A direct approach to cross market spillovers

Transcription

1 A direc approach o cross marke spillovers Kjell Jørgensen Siri Valseh July 1, 2011 Absrac This paper inroduces a framework ha direcly quanifies informaion spillovers beween financial markes. Informaion spillovers occur when marke specific informaion, defined as informaion ha direcly affecs he reurn or volailiy in one marke only, indirecly affecs reurns or volailiy in oher markes hrough some channel(s) of ransmission. By using marke specific order flow as a measure of marke specific informaion, we esimae he spillover effecs from he sock marke o he bond marke and vice versa. We examine spillovers under differen marke condiions by employing a regime-swiching framework. We find evidence of spillovers in reurns and volailiy across he wo markes especially when he volailiy in he sock marke is high. Our findings are consisen wih fligh-o-qualiy and rebalancing as channels of ransmission. Keywords: Cross Marke spillovers, Regime-swiching, Marke Microsrucure. JEL classificaions: G12, G14. BI School of Managemen, kjell.jorgensen@bi.no BI School of Managemen, siri.valseh@bi.no We are graeful o Richard Priesley for many suggesions and commens. We also wan o hank Carol Osler, Chrisian Heyerdal-Larsen, Ilan Cooper and Bern Arne Ødegaard for useful commens.

2 1 Inroducion Marke specific informaion is defined as informaion ha direcly affecs reurns in one marke only. Someimes, however, marke specific informaion indirecly affec reurns and volailiy in oher markes. Falling prices in he U.S. housing marke in 2006 are an example of his. This informaion was relevan for reurns in he marke for morgage backed bonds, bu urned ou o affec financial markes worldwide. This indirec effec of marke specific informaion is ofen referred o as cross marke spillover or conagion. There is no consensus on he exac definiion of spillovers and conagion in he lieraure. We follow Fleming, Kirby and Osdiek (1998) and define spillovers as changes in reurns or volailiy in one marke due o a ransmission of marke specific informaion from anoher marke. In accordance wih Allen and Gale (2000) we define conagion as srong spillover effecs relaed o crisis periods. Marke specific informaion spills over o oher markes hrough differen ransmission mechanisms, ofen referred o as channels of ransmission. Three possible channels of ransmission will be considered in his paper; rebalancing, cross marke hedging and fligh-o-qualiy. We examine he exen of spillovers under differen marke condiions and relae our resuls o hese hree channels. A beer undersanding of how and when spillovers occur is imporan as spillovers can conribue o significan comovemens beween asses and hus resul in unexpeced increases in porfolio risk. This can resul in financial losses and sricer financing condiions for invesors which in urn can lead o less invesmen, lower growh, and higher unemploymen in he economy. However, empirically i is diffi cul o measure he effecs of cross marke spillovers. Many sudies, for example Forbes and Rigobon (2002), define and measure spillovers indirecly as a significan increase in he level of correlaion beween markes. One problem relaed o he use of correlaions is ha boh common informaion and spillovers of marke specific informaion will influence he level of correlaion. Since informaion flows are unobservable, he relaive conribuion of common informaion and he spillover of marke specific informaion o changes in correlaions is indiscernible. Bekaer, Harvey and Ng (2005) seek o eliminae he effec of common informaion by using a facor model reflecing economic fundamenals and measure spillovers as correlaions in he model residuals. However, as here is no agreemen in he lieraure 2

3 on which facors represen common informaion, here is a possibiliy ha his indirec approach also can include some effecs of common informaion. This paper has wo main conribuions. Firs, i proposes an approach o measure spillover effecs ha overcomes he problems relaed o he use of correlaions. We use marke specific order flow as a measure of marke specific informaion o capure spillovers in reurns and volailiy direcly. We are hus able o isolae he effecs of spillovers from he effecs of common informaion. According o marke microsrucure heory order flow conains privae informaion ha can include heerogeneous inerpreaions of macroeconomic fundamenals as well as non-fundamenal informaion held by marke paricipans. To make sure we remove any privae informaion ha is common across markes we orhogonalize he order flow in each marke and label his marke specific order flow. This implies ha heerogeneous inerpreaions of marke specific public informaion is included in our measure. Second, our paper conribues by applying a dynamic framework o examine wheher spillovers are sronger in periods of high volailiy. Spillover effecs are ofen associaed wih periods of uncerainy and financial crises. By using a regime-swiching model we are able o compare he exen of spillovers in periods of high volailiy wih periods of normal volailiy. We apply he proposed framework o he Norwegian sock and governmen bond markes and employ a daa se covering all rades in Norwegian socks and governmen bonds during he period Sepember 1999 o March The bond marke is divided ino hree differen mauriy segmens for shor, medium and long erm bonds. We define spillover effecs in reurns as posiive when marke specific order flow ha leads o higher (lower) reurns in he originaing marke also leads o higher (lower) reurns in he oher marke. Spillover effecs are negaive when marke specific order flow has opposie effecs in he originaing marke and he affeced marke. Our resuls show ha here are significan spillover effecs across he sock and bond markes. We find negaive spillover effecs from he bond marke o sock reurns when sock marke volailiy is high. We also find ha here are negaive spillover effecs from he sock marke o bond reurns when bond marke volailiy is normal and ha periods of normal volailiy in he bond marke correspond o periods of high volailiy in he sock marke. Our resuls hus indicae ha spillover effecs are relaed o periods characerized by high risk in he 3

4 sock marke. Our findings furher indicae ha while here are some spillover effecs o volailiy, hese are of less significance han spillovers o reurns in boh markes. Our resuls are consisen wih fligh-o-qualiy and porfolio rebalancing as channels of ransmission. Fligh-o-qualiy occurs when sock marke uncerainy is high and refers o episodes when invesors sell asses perceived as risky and buy he safes and mos liquid asses, such as governmen bonds, insead. Episodes of fligh-o-qualiy are ofen relaed o financial crises and imply negaive spillover effecs in reurns across he sock and bond markes. Porfolio rebalancing refers o a change in he composiion of a porfolio, for example o aler porfolio risk, and involves a purchase of one asse and a sale of anoher asse. If an invesor becomes more risk averse and wans o reduce porfolio risk, she can sell socks and buy bonds o increase he porfolio share in bonds. If she wans o increase he expeced reurn of her porfolio she will do he opposie ransacion. Thus, porfolio rebalancing also implies negaive spillover effecs in reurns. The hird channel of ransmission we consider is cross marke hedging, which refers o he purchase or sale of an asse in order o insure a posiion in anoher asse. Our resuls are no consisen wih his channel. Sock and bond reurns are negaively correlaed in our sample period, and using bonds o hedge a sock posiion hen implies posiive spillover effecs in reurns. Our resuls imply ha he correlaion beween sock and bond reurns becomes more negaive when swiching from he normal volailiy regime o he high volailiy regime in he sock marke. By employing he dynamic condiional correlaion (DCC) framework of Engle (2002) we documen ha he ime varying correlaion beween reurns on socks and long bonds and socks and medium erm bonds become more negaive when he volailiy in he sock marke swiches from he normal o he high volailiy regime. This is in line wih he resuls of previous sudies using changes in he level of correlaion as a measure of spillover effecs. The paper is organized as follows: Secion 2 discusses relaed lieraure, secion 3 presens he framework for measuring cross-marke spillovers, secion 4 describes he daa se and secion 5 presens and discusses he resuls. Secion 6 concludes. 4

5 2 Relaed lieraure Our sudy is relaed o wo fields of research. Firs, i is relaed o he lieraure on financial marke linkages, including he lieraure on financial conagion. Second, i is relaed o he marke microsrucure lieraure focusing on he role of order flow as an informaion aggregaor. From he firs field our paper is relaed o several sudies. Connolly, Sivers and Sun (2005) invesigae he sources of he ime varying correlaion beween socks and bonds by examining wheher he sock-bond reurn relaion varies wih wo measures of sock marke uncerainy suggesed by he lieraure, namely he VIX index and abnormal sock urnover. They conclude ha sock marke uncerainy may generae imporan cross-marke pricing influences, suggesing ha sock marke specific informaion could spill over o bond reurns. Our sudy differs from heirs by direcly quanifying he spillover effecs. We also include spillovers from he bond marke o he sock marke and measure he spillover effecs in boh reurns and volailiy. Forbes and Rigobon (2002) ask wheher conagion can explain highly correlaed sock marke movemens. They find no evidence of conagion during differen periods of crises. Bekaer, Harvey and Ng (2005) examine changes in correlaions in sock marke reurns beween counries and invesigae wheher here has been episodes of conagion. They use a facor model reflecing economic fundamenals and measure conagion as he correlaions in he model residuals. Our framework differs from hese sudies in a fundamenal way because we do no examine he indirec measure of correlaions, bu quanify he informaional spillover effecs direcly by using marke specific order flow as a proxy for marke specific informaion. Our approach capures he effecs of marke specific informaion in one marke on reurns and volailiy in he oher marke by adding marke specific order flow as an explanaory variable in regime-swiching models. As marke specific informaion indirecly spills over o oher markes, he lieraure is concerned wih how his acually happens. A number of sudies have invesigaed possible ransmission mechanisms linking markes ogeher. These mechanisms are ofen referred o as channels of ransmission or channels of conagion. Prisker (2001) and Longsaff (2010) provide a descripion of he main channels. Kodres and Prisker (2002) focus on he channel of cross marke rebalancing. Rebalancing refers o a change in he composiion 5

6 of a porfolio and involves a purchase of one asse and a sale of anoher asse. Rebalancing occurs when new informaion affecing reurns in one marke makes an invesor wan o change porfolio holdings in ha marke. This change can lead o a change in porfolio holdings in oher markes also even hough here was no new informaion abou hese markes. Underwood (2009) finds evidence of cross marke hedging as a channel of ransmission. Hedging is underaken o insure a posiion in an asse and involves he purchase or sale of a posiion in anoher asse which has a posiive reurn when he insured posiion has a negaive reurn and vice versa. If he correlaion beween he wo asses is posiive, and he invesor has a long posiion in he asse o be hedged, he hedge will be esablished as a shor posiion. If he correlaion beween he wo asses is negaive, and he invesor has a long posiion in he asse o be hedged, he hedge will be esablished as a long posiion. Connolly, Sivers and Sun (2005) explore wheher fligh-o-qualiy can be a channel of ransmission. Fligh-o-qualiy occurs when marke uncerainy is very high and refers o episodes when invesors sell asses perceived as risky and buy he safes and mos liquid asses insead. Examples of safe and liquid asses are shor erm governmen bonds. Episodes of fligh-o-qualiy are ofen relaed o financial crises iniiaed by negaive informaion in a high risk marke. Our paper is relaed o hese sudies as we invesigae wheher our resuls are consisen wih rebalancing, hedging or fligh-o-qualiy as channels of ransmission. From he second field, he marke microsrucure lieraure, our paper is relaed o sudies on he informaion conen of order flow. A large number of sudies documen ha order flow conains informaion abou conemporaneous asse prices. Hasbrouck (1991) provides evidence ha sock marke order flow influences sock reurns, Evans and Lyons (2002) documen ha currency marke order flow has a srong effec on exchange raes and Brand and Kavajecz (2004) show ha Treasury marke order flow explain bond yields. More recen sudies show ha order flow also conains informaion abou fuure asse prices and fuure economic fundamenals. Evans and Lyons (2005) and Valseh (2011) show ha order flow has ou-of-sample predicive power for exchange raes and governmen bond yield changes, respecively. Evans and Lyons (2009) find ha order flow in he foreign exchange marke predics fuure macro variables such as GDP growh and inflaion. Beber, Brand and Kavajecz (2010) provide evidence ha sock marke order flow predics 6

7 economic fundamenals measured by he Chicago Fed Naional Aciviy Index. In all, hese sudies suppor a fundamenal view in he marke microsrucure lieraure, namely ha order flow conains privae informaion abou asse prices. This is imporan because while informaion flows are unobservable, order flows are observable. By using marke specific order flow as a direc measure of marke specific informaion we overcome he problem conneced o he use of he indirec measure, correlaion, which is ha common informaion and spillover effecs are indisinguishable as drivers of correlaion. Underwood (2009) employs sock and bond marke order flow o explain cross marke reurns. He finds ha he correlaion beween sock marke order flow and bond marke order flow is negaive in periods of negaive reurn correlaion and posiive in periods of posiive reurn correlaion. He concludes ha cross marke hedging is an imporan source of linkages beween he wo markes. Underwood (2009) does no differeniae beween informaion spillover and common informaion. Our sudy differs from Underwood (2009) in ha we focus on spillovers only and invesigae he effecs on boh reurns and volailiy. 3 Framework for measuring cross marke spillovers 3.1 Marke specific order flow We use marke specific order flow as a proxy for marke specific informaion. I is imporan ha our proxy reflecs marke specific informaion only as his informaion should be independen from informaion ha has a direc impac on he oher marke also. Our proxy for sock marke specific informaion is herefore sock marke specific order flow which is defined as he par of he sock marke order flow ha is orhogonal o he shor, medium and long erm order flow in he bond marke. Common informaion ha affecs reurns in boh he sock marke and he bond marke is hus by consrucion removed from our proxy. Bond marke specific informaion is defined by hree variables; shor erm bond marke specific order flow, medium erm bond marke specific order flow and long erm bond marke specific order flow. This is useful because reurns on bonds wih a long ime o mauriy could be deermined by differen facors han reurns on bonds wih shorer ime o mauriy. Invesors could also specialize in differen mauriy bonds and spillover effecs could herefore vary according o bond duraion. 7

8 In order o idenify he marke specific par of sock marke order flow, we orhogonalize sock marke order flow by running he following regression OF S = α 1 + β 1 OF BS + β 2 OF BM + β 3 OF BL + e (1) where OF S is he order flow in he sock marke, α 1 is a consan, OF BS bond marke order flow, OF BM erm bond marke order flow and e is he residual. e is medium erm bond marke order flow, OF BL is shor erm is long is he par of he sock marke order flow ha is no relaed o bond marke order flow and hus a measure of he sock marke specific informaion. We label his par of he order flow OF S,MS. In order o idenify he marke specific par of he hree segmens of bond marke order flow, we orhogonalize shor, medium and long erm bond marke order flow by running he following regressions OF BS = α 2 + β 4 OF S + ε (2) OF BM = α 3 + β 5 OF S + (3) OF BL = α 4 + β 6 OF S + π (4) where ε, and π are he bond marke specific pars of he bond marke order flows and hus a measure of shor, medium and long erm bond marke specific informaion. We label he marke specific order flow of he hree segmens OF BS,MS, OF BM,MS OF BL,MS respecively. and 3.2 Informaional spillover models We use regime-swiching models based on Gray (1996) o measure he degree of informaional spillovers across differen volailiy regimes. Since we are invesigaing possible cross marke spillovers in boh reurns and reurn volailiies a he same ime, we consider wo models ha allow for changes in volailiy. Firs, we esimae a consan variance regimeswiching model which allows for differen levels of volailiy in each regime. Second, we esimae a regime-swiching GARCH model which allows he levels of volailiy in each regime o vary according o GARCH(1,1) processes. In he GARCH(1,1) model we include he marke specific order flows as regressors in boh he condiional mean and variance 8

9 equaions. We sar by describing a convenional GARCH(1,1) model modified o include spillovers. The equaions for a model including spillovers from he bond marke o he sock marke are r s, = a 0 + a 1 OF S + a 2 OF BL,MS + a 3 OF BM,MS + a 4 OF BS,MS + u s,, (5) and h s, = b 0 + b 1 u 2 s, 1 + b 2 h s, 1 + b 3 OF BL,MS + b 4 OF BM,MS + b 5 OF BS,MS (6) where (5) is he mean equaion, r s, is daily sock marke reurn, and OF BL,MS, OF BM,MS and OF BS,MS are daily bond marke specific order flows as defined in he previous secion. Equaion (6) is he condiional sock marke variance modified o include he marke specific order flows as regressors. Accordingly, he equaions in he GARCH(1,1) model for spillovers from he sock marke o he differen bond marke segmens, j, are r bj, = a o + a 1 r bj, 1 + a 2 OF Bj + a 3 OF S,MS + u bj,, (7) and h bj, = b 0 + b 1 u 2 bj, 1 + b 2h bj, 1 + b 3 OF S,MS. (8) where (7) is he mean equaion wih r bj, as he daily marke reurns for he differen bond segmens, j = s, m and l, and OF S,MS defined in he previous secion. modified o include OF S,MS represens he sock marke specific order flow as Equaion (8) is he condiional bond marke variance as a regressor. These models are single regime models in he sense ha hey assume a single srucure for he condiional mean and variance. The srucural form of he condiional mean and variance equaions, including he spillover coeffi ciens, are assumed fixed and linear hroughou he enire sample period. Hence, his model has he implici assumpion ha any spillover effecs are consan hroughou he enire sample period. However, reurn 9

10 correlaions exhibi a grea deal of ime variaion as we will show in he resuls secion. This ime variaion could be influenced by varying degrees of informaional spillovers beween he wo markes. We herefore check wheher he degree of informaional spillover is differen across volailiy regimes, and in paricular wheher informaional spillovers are more pronounced when reurn volailiy is high. Since spillover effecs imply changes in reurns and volailiy, we expec spillovers o occur in a marke when he volailiy in his marke is high. Also, fligh-o-qualiy is relaed o periods of high risk in he sock markes and we expec spillovers hrough his channel o occur when sock marke volailiy is high. Prior research such as Clark (1973), Ross (1989) and Andersen (1996) argue ha he level of informaion flows ino a marke is direcly relaed o is level of reurn volailiy. Also, following he works of Cai (1994) and Hamilon and Susmel (1994) several sudies have suppored he view ha asse prices could be characerized by wo regimes: a normal volailiy regime and a high volailiy regime. Shalen (1993) and Harris and Raviv (1993) provide heoreical argumens suggesing ha high volailiy periods are characerized by a dispersion of beliefs abou asse values among invesors. This dispersion may be due o asymmeric informaion or o heerogenous inerpreaions of symmeric informaion. In addiion o provide an explanaion for increased volailiy, he level of disagreemen among invesors could impac he role of order flow as an informaion aggregaor. Order flow would be more informaive when dispersion is large as i conains privae informaion reflecing heerogenous inerpreaions of public news. If his is he case one should see a larger impac of order flow on reurns in periods of high volailiy. 1 A larger impac on reurns in he iniiaing marke will provide a larger incenive for invesors o change porfolio weighs by rebalancing heir porfolios. More rebalancing by invesors would resul in larger spillover effecs. Thus, if order flow carries more informaion in imes of high volailiy we would expec ha he exen of informaional spillovers is larger in high volailiy regimes han in normal volailiy regimes. We herefore wan o relax he imposed lineariy of he spillover effecs of he single regime specificaions above and le he coeffi ciens of he above models be differen in differen volailiy regimes if such exis. The regimes are never observed, 1 Pasquariello and Vega (2007) observe his in he U.S. Treasury bond marke. 10

11 bu probabilisic saemens will be made abou heir relaive likelihood of occurring, condiional on an informaion se. This is done according o an endogenous classificaion rule based on a Markov swiching model. We follow he mehodology developed by Gray (1996) which builds on Cai (1994), Hamilon (1994), and Hamilon and Susmel (1994). Firs, we invesigae if regime-swiching alone could accoun for he observed condiional heeroscedasiciy in he bond and sock markes. This is done by esimaing a consan variance firs-order Markov regime-swiching model wih wo regimes. In his model, assuming condiional normaliy for each regime, he sock reurns, r si,, and bond reurns, r bji,, are disribued as N(a 0i + a 1i OF S + a 2i OF BL,MS + a 3i OF BM,MS a 4i OF BS,MS, b 0i ) (9) and N(a oi + a 1i r bj, 1 + a 2i OF Bj + a 3i OF S,MS, b 0i ) (10) respecively in regime i where i = 1, 2. Hence, he variance is consan in each regime. We refer o his model as he consan variance regime-swiching model. Any condiional heeroscedasiciy can only be driven by swiches beween regimes. We hen relax he assumpion of consan variances wihin each regime, allowing he condiional variances o be GARCH(1,1) processes. We follow Gray (1996) and assume condiional normaliy for each regime. The variance of he reurn series a ime is hen given by h k, = E[r 2 k, Φ k,] E[r k, Φ k, ] 2 = p k,1 (µ 2 k,1 + h k,1) + (1 p k,1 )(µ 2 k,2 + h k,2) [p k,1 µ k,1 + (1 p k,1 )µ k,2 ] 2, (11) where µ k,i is he condiional mean for marke k, k=s (socks), BL (long erm bonds), BM (medium erm bonds), BS (shor erm bonds), in regime 1 and 2 respecively and Φ k, represens he informaion se available in marke k a ime. The sae probabiliy p k,1 11

12 gives he probabiliy ha marke k is in regime 1 a ime and is defined as [ ] g k,2 1 (1 p k,1 1 ) p k,1 = (1 Q k, ) g k,1 1 p k,1 1 + g k,2 1 (1 p k, 1 ) [ ] g k,1 1 p k,1 1 +P k,, g k,1 1 p k,1 1 + g k,2 1 (1 p k,1 1 ) (12) where p k,1 = Pr(S k, = 1 Φ k, ), g k,1 = f(r k, S k, = 1), g k,2 = f(r k, S k, = 2), P k, = Φ(X k, β 1 ), Q k, = Φ(X k, β 2 ). S k, is he laen regime indicaor while P k, and Q k, are probabiliies of remaining in regime 1 and regime 2, respecively. The ransiion probabiliies are ime varying and dependen on he level of he explanaory variables in he condiional mean equaions in he sock and bond marke segmens. β 1 and β 2 are marices of unknown parameers o be esimaed and Φ( ) is he cumulaive normal disribuion funcion ha guaranees 0 < P k,, Q k, < 1. The erms in he square brackes in (12) represens Pr[S k, 1 = 2 Φ k, 1 ] and Pr[S k, 1 = 1 Φ k, 1 ], respecively. Now h k,, which is pah-independen, can be used as he lagged condiional variance in consrucing h k,1+1 and h k,2+1 which follow GARCH(1,1) processes. Thus we have h k,i = ω k,i + a k,i ε 2 k, 1 + b k,ih k, 1, h k, 1 = p k,1 1 [µ 2 k,1 1 + h k, 1] + (1 p k,1 1 )[µ 2 k,2 1 + h k,2 1] [p k,1 1 µ k,1 1 + (1 p k,1 1 )µ k,2 1 ] 2, (13) ε k, 1 = r k, E[r k, Φ k, 1 ] = r k, [p k,1 µ k,1 + (1 p k,1 )µ k,2 ]. We refer o his model as he regime-swiching GARCH model. 12

13 The regime-swiching models for he sock marke quanify any spillover effecs from he bond marke o sock reurns when sock marke volailiy is high and when i is normal. The models for he bond marke segmens quanify any spillover effecs from he sock marke o bond reurns when bond marke volailiy is high and when i is normal. The wo regimes in our models hus capure he periods of high and normal volailiy in he marke where he spillover effecs can occur, bu no in he marke where he spillover effecs can be iniiaed. However, in some cases we would be ineresed in he volailiy condiions in he marke iniiaing he spillover effecs also. For example, if sock marke specific informaion leads o large changes in sock marke reurns, invesors would be more prone o change heir porfolio weigh in socks han oherwise. This implies ha spillover effecs from he sock marke o bond reurns would be more likely when he sock marke is in he high volailiy regime. Also, if here is fligh-o-qualiy, high uncerainy in he sock marke will iniiae sales of risky socks and purchases of safer asses such as governmen bonds. To idenify wheher fligh-o-qualiy causes spillover effecs we are ineresed in knowing wheher spillover effecs from socks o bonds occur when sock marke volailiy is high. Our regime-swiching models will idenify wheher spillover effecs from he sock marke o bond reurns occur in he high volailiy or normal volailiy regime in he bond marke, bu no wheher hey occur during he high volailiy or normal volailiy regime in he sock marke. In order o invesigae wheher spillover effecs from socks o bonds occur when volailiy in he sock marke is high we esimae he following regression model: r bj, = α + β 1 r bj, 1 + β 2 OF bj + β 3 OF S,MS P s, + β 4 OF S,MS Q s, + ε, (14) where OF S,MS P s, and OF S,MS Q s, are ineracion erms capuring he probabiliy weighed spillover effecs from he sock marke o he bond segmens. P s, and Q s, are he ime-varying probabiliies ha he sock marke is in a high volailiy regime and a normal volailiy regime respecively. 13

14 3.3 Tesable predicions We invesigae wheher spillovers occur across sock and bond markes, and wheher hey are consisen wih porfolio rebalancing, hedging or fligh-o-qualiy as possible channels of ransmission. We can es wheher spillover effecs from he sock marke o he bond marke occur by esimaing he effecs of sock marke specific order flow on bond reurns and bond volailiy. Similarly we can es wheher spillover effecs from he bond marke o he sock marke occur by esimaing he effecs of bond marke specific order flows on sock reurns and sock volailiy. The sign of he spillover effecs will indicae which channel of ransmission would be mos likely. Rebalancing is consisen wih negaive spillover effecs in reurns as i involves a purchase of one asse and a sale of anoher asse. Hedging is consisen wih posiive spillover effecs in reurns if he hedging porfolio is esablished in a negaively correlaed marke. Hedging is consisen wih negaive spillover effecs in reurns if he hedging porfolio is esablished in a posiively correlaed marke. Fligh-o-qualiy as a channel of ransmission is consisen wih negaive spillover effecs from he sock marke o bond reurns when sock marke volailiy is high. We es for his by esimaing wheher spillovers from he sock marke o bond reurns depend on he regime probabiliies in he sock marke. The signs of any spillover effecs o volailiy are no clear for he ransmission channels we discuss. Posiive spillover effecs in reurns conribue o posiive correlaion and negaive spillover effecs conribue o negaive correlaion beween he wo markes. According o his we expec any spillover effecs o be posiively relaed o he absolue level of reurn correlaions. Also, Fleming, Kirby and Osdiek (1998) argue ha informaion spillovers should be sronges when hedging incenives are high which are in periods wih a high absolue level of correlaion. In order o check his we esimae he ime varying reurn correlaions beween he sock marke and he differen bond marke segmens and compare he level of correlaion o he probabiliy for he sock marke o be in he high volailiy regime. The ime varying reurn correlaions are esimaed using he dynamic condiional correlaion (DCC) esimaor of Engle (2002). The appendix explains how he DCC esimaor is se up. 14

15 4 Daa We use daa from he Norwegian sock and governmen bond markes for he years 1999 o The Norwegian sock marke ranked as he 24h larges world equiy marke by marke capializaion by he end of A ha ime 219 firms were lised on he Oslo Sock Exchange (OSE) wih a oal marke value of abou billion NOK. 2 The Norwegian governmen bond marke is organized in he same way as major governmen bond markes, bu he number of bonds is smaller due o he oil driven financial surpluses of he Norwegian economy. In 2005, ousanding domesic governmen deb amouned o 207 billion NOK, of which six benchmark bonds accouned for 152 billion NOK. In Sepember 1999, an elecronic order book was esablished for rading in governmen bonds. Bond marke rades can be agreed on eiher in he elecronic order book or in he over-hecouner marke. The share of elecronic rading and he average elecronic rade size in bonds increased gradually afer he incepion of he limi order book. In he inerdealer marke, elecronic rades and over-he-couner rades consiued roughly one half each over he period. The OSE is he only regulaed marke place for securiies rading in Norway and all rades are regisered in he OSE rading sysem. In January 1999 he OSE inroduced an elecronic rading sysem for socks. Since hen a fully compuerized cenralized limi order book sysem has been in place for equiy rading. The sysem is similar o he public limi order book in Paris, Torono, Sockholm and Hong Kong. All rades are agreed upon wihin his sysem. Our daa se consiss of daily reurn daa and all ransacions in socks and governmen bonds over he period Sepember 1999 o March The ransacions daa include dae, ime, price and amoun in NOK. For sock ransacions he iniiaing side of he rade is known. For governmen bond ransacions, he mehod of Lee and Ready (1991) is used o idenify he iniiaing dealer. 3 We consruc daily order flow series in socks and bonds from he signed ransacions daa. Bond marke order flow consiss of hree mauriy groups. Shor-erm order flow is based on rades in bonds wih a remaining ime o 2 Equvialen o a value of USD 207 billion. The USDNOK exchange rae was 6.77 a he end of According o his mehod, rades execued a a price above he middle of he bid-ask spread are classified as buyer-iniiaed rades. Trades execued a a price below he middle of he prevailing bid-ask spread are classified as seller-iniiaed rades. When rades are execued a he mid price, he ick rule is used. According o his rule he direcion of change from he las ransacion price deermines wheher he rade is classified as seller-iniiaed or buyer-iniiaed. 15

16 mauriy from 1 year o 4 years, medium erm order flow is based on rades in bonds wih a remaining ime o mauriy greaer han 4 years up o 7 years and long-erm order flow is based on rades in bonds wih a remaining ime o mauriy greaer han 7 years up o 11 years. Daily order flow is he number of buyer-iniiaed rades minus he number of seller-iniiaed rades during a day and reflecs he ne buying pressure in he marke. We use a sock marke index including all socks a he OSE and hree bond oal reurn indices o compue daily sock and bond reurns. The indices are published by he OSE and he bond indices reflec he reurns on governmen bonds wih a consan duraion of five years, hree years and one year. The indices are consruced on he basis of he ousanding benchmark bonds, which are normally four o six bonds. 4 Summary saisics for he reurn and order flow daa are presened in Table 1, Panels A, B, and C. Panel A shows ha he univariae properies of he reurn daa conain he ypical properies of financial reurn series. In oher words, boh sock and bond reurns are lepokuric wih sock reurns having a negaive skew and bond reurns having a posiive skew. The annualized mean reurn for he sock marke is 10.2 percen for he period while i ranges from 5.7 percen for he bonds wih 1 year duraion o 7.6 percen for he bonds wih 5 year duraion, in line wih a ypically upward sloping yield curve. According o he firs order auocorrelaion, bond reurns, especially for he shor and medium erm duraions, are persisen wih coeffi ciens beween 9 and 14 percen. Sock marke reurns do no show any persisence. In addiion here is clear evidence of condiional heeroscedasiciy in all reurn series as he LM es for ARCH-effecs sysemaically rejecs he null of no such effecs a a horizon up o a leas a week. Panel B shows he properies of he order flow variables. Average order flow in he sock marke, OF S, is posiive indicaing a ne buying pressure in he marke over he sample period. On average here have been 187 more buy-iniiaed rades per day han sell-iniiaed rades. The order flow variables for he bond marke, OF BS, OF BM OF BL, all show a sligh negaive mean value indicaing a small ne selling pressure in he bond marke in he sample period. Panel C displays he uncondiional correlaions beween reurns and order flow. The 4 The sock index daa are from Daasream and are based on he oal marke index, TOTX, o he end of 2001, and he all share index, OSEAX, hereafer. Bond yield indices wih a fixed duraion of 1 year (ST3X), 3 years (ST4X) and 5 years (ST5X) are calculaed daily by OSE. and 16

17 correlaion beween he differen mauriy bond marke reurns and he sock marke reurn is fairly low and negaive, bu increasing wih duraion. A low value of he uncondiional correlaion beween bond and sock reurns is in line wih oher sudies like Connolly, Sivers and Sun (2005). As for he relaionship beween order flow and reurns, we find ha sock marke order flow is negaively, bu weakly relaed o bond reurns. Shor, medium and long erm bond marke order flows are weakly and negaively correlaed o sock reurns. The relaionship beween sock marke order flow and sock marke reurns is srong and posiive. The relaionship beween bond marke order flow and bond marke reurns is also srong and posiive, albei weaker han in he case of he sock marke. Figures 1 o 4 display he cumulaive order flow in he sock marke and he hree segmens of he bond marke. The cumulaive order flow is consruced by adding up daily order flow. Figure 1 illusraes an almos homogenous buying pressure in he sock marke hrough he whole sample period. A he end of he period he amoun of buyer iniiaed rades in excess of seller iniiaed rades has accumulaed o rades which is equivalen o almos 90 billion Norwegian kroner. Figure 2 shows ha here was a clear selling pressure in he marke for long bonds from 2001 o mid Figure 3 displays a very differen paern for medium erm bonds wih ne selling up o mid 2001 and ne buying for mos of he period from mid 2001 unil early From mid 2001 o he beginning of 2004 long and medium erm bonds were experiencing opposie ne order flows. Figure 4, illusraing he shor end of he bond marke, shows ha he amoun of seller iniiaed rades in excess of buyer iniiaed rades accumulaed o 1100 which in value equals 40 billion Norwegian kroner by spring Overall, hese figures show ha he acive side of he bond marke has been selling, excep for he above menioned buying period for medium erm bonds, while he acive side of he sock marke has been buying. 5 Resuls We invesigae wheher here are spillover effecs across he sock marke and he bond marke and if so, wheher hey vary across volailiy regimes. We do his by esimaing he models presened in secion 3.2. The resuls of hese models are repored and discussed 17

18 below. 5.1 Consan variance models We firs esimae he consan variance regime-swiching model and compare i wih a sandard single regime consan variance model. This will provide us wih valuable insighs ino he characerisics of he wo regimes and how spillover effecs vary wih he regimes. In addiion, i will provide evidence on wheher regime-swiches can explain he ARCH effecs found in sock and bond reurns. Panel A of Table 2 repors he resuls for he sock marke. The firs column gives he parameer esimaes of a single regime consan variance model which is a convenional regression model. The spillover coeffi ciens from he bond marke, a 21, a 31 and a 41, are all negaive. The coeffi ciens for he shor and long erm segmens are significan and indicae ha here are negaive spillover effecs from he shor and long erm bond markes o sock marke reurns. There is serial correlaion in he squared residuals as indicaed by he large ARCH es saisic. As expeced, given he level of condiional heeroscedasiciy in sock reurns, his consan variance model does a poor job in modeling he volailiy of sock reurns. The second column repors he resuls from he consan variance regime-swiching model which allows for wo possible levels of volailiy, one for each regime. The volailiy measured by he sandard deviaion in regime 1, b 01, is wice he size of he volailiy in regime 2, b 02. The average daily reurns in he sock marke are also significanly negaive in his regime while hey are saisically zero under regime 2. Regime 1 is hus a high volailiy negaive reurn regime in he sock marke. Regime 2 is a normal volailiy regime. Alhough he spillover coeffi cien for he long erm bond segmen is marginally significan a he 10 percen level, he coeffi ciens for he oher segmens are highly significan and economically much larger. This indicaes ha posiive (negaive) news in he bond marke ends o reduce (increase) sock marke reurns. None of he spillover coeffi ciens in he normal volailiy regime, a 22, a 32 and a 42 are significan and he coeffi ciens here are much smaller. In oher words, spillover effecs from he bond marke o he sock marke appear o be negaive and resriced o periods of high sock marke volailiy. We also find ha he high volailiy regime is much less persisen han 18

19 he normal volailiy regime. While he high volailiy regime has an average duraion of 1/(1 P ) = 7.73 days, he normal volailiy regime has an average duraion of 1/(1 Q) = days. This indicaes ha periods of high sock volailiy usually are shor. The ARCH es saisic is subsanially lower in he regime-swiching model indicaing ha his model is more adequae han he single regime model. Panels B, C and D of Table 2 repor he resuls for he shor, medium, and long erm bond marke segmens, respecively. The firs column of Panel B shows ha in he single regime model he spillover coeffi cien measuring he effecs of sock marke specific order flow on shor bond reurns, a 31, is negaive and significan a he 5 percen level. The second column, presening he resuls for he consan variance regime-swiching model, shows ha whereas he spillover coeffi cien in regime 1, a 31, is insignifican, he spillover coeffi cien in regime 2, a 32, is negaive and highly significan. The size of he coeffi cien in regime 2 is considerably larger han he coeffi cien in he single regime model. Average daily shor bond reurns are posiive in boh regimes, bu higher in regime 1. The volailiy in regime 1 for shor bonds, b 01, is 2.8 imes higher han he volailiy in regime 2, b 02. Panel C repors he resuls for medium erm bonds. The firs column reveals ha he spillover coeffi cien, a 31, is negaive and significan a he 1 percen level in he single regime model. The second column shows ha in regime 1 he spillover coeffi cien is insignifican while i is negaive and highly significan in regime 2. The resul for he spillover coeffi cien a 32 implies ha a one sandard deviaion increase (decrease) in sock marke specific order flow reduces (increases) medium erm bond reurns by 1.1 basis poins in regime 2. Daily medium bond reurns are also posiive in boh regimes, bu on average higher in regime 1. The volailiy in regime 1 for medium erm bonds is 2.4 imes higher han he volailiy in regime 2. Finally, Panel D of Table 2 shows he resuls for long bonds. Also for long bonds he coeffi cien measuring he spillover from he sock marke, a 31, is negaive and significan in he single regime model. In he regime-swiching model he coeffi cien is only significan in he normal volailiy regime, and he value is higher han in he single regime model. Average daily long bond reurns are posiive and more han 2 imes higher in regime 1 han in regime 2. The volailiy in regime 1 for long erm bonds is 2.3 imes higher han he volailiy in regime 2. In all hree panels he ARCH es saisic is subsanially lower 19

20 in he regime-swiching model han in he single regime model. This indicaes ha he regime-swiching model is more adequae for all hree bond segmens. The resuls from he regime-swiching model for he shor, medium and long erm bond segmens indicae ha regime 1 is a high volailiy high reurn regime in he bond marke. Regime 2 is a normal volailiy regime. The spillover coeffi cien from he sock marke in he high volailiy regime, a 31, is no significan for any of he bond segmens while he coeffi cien in he normal volailiy regime, a 32, is highly significan and negaive for all hree segmens. This implies ha here are negaive spillover effecs from he sock marke o he bond marke only in normal imes which is opposie of wha we find for he sock marke, where here are spillover effecs in he high volailiy regime only. An explanaion for his asymmery beween he sock and bond markes could be ha spillovers from he sock marke o he bond marke are mainly relaed o he volailiy regime in he sock marke. If normal volailiy regimes in he bond marke coincides wih periods of heighened volailiy in he sock marke i could explain he resuls in Table 2. Figures 5 o 7 plo he probabiliy ha he sock marke is in a high volailiy regime agains he probabiliies ha he differen bond segmens are in a high volailiy regime. Figure 5 shows he probabiliy ha socks and long erm bonds will be in he high volailiy regime and we see ha he probabiliies ofen are high a differen imes. This is more pronounced in Figure 6 which includes socks and medium erm bonds. I appears ha when medium erm bonds are in he high volailiy regime he sock marke is in a normal volailiy regime and vice versa. Figure 7, including socks and shor erm bonds, also shows ha he high volailiy regimes are no idenical in he wo markes. The figures hus confirm ha he differen bond segmens frequenly are in a normal volailiy regime when he sock marke is in a high volailiy regime. The resuls in Table 2 are based on a regime-swiching model where he regimes reflec he volailiy level in he marke "receiving" he spillover effec. This model canno address he quesion of wheher spillover effecs from socks o bonds occur when volailiy in he sock marke is high. In order o invesigae his quesion we herefore employ he regression model presened in equaion (14). The resuls from his model are presened in Table 3. The firs column repors he resuls for he long erm bond segmen. The coeffi ciens for lagged reurns and long erm bond marke order flow are posiive and 20

21 significan. The coeffi ciens for he ineracion erms capuring he probabiliy weighed spillover effecs from he sock marke o long bonds, OF S,MS P s, and OF S,MS Q s,, are boh negaive and significan. The economic imporance is much higher for he firs erm which indicaes spillovers when he sock marke is in he high volailiy regime. The second column repors he resuls for he medium erm bond segmen. The coeffi ciens for lagged reurns and medium erm bond marke order flow are posiive and significan. However, only he ineracion erm capuring he probabiliy ha he sock marke is in he high volailiy regime is significan. This implies ha here is a negaive spillover effec from he sock marke only when he sock marke is in a high volailiy regime. The hird column repors he resuls for he shor erm bond segmen. Here, he coeffi ciens for lagged reurns and own order flow are also posiive and significan, bu only he coeffi cien for he ineracion erms capuring he probabiliy ha he sock marke is in he normal volailiy regime is significan. Thus here are only negaive spillover effecs from he sock marke o shor bonds when he sock marke is in a normal volailiy regime. The explanaory power measured by R 2 is significanly higher for he long and medium erm bonds models han for he shor erm bond model. The resuls in Table 3 documen ha here are negaive spillover effecs from socks o medium and long erm bonds when sock marke volailiy is high. 5 This finding is consisen wih fligh-o-qualiy as a channel of ransmission. Anoher explanaion for spillovers from sock o bonds in normal imes only is ha he normal volailiy regime appears o be relaively much more persisen han he high volailiy regime. Periods wih high volailiy only have an average duraion beween 1 and 6 days in he bond marke. This can be due o he fac ha we in his specificaion have forced he condiional variance ino jus wo levels and hereby making he condiional variance mimic he regime probabiliies. The regime-swiching GARCH model in he nex secion overcomes his limiaion wih a richer parameerizaion of he condiional variance wihin each regime. We consruc a likelihood raio es (LRT) o invesigae wheher he consan variance regime-swiching model or a GARCH(1,1) regime-swiching model is he mos suiable 5 The shor erm bond marke, including governmen securiies wih an average duraion of 1 year, was less liquid han he marke for bonds wih a duraion over 1 year in our sample period. 21

22 model for each marke. We hen compare he significance of he regime swiching GARCH model relaive o he consan variance regime swiching model. We find ha he consan variance regime-swiching model is mos adequae for he hree bond marke segmens, while he GARCH model is clearly bes for he sock marke. 5.2 GARCH models We now drop he assumpion of consan variances wihin each regime and allow he condiional variances o be GARCH(1,1) processes. The condiional variance equaions will also conain marke specific order flow variables as addiional regressors. Table 4 repors he resuls for he sock marke. The firs column gives he parameer esimaes of a convenional single regime GARCH(1,1) model. The spillover coeffi ciens in he mean equaion, a 21, a 31 and a 41 are all negaive and he coeffi ciens for he long and shor erm segmens are significan. This is in line wih he single regime model in Table 2. None of he spillover coeffi ciens in he variance equaion, b 31, b 41 and b 51 are significan. The second column of Table 4 repors esimaes of he regime-swiching GARCH(1,1) model. The spillover coeffi ciens in he mean equaion are all negaive and significan in he high volailiy regime. For example, we find ha a one sandard deviaion increase (decrease) in medium erm bond marke specific order flow reduces (increases) sock reurns by 14 basis poins. This is in line wih he consan variance regime-swiching model in Panel A of Table 2. Noe he almos idenical economic impac in he spillover from all bond segmens o he sock marke reurns. In he normal volailiy regime only medium erm bond marke informaion spills over o he sock marke. The coeffi cien, a 32, is posiive and highly significan. Thus, in normal imes posiive informaion in he medium erm bond marke increase sock marke reurns. The condiional variance equaion shows ha here is no spillover o he condiional sock marke volailiy from any of he bond segmens when he volailiy is a a high level. None of he spillover coeffi ciens, b 31, b 41 and b 51 are significan. In he normal volailiy regime however, here are negaive spillovers o he condiional volailiy of he sock marke from he long and medium erm bond segmens. The coeffi ciens, b 32 and b 42, are boh significanly negaive. This means ha when he sock marke is in a normal volailiy regime, posiive news in hese bond segmens will ypically dampen 22

23 he condiional volailiy in he sock marke. Negaive news in hese bond segmens will correspondingly increase he condiional volailiy in he sock marke. By allowing for a ime varying variance wihin each regime he condiional variance esimaes are no longer forced o mimic he regime probabiliies. Hence, he esimaes of he ransiion probabiliies P and Q should be more realisic if he GARCH specificaion is more adequae. The LRT saisic, which is disribued χ 2 (10) under he null, is This is significan a any sandard level, indicaing ha GARCH effecs wihin each regime is an imporan feaure of he sock marke. 6 The regimes now appear o be more persisen han was he case wih he consan variance regime-swiching model. The high volailiy regime in he sock marke now has an average duraion of 1/(1 P ) = days while he normal volailiy regime has an average duraion of 1/(1 Q) = days. 5.3 Discussion Our resuls based on he regime-swiching models documen ha here are significan negaive spillover effecs in reurns across he sock and bond markes. In he sock marke hese spillovers occur in he high volailiy regime and in he bond marke segmens hey occur in he normal volailiy regime. By comparing he ime varying probabiliies of being in he high volailiy regime we find ha he normal volailiy regime in he bond marke frequenly coincides wih high volailiy regimes in he sock marke. These findings indicae ha spillover effecs from he sock marke o bond marke reurns occur when he sock marke is in a high volailiy regime. This is confirmed by he resuls from he regression model which separaes spillovers from socks o bonds according o he volailiy regime in he sock marke. They show ha spillover effecs from he sock marke o medium and long erm bond marke reurns are negaive and significanly sronger when he sock marke is in a high volailiy regime han in a normal volailiy regime. This is consisen wih fligh-o-qualiy as a channel of ransmission. Episodes of fligh-o-qualiy occur when he uncerainy in he sock marke is very high. Risk averse 6 I should be noed ha he likelihood raio es here is only indicaive. This is because he parameers associaed wih he second regime is no idenified under he null of a single regime. The LRT saisic can herefore only be assumed o be χ 2 disribued under he null. Hansen (1992) has developed a sandardized LRT procedure ha overcomes his diffi culy. This procedure is however exremely roublesome unless he model is very simple. In our siuaion his procedure is pracically infeasible. In pracice, we are herefore judging he large difference in log-likelihood values as saisical evidence in favour of he regime swiching GARCH model. 23