes a 5:40 p.m. CET (Cenral European Tme). Prague (PX ndex) rades from 9:00 a.m. o 4:30 p.m., Budapes (BUX ndex) rades from 9:00 a.m. o 5:00 p.m. whle he NYSE (S&P 500 ndex) rades from 3:30 p.m. o 10:00 p.m. CET 3. The radng overlap beween he CEEC 3 and New York markes s approxmaely equal o one and a half hours,.e. lae radng n Warsaw, Prague or Budapes corresponds o early radng n New York. We advocae o use daly open o close logarhmc reurns, as hese reurns nform abou he suaon on a gven sock marke beween he openng and closng me. We compue daly close o close, close o open, and open o close logarhmc reurns for he four sock ndexes. Followng Hamao e al. (1990), we dvde daly close-o-close (C C) logarhmc reurns no her close o open (C O) and open o close (O C) componens: C O C C C = ln, C O = ln, O C = ln, (9) C C O 1 1 )]. (8) 3 Sources: hp:// ; hp:// ; hp:// ; hp://bse.hu/.

9 Asymmerc Impac of Innovaons on Volaly 41 we oban consequenly ha a daly close o close logarhmc reurn can be expressed as: O C O C C ln + ln = ln = ln, (10) C 1 O C 1 O C 1 where C and C 1 are he closng prces of days and ( 1), respecvely, and O s he openng prce of day. Noe ha on a gven day, because he CEEC 3 markes open before he US marke, dayme nformaon se from he US marke would have an nfluence on he CEEC 3 markes on he nex day. An nformaon se can be seen n broad erms as he se of all nformaon relevan for prcng an asse a a gven me (Baumöhl, Výros, 2010). Therefore, he nformaon on he openng and closng values of he CEEC 3 and US sock markes ndexes does no belong o he same nformaon se, however, he nformaon se for he CEEC 3 markes s overlappng. Table 1 repors summarzed sascs for he close o close, close o open, and open o close logarhmc reurns for four sock ndexes: S&P 500, WIG, PX, and BUX, as well as sascs esng for normaly and nerdependence. The sample means are no sascally dfferen from zero. The measures for skewness and excess kuross show ha all reurn seres are negavely skewed and hghly lepokurc wh respec o he normal dsrbuon. Lkewse, he Doornk Hansen (2008) es rejecs normaly for each of he reurn seres a he 5 per cen level of sgnfcance. The Ljung Box (1978) sasc a he lag q lnt, where T s he number of daa pons (Tsay, 2010, p. 33), calculaed for boh he reurn and he squared reurn seres, ndcaes he presence of sgnfcan lnear and non-lnear dependences, respecvely, excep he WIG O C and PX O C seres. The lnear dependences may be due o he nonsynchronous radng effec I of he socks ha make up each ndex (e.g. Campbell e al., 1997). The non lnear dependences may be due o he auoregressve condonal heeroskedascy (e.g. Nelson, 1991; Koumos, Booh, 1995; Booh e al., 1997). All calculaons were done usng Grel (Adkns, 2012).

10 42 Joanna Olbryś Table 1. Summarzed sascs for he close o close, close o open, and open o close logarhmc reurns for four sock ndexes: S&P 500, WIG, PX, and BUX S&P 500 C C S&P 500 C O S&P 500 O C WIG C C WIG C O WIG O C PX C C PX C O PX O C BUX C C BUX C O BUX O C Number of obs. Mean Sandard devaon Skewness Excess kuross * 6.53* * 7.29* * 6.62* * 2.63* * 5.38* * 2.83* * 12.66* * 13.35* * 12.00* * 5.67* * 9.61* * 3.81* Doornk Hansen es * * * * * * * * * * * * LB(7) LB 2 (7) 34.42* * 28.13* * 33.84* * 17.57* * 27.44* * * 31.08* * 28.21* * * 52.16* * 49.11* * 19.77* * Noe: he able s based on all sample observaons durng he perod Jan 2, 2007 Dec 31, C-C, C-O, and O-C sand for close-o-close, close-o-open, and open-o-close logarhmc reurns for four sock ndexes (S&P 500, WIG, PX, BUX), respecvely. * denoes sgnfcance a he 5 per cen level. The es sasc for skewness and excess kuross s he convenonal -sasc. The Doornk-Hansen es (2008) has a χ 2 dsrbuon f he null hypohess of normaly s rue. Numbers n brackes are p-values. LB(q) and LB 2 (q) are he Ljung-Box (1978) sascs for reurns and squared reurns, respecvely, dsrbued as χ 2 (q), q lnt, where T s he number of daa pons (Tsay, 2010). The χ 2 (7) crcal value s (5%) Asymmerc Impac of Innovaons on Volaly To examne asymmerc effecs beween posve and negave ndex reurn nnovaons, we frs esmae he unvarae AR(1) EGARCH(1,1) models of he four sock ndexes: S&P 500, WIG, PX, and BUX, n he whole sample perod from Jan 3, 2007 o Dec 30, The robus QML

11 Asymmerc Impac of Innovaons on Volaly 43 (Bollerslev, Wooldrdge, 1992) esmaes of he parameers of he model (8) are presened n Table 2 4. Table 2. Resuls from he AR(1) EGARCH(1, 1) models of he four sock ndexes: S&P 500, WIG, PX, and BUX. Full sample perod from Jan 3, 2007 o Dec 30, 2011 (1181 daly open o close percenage logarhmc reurns) New York ( = 1) Warsaw ( = 2) Prague ( = 3) Budapes ( = 4) Condonal mean equaon φ (0.033) 0.060* (0.029) 0.052* (0.026) 0.092* (0.039),0 φ 0.084* (0.027) (0.026) (0.030) (0.031) Condonal varance equaon α 0.101* (0.020) 0.108* (0.028) 0.166* (0.034) 0.117* (0.030) *,0 α 0.978* (0.007) 0.983* (0.007) 0.977* (0.011) 0.979* (0.010) θ 0.141* (0.020) 0.083* (0.019) 0.047* (0.020) (0.020) γ 0.142* (0.026) 0.144* (0.037) 0.227* (0.049) 0.179* (0.044) Condonal densy parameers ν 7.515* (1.713) * (2.989) 5.743* (0.846) 6.538* (1.178) λ 0.227* (0.041) (0.033) 0.078* (0.039) (0.043) Asymmery effec for marke δ = θ / γ Half lfe (HL) Log lkelhood BIC AIC LB(20) [0.93] [0.82] 7.97 [0.99] [0.67] LB 2 (20) [0.17] [0.81] [0.68] [0.84] Noe: he able s based on all sample observaons durng he perod Jan 3, 2007 Dec 30, 2011; * denoes sgnfcance a he 5 per cen level; he heeroskedasc conssen sandard errors are n parenheses; he varance-covarance marx of he esmaed parameers s based on he QML algorhm; he dsrbuon for he nnovaons s supposed o be skewed ; ν and λ are condonal densy parameers (Lucche, Bale S, 2011, p. 3); he asymmery coeffcen s defned n he ex; he half-lfe s defned n he ex and represens he me akes for he shock o reduce s mpac by one-half; BIC and AIC are he nformaon crerons; LB(20) and LB 2 (20) denoes he Ljung-Box (1978) sascs for sandardzed nnovaons and squared sandardzed nnovaons, respecvely (Balle, Bollerslev, 1990); numbers n brackes are p-values. 4 In he case of all perods analyzed, he choce of an approprae verson of he EGARCH model was conduced based on he BIC and AIC nformaon crerons, and dsrbuons for he nnovaons were supposed o be normal, -Suden, or skewed. As urned ou, he unvarae AR(1) EGARCH(1, 1) models wh skewed as he dsrbuon for he nnovaons are he mos adequae. Due o he space resrcons, deals and calculaons are avalable upon reques.

12 44 Joanna Olbryś For model checkng, he Ljung Box sascs LB(20) for he sandardzed nnovaon process, and LB 2 (20) for he squared sandardzed nnovaons were appled (Balle, Bollerslev, 1990). The evdence s ha here s no seral correlaon or condonal heeroskedascy n he sandardzed nnovaons of he fed models. The esmaed AR(1) EGARCH(1, 1) models are adequae (Tsay, 2010, p. 146). Several resuls presened n Table 2 are worh specal noce. The auoregressve coeffcens ϕ are negave, and hs coeffcen s sascally sgnfcan only for he New York marke. The condonal varance s a funcon of pas condonal varances and pas nnovaons. The relevan coeffcens α, θ, and γ are sascally sgnfcan a he 5 per cen level n he case of all models (excep θ 4 ). In addon, all of he γ coeffcens are posve. For posve γ, f δ = θ / γ < 0, hen negave nnovaons have a hgher mpac on volaly han posve nnovaons; f δ = 0 ( θ = 0 and γ > 0 ), hen he magnude erms rases (lowers) volaly when he magnude of marke movemens s large (small); f 0 < δ < 1, hen posve nnovaons would ncrease volaly bu negave nnovaons decrease volaly. These pronounced negave asymmery effecs are presen n Table 2. For New York, Warsaw, Prague, and Budapes, negave nnovaons ncrease volaly consderably more han posve nnovaons. Our fndngs sugges ha he four sock markes are more sensve o bad han good news. The perssence of volaly may be nerpreed by usng he half lfe concep (7), whch measures he me akes for an nnovaon o reduce s mpac by one half. Numercally, he HL coeffcens for he New York, Warsaw, Prague, and Budapes ndexes are equal o: 31.16, 40.43, 29.79, and days, respecvely. I s worh sressng ha he half lfe coeffcens are surprsngly hgh, however Schecher (2001, p. 37) documens half lfe coeffcens for he CTX, HTX, and PTX ndexes 5, whch are equal o: 16.39, 1.95, and (!) days. For example, Bhar (2001) documens half lfe coeffcens equal o 2.63 and 3.86 days for wo Ausralan spo and fuures markes, respecvely. Fgure 1. presens me plos of condonal varances from he unvarae AR(1) EGARCH(1, 1) models for he S&P 500, WIG, PX, and BUX ndex- 5 CTX, HTX, and PTX are he Czech, Hungaran, and Polsh Traded Indexes, whch are compued by he Cenral European Clearng Houses and Exchange (CECE) n Venna (Schecher (2001, p. 28).

13 Asymmerc Impac of Innovaons on Volaly 45 es, n he whole sample perod from Jan 3, 2007 o Dec 30, The global fnancal crss was refleced evdenly n all sock exchanges (cf. Fgure 1). Condonal Varances from EGARCH(1, 1) (S&P 500) Condonal Varances from EGARCH(1, 1) (WIG) Condonal Varance 15 Condonal Varance Condonal Varances from EGARCH(1, 1) (PX) Condonal Varances from EGARCH(1, 1) (BUX) Condonal Varance 15 Condonal Varance Fgure 1. Condonal varances from he unvarae AR(1) EGARCH(1, 1) models for he S&P 500, WIG, PX, and BUX ndexes, n he whole sample perod from Jan 3, 2007 o Dec 30, 2011 (Table 2). Tables 3a 3b presen furher analyss, ncludng deals abou resuls from he AR(1) EGARCH(1, 1) models of he four sock ndexes n: he down marke perod from Feb 27, 2007 o Mar 9, 2009 (Table 3a), he up marke perod from March 10, 2009 o Mar 10, 2011 (Table 3b).

14 46 Joanna Olbryś Table 3a. Resuls from he AR(1) EGARCH(1, 1) models of he four sock ndexes: S&P 500, WIG, PX, and BUX. The down marke perod from Feb 27, 2007 o Mar 9, 2009 (476 daly open o close percenage logarhmc reurns) New York ( = 1) Warsaw ( = 2) Prague ( = 3) Budapes ( = 4) Condonal mean equaon φ (0.060) 0.139* (0.056) (0.047) (0.061),0 φ 0.141* (0.041) (0.043) (0.048) (0.047) Condonal varance equaon α 0.069* (0.028) (0.034) 0.131* (0.052) 0.162* (0.058) *,0 α 0.965* (0.009) 0.970* (0.011) 0.960* (0.013) 0.972* (0.016) θ 0.182* (0.035) 0.127* (0.029) 0.136* (0.043) 0.048* (0.038) γ 0.117* (0.034) 0.098* (0.040) 0.188* (0.068) 0.250* (0.082) Condonal densy parameers ν (14.100) (10.273) 6.484* (1.710) 6.026* (1.651) λ 0.253* (0.059) (0.062) (0.080) (0.059) Asymmery effec for marke δ = θ / γ Half lfe (HL) Log lkelhood BIC AIC LB(20) [0.76] [0.27] [0.93] [0.27] LB 2 (20) [0.13] [0.85] [0.65] [0.91] Noe: he able s based on observaons durng he down marke perod February 27, 2007 March 9, 2009; * denoes sgnfcance a he 5 per cen level; he heeroskedasc conssen sandard errors are n parenheses; he varance-covarance marx of he esmaed parameers s based on he QML algorhm; he dsrbuon for he nnovaons s supposed o be skewed ; ; ν and λ are condonal densy parameers (Lucche, Bale S, 2011, p. 3); he asymmery coeffcen s defned n he ex; he half-lfe s defned n he ex and represens he me akes for he shock o reduce s mpac by one-half; BIC and AIC are he nformaon crerons; LB(20) and LB 2 (20) denoes he Ljung-Box (1978) sascs for sandardzed nnovaons and squared sandardzed nnovaons, respecvely (Balle, Bollerslev, 1990); numbers n brackes are p-values. The resuls n Tables 3a 3b clearly show ha he asymmerc effecs beween posve and negave ndex reurn nnovaons are especally srong n he down marke perod (cf. Table 3a). All of he γ coeffcens are sgnfcanly posve, all of he θ coeffcens are sgnfcanly negave, and hen suable δ = θ / γ coeffcens are negave, herefore we conclude ha negave nnovaons have a hgher mpac on he volaly han posve nnovaons. I s worhwhle o noe ha he asymmery effec s exremely srong

15 Asymmerc Impac of Innovaons on Volaly 47 n he case of he New York ( δ 1 = ) and Warsaw ( δ 2 = ) markes. Suable half-lfe coeffcens for he New York, Warsaw, Prague, and Budapes ndexes are equal o: 19.46, 22.76, 16.98, and days, and are numercally comparable. Table 3b. Resuls from he AR(1) EGARCH(1, 1) models of he four sock ndexes: S&P 500, WIG, PX, and BUX. The up marke perod from Mar 10, 2009 o Mar 10, 2011 (476 daly open o close percenage logarhmc reurns) New York ( = 1) Warsaw ( = 2) Prague ( = 3) Budapes ( = 4) Condonal mean equaon φ 0.101* (0.000) (0.042) (0.043) (0.067),0 φ 0.065* (0.000) (0.049) (0.039) (0.052) Condonal varance equaon α 0.159* (0.034) 0.129* (0.054) 0.146* (0.068) (0.049) *,0 α 0.971* (0.016) 0.984* (0.013) 0.962* (0.032) 0.989* (0.015) θ 0.112* (0.041) (0.034) (0.036) (0.025) γ 0.216* (0.048) 0.162* (0.071) 0.193* (0.096) (0.075) Condonal densy parameers ν 5.439* (1.183) 9.942* (3.997) 5.412* (1.215) * (3.981) λ 0.148* (0.051) (0.070) (0.064) (0.066) Asymmery effec for marke δ = θ / γ Half lfe (HL) Log lkelhood BIC AIC LB(20) [0.47] [0.39] [0.95] [0.14] LB 2 (20) [0.26] [0.95] [0.52] [0.94] Noe: he able s based on observaons durng he up marke perod March 10, 2009 March 10, 2011; * denoes sgnfcance a he 5 per cen level; he heeroskedasc conssen sandard errors are n parenheses; he varance-covarance marx of he esmaed parameers s based on he QML algorhm; he dsrbuon for he nnovaons s supposed o be skewed ; ; ν and λ are condonal densy parameers (Lucche, Bale S, 2011, p. 3); he asymmery coeffcen s defned n he ex; he half-lfe s defned n he ex and represens he me akes for he shock o reduce s mpac by one-half; BIC and AIC are he nformaon crerons; LB(20) and LB 2 (20) denoes he Ljung-Box (1978) sascs for sandardzed nnovaons and squared sandardzed nnovaons, respecvely (Balle, Bollerslev, 1990); numbers n brackes are p-values. As for he up marke perod he evdence s ha he esmaed unvarae EGARCH models are qualavely raher poor. Mos of he parameers are no sascally sgnfcan a he 5 per cen level. Essenally, he research provdes evdence ha he four markes are no homogeneous

16 48 Joanna Olbryś regardng he asymmerc mpac of nnovaons on volaly n he up marke perod, as well as he half-lfe coeffcen sze. The asymmerc effecs beween posve and negave ndex reurn nnovaons are presen n he case of hree markes (.e. New York, Warsaw, and Budapes). Suable half lfe coeffcens for he New York, Warsaw, Prague, and Budapes ndexes are equal o: 23.55, 42.97, 17.89, and days, and are subsanally hgher compared hose n he down marke perod. Ths evdence confrms ha he four sock markes are more sensve o bad han good news. Conclusons Our research provdes evdence for pronounced asymmerc mpac of nnovaons on volaly n he case of he US and CEEC 3 markes, especally n he down marke perod (Feb 27, 2007 March 9, 2009). We conclude ha negave nnovaons have a hgher mpac on volaly han posve nnovaons. Our fndngs sugges ha he four sock markes are more sensve o bad han good news. A possble and neresng drecon for furher nvesgaon would be an asymmery effecs nvesgaon n he case of he US and CEEC 3 markes, n erms of oher asymmerc GARCH ype models (cf. Engle, 2000; Bauwens e al., 2006). References Adkns, L. C. (2012), Usng Grel for Prncples of Economercs, 4h Edon, Verson Balaban, E., Bayar, A. (2005), Sock Reurns and Volaly: Emprcal Evdence from Foureen Counres, Appled Economcs Leers, 12, , DOI: hp://dx.do.org/ / Balle, R. T., Bollerslev, T. (1990), A Mulvarae Generalzed ARCH Approach o Modelng Rsk Prema n Forward Foregn Exchange Rae Markes, Journal of Inernaonal Money and Fnance, 9, , DOI: hp://dx.do.org/ / (90)90012-o. Baumöhl, E., Výros, T. (2010), Sock Marke Inegraon: Granger Causaly Tesng wh Respec o Nonsynchronous Tradng Effecs, Fnance a Uver: Czech Journal of Economcs and Fnance, 60(5), Bauwens, L, Lauren, S., Rombous, J.V.K. (2006), Mulvarae GARCH Models: A Survey, Journal of Appled Economercs, 21, , DOI: hp://dx.do.org/ /jae.842. Bhar, R. (2001), Reurn and Volaly Dynamcs n he Spo and Fuures Markes n Ausrala: an Inervenon Analyss n a Bvarae EGARCH X Framework, Journal of Fuures Markes, 21, , DOI: hp://dx.do.org/ /fu Black, F. (1976), Sudes of Sock Marke Volaly Changes, 1976 Proceedngs of he Amercan Sascal Assocaon, Busness and Economc Sascs Secon,

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18 50 Joanna Olbryś Lucche, K., Bale, S., (2011), The gg package, Verson 2.2. Mun, M., Brooks, R. (2012), The Roles of News and Volaly n Sock Marke Correlaons durng he Global Fnancal Crss, Emergng Markes Revew, 13, 1 7, DOI: hp://dx.do.org/ /j.ememar Nelson, D. B. (1991), Condonal Heeroskedascy n Asse Reurns: A New Approach, Economerca, 59, , DOI: hp://dx.do.org/ / Olbryś, J. (2013), Prce and Volaly Spllovers n he Case of Sock Markes Locaed n Dfferen Tme Zones, Emergng Markes Fnance & Trade, 49(2), , DOI: hp://dx.do.org/ /ree x4902s208. Reyes, M.G. (2001), Asymmerc Volaly Spllover n he Tokyo Sock Exchange, Journal of Economcs and Fnance, 25(2), , DOI: hp://dx.do.org/ /bf Schecher, M. (2001), The Comovemens of Sock Markes n Hungary, Poland and he Czech Republc, Inernaonal Journal of Fnance and Economcs, 6, 27 39, DOI: hp://dx.do.org/ /jfe.141. Syczewska, E. M. (2010), Changes of Exchange Rae Behavor Durng and Afer Crss, Quanave Mehods n Economcs, WULS Press, 11(1), Syropoulos, T. (2007), Dynamc Lnkages beween Emergng European and Developed Sock Markes: Has he EMU any Impac?, Inernaonal Revew of Fnancal Analyss, 16, 41 60, DOI: hp://dx.do.org/ /j.rfa Tsay, R. S. (2010), Analyss of Fnancal Tme Seres, John Wley, New York. Tse, Y., Wu, C., Young, A. (2003), Asymmerc Informaon Transmsson beween a Transon Economy and he U.S. Marke: Evdence from he Warsaw Sock Exchange, Global Fnance Journal, 14, , DOI: hp://dx.do.org/ /j.gfj Asymeryczny wpływ dodanch ujemnych sóp zwrou na zmenność w przypadku rynków Sanów Zjednoczonych, Polsk, Czech Węger: podejśce opare na modelu EGARCH Z a r y s r e ś c. Arykuł przedsawa badana dokumenujące asymeryczny wpływ dodanch ujemnych sóp zwrou na zmenność w przypadku rynków Sanów Zjednoczonych, Polsk, Czech Węger, z wykorzysanem jednorównanowych wykładnczych model EGARCH (Nelson, 1991). Porównawcze analzy empryczne doyczą okresu syczeń 2007 grudzeń 2011 oraz dwóch jednakowo lcznych podokresów: spadków ( ) wzrosów ( ). Swerdzono wyraźny efek asymer na wszyskch badanych rynkach, szczególne slny w wyróżnonym okrese spadkowym, wyznaczonym w oparcu o zmany warośc ndeksu S&P500 ścśle zwązanym z okresem kryzysu fnansowego w Sanach Zjednoczonych. S ł o w a k l u c z o w e: zmenność, efek asymer, okresy spadków wzrosów, wspólny zbór nformacj, model EGARCH. Acknowledgemens I would lke o hank prof. Evzen Kocenda and prof. Jan Hanousek for provdng me wh he daa on Prague Sock Exchange Index. GACR gran No. 403/11/0020 as a source of he daa s acknowledged. I am especally ndebed o anonymous referees for her valuable commens and suggesons whch grealy mproved he paper.