How To Calculate The Volailiy Of A Sock Marke

Transcription

1 News Inensiy and Condiional Volailiy on he US sock marke Jean-Gabriel Cousin a, Tanguy de Launois b* a ESA, Universié de Lille II, France b FNRS Fellow a he Universié caholique de Louvain, Belgium ABSTRACT The relaion beween informaion flow and asse prices behavior is one of he key issues of modern finance. Our sudy invesigaes more closely he link beween frequency of informaion arrivals and sock reurn volailiy. I aims precisely o es empirically he mixure of disribuion hypohesis and o check wheher he sock reurns disribuion is driven by he frequencies of informaion arrivals on he US marke. We analyze he impac of news on volailiy a he firm-level. We op for a model wih wo (Markov swiching) regimes of volailiy ha we apply o all socks belonging o he S&P 500 index from May 1998 o December We exploi he panel srucure of our daa and we find a posiive and significan bu marginally decreasing impac of he daily frequency of informaion arrivals on he probabiliy o be in a sae of high volailiy for he 458 companies considered. Subsequen ess allow us o conclude ha his impac crucially depends on he iming and he opic of he news release. Ineresingly, news announcing sronger public inervenion increases he uncerainy he mos, whereas announcemens abou fuure privaizaion lead o he sronges reducion in he sock volailiy. We finally perform a cross-secional regression of he ransiion probabiliies on differen measures of news inensiy, regulariy and persisence. We find a posiive relaion beween he ransiion probabiliies and hese characerisics of informaion. JEL codes: G14 EFA Classificaion Code: ME Keywords: News, (condiional) Volailiy, Public informaion arrivals, Mixure of disribuion hypohesis, Communicaion inensiy, Markov Swiching Regression Model. * Corresponding auhor: Oher auhor : 1, Place des Doyens 1 1 Place Délio 1348 Louvain-la-Neuve Lille Belgium France address: anguy.delaunois@uclouvain.be address: jgcousin@univ-lille2.fr We are graeful o Jacques Chardon and Faciva for having offered access o heir daa base. We especially wish o hank E. de Bod for his guidance and advice. All errors remain ours.

2 1 Inroducion The relaion beween informaion flow and asse prices behavior is one of he key issues of modern finance. How, why and under which condiions do financial news impac sock price volailiy, coun among he classical (and sill debaable) quesions in his research area. The clear knowledge and he good undersanding of such imporan issues are of firs imporance for lised companies. The behavior of sock prices around profi warning announcemens is a ypical (and probably exreme) example of hese phenomena. Carl-Henric Svanberg, Ericsson Chief Execuive, sill probably remembers he disasrous consequences of his injudicious profi warning of Ocober 16, A firs sigh, he news release looked quie innocen: i said ha Ericsson s operaing earnings dropped 36% o 5.6bn Swedish crowns ($876m), from 8.8bn crowns a year ago. The problem was ha analyss had been expecing earnings of abou 8.9bn crowns for he quarer. The marke showed no mercy: shares of he company los 24% in one day, involving ha no less han 15.7 billion of Ericsson s marke capializaion vanished in a couple of hours. "This is a day o be humble, concerned and disappoined," said Svanberg during a Webcas press conference in he morning. "This is a dynamic business environmen... We should have alked more abou i and undersood more abou i. We have underesimaed he impac" of changes in he marke, added he CEO 1. Tha kind of news hardly makes only one vicim. Secor spill over effecs of such announcemens have been quie common. On Sepember 16, 2004, afer Celesica, a large-cap elecronics manufacurer, cu is oulook for he hird quarer, he whole secor of makers of elecric pars and equipmen as well as providers of relaed services dropped: Power-One umbled 6.4%, Plexus fell 5.4%, Lilefuse shed 3.3% and

3 Benchmark Elecronics los 10% on he New York Sock Exchange. The communicaions-echnology secor was affeced he same way, since Sraex Neworks dropped 4.4%, Mindspeed Technologies los 3.3% and MRV Communicaions fell 3.2%. Financial communicaion may hus srongly impac sock reurn, volume and volailiy of any company. Such a poin deserves o be sudied and analyzed carefully. Our primary objecive is o invesigae he relaion beween public informaion and sock volailiy. To wha exen does he disconinuous frequency of news releases affec he volailiy of he daily sock reurns? And wha are he facors srenghening or weakening his relaion? These are precisely he main quesions ha we aim o answer in his paper. They are crucial from boh a pracical and an academic perspecive, since recen academic works have pu ino ligh he imporance of developing a beer undersanding of he deerminans of reurn volailiy. Easley and O Hara (2001) bring some evidence ha he less ransparen and disclosing a company is, he higher is cos of capial will be. Such a conclusion already offers some insigh of how significan he influence of news releases (in qualiy and in quaniy) on sock prices can be. Campbell, Leau, Malkiel and Xu (2001) find ha he proporion of firm-specific variance in he oal sock variance has seadily been increasing for he las hiry years and hus provides us wih anoher good reason o invesigae he relaion beween firm-specific news and idiosyncraic volailiy. As a maer of fac, one may wonder wheher he regular increase in idiosyncraic variance deeced by Campbell and al. (2001) could possibly be linked wih he obvious conemporaneous increase in he financial communicaion inensiy. Our resuls seem o suppor such an asserion. Evenually, Goyal and Sana Clara (2002) deec a posiive relaion beween idiosyncraic variance and expeced sock reurn. For idiosyncraic risk is no perfecly diversifiable and 1 Sources: lighreading :hp:// BBC news: hp://news.bbc.co.uk/1/hi/business/ sm and he Guardian: hp:// 3

4 invesors are assumed risk-averse, an increase in he firm-specific par of he sock volailiy can induce an increase in he cos of capial 2. Since we focus on he sock volailiy, an adequae model of is dynamics is obviously of prime imporance. If GARCH models coun undoubedly among he mos famous condiional volailiy models, alernaive frameworks exis and deserve o be considered. The Markov swiching regression (MSR) approach is one of hem: his raher original approach avoids he classical drawbacks of he GARCH models and allows us o indirecly es he Mixure of Disribuion Hypohesis (MDH), which argues ha he sock volailiy is direcly relaed o he informaion frequency. Alhough GARCH and MSR models give useful and quie reliable esimaes of he condiional sock variance, hey sill remain reduced form models no dedicaed o explain observed changes in sock volailiy and o poin ou he core facors driving is behavior. In our ques for an innovaive explicaive model of he sock volailiy, he MDH may well be of grea help, since i suggess explicily ha he sock volailiy is closely linked o he informaion frequency. Therefore i largely jusifies he inroducion of he daily number of press releases on a sock as he mos appropriae explanaory variable in he basic equaion of our inended explicaive model. Wih regard o he exising lieraure, our conribuions are of hree kinds: hey concern he daa used as well as he mehodology adoped and he resuls obained. In order o es empirically wheher informaion flows drive sock reurn volailiy, we apply our economerical model o all socks peraining o he S&P 500 index from May 13, 1998 o December 31, CRSP-apes provide us wih he series of daily sock 2 However, his poin remains conroversial. In obvious conradicion wih Goyal and Sana Clara (2002), Wei and Zhang (2004) claim ha idiosyncraic risk does no maer. 3 In a previous work (see Cousin and de Launois (2006)), we had conduced he same kind of analysis on he French marke, i.e. on all socks members of he CAC 40 index beween January 1999 and December

5 prices, while Faciva gives us access o a paricularly rich and advanageous news sample composed of all ime-samped socieal and indusrial Reuers and Dow Jones news releases concerning all companies seleced above. This kind of financial communicaion couns undoubedly among he mos up o dae and relevan public informaion ha invesors can collec when rading on he marke. Furhermore, since we are only ineresed in he impac of informaion inensiy on he idiosyncraic sock variance, we resric our invesigaion o firm-specific and indusrial-specific news and chose no o inroduce any marke or macroeconomic news in he sample (as i will be explained below, we will conrol for possible marke and macroeconomic shocks on sock variance hrough conrolling for he marke variance in he regression equaion). Finally, for we wan o es he link beween he daily number of firm-specific news releases and he corresponding sock volailiy, i is necessary o know which company (or companies) is (or are) concerned by each news release. Our sample provides us wih such an ineresing iem, among many ohers. I allows us o refine he classical aggregae marke-level analysis ino a more suble and accurae firm by firm sudy. Our mehodology differs in many respecs from he previous sudies on he opic menioned in Secion 2. We analyze he impac of news on volailiy a he firm-level, i.e. company by company, and no a he marke-level, i.e. impac of news on he index. I allows us o capure he enire firm-specific effec conained in he news which is obviously los a he aggregae level. We also employ condiional volailiy measures (insead of uncondiional volailiy measures) in order o ake he volailiy persisence effec ino accoun. We firs replicae on a daily basis he GARCH approach of Kalev, Liu, Pham and Jarnecic (2004) wih our specific daa se a he firm-level. We hen op for a marke model wih wo (Markov swiching) regimes of volailiy, which is more robus and general han he GARCH model used by Kalev and al. (2004) because i needs less srong assumpions on he condiional volailiy process. Moreover, such a 5

6 MSR model allows us o explicily ake advanage of he cenral Roll (1988) s idea 4 of a mixed reurn disribuion ( wih news and no news ) driven by news arrivals and o es he relevance of such an inuiion. The subsequen economeric mehodology consiss basically of wo seps: esimaing he daily probabiliies of being in a high volailiy sae hanks o he developed wo-sae marke model and regressing in a panel framework hese obained probabiliies on some possibly explicaive variables (like he daily number of news wires) in order o undersand he deerminans driving he sock reurns volailiy. Like Kalev and al. (2004), we conrol for he daily volume of rades, a possible proxy of privae informaion, and we find i o be significan. Unlike Kalev and al. (2004), we conrol for facors such as he marke condiional volailiy and he secor condiional volailiy, which urn ou o be highly significan. Furhermore, we conrol for possible ime effecs, boh alone and in ineracion wih our news variables. Only he firs ype of ime effecs appears o be significan. We also choose o perform he same regressions on differen news subses seleced on he basis of various crieria, like he subjec or he iming of he news release. In a las analysis, we invesigae impac of various characerisics of he company (he inensiy, regulariy and persisence of he communicaion, as well as he size of he company) on he probabiliies of ransiion from one regime (low or high) o anoher regime of volailiy (low or high). Our main finding is ha public informaion flows srongly affec he sock reurns disribuion. In he GARCH framework, our resuls are consisen wih hose of Kalev and al. (2004). The news frequency seems o be largely responsible for he persisence volailiy effec, and is impac on he volailiy level is subsanial. In he MSR model framework, we find a posiive and significan impac of he daily frequency of informaion arrivals on he probabiliy o be in a sae of high volailiy for each of he 458 companies considered. Moreover, we observe ha his impac is marginally 4 The MDH in fac. 6

7 decreasing. The regressions on various daa subses offer very ineresing resuls: news released during rading hours seems o have a much sronger impac han news released during non-rading hours. In erms of subjec, wih a coefficien of 0.32, press releases concerning earnings surprises appear o have he greaes impac on he sock volailiy. This confirms us in he common view ha invesors do no like being surprised a all. Oher kinds of news, in paricular Regulaion and governmen policy and earnings projecions (especially he subse of analys commens and recommendaions) presen much more moderae posiive impacs (wih a coefficien around 0.05), bu sill very significan. Ineresingly, news announcing sronger public inervenion increases he uncerainy he mos (afer he earnings surprises caegory), whereas announcemens abou fuure privaizaion lead o he sronges reducion in he sock volailiy. We finally end his sudy wih cross-secional regressions of he ransiion probabiliies on differen measures of news inensiy, regulariy and persisence. We find a posiive relaion beween he ransiion probabiliies and hese characerisics of informaion. The more frequenly and regularly informaion is released, he higher he ransiion probabiliies. And he impac is sronger on he ransiion probabiliy from he low o he high volailiy regime han he oher (high o low). Our paper is organized as follows. Secion 2 provides a brief review of he lieraure abou he relaion beween informaion and condiional volailiy. Secion 3 describes he used daa ses: sock prices and Reuers and Dow Jones news wires. Secion 4 presens he GARCH and he Markov swiching regimes models used in he subsequen empirical par. Secion 5 displays and commens resuls. Secion 6 concludes and provides some perspecives for fuure research. 7

8 2 Informaion and condiional volailiy 2.1 Modeling he condiional volailiy In he lieraure, he ime-varying naure of he volailiy is a well-known empirical fac. Presence of condiional heeroscedasiciy is well documened in mos financial imeseries. As a naural consequence, several auhors have ried o accoun for his volailiy persisence effec in alernaive economeric frameworks like ARCH (see Engle (1982)) and GARCH 5 (see Bollerslev (1988)) approaches. By expressing he sock idiosyncraic variance a ime as a linear funcion of he pas sock idiosyncraic variances and innovaions (a -1, -2, ec.), hese models provide condiional esimaes of he sock volailiy while aking he persisence volailiy effec ino accoun. Markov swiching regression models (MSR) appear as anoher ineresing way o capure condiional heeroscedasiciy evoluions. In such a non-linear dynamic framework, sock reurns disribuion is supposed o swich from a low o a high volailiy regime (and vice-versa) according o some fixed ransiion probabiliies. MSR models exhibi a more general srucure han he GARCH models, since hey impose fewer assumpions on he funcional form of he condiional volailiy. Moreover, GARCH models may someimes presen some annoying convergence problems, while MSR models are generally more reliable in his respec. Evenually, GARCH models do no res on a clear heoreical jusificaion (hey are sor of reduced form models), whereas MSR models are implicily based upon such a powerful argumen, which is known as he Mixure of Disribuion Hypohesis (MDH). Suggesed for he firs ime by Clark (1973), i posis ha he join disribuion of daily reurn and volume can be modeled as a mixure of bivariae normal disribuions. Specifically, hey are conemporaneously dependen on an underlying mixing variable ha represens he flow of informaion. As 5 ARCH and GARCH sand respecively for auoregressive condiional heeroscedasiciy and generalized auoregressive condiional heeroscedasiciy (models). 8

9 a consequence, he variance of reurns a a given inerval is expeced o be proporional o he rae of informaion arrival a he marke. Abou fifeen years laer, Roll (1988) shows empirically ha he sample variance and he kurosis for example can reveal somehing abou he probabiliy of informaion and he difference beween he informaion-relaed disribuion and he non-informaion-relaed disribuion of reurns, which is oally consisen wih he MDH. One year laer, Ross (1989) brings some convincing heoreical evidence supporing he MDH and demonsraes ha in an arbirage-free economy, he volailiy of prices is direcly relaed o he rae of flow of informaion o he marke. An avowed objecive of our sudy is precisely o es empirically ha mixure of disribuion hypohesis and o check wheher he sock reurns disribuion is driven by he frequency of informaion arrivals on he Paris sock Exchange (Euronex). In his conex, he MSR model urns ou o be he mos suiable specificaion, since i is he closes ranslaion of he mixure of disribuion hypohesis ino an empirical esimaion. Chauve and Hamilon (2005) shows ha a simple Markov swiching model fis paricularly well he daa when hese are suspeced o follow a mixure of disribuions. In our case, Davies s es confirms ha a Markov swiching model wih wo regimes mus be preferred o a simple marke model. We could consider more han wo regimes, bu in absence of srong and annoying ouliers, he addiion of a hird regime does no bring anyhing valuable and will only increase he complexiy of he model. 2.2 News arrivals and marke reacions If many auhors ried o esablish he realiy of he posiive relaion beween flows of informaion and sock (or marke) volailiy, he empirical evidence of such a posiive relaion is everyhing bu overwhelming, probably because of he difficuly o find good 9

10 empirical proxy of informaion arrivals and of he poor volailiy esimaes ha were radiionally used. The difficuly o precisely measure informaion arrivals appears in he variey of proxies employed by previous empirical sudies on he opic. Berry and Howe (1993) use he number of daily newspaper headlines and earnings announcemens and Ederingon and Lee (1993) invesigae he imporance of macroeconomic news, whereas Michell and Mulherin (1994) employ he number of specific sock marke announcemens in order o es he impac of he rae of informaion on he marke volailiy. «However, he use of uncondiional volailiy measures such as absolue daily marke reurns in hese sudies ofen generaes weak or inconclusive resuls regarding he news volailiy relaion» 6. Indeed, such a proxy is known o be quie noisy, and he presence of condiional heeroscedasiciy in he reurns ime-series may significanly aler he qualiy of he resuls. I is precisely o accoun for his well-known phenomenon of condiional heeroscedasiciy ha Kalev and al. (2004) choose o es he relaion beween firm-specific announcemens (as a proxy for informaion flows) and volailiy on he Ausralian Sock Exchange in a GARCH framework. Their analysis reveals a posiive and significan impac of he arrival rae of he seleced news variable on he condiional variance of sock reurns, even afer conrolling for he poenial effecs of rading volume and high opening volailiy. They find he respecive coefficiens of hese wo las conrol variables o be posiive and significan, excep on a daily basis. Evenually, hey spli all heir press releases ino differen caegories according o heir subjec, since Andersen (1996) argues ha differen ypes of news have differen sochasic arrival processes, so ha we may legiimaely expec hem o have a differen impac on he condiional sock volailiy. 6 Kalev, Liu, Pham and Jarnecic (2004), p

11 I is worh noicing ha some auhors have worked specifically on he French marke, like Lardic and Mignon (2003) and Lespagnol and Teïelche (2005), as we did in a previous sudy (Cousin and de Launois (2006)). 3 Sample selecion Our final sample covers a period ranging from May 13, 1998 o December 31, 2003 (i.e rading days). Our firms universe is composed of he 458 US socks ha were par of he S&P 500 index in May 2006 and which survived he filering process. We have indeed deleed all socks (i.e. 42) ha were acquired, merged or ha have purely vanished over he seleced period, as well as socks wih insufficien news or financial daa. We do no consider news prior o May 13, 1998, because he ime of arrival of news is a relaively new feaure of Faciva and was no sysemaically provided before his dae. As his iem appears o be useful in he aggregaion process of announcemens and he subsequen regressions, and since we wish o work on a daase as homogenous as possible, we decide o resric our aenion o his specific ime range, as well as o 458 companies ou of he 500 iniially considered, for some necessary daa lack for 42 of hem. Evenually, we are lef wih a broad and represenaive sample of he US marke since i accouns for no less han 75% of he US marke value. The average oal marke value of our sample is $25, billion. The mean (median) company marke value is $ billion ($2.175 billion). For all firms included in his sample, we use daily closing prices from May 13, 1998 o December 31, The hree larges secors in he sample are he commercial banking (5,8%), Elecriciy/Gas Uiliies (3,8%) and Semiconducors (3,4%). We use as a marke porfolio he CRSP EW. The daa are obained from he CRSP-apes. 11

12 All press releases were colleced hrough he Faciva daa base web sie 7. Faciva is a Dow Jones and Reuers company ha provides professionals wih business news and informaion sources like The Wall Sree Journal or The Financial Times for example. Our sample is composed of all corporae and indusrial news wires concerning firms included in he S&P 500 index and recorded by Dow Jones and Reuers from May 13, 1998 o December 31, Dow Jones and Reuers news wires are he wo major sources of news available in Faciva and are of course redundan. We have performed he whole analysis wih each daase separaely, and we have founded very close resuls. Therefore, we have chosen o presen only he saisics and resuls concerning Reuers news in his work. For each news wire, we have go he following fields: he accession number (AN), headline (HD), word coun (WC), publicaion dae (PD) and ime (ET), source name (SN) and code descripor (SC), lead paragraph (LP), company (concerned by he news release) code (CO), indusry code (IN), subjec code (NS), region code (RE), Dow Jones codes (DJIC) and descripors (DJID), informaion provider codes (IPC) and Reuers codes (RBBCM). Company, indusry and subjec codes are he main fields of ineres, since hey allow us o classify each news release in secor and in opic. One piece of news can of course concern several companies, indusries and subjecs. To avoid any redundancy and duplicae announcemens ha do no bring any addiional informaion value, we resric he sample o news released by Reuers only (or Dow Jones only when we consruc he Dow Jones sample). For he same reason, we eliminae all news releases wih he same headlines and lead paragraphs. Evenually, afer having excluded news iems wih one missing field or more, we are lef wih 7 hp:// 12

13 335,202 Reuers financial communicaions over he whole sample period Nov 1998 Dec Figure 1 (resp. Figure 2) displays he evoluion over ime of he oal daily (resp. weekly) number of news wires. We can disinguish hree differen regimes. The firs one ranges from November 1995 o May 1998 and presens a relaively low news arrival rae. Indeed, a ha ime, he ime of he news release was no ye sysemaically provided. Since May 1998 his feaure has been generalized and he frequency of announcemens becomes much more significan. Tha is why we begin our sample in May 1998 in order o have a homogenous sample. Laer years exhibi a decline in he number of announcemens, because he news releases are no inegraed immediaely in Faciva bu progressively, and i may occur ha some pieces of news daing back o 2003 are only incorporaed in he Faciva daabase in 2006 only. Tha is why we sop he sample on December 30, 2003, in order o ensure a minimal homogeneiy. From now, all subsequen figures and ables will be given for his specific sample ha ranges from May 13, 1998, o December 31, A firs sigh, he absence of any clear rend in Figure 1 and Figure 2 indicaes ha he news ime-series is raher saionary 8. This characerisic of our daa presens he advanage o eliminae he risk of spurious resuls due o a possible simulaneous increase over ime of he sock volailiy. No surprisingly a all, he Chrismas-New Year period experiences a news arrivals rae much below he average. Finally, here are recognizable picks every quarer (around each January, April, July and Ocober 20), ha probably correspond o he wave of he quarerly releases of he inermediae figures and earnings of companies. 8 We have checked his saionariy hypohesis more formally hrough he uni roo es of Dickey-Fuller ha rejecs he hypohesis of uni roo a a 0.1% level. So we can conclude ha he series is saionary. 13

14 Figure 3 focuses on a possible and expeced weekly seasonaliy in he daa and shows indeed ha he average number of news announcemens released during he week-end is much lower han he one of he oher weekdays. Since he sock exchange is closed during he week-end, his seasonaliy is no problemaic: news released during he week-end will simply be aggregaed o news published on he nex Monday. I can also be noiced ha he number of announcemens released on Tuesday, Wednesday and Thursday is roughly he same, wih Monday and especially Friday lower han he former. Figure 4 depics he evoluion of he frequency of announcemens arrivals hroughou he day, a New-York s ime. There are picks a 9 am and 4 pm, and he aciviy seems o be globally more susained in he morning han in he afernoon. The lunch drop is easily recognizable. Fields like company, indusry and subjec deserve o be examined in deail. Table 1, Table 2 and Table 3 provide an exensive overview of wha hese fields precisely conen. They respecively give he Faciva classificaion of companies, indusries and opics. Neverheless, because of he high number of companies in he sample (458), Table 1 is resriced o he 50 mos imporan companies ranked by heir sales in May There were iniially 500 differen companies in he sample (all consiuens of he S&P 500 in May 2006). However, only 458 ou of hese 500 firms will be analyzed in he subsequen GARCH and MSR economeric models, since some of hese companies were creaed, merged, or acquired during he sample period, or presen insufficien financial or news daa. Figure 5 shows ha news releases inensiy was he highes for Microsof (5.19% of all news releases concerned Microsof in some way), General 14

15 Moors (4.52%), Inel (3.59%), Ford (3.53%) and Time Warner (3.21%) 9. Conrary o he French marke for example, he sample is quie homogeneous: we do no observe one or wo firms presening news inensiy levels much above he res of he marke. Concerning indusry secors, hey are spli ino en general caegories and 56 subcaegories. Figure 6 shows ha he hree secors wih he highes news frequency from May 1998 o December 2003 were Meal, Goods and Engineering (44.98%), Financial and Business Services (36.01%) and Transpor and Communicaion (22.96%). Subjecs have also been divided ino 5 general caegories and 105 more specific ones, bu only he general caegory corporae and indusrial news is reained in our sample. From Figure 7 one can observe ha he 9 mos common news subjecs are earnings projecions (22.44%), earnings (17.99%), ownership changes (17.51%), mergers and acquisiions (hereafer M&A, which is in fac a sub-caegory of ownership changes) (16.07%), funding/capial (6.65%), capaciy/faciliies (4.80%), analys commen/recommendaion (a subcaegory of earnings projecions) (4.33%), conracs/orders (4.26%) and regulaion/governmen policy (3.67%). According o Andersen (1996), we expec he impac of various news releases o be differen across caegories. One of he purposes of he subsequen economeric analysis will be o give some empirical suppor o such a heoreical predicion. Table 4 provides an exensive se of summary saisics (mean, min, max, sandard deviaion, skewness, excess kurosis and sum), for he whole sample and by company (Panel A), by indusry (Panel B), by subjec (Panel C) and by iming (Panel D). Noe ha only he 10 general caegories of indusries and all subcaegories of opics of corporae/indusrial news (CCAT) are considered in Panels B and C. Concerning Panel D, he iming classificaion of a news release depends wheher i is published when 9 Percenages do no sum up o 100%, because one news release ofen concerns more han one company, indusry or subjec. I follows ha caegories are no exclusive (bu hey are exhausive). 15

16 he marke is open (rading hours) or no (namely overnigh and week-end). Daily news frequency ranges from 25 o 943 news releases a day 10, wih an average and a sandard deviaion of respecively and The skewness and excess kurosis (momens of order hree and four) are moderae and indicae ha he oal news probabiliy disribuion is asympoically roughly Gaussian, even if i presens some subsanial ails. Panels A, B, C and D are quie ineresing since hey offer valuable informaion abou possible cross-secional differences in he news arrival rae. One of he main conclusions ha can be drawn from he analysis of Table 4 is he following: he greaer he oal number of news releases concerning a company (or an indusry, or a subjec), he higher he sandard deviaion and he lower he skewness and kurosis of he disribuion of he daily number of news releases. Indeed, he behavior of he discree random variable number of news releases is a priori bes described by a Poisson probabiliy disribuion, and his disribuion is known o converge o a Gaussian disribuion as he number of observaions increases. 4 Model specificaion One of he core inermediae objecives of our work is o obain adequae esimaes of he daily sock volailiy. In his aim, we choose o apply wo differen frameworks: GARCH(1,1) model, as used in Kalev and al. (2004), and Markov swiching model ha is hough o be more relevan and appropriae han he former. 10 We only consider rading days, i.e. days when he marke is open. If a piece of news is released on Saurday, i will be aggregaed o he news releases of he nex rading day (here, if here is no holiday, Monday). 16

17 4.1 The GARCH model Firs of all, we propose o simply replicae he sudy of Kalev and al. (2004) on our exensive daa se. Their aricle aimed a esing he relaion beween firm-specific announcemens (as a proxy for informaion flows) and volailiy on he Ausralian Sock Exchange in a GARCH framework. By esing he same relaion in he same framework on a richer and more exensive daase (namely Euronex news), we wan o check ha we ge resuls consisen wih hose of Kalev and al. (2004). However, he sudy we inend o perform is differen from heirs in wo respecs: while Kalev and al. (2004) invesigae he volailiy behavior on an inraday and daily scale and were mainly ineresed in he marke volailiy, we choose o focus on a daily scale on he individual sock volailiy. GARCH model have now become quie common in he modeling of uncerainy in financial asse reurns. We will use i as follows11: MM MM R i, α i + β i Rm, + ε i, σ 2 = where ε i, Ω 1 ~ N(0, σ i, ) i, = ωi + α i ε i, 1 + βiσ i, 1 (4-1) (4-2) where: R i, is he reurn of sock i a inerval ; R m, is he reurn of marke index a inerval ; MM α i and MM β i are he marke model parameers for he sock i; ε i, are he serially uncorrelaed errors of sock reurns i wih mean zero; 2 and σ i, is he condiional variance of ε i,. 11 We use a GARCH model of order 1 since we wan o rigorously replicae he sudy of Kalev and al. (2004). The GARCH(1,1) model is predominan in he volailiy lieraure. Hansen and Lunde (2001) esablish a forecas comparison of volailiy models and conclude ha he bes models do no provide a significanly beer forecas han he GARCH(1,1) model. 17

18 The coefficiens α i and β i reflec he dependence of he curren volailiy of sock i upon is pass levels and he sum α + β indicaes he degree of volailiy persisence. i i According o Lamoureux and Lasrapes (1990) and Kalev and al. (2004) s resuls, he ime-varying paern of condiional volailiy may be generaed by serial correlaion in he informaion arrival process. Informaion clusering is indeed a well-known phenomena: news releases are no independen and are ofen concenraed around cerain daes. In our daa, he daily (resp.weekly) order-one serial correlaion of our announcemens is 71.09% (resp %) and remains high for superior orders. This argumen implies ha when a proxy for informaion flows is insered direcly ino he condiional variance equaion, mos of he observed volailiy persisence is expeced o disappear. Like Kalev and al. (2004), we adop as a proxy he number of all firmspecific news evens announced o he sock marke per inerval (N ), bu conrary o hem we run he analysis a he individual firm level (N i, ) raher han a he marke level in order o beer and more precisely capure he impac of news announcemens on he sock volailiy. Imporanly, N i, canno accoun for he flow of privae informaion, i does jus encompass a major componen of he public informaion se ha drives sock prices and volailiy. In our firs analysis N i, is se as an exogenous variable in he condiional variance equaion of he GARCH (1,1) specificaion as follows 12 : i, = ωi + αiε i, 1 + β iσ i, 1 λi Ni, σ + (4-3) Two imporan resuls follow from he esimaion of he above equaion. Firsly, he significance of he coefficien λ i provides evidence abou wheher he rae of public informaion arrival influences volailiy of he sock i in he presence of condiional 12 Noice ha variables N i,, R i, and σ i, are exacly synchronized. R i, is he reurn beween he closing price of oday and he previous closing price, and N i, is simply he number of press releases ha occurred beween hese wo daes. 18

19 heeroscedasiciy. Secondly, if he presence of GARCH effec is largely induced by he naure of he informaion flows, we may legiimaely anicipae a significan decrease in he persisence of volailiy, α + β. This would sugges ha he posiive serial i i correlaion in he daily volailiies is parly due o he posiive serial correlaion in he news arrivals. Since N i, does no cover all sources of informaion, we do no expec volailiy persisence o disappear enirely afer he inclusion of N i,. Afer his brief work of replicaion, we will coninue our ques for an innovaive explicaive model of he sock volailiy and develop one of he basic pieces of our work: he Markov Swiching Regression. 4.2 The wo-sae marke model (TSMM) We propose a new way o model he sock s variance behavior ha is perfecly in line wih he MDH and Roll s (1987) resuls. According o Roll, he rue reurn generaing process seems o be beer described by a mixure of wo disribuions: one corresponding o a sae of informaion arrival, and he oher o he normal reurn behavior. In order o sudy he impac of news on volailiy a he firm level, our new approach is based on a combinaion of he well-esablished marke model (Sharpe, 1963) and he more recen Markov Swiching Regression models (MSR), largely inroduced and developed by Hamilon (1989 and 1994), and significanly exended in Krolzig (1997). Our iniial inuiion is simple: if he occurrence of firm-specific evens may have a significan impac on he variance of he firm s reurn generaing process, we mus capure his perurbaion by using a regime swiching model. In his framework, we assume ha he error ε i, is sae dependen. S denoes our sae variable. We consider he general and concepual case of a wo-sae regime model 19

20 (mixure of wo disribuions wih differen variances) wih a low-variance regime (S = 1) and a high-variance regime (S = 2): Y = Xδ + ε Y = Xδ + ε 1 2 if S = 1 (4-4) if S = 2 wih Y he vecor of dependen variables and X he vecor of explanaory variables. The variance of he residuals for each sae is given by: E 2 [ ε1ε1' X ] = σ 1 I if S = 1 2 [ ε ε ' X ] = σ I if S = 2 E (4-5) 2 2 where σ > and I is he ideniy marix. 2 σ 1 We assume ha he ransiion beween he wo regimes is governed by a Markov chain of order 1, for which he ransiion marix is given by: p11 P = 1 p 11 1 p p (4-6) where p ij = p(s = i S -1 = j) corresponds o he probabiliy of going from sae j o sae i. The uncondiional probabiliy of he regime is given by (Hamilon, 1994, p. 683): p(s p(s 1 p22 = 1) = 2 p p 11 1 p11 = 2 ) = 2 p p (4-7) The inuiion underpinning our choice is simple: we anicipae ha firm-specific evens will impac he reurn variance. We will suppose ha he reurn generaing process can be adequaely modeled using a wo-regime process 13, one regime wih normal variance and one regime wih high variance (firm-specific even regime). Noe ha, in boh 13 We have realized likelihood raio es (LR es) o compare he wo-sae marke model (TSMM) and he classical one-sae marke model (MM). Since we are in he presence of nuisance parameers under he alernaive hypohesis, we have implemened he procedure advocaed by Davies (1977). Our resuls (available on reques) show ha he TSMM dominaes he MM in all cases (i.e. for each firm) a a confidence level of 5%. Since a hree-regime decomposiion appears o be jusified only in he presence of srong ouliers, we conclude ha he wo-regime model is an adequae represenaion of he reurn generaing process. (Noe also ha a wo-regime model is closer o he concep of a mixure of wo disribuions (MDH)). 20

21 regimes, he MM (marke model) parameers are assumed o be he same 14. Therefore he reurn generaing process is: R R i, i, and = α + β R = α + β R σ i j i,2 i i > σ m, i,1 m, + ε + ε i,1, i,2, if S if S = 1wih ε i,1, = 2 wih ε i,2, ~ N(0, σ i,1 ~ N(0, σ ) i,2 ) (4-8) where R i, is he reurn of sock i, R m, is he marke reurn and S is a sae variable aking he value 1 if we are in he low variance regime and he value 2 if we are in he high variance regime. In he sequel, we will refer o equaion (8) as he wo-sae marke model (TSMM). The proposed model is a direc and parsimonious exension of he classical MM. As he regime sae variable S is no direcly observable, we have o specify is saisical properies. The model we propose is herefore based on he esimaion of six parameers (α, β, σ 1, σ 2, p 11 and p 22 ) and, while much more flexible han he classical MM model, remains parsimonious. The esimaion of Markov Swiching Regression models is fully presened in Hamilon (1994). I is based on a maximum likelihood approach, for which an efficien esimaion algorihm has been developed. The esimaed probabiliy of being in a specific sae a a specific dae is one of he ineresing by-producs of he advocaed approach. I allows one o look for he reasons explaining an increase in he variance of sock reurns; in our case, o look for he link beween informaion flow and condiional variance. The use of his Markov Swiching Regression model provides numerous ineresing feaures. Beyond he above-quoed possibiliy of obaining he esimaed probabiliy of being in a specific regime a a specific dae, his specificaion is in line wih Roll s (1987) inuiion. In his Presidenial Address o he American Finance Associaion, he clearly highlighed ha he rue reurn-generaing process seems o be beer described 14 This hypohesis is suppored by unrepored resuls (available on reques). We allow he marke model parameers o vary across he wo regimes hrough he esimaion of a MSIAH model (Markov Swiching Inercep Auoregressive Heeroscedasiciy) (see Krolzig (1997)) and we find resuls very similar o he previous ones, excep ha he marginal impac of news is slighly sronger by less han one basis poin. 21

22 by a mixure of wo disribuions, he firs one corresponding o a sae of informaion arrival and he oher o he normal reurn behavior: i s clearly a good candidae for esing he mixure of disribuion hypohesis. Once we have esimaed he probabiliy for a firm of being in a high variance regime a a specific dae, we can es wheher i is linked o he informaion flow. The specificaion has oher aracive feaures: - he Gaussian condiional disribuion of reurns could be misleading. While he model imposes a Gaussian assumpion for he reurn disribuion in each sae, as shown in Hamilon (1994) and Krolzig (1997), i allows o capure skewness and kurosis in he uncondiional disribuion; - he Markov Swiching Regression framework also akes condiional heeroscedasiciy ino accoun wihou imposing a specific form on he condiional dependence of he variance (as in he (G)ARCH framework); - finally, he esimaion process provides us wih he esimaed variance in each regime, he probabiliy of being in a specific regime a a specific dae, and he esimaed ransiion probabiliies in a cerain manner, he TSMM, once we have esimaed he probabiliy for a firm of being in a high variance regime a a specific dae, could be a beer framework han he GARCH model (via he esimaed λ i ) in order o esimae he impac of he public informaion rae on he sock volailiy a he individual firm level. This may also give some addiional robusness o he news-volailiy relaion in he paern of he daily sock reurn volailiy. 15 All esimaions presened in his paper have been realized under he Ox economeric sofware, using he Krolzig MSVAR package. We hank Professor J. Hamilon for advising he use of his package. I is freely downloadable a: hp:// 22

23 5 The resuls 5.1 GARCH framework We begin wih he GARCH specificaion. In a firs sep, we merely reproduce he mehodology commonly used in he lieraure (see Kalev e al. (2004) and Janssen (2004)). I sums up o inser he number of daily announcemens concerning a sock ino he equaion of is variance in a GARCH (1,1) model. The esimaion of he laer afer inclusion of he variable NBN (daily number of news releases) converges for 445 socks. Ou of hose 445 esimaions, he coefficien associaed o he NBN variable is significan a he 5% (resp. 10%) level in 161 (resp. 212) cases and is inclusion decreases he persisence (alpha + bea) in 403 cases. I is imporan o noice ha he esimaion of a GARCH on such a long period may no be wihou problems. Therefore, resuls are probably no oally exemp of mehodological biases. Beyond his reserve, i gives a firs insigh of how he informaion sream affecs he condiional volailiy and o which exen i can explain he well-known persisence of he laer. I is unfeasible o give exensively here he resuls for each of he 458 companies of he sample, bu hey are available upon reques. 5.2 MSR framework: he wo-sae marke model (TSMM) Panel daa analysis wih he smooh probabiliy Global analysis For he many reasons brough up in Secion 2.1, an MSR framework is expeced o be a more appropriae specificaion and o fi much beer han a GARCH model. As i was horoughly explained in he same secion, such an approach leads us o develop a wosae marke model ha provides us wih he (daily) probabiliies of being in a high 23

24 volailiy regime on a specific day for each sock of he sample. Once hese probabiliies have been obained, i is possible o regress hem over our explicaive and conrol variables, in a panel framework. The main advanage of he panel analysis is o work globally and o analyze he combinaion of ime and cross-secional effecs. Modeling in his seing calls for some complex sochasic specificaion. We herefore use he mos common echniques: he fixed effecs and random effecs approaches. The fixed effecs approach akes he consan model o be a group-specific erm in he regression model. The consan is differen for any securiy. I should be noed ha he erm fixed as used here indicaes ha he consan erm does no vary over ime. The random effecs approach assumes ha he residual is a group specific random elemen. In his model, he consan is he same for all securiies included in he sample. The crucial disincion beween hese wo cases is wheher he unobserved individual effec embodies elemens ha are correlaed wih he regressors in he model, no wheher his effec is sochasic or no. In our case, he fixed effecs model is probably beer specified. Indeed, from he relaively high heerogeneiy across socks observed in he individual regressions, we may hink ha he fixed effecs approach fis beer, since i assumes he consan o be differen for each sock. Moreover, from a saisical perspecive, Hausman s es (available on reques) indicaes ha he fixed effecs model performs much beer han he random effecs one. As a regression mehod, we op for a General Mehod of Momens (GMM) regression 16 raher han a classical OLS regression because we expec he residuals of our regression 16 Before adoping he GMM framework, we firs used an «improved» OLS approach like «weighed leas squares»: resuls are very similar o hose obained by GMM, and even more significan. However, we hink ha a GMM regression mus be preferred o an (even improved) OLS regression since he former is known o be much more robus han he laer o heeroscedasiciy and serial correlaion problems apparen in our daa. Moreover, GMM coefficiens are direcly inerpreable as such, whereas 24

25 o presen subsanial heeroscedasiciy and serial correlaion problems. The coefficiens obained by his approach are he same as he coefficiens delivered by he classical OLS regression, bu he GMM procedure provides Suden saisics robus o heeroscedasiciy and serial correlaion of order one. The esimae of he covariance marix is obained hanks o he convergen esimaor of Newey and Wes (1987). We conduc hus he following fixed-effec panel GMM regression in order o measure he impac of he announcemens arrivals on he probabiliy o be in he high volailiy regime (he smooh probabiliy): Prob = C + C + β x +, i, i i, ε i (5-1) where Prob i, sands for he probabiliy of sock i a ime o be in he high volailiy regime and x i, he variables for which we anicipae some kind of associaion wih Prob i,. The heerogeneiy, i.e. he cross-secional effec beween socks, is modeled by C i where C i is a consan erm specific o individuals. We also add a ime effec, C, in order o ake ino accoun he possible evoluion of he inercep hrough ime. Specifically, we code his variable C as four annual dummies. The use of a probabiliy as a dependen variable mainly raises an issue of heeroscedasiciy (see Greene (2002)). We solve i by using he Newey-Wes robus esimaor of he covariance marix. In our firs specificaion, our proxy for he informaion flow is a dummy equal o one if here is a leas one news release concerning sock i in and 0 oherwise. The conrol variables which are no accouned for by he fixed effec, because hey are no consan on he seleced period, are he condiional volailiy of he marke and of he secor index (he laer is formed on he basis of he wo firs digis of he SIC code). Boh weighed leas squares coefficiens are no, since he variables have been logi-ransformed because hey are proporions. 25

26 condiional variances of he marke porfolio and of he secor index are esimaed via a GARCH (1,1) model. Prob = C + β D + varmrk + varsec +, i, i 1 i, β 2 β 3 i, ε i (5-2) I follows from Table 5 ha afer conrolling for annual, fixed, marke and secorial effecs, he fac o be on a dae where a leas one Reuers news release has been recorded for a sock increases he probabiliy o be in he high variance regime of abou 6.75 poins for his sock. No surprisingly, he coefficiens of he marke and secor variances appear o be posiive and significan, since he sock volailiy is known o convey some marke componen. Such conrol variables allows us o accoun (a leas parially) for all macroeconomic shocks ha affec he sock volailiy and ha are no covered by our se of firm-specific press releases. I also appears (from resuls available on reques) ha he annual dummies denoed by C are sysemaically significan when hey are inroduced, which seems o sugges ha he probabiliy o be in he high variance regime exhibis some paern hrough ime and canno be aken as independen of ime. Therefore, we will perform our regressions of Secion (excep in Table 10 in order o be able o compare US resuls o he French ones) by sysemaically including his variable C in order o conrol for he ime paern of he probabiliy of being in he high variance regime. As a nex sep we wish o measure he impac of he informaion volume on his laer probabiliy. Our idea is o inroduce four dummies D k,i, (k=1,, 4) in order o spli he rading days in differen caegories according o he level of communicaion observed everyday: D 1,i, (resp. D 2,i,, D 3,i,, D 4,i, ) = 1 if he rading day is in he op 20% (resp. 10%, 5%, 1%) of he days presening he highes number of news releases concerning sock i, and 0 oherwise. 26

27 Prob = C + β D + varmrk + varsec +, i, i 1 k, i, β 2 β 3 i, ε i (5-3) Resuls of Table 6 show clearly ha he probabiliy o be in he high variance regime increases wih he volume of announcemens: a rading day siuaed in he op 1% of he mos news-inensive rading days brings 26.6 exra poins o he variance of he concerned sock, which canno be considered as negligible, boh from a saisical and economical poins of view. This new evidence leads us o propose a specificaion including direcly he number of announcemens in he regression equaion: Prob = C + β NBN + NBN + varmrk + varsec +, 2 i, i 1 i, β 2 i, β 3 β 4 i, ε i (5-4) NBN i, is he oal number of announcemens observed for sock i on day while 2 NBN i, is simply he square of i NBN,. This las variable is inroduced in order o ake ino accoun he possibiliy of a marginally decreasing (or increasing) effec of he number of news releases on he probabiliy of high variance regime. Resuls of Table 7 demonsrae he posiive and significan impac of he volume of specific announcemens on he condiional volailiy of each sock. The significan negaive sign associaed o NBN² suggess he exisence of a marginally decreasing effec, wih maximum siuaed around 64.5 news releases. In line wih Kalev e al. (2002), p. 1444, we inroduce he rading volume in value ($) ino he regression equaion, as his variable does, o a limied degree, conain privae informaion no ye refleced in public news. I could also influence volailiy in ways ha are unrelaed o he informaion arrival. Indeed, our variable NBN, because i is of public knowledge, does no ake ino accoun he privae dimension of informaion. In order o avoid any endogeneiy problem, we lag his volume variable by one period: 27

28 Prob 2 i, = Ci + β 1NBN i, + β 2 NBN i, + β 3Voli, 1 + β 4varmrk + β 5varseci, + ε i, (5-5) According o Table 8, he impac of rading volume on he probabiliy of high variance regime urns ou o be posiive and significan, which is a well-known resul of he lieraure. We refer he ineresed reader o Karpoff (1987) for a deailed survey of earlier empirical work, mos of which shows evidence ha higher volailiy is accompanied by higher rading volume. More recen sudies such as Jain and Joh (1988), Schwer (1989), Gallan e al. (1992), Richardson and Smih (1994), Foser and Viswanahan (1995), and Andersen (1996) also documen a similar relaion. Noice ha his impac of he volume rading remains significan afer he inclusion of our public informaion proxy (NBN) Inroducion of a ime effec Up o now, we have no considered he possibiliy ha he impac of he announcemens frequency on he smooh probabiliy could vary hrough ime. We herefore propose o perform he following panel regression: Prob i, = C + C + β β β β β i 2 1NBNi, + 2NBNi, + 3 D1999 NBNi, + 4 D2000 NBNi, + 5 D2001 NBN i, + β + 6 D 2002 NBN i, + β 7 D2003 NBN i, + β 8varmrk + β 9varsec i, ε i, (5-6) C akes ino accoun as before he possible evoluion of he inercep hrough ime, while he coefficiens β 3 o β 7 conrol for he poenial evoluion hrough ime of he coefficien of our main variable of ineres. 28