The effects of sovereign rating drifts on financial return. distributions: Evidence from the European Union

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1 The effec of overegn rang drf on fnancal reurn drbuon: Evdence from he European Unon Hung Do a, Rober Brook a, Srmon Treepongkaruna b, Elza Wu c a Deparmen of Economerc and Bune Sac, Monah Unvery, Aurala b Accounng and Fnance, UWA Bune School, The Unvery of Weern Aurala, Aurala c Fnance Dcplne Group, UTS Bune School, Unvery of Technology Sydney, Aurala ABSTRACT We develop a framework ha allow a mulvarae yem of long memory procee o be condonal on pecfc regme o nvegae he effec of cred rang agence CRA overegn cred re-rang on European ock and currency reurn drbuon over he perod from 996 o 202. We fnd evdence acro rang regme o uppor he uefulne of our propoed model n accommodang boh long memory and regme wchng feaure. Furhermore, we reveal ha he oal effec boh drec and ndrec force of overegn cred aemen on he fr four realzed momen of reurn drbuon can be dfferen o her drec effec on ndvdual momen. Thu, we fnd he rank order among he hree major CRA o dffer for each realzed momen and ae marke. Keyword: Soveregn cred rang; cred rang agence; nraday daa; hgher momen; Markov regme wchng; long memory JEL clafcaon: C32, F30, G5. Correpondng auhor. Tel: Emal addree: hung.do@monah.edu Hung Do, rober.brook@monah.edu Rober Brook, rmon.reepongkaruna@uwa.edu.au Srmon Treepongkaruna, elza.wu@u.edu.au Elza Wu.

2 . Inroducon Soveregn cred rang, whch publcly reveal opnon of pecal nformaon nermedare abou he cred qualy of a naonal governmen, are expeced o nfluence he behavor of ae prce, epecally durng perod of marke uncerany and fnancal nably. Ye, he Cred Rang Agence CRA ha provde h nformaon, have ofen been crczed for her low repone o fnancal cre a well a her nably o forewarn marke parcpan ee Mora, 2006 and Goron, I, herefore, neceary o ae he mpac of cred rang decon provded by CRA on he behavor of fnancal marke. Th paper develop a new approach o accuraely capure he mpac of overegn cred aemen on fnancal reurn drbuon. Focung on fnancal reurn drbuon enable an mproved underandng of fnancal marke parcpan reacon o overegn rang nformaon and can alo beer nform oher fnancal decon for rk managemen and ae allocaon purpoe. The dynamc of hgher reurn momen uch a varance, kewne and kuro are documened o nfluence ae prce ee among oher, Harvey and Sddque, 2000, Ahayde and Flôre, 2003 and Mandelbro and Hudon, The aymmery and more generally, he al behavour of reurn drbuon are known o be mporan for ae prcng and nvemen managemen. Ye he exan leraure ha radonally examned he effec of overegn rang change on he fr momen of ae reurn drbuon ee for example, Brook e al., 2004, Gande and Parley, 2005, Ferrera and Gama, 2007; Hll and Faff, 200a, Alakka and ap Gwlym, 202a,b or ae correlaon durng fnancal cre Chang e al., 2007 bu here a dearh of aenon on he mpac of cred rang change on hgher ae reurn momen. A poenal reaon for h vod n he leraure he lmaon of he paramerc mehod ued n emang he condonal hgher momen 2. In recen me, an ncreang avalably of nra-day daa ha 2 Due o he lmed avalably of hgh frequency daa, he hgher momen were ofen emaed condonally baed on he well-known Generalzed Auoregreve Condonal Heerokedac GARCH model and varan. The 2

3 provded a beer alernave for meaurng he hgher momen of ae reurn ung nonparamerc mehod. The ue of nraday daa compared o daly daa can gve u a beer repreenaon and more robu emae of acual ae prce behavor ee for nance, Anderen e al., In h paper, realzed hgher momen conruced from nraday reurn, are reaed a obervable varable and, herefore, can be modelled drecly whn an economerc framework. Furhermore, we accoun for he propere of he realzed hgher momen n he emprcal modellng proce. Our prelmnary analye how ha realzed reurn and kewne exhb hor memory behavor; wherea realzed volaly and kuro are more lkely o be long memory procee 3. A long memory proce condered a an nermedae beween wo clacal procee, he hor-memory I0 and he un roo proce I. More precely, defned correpondng o he cae of a fraconal degree of negraon. Our propoed emprcal model can accommodae fraconal degree of negraon hereby capurng boh hor- and long-memory behavor n realzed momen. A gnfcan number of ude have modelled overegn cred rang ranon due o crcal role n modern cred rk managemen, valuaon and nernaonal ae allocaon ee among oher, Banga e al., 2002, Lando and Skødeberg, 2002, Fuere and Kaloychou, 2007 and Hll e al., 200b. The emaon of he rang ranon probable marx ha ndcaed a regme wchng behavor n cred rang whch need o be accouned for n he modellng of overegn emae of condonal volaly, kewne and kuro, herefore, rely heavly on hee model underlyng aumpon. In addon, he problem magnfed whn a mulvarae yem due o he large number of parameer ha need o be emaed for exracng he oupu of condonal hgher momen. 3 Fgure 3 llurae he long memory behavor of realzed volaly and kuro nce her auocorrelaon de ou lowly and her pecral dene are unbounded a he orgn; wherea, he realzed reurn and kewne evolve a hor memory procee becaue of her mmedae ded ou auocorrelaon and her bounded pecral dene a he orgn. 3

4 cred rang fnancal marke mpac. In eence, cred rang, eher n level or fr dfference.e., rang change, can be caegored no regme ae, for example, ae of rang level can be defned a each of leer degnaon AAA, AA+, ; wherea, ae of rang change may nclude able.e. no change, downgrade or upgrade. The conderaon of rang regme or rend n rang change whch we call drf boh ueful and novel a h conen wh nveor ue of menal accounng n behavoral fnance Hrchlefer, 200. Inveor are lkely o repond dfferenly o rang revon dependng on he phae of he cred rang cycle and h uppored by he eablhed aymmerc reacon of ock and currency marke reurn o rang downgrade relave o upgrade Brook e al., Hence, we develop an emprcal framework ha no only allow a flexble e of fraconal degree of negraon for endogenou varable a menoned earler bu ha alo capure he perceved regme wchng behavor of overegn cred rang. Our udy conrbue a new emprcal framework o he curren leraure on he marke mpac of overegn rang. We allow a mulvarae yem of long memory procee o be condoned on obervable regme ha are baed on he characerc of overegn cred qualy aemen acro he European regon o accoun for common rang nformaon. I concevable ha nveor whn he European Unon EU would no only repond o cred aemen for her own naonal marke bu alo hoe gven for oher EU counre. By accommodang boh he long range dependence of realzed hgher momen and he regme wchng feaure of common overegn cred rang nformaon, he propere of hee meaure can be properly accouned for. The necey of ncludng hee feaure whn one framework ha been uppored n he recen leraure, for nance, Debold and Inoue 200, Haldrup and Nelen 2006 and Haldrup e al Our approach dnguhed from exng model a alo allow for he preence of exogenou varable. Th feaure mporan for aeng he effec of overegn rang whch are no deermned by he yem of endogenou varable.e. he realzed momen. Lkewe, he feaure alo ueful a allow many conrol varable o be 4

5 ncluded alongde overegn cred aemen. Furhermore, we dfferenae our approach furher by ung an alernave emaon procedure. The propoed echnque, whch concenrae he lkelhood funcon on fraconal degree of negraon, may help o faclae our model n nance wh hgher dmenon nce he objecve funcon numercally opmzed over a maller number of parameer n comparon wh exng echnque. We llurae our new approach by emprcally nvegang he mpac of overegn cred aemen on European ock and foregn exchange FX reurn drbuon. Alakka and ap Gwlym 203 provded evdence ha overegn cred aemen preened mporan gnal of mpendng fcal problem for currency marke parcpan durng n he European Deb Cr up o 200. We examne a longer perod from January 996 o July 202, o cover he lead up o he nroducon of he Euro a well a he hegh of he European overegn deb cr hereafer, EDC n when he European Cenral Bank ECB wa forced o nervene n European fnancal marke wh a long erm refnancng operaon LTRO o njec lqudy and lower borrowng co. Prevou ude on he EDC lke Calce e al. 203 have documened wdenng cred pread up o 200 acro Europe bu he ubequen developmen n European fnancal marke are le clear. No urprngly, all CRA have been parcularly acve n downgradng European overegn durng he recen deb cr wh on average, nearly 70% of all rang downgrade n our ample akng place nce December 2008 he one of he EDC ee Fg.. We conrbue comprehenve and new evdence of overegn rang mpac on European fnancal marke durng he EDC. We employ overegn rang daa from Sandard and Poor, Moody and Fch he hree man CRA n he world - n order o fnd ou whch agency ha he greae mpac on fnancal reurn drbuon va her fr four realzed momen. Alhough prevou ude have ndcaed he large mpac from Sandard and Poor e.g., Reen and Malzan, 999, and Brook e al., 2004, recen acve of he CRA durng he EDC may change her rank order. In lne wh h vew, Alakka and ap Gwlym 202a, 203 fnd ha over he perod from , Fch overegn cred gnal nduced he mo mely currency marke 5

6 repone. In addon, prevou ude nvegaed he ue baed on caualy e and conduced even ude, whch may only capure he drec effec of he CRA re-rang acve. We argue ha he marke mpac of he CRA hould be meaured n erm of her oal effec, whch nclude boh drec and ndrec force. In a mulvarae framework, where he ner-relaonhp among realzed momen are capured, we defne he ndrec effec of he CRA on a realzed momen a he pllover effec ha goe hrough oher realzed momen. Th effec ha been gnored n he leraure bu mporan for gaugng he full effec of overegn cred aemen on fnancal reurn drbuon. Laly, n h paper, we furher conrbue o he leraure by developng a ool ha can capure he oal effec of he CRA o reveal whch agency elc he greae marke reacon.e., ha he mo nfluence on fnancal reurn drbuon n our conex. We beleve h he fr udy o dnguh beween he drec and ndrec effec of cred rang agence acon whn fnancal marke and mporan o conder boh manfeaon on fnancal marke ably. The remander of h paper organzed a follow. We decrbe he daa conrucon n econ 2. Secon 3 propoe our new economerc model and emaon procedure. We dcu he fndng of our emprcal analy of he European fnancal marke n econ 4. An mpule repone of a ranfer funcon developed o reveal he mo powerful CRA n econ 5. Fnally, we conclude our reearch n econ Daa We capure 5-mnue nraday ock and FX marke prce n ome European Unon EU counre from he Thomon Reuer Tck Hory TRTH daabae provded by he Secure Indury Reearch Cenre of Aa-Pacfc SIRCA. By ung 5-mnue nraday daa, we can mnme he problem of meauremen error due o a reducon of mcrorucure bae 4. The 4 I commonly known ha mcrorucure bae e.g., bd-ak bounce, prce dcreene and nonynchronou radng caue meauremen error n he compuaon of realzed volaly. However, Anderen e al. 200 demonraed ha 6

7 ample perod uded from January 996 o July 202, whch cover he perod from pre- Aan Fnancal Cr unl he recen European Soveregn Deb cr EDC. We employ he FX daa quoed agan he USD from 2 counre: Aura, Belgum, Bulgara, Cypru, Czech, Denmark, France, Germany, Greece, Hungary, Ireland, Lava, Mala, Neherland, Poland, Porugal, Romana, Slovaka, Span, Sweden and he Uned Kngdom. However, due o lmed avalably of he hgh frequency daa, our daae for ock marke only con of 0 ock marke ndce from whn he European Unon EU, ncludng Aura, France, Germany, Greece, Hungary, Ireland, he Neherland, Romana, Span and he Uned Kngdom. In addon, we employ horcal long-erm foregn currency overegn cred rang and cred oulook and wache from hree leadng CRA - Sandard and Poor, Fch and Moody. Th wll enable an aemen on whch CRA nfluence European ock marke reurn he mo va overegn rang acon. Due o he rregular mng of rang announcemen, we focu our analy on a monhly ba. We follow he approach of Gande and Parley 2005 and Ferrera and Gama 2007 among oher o ranform he overegn rang and cred oulook and wache no lnear core 5. We ummarze all rang new releaed durng each monh ung he comprehenve cred rang CCR meaure 6. Fgure llurae how acve he CRA are n re-rang EU overegn oblgor. A can be een, he CRA have more ofen upgraded han downgraded EU counre over he enre ample perod bu no urprngly mo of he downgrade new on EU naon were releaed durng he mo recen overegn deb cr around 70% of all downgrade rang new n our ample. Among he hree CRA, Fch eem o be he lea acve agency n downgradng EU overegn; wherea, he number of upgrade releaed by Moody for EU counre he malle mulaon of he 5-mnue amplng nerval produce mean quare error relavely cloe o he opmal nerval. Bede, he ue of 5-mnue daa o conruc realzed kewne and kuro uggeed by Amaya e al Deal wll be avalable upon reque. 6 The CCR calculaed a he um of lnearzed overegn cred rang and he cred oulook/wache followng he approach of Gande and Parley

8 uggeng ha hey are he mo conervave of he major CRA. Overall, he abolue number of rang announcemen ha ndcaed ha Sandard and Poor can be condered a he mo acve rang agency for counre n he EU corroborang wh pror ude ha compare acro rang agence uch a Brook e al., [Iner Fgure here] To conruc a proxy for he opnon of a CRA abou he overegn cred qualy of he EU overall, we ule he overegn rang drf meaure, whch he average change n cred qualy acro all EU member counre. The rang drf acro he EU can be calculaed for each CRA a, SRD m CCR m where CCR he fr dfference of he CCR meaure of counry, and m he number of counre ued o conruc he rang drf. Snce we am o ae he opnon of a CRA abou he whole EU overall, we nclude horcal overegn rang daa of all 27 EU counre o conruc he drf meaure. The overegn rang drf adequaely reflec he vew of a CRA on he average rend n he cred qualy of all overegn oblgor n he EU regon a a whole. The plo of he overegn cred rang drf for he hree major CRA hown n Fgure 2 ndcae ha he rang drf can be clafed no hree obervable regme or ae over me, whch are zero, pove and negave zone. Thee hree zone can be nferred a he regme of able, upward and downward rend n overegn cred qualy acro he EU a perceved by each of he CRA. Furhermore, can be oberved ha mo of he negave rang drf are n he perod of he overegn deb cr, conen wh wha ha been hown n Fgure. We can, herefore, conder he regme of downward overegn cred qualy a prmarly he epode of he European overegn deb cr EDC. 7 Over he enre ample perod, Sandard and Poor releaed 2 downgrade and 24 upgrade. Meanwhle, Moody made 09 downgrade and 09 upgrade. Alongde hee, Fch announced 9 downgrade and 5 upgrade. 8

9 [Iner Fgure 2 here] To model he ock marke and FX reurn drbuon, we conruc her hgher momen baed on nraday reurn raher han employng daly cloe o cloe prce nce he ue of nraday daa wdely documened o provde more conen and effcen emae ee Anderen and Bollerlev, 998, Barndorff-Nelen and Shephard, 200 and Anderen e al., 2003 among oher. The daly realzed reurn conruced from nraday reurn are dencal o he uual daly reurn calculaed from daly cloe o cloe prce, D r r, 2 where r, denoe he h 5-mnue logarhmc reurn durng day and D denoe he oal number of 5-mnue logarhmc reurn nerval durng any radng day. We follow Anderen e al and Amaya e al. 203 o defne he realzed volaly RV, realzed kewne RS and realzed kuro RK repecvely a 8, D RV r 2, 3 RS D D 3 / 2 RV r 3, 4 RK D D 4 r, 2 RV 5 To faclae emprcal eng, he monhly realzed meaure are hen conruced a average of correpondng daly realzed ere. We graph he ample auocorrelaon and pecral dene of realzed reurn, logged realzed volaly, realzed kewne and logged realzed kuro for a lag of 50 monh n Fgure 8 The propere of realzed volaly a defned n Eq. 3 are well analyzed n he leraure e.g., Anderen and Bollerlev, 998 and Anderen e al., Meanwhle, he lm of realzed kewne and kuro under he form of Eq. 4 and Eq. 5 are recenly aeed n Amaya e al.,

10 3 9. There evdence of long memory behavor n he realzed volaly and realzed kuro ere e., econd and fourh momen revealed by he low hyperbolc auocorrelaon decay and he mo ma a he zero frequency of he pecral dene. Meanwhle, he ample auocorrelaon of realzed reurn and realzed kewne flucuae around zero durng he dplacemen of 50 monh, exhbng he propery of hor memory procee. [Iner Fgure 3] 3. Economerc modellng The propere and feaure of he four realzed momen of fnancal reurn and he overegn rang drf dcued n he prevou econ, movae u o develop a flexble mulvarae framework ha can capure boh long memory and regme wchng behavor n hee ere. Alhough here have been ome ude debang he nerchange beween long memory and non-lnear model 0, neceary n our cae o mulaneouly accommodae boh long range dependence and regme wchng behavor n order o adequaely accoun for he propere of our varable of nere. The recen leraure alo uppor he mporance of ncludng hee feaure whn a ngle framework, for nance, Debold and Inoue 200, Haldrup and Nelen 2006 and Haldrup e al In our cae, he overegn rang drf are clearly dnguhed by hree eparae regme, whch repreen he perod of able, upward and downward rend n overegn cred qualy. In he able perod, overegn rang drf ha no mpac on he fnancal reurn drbuon a equal o zero. On he oher hand, n he upward and downward regme, 9 We ulze he naural logarhm of realzed volaly and kuro n our analy conen wh he exan leraure e.g., Anderen and Bollerlev, 998 and Anderen e al., Furhermore, he ue of realzed logarhmc volaly and kuro help u o avod he non-negavy condon n modelng. Therefore, when we refer o he realzed volaly and kuro meaure, hey are n naural logarhmc form. 0 See for example, Granger and Dng 996, Bo e al. 999 and Granger and Hyung We can alo nerpre hee regme a he perod n whch CRA releae good new and bad new regardng overegn cred qualy acro he EU. 0

11 he mpac of overegn rang drf on fnancal reurn drbuon and he characerc of he fnancal reurn drbuon elf can be very dfferen. Accordngly, he long memory behavor of he realzed momen of ae reurn hould no be fxed acro he hree regme. Inead, we allow long memory behavor under he form of fraconal negraon o vary acro hee regme of overegn rang drf. Tha, o examne how fnancal reurn drbuon behave durng he perod of upward and downward rang drf, we conder he ex-ane regme ha are defned by he drecon of he overegn rang drf. We ule a mulvarae long memory model wh exogenou varable ha are allowed o wch beween dfferen regme. We model he realzed momen of ae reurn a endogenou varable n he yem and we ake he vew ha he overegn rang drf no necearly explaned by he yem of hoe realzed momen. Th aumpon uppored by he myrad of pror ude howng he gnfcan marke mpac of overegn cred rang nformaon ee ner ala, Alakka and ap Gwlym, 202a, Brook e al., 2004, and Hll and Faff, 200a. The overegn rang drf raher deermned by publc nformaon a well a he prvae nformaon owned and ubjecvely aeed by he CRA. Therefore, we rea he overegn rang drf a an exogenou varable, whch defne he ae regme and may help o explan he realzed reurnbaed meaure. Our model dfferen o he exng model n he leraure e.g., Haldrup and Nelen, 2006 and Haldrup e al., 200 n he ene ha allow for he exence of exogenou varable. We furher dnguh our model by propong a dfferen echnque ued n he emaon procedure. Th echnque enable our model o be applcable for a hgher dmenonal yem, whch alo an advanage over exng model a we can model he fr four realzed reurn momen mulaneouly. Inead of numercally opmzng he objecve lkelhood funcon wh regard o all parameer a n he leraure, we furher concenrae he objecve funcon wh regard o he degree of fraconal negraon. Hence, he numercal opmzaon procedure much faer and, perhap, more relable han prevouly poble. 3. Model pecfcaon and aumpon

12 Le he K-dmenonal me ere, Y K Y,..., Y, follow a Markov Regme Swchng and Fraconally Inegraed Vecor Auoregreve model wh n exogenou varable MS-FIVARX, R 2 n R,,..., R R : A R + ε, L D L Y,2,..., T 6 We defne {,2,..., M} a he obervable regme varable whch characerzed by he behavor of one of he exogenou varable R and follow an ergodc M-ae Markov chan proce wh a M M rreducble ranon probably marx, P { p j ;, j,2,..., M}. We defne p Pr + j and p j M j j,, j {,2,..., M}. In oher word, pj he probably ha a regme followed by a regme j. The operaor, A L I K p A L, where p he lag order of he lag polynomal and A he K K marx of coeffcen aocaed wh he endogenou varable. he K n marx of coeffcen aocaed wh he exogenou varable. The operaor D L a d d2 d K dagonal K K marx formed a, D L dag{ L, L,..., L }. We can employ he bnomal expanon o operaonally generae he erm L d j a, L d j 0 Γ + d j L Γ d Γ + j 0 ψ d j L where Γ. he gamma funcon; ψ, and ψ 0, for 0. 0 A n he repreenaon of he MS-FIVARX, all he coeffcen marce, he degree of fraconal negraon a well a he varance covarance marx of error erm are aumed o be regme dependen, whch mean ha hey are condonal on, for example, 2

13 M f f M To enure he adequacy, aonary and o avod he mulcollneary problem, he followng addonal aumpon have been made for our MS-FIVARX model: Aumpon 3.: ~ 0, ε N Σ ; Σ { σ ;, j,2,..., K} are K K pove defne marce, E ε ε 0, for all r. r ε ε j Aumpon 3.2: All he roo of A z p I K A z 0 fall oude he un crcle and d 0.5, 0.5 for all j,2,..., K. j Aumpon 3.3: Y ha no deermnc rend. Y, Y 2,..., Y p are no perfecly collnear and each elemen of R 2 n R,,..., R R ndependen of each oher. 3.2 Emaon of ranon probable Snce he regme varable aumed o be obervable and deermned by he behavor of he exogenou varable R, we may explo R o coun he number of he obervaon n each regme a well a he number of ranon among regme. Thee fgure ubequenly can be ued o emae he ranon probably marx P. Therefore, he maxmum lkelhood emae MLE of he ranon probable are mply gven a, p j M n m j n m,, j {,2,..., M} 8 where nj he number of me ha we oberve a regme ha followed by a regme j. 3.3 Emaon of he model parameer We oban he emae of remanng parameer n he model by ung he qua maxmum lkelhood va he concenraed log-lkelhood funcon CLF. For a pecfc regme, model 3

14 pecfcaon 6 follow a Fraconally Inegraed Vecor Auoregreve framework wh exogenou varable FIVARX. Hence, he CLF of our MS-FIVARX model n a pecfc regme can borrow he form of he CLF of a FIVARX model. For mplcy, we gnore he erm n conrucng he CLF of a MS-FIVARX model n a pecfc regme nce n fac under he repreenaon of a FIVARX model. Le u conder, A L D L Y R + ε,,2,..., N 9 Furher, we aume ha he p pre-ample value of each endogenou varable, avalable. The followng noaon are employed o faclae our dervaon, X D L Z Kp+ n Lemma 3.: Y X X p R, X X, X,..., X, B A, A,..., A,, K N + 2 N K Kp+ n 2, Z Z 0,..., Z N, U ε, ε 2,..., ε N, Kp+ n N K N Le he aumpon 3., 3.2, 3.3 hold and he varance-covarance marx of error erm wren a a funcon of all parameer a, Σ N ε d, B N ε ε For a gven memory parameer d, Σ d, B can be denoed a d,, hen he followng reul hold, N N [ A L D L Y ][ ] R A L D L Y R ε p Σ ε d B Y p+,...,y 0, are d, Σ ε d B mnmzed a ˆ B XZ ZZ, and, Σ d, B N X BZ ˆ X BZ ˆ. ε d mn Followng Lemma 3., we can oban he CLF wh regard o he memory parameer d of a FIVARX model a preened n he propoon, Propoon 3.: 4

15 Le he aumpon 3., 3.2, 3.3 hold, he concenraed log-lkelhood funcon wh repec o he vecor of memory parameer d d,..., d K of a FIVARX model, l c FIVARX KN N d ε d 2 2 [ ln2π + ] ln Σ where, Σ d T X I N Z ZZ Z X and he emaor are obaned by, ε dˆ arg max l d 0.5,0.5 c FIVARX d, and B ˆ XZ ˆ ˆ Zˆ Zˆ Accordng o Propoon 3., we can oban he condonal log-lkelhood funcon of our MS-FIVARX model, apar from conan, for a pecfc regme a follow, where I he ndcaor funcon reurnng f and 0 oherwe. The full-ample CLF of a MS-FIVARX model wh repec o he vecor of memory c c parameer gven by l d l d. l M I T c d ln Σε 2 Alernavely, we collec all he nformaon of he regme durng he ample perod n a d, M ξ I, I 2,..., I M vecor, [ ], and, he varance-covarance marce of error erm concenraed on Σ d K MK d, ε, for M regme n he marx, Σ [ Σ ε d,..., Σ d M ε MS-FIVARX model a 2, ]. We have he ulmae repreenaon of he full-ample CLF of a T c l d ln Σ ξ I K Dealed proof of Lemma 3. and Propoon 3. a well a dervaon o acheve he form of 0 are avalable upon reque. 5

16 A he fr age, he memory parameer he l c d wh repec o d, ˆ d c arg max l d. can be obaned by numercally maxmzng Remanng parameer Bˆ for each regme are exraced condonal on emaor d ung he reul obaned n Propoon Emprcal reul We ule our propoed model by employng realzed reurn-baed meaure conruced n econ 2 o nvegae he mpac of he overegn rang drf on ock marke and FX reurn drbuon whn he EU. Snce he prelmnary analye performed n econ 2 affrmed he hor memory behavor of realzed reurn and kewne, we rerc her memory parameer o be zero. The fraconal degree of negraon for realzed volaly and kuro are allowed o vary acro regme. A dcued n prevou econ, we dnguh he relaonhp beween realzed reurn momen and CRA overegn rang change no hree regme whch are defned by he propere of he overegn rang drf. Thee regme can be condered a he perod of able, upward and downward aemen of overegn cred qualy, correpondng o zero, pove and negave value on overegn rang drf repecvely. We focu on he reul obaned n he upward and downward regme. Alo, a noed n econ 2, he me ere plo of he overegn rang drf Fgure 2 ndcae ha he perod of he EDC promnen and cover almo he enre downward regme. We, herefore, conder he downward ae a a repreenaon of he European overegn deb cr. d 0.5,0.5 d More mporanly, o faclae he nerpreaon of he effec of downward overegn rang drf on each realzed momen, we employ he abolue value of he downward drf n modellng. Hence, a pove relaonhp beween he drf and he realzed reurn n he downward regme, for example, can be nerpreed a more negave aemen of overegn cred qualy wll lead o an ncreae n he realzed reurn conen wh he bac rk-reurn rade-off n Fnance heory. ˆ 6

17 We chooe he opmal lag lengh p for he model o ha he nnovaon mmc he whe noe procee and he parmonou crera afed. We, herefore, end up wh he lag lengh of order for our model. Th reul reaonable a boh characerc of he meaure, he long memory and regme wchng feaure, whch may requre a large number of lag order have been capured by he pecfcaon of he propoed model. The emaed reul how ha all he roo fall oude he un crcle and he memory parameer are n he range from -0.5 o 0.5, an ndcaon of aonary The ranon probably marce A he regme are obervable, we can ealy calculae he emae of ranon probable for each regme accordng o formula 8. We preen he emaed reul of he ranon probably marce n Table. [Iner Table ] The emae ndcae an average level of perence of he regme. The probable ha he overegn rang drf ay n one regme are a mo 0.5. Among all, he probable of ayng n he upward regme are he lowe.e., 0.25, 0.38 and 0.28 for he Sandard and Poor, Fch and Moody repecvely. There a relavely hgh lkelhood of remanng n he able ae.e., 0.38, 0.48 and 0.49 for Sandard and Poor, Fch and Moody repecvely compared o eher upward or downward ae, conen wh he vew ha CRA provde long-erm aemen on overegn cred qualy and he pracce of rang hrough he cycle. Thee fgure n conjuncon wh he probable of redng n he upward regme, however, mply omewha ha he CRA have no been acve n re-aeng overegn cred qualy acro he EU pror o he one of he EDC. In conra, here are relavely hgh level of perence n he downward regme.e., 0.45, 0.50 and 0.39 for Sandard and Poor, Fch and Moody repecvely ndcang ha CRA eem 3 We do no repor he full e of our emaon reul o conerve pace. However, full deal are avalable upon reque. 7

18 o have learn leon from he Global Fnancal Cr and have become more acve n downgradng overegn cred qualy hroughou he EDC. 4.2 Impac of he overegn cred aemen on fnancal reurn drbuon In h econ, we analye he drec mpac of he overegn rang drf on each realzed momen of he EU ock and FX reurn drbuon by ung he Granger Caualy e. Hence, we exrac he emae of he vecor and her correpondng -ac. 4 Drec mpac on European ock and FX realzed reurn We repor he effec of overegn cred qualy aemen on realzed reurn acro boh he upward and downward regme n Table 2. A can be een, he overegn rang drf are lkely o have ngnfcan mpac on ock marke realzed reurn n boh upward and downward regme. Th reul mple ha he overall aemen of CRA on European overegn credworhne have lmed drec conrbuon o change n realzed ock marke reurn acro he EU. However, f we focu on he drecon nead of he gnfcance of he relaonhp, we fnd a negave mpac of he upward rang drf on realzed ock marke reurn whle downward rang drf end o have pove effec. Th fndng conen wh he bac rk-reurn rade off heory n Fnance nce he upward rend n he overegn cred qualy evaluaon reveal a endency of lower cred rk; wherea, he downward rend ndcae ncreang cred rk. [Iner Table 2] We fnd ha realzed FX reurn reac gnfcanly o Sandard and Poor re-rang n he upward regme bu repond more o Moody re-rang n he downward regme durng he EDC. Inerengly, h reul dffer from prevou ude n wo way. Frly, our reul ndcae ha FX reurn reac povely o only Sandard and Poor upward rang drf; wherea Alakka and ap Gwlym 200, 203 fnd a domnan role of Moody pove new. Secondly, whle Alakka 4 For he purpoe of calculang he -ac, we oban he aympoc covarance marx of he concenraed maxmum lkelhood emae a he negave nvere of he oberved Hean marx. 8

19 and ap Gwlym 203 repor an aocaon beween negave rang new and gnfcan currency deprecaon, we fnd a pove mpac of Moody downward rang drf on FX reurn. Our reul, neverhele, conen wh he bac rk-reurn rade off heory a noed prevouly. One poble explanaon for our dfferen reul wh he leraure our focu on he mpac of he overall EU credworhne aemen, whle prevou ude look a he effec of overegn rang of ndvdual counre. Hence, we conrbue new evdence on overegn rang mpac a a regonal level o caer for he unque economc arrangemen whn he EU. Drec mpac on European ock marke and FX realzed volaly The effec of overegn cred aemen on realzed volaly acro boh upward and downward regme are hown n Table 3. I can be oberved ha he overegn rang drf have lmed mpac on boh ock and FX realzed volaly n he upward regme. However, here more evdence of her gnfcan effec n he downward regme. Th reul ndcae ha he aemen of he CRA on overegn cred qualy acro he EU have greaer effec on he uncerany and/or he dperon of opnon wh repec o he value of European ock and currence durng he recen EDC. [Iner Table 3] A expeced, we fnd a conenly negave relaonhp beween he upward rang drf and realzed volaly n boh ock and FX marke. Meanwhle, he downward rang drf have gnfcan and pove effec on realzed volaly. The reul unambguouly ndcae ha mprovemen n CRA aemen on overegn cred qualy acro he EU reduce ock and FX marke uncerany; wherea connung negave aemen wll ncreae marke uncerany. Th fndng conen wh he emprcal reul whch we obaned n analyng he drec mpac of rang drf on realzed reurn from he prevou ub-econ. The explanaon for h conency can be baed on he rk-reurn rade off heory n Fnance. Drec mpac on European ock and FX realzed kewne 9

20 Table 4 repor he effec of overegn cred aemen on realzed kewne n ock and FX marke acro boh upward and downward regme. For he ock marke, we fnd ha he cae of Sandard and Poor overegn rang drf provde rong evdence of he drec effec n he upward regme; wherea, n he downward regme, more evdence of he drec effec revealed for Fch overegn rang drf. Th reul ndcae ha Sandard and Poor aemen on overegn credworhne whn he EU have relavely broader mpac on he aymmery of ock marke reurn drbuon durng perod of fnancal ably. Meanwhle, Fch ha evdenly played a more crcal role n h regard durng he recen EDC. In he FX marke, we oberve he revere uaon nce Fch rang delver greaer drec effec n he upward regme; wherea, Sandard and Poor rang effec are ronger n he downward regme. [Iner Table 4] Inerengly, n erm of boh ock and FX marke, we moly fnd a pove relaonhp beween overegn rang drf and realzed kewne n boh upward and downward regme. Hence, regardle of he upward or downward drecon, a long a he rang drf change.e., more rang new are releaed, he magnude of he pove exreme reurn n EU ock and FX marke larger more rgh-kewed. Drec mpac on European ock and FX realzed kuro The effec of overegn cred aemen on realzed kuro acro boh upward and downward regme are ummarzed n Table 5. We fnd lmed evdence of gnfcan effec n he upward regme bu greaer evdence of he gnfcan relaonhp beween overegn rang drf and realzed kuro can be found n he downward regme. Hence, he reul how ha he aemen of he CRA on overall overegn credworhne acro he EU have greaer mpac on he occurrence of exreme reurn n ock and FX marke durng he EDC. [Iner Table 5] In addon, we moly fnd he negave relaonhp beween he overegn rang drf and realzed kuro n he downward regme; wherea, he upward rang drf end o povely affec 20

21 realzed kuro. Thee reul ndcae ha an upurge n he downward upward rend of he CRA aemen on EU overegn oblgor wll gnfcanly lower ncreae he peak of ock and FX reurn drbuon for European counre. Th reul conen wh wha we have found n he analy of he drec mpac of overegn cred aemen on realzed volaly. Th becaue a reurn drbuon wh a lower hgher peak correpond o a drbuon wh more le reurn dperon. Bede, a menoned n he prevou ub-econ, we noe ha an ncreae n he downward upward rang drf wll heghen decreae ock and FX marke volaly acro he EU. 5. The mo domnan cred rang agency The emprcal reul dcued o far confrm ceran mpac of each CRA overegn rang on fnancal reurn drbuon va fr four realzed momen. I, however, reman queonable whch CRA ha he large effec on fnancal marke. In econ 4, we aeed he drec mpac of CRA aemen ung Granger Caualy e. Ye, h mehod no applcable o addre he ue of domnance among he CRA a h hould be refleced by her oal effec ncludng boh drec and ndrec force. Becaue of he ner-relaonhp among realzed momen, whch alo capured n our mulvarae yem, he ndrec effec of he overegn rang drf on a realzed momen he pllover effec ha goe hrough oher realzed momen n he yem. In h econ, we develop a ool, whch we call he mpule repone of a ranfer funcon IRTF, o capure hoe oal effec of he CRA aemen. The IRTF decrbe how endogenou varable reac when here an exogenou hock o he exogenou varable. The funcon, herefore, deal for capurng he oal repone of a fnancal reurn drbuon o a change n he overegn rang drf nce uch a change uually caued by a hock from oude arrvng under he form of publc or prvae nformaon whch aeed by he CRA. 5. Impule repone of a ranfer funcon 2

22 Under he bac aumpon whch have been made n prevou econ, we can rewre model pecfcaon 6 under an nfne movng average repreenaon MA. Smlar o wha ha been derved n Do e al. 203, we can ealy oban: where, and, The K K coeffcen marx can be calculaed ung he followng relaonhp,, where he dagonal K K marx wh noed n formula 7 a he j h elemen, and obaned accordng o he followng recurve relaonhp, Baed on he MA repreenaon of a MS-FIVARX model, we employ he generalzed approach propoed by Koop e al. 996 o develop our IRTF. The IRTF a a horzon h, herefore, defned a he dfference beween he condonal expecaon of Y+h, gven he nformaon e avalable a me - afer ncorporang he effec of he hock on exogenou varable and he condonal expecaon whou he effec of he hock,, where n vecor of exogenou hock on he exogenou varable R. L R L Y ε + Φ Φ Φ + Φ h h L L Φ + Φ h h K L I L Φ h Π Π Ψ Φ 0,2, h h h h d h d Ψ d j ψ Π > Π Π Π 0,2,..., I p A p A K p j j j j j j, + + Ω Ω h h h Y E R Y E IRTF δ,..., n δ δ δ 22

23 Under an addonal aumpon ha E 0, we ulmaely oban he full marx of R mpule repone of a ranfer funcon a 5, IRTF h Φ h Ξ where Ξ* dag{ δ, δ 2,..., δ n} a n n dagonal marx characerzed by elemen of he hock o R 6. Accordngly, we can nerpre he, j elemen of IRTF h a he repone of he h endogenou varable a horzon h.e., a me +h o a hock hng he j h exogenou varable a me. I can be ealy een ha under equaon, he ndrec effec of he exogenou hock n Φ h R on Y are capured n he marx ; wherea, he drec effec are capured by he marx. 5.2 Emprcal reul on mpule repone analye We calculae he IRTF baed on a one andard devaon hock n he overegn rang drf a h he uual choce n he leraure feaurng mpule repone analye. We repor he average repone of EU ock marke and FX realzed momen o he hock n he overegn rang drf for 20 perod ahead n Fgure 4 and 5, repecvely. [Iner Fgure 4 & 5] A can be een, Sandard and Poor aemen have he greae mpac on ock marke realzed reurn and kewne for he fr 5 perod ahead n he upward regme. Th reul conen wh he leraure, for example, Reen and Malzan, 999, and Brook e al., 2004, alo fnd ha he rang acon of Sandard and Poor affec ock marke reurn more han oher CRA. However, he cae of hgher momen ha no been nvegaed o dae. In our analy, he 5 We ue he MA repreenaon of Y o derve he dfference beween he wo condonal expecaon and oban he fnal form of he IRTF accordngly. Snce he ep nvolved are rval, we kp o he reul o conerve pace. 6 Followng Koop e al. 996 and Pearan and Shn 998, we e he un hock a a one andard devaon hock. 23

24 emprcal reul how ha he overegn rang drf conruced from Fch rang have he large effec on ock marke realzed volaly n he upward regme; wherea, he magnude of effec on ock marke realzed kuro no clearly dnguhable among he major CRA. In he mo recen overegn deb cr repreened largely by he downward regme, he rank of he CRA regardng he magnude of he effec on realzed momen ha changed. We fnd nereng reul ha Moody aemen on overall EU overegn credworhne have he greae mpac on almo all ock marke realzed momen around he fr 5 perod. The only excepon he effec on realzed volaly, for whch Moody hare he rankng wh Fch rang nce her effec are que comparable. In erm of he FX marke, we conenly oberve ha Sandard and Poor and Fch rang drf have he greae mpac on FX realzed hgher momen n boh upward and downward regme. Meanwhle, he magnude of he effec on FX realzed reurn durng he EDC abou fve fold greaer han n able perod. Thee fndng are n lne wh he fndng of Alakka and Gwlym 202a, 203 bu we dffer n denfyng a rong mpac for Sandard and Poor a well a Fch rang when ndrec effec on hgher momen are condered. In addon, we noe ha here a conradcon n he reul beween he IRTF n h econ and he Granger Caualy e n he prevou econ n he cae of he effec on realzed reurn n an upward regme. For example, we fnd a negave relaonhp beween overegn rang drf and he ock marke realzed reurn n he upward regme ung he Granger Caualy e. However, he IRTF confrm h a pove relaonhp. The dfference n reul uppor her complemenary propery. Whle he Granger Caualy only e he drec caual effec, he IRTF capure boh he drec and he ndrec effec and provde a more complee pcure of he rang mpac. 24

25 6. Concluon In h udy we nvegae he effec of rend n overegn cred aemen on ock marke and FX reurn drbuon whn he European Unon EU va her fr four realzed reurn momen. To do o, we develop a mulvarae framework o precely capure he full effec of CRA overegn cred aemen on fnancal reurn drbuon by allowng endogenou long memory varable o be condonal on obervable regme wchng n exogenou varable. The model movaed by he necey o fully nvegae he mpac of overegn cred qualy aemen on fnancal reurn drbuon a here a dearh of aenon on he mpac of CRA announcemen beyond he uual fr and/or econd momen of ae reurn. The conen and robu emae of momen of he reurn drbuon.e., he realzed momen exhb long memory behavor whl he regme wchng feaure of overegn rang ha been wdely documened. Thu, our propoed model degned o capure boh of hee feaure n order o eparaely accoun for he propere of hee varable of nere. Our emprcal reul confrm he heerogeneou effec of rang acon acro regme, whch are defned o correpond o he upward and downward rend n overegn cred aemen by ndvdual CRA. Hence, hee reul llurae he uefulne of he propoed model nce mleadng concluon may be made f he proce no allowed o be condonal on eparae ae of credworhne. More pecfcally, we moly fnd a negave relaonhp beween he overall EU overegn cred aemen and realzed reurn n he upward regme, ye he pove relaonhp are oberved n he downward regme. Thee fndng are conen wh he bac rk-reurn rade-off n fnance heory, and are furher confrmed by he reul of overegn rang mpac on realzed volaly. The evdence moly how negave effec of rang drf on realzed volaly n he upward regme bu pove effec n he downward regme. Furhermore, change n he overall rang rend boh upward and downward reul n ock and FX reurn drbuon beng more rgh-kewed. Meanwhle, n erm of realzed kuro, we fnd an upurge n he downward upward EU overegn rang drf wll gnfcanly lower ncreae he peak of 25

26 he EU ock and FX reurn drbuon. The fndng conen wh emprcal reul obaned n analyng he mpac on realzed volaly. In h paper, we alo noe ha he oal effec of he overegn cred aemen on realzed momen can be dfferen from her drec effec alone. Th due o he ndrec effec, whch are caued by he ner-relaonhp and pllover beween he realzed reurn momen. Therefore, we argue n h paper ha he oal effec, raher han he drec one, hould be employed o nvegae whch CRA provde he greae mpac on fnancal reurn drbuon. We fnd ha he rank order among he CRA dffer for each realzed momen and ae marke. In he perod of fnancal ably, he aemen of S&P have he greae effec on ock marke realzed reurn and kewne; wherea Fch rang acon have he large mpac on ock marke realzed volaly acro he EU. Meanwhle, Moody rang acve domnae durng he recen European overegn deb cr. Bede, we conenly fnd ha S&P and Fch hare he rank order n havng he large effec on FX realzed hgher momen. Th pobly due o Fch beng he only major CRA baed oude of he US. 26

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29 APPENDIX Fgure - Rang acve of he hree cred rang agence 400 Rang acve durng he ample Moody' Fch S&P Downgrade Upgrade Proporon of rang new releaed durng he EU overegn deb cr S&P Fch Moody' Upgrade Downgrade Noe: The fr char ummarze he number of rang downgrade and upgrade releaed by he hree cred rang agence CRA, namely Sandard and Poor S&P, Fch and Moody durng our full ample perod. The econd char repor he proporon of rang even ha he CRA releaed durng he European overegn deb cr begnnng from Ocober

30 Fgure 2-The European Unon overegn rang drf 0.25 Sandard and Poor Fch Moody' Noe: Th fgure repor he overegn rang drf conruced accordng o formula from horcal long-erm foregn currency overegn cred rang daa for all 27 EU counre covered by Sandard and Poor, Fch and Moody. Fgure 3-Sample auocorrelaon funcon and pecral dene of he realzed momen Specral deny ACF-Realzed Reurn 2 Realzed Reurn ACF-Realzed Volaly Specral deny 2 Realzed Volaly ACF-Realzed Skewne Specral deny 2 Realzed Skewne ACF-Realzed Kuro Specral deny 2 Realzed Kuro Noe: Th frgure preen ample auocorrelaon and pecral dene of a repreenave ock marke realzed reurn, logged realzed volaly, realzed kewne and logged realzed kuro for a lag of 50 monh. 30

31 Fgure 4-Average repone of he EU ock realzed momen o he overegn rang drf Average repone of he EU ock realzed reurn Average repone of he EU ock realzed volaly Average repone of he EU ock realzed kewne Average repone of he EU ock realzed kuro S&P Fch Moody' Fgure 4a: Average repone of he EU ock realzed momen o he hock n upward rang drf Average repone of he EU ock realzed reurn Average repone of he EU ock realzed volaly Average repone of he EU ock realzed kewne Average repone of he EU ock realzed kuro S&P Fch Moody' Fgure 4b: Average repone of he EU ock realzed momen o he hock n downward rang drf 3

32 Fgure 5-Average repone of he EU FX realzed momen o he overegn rang drf Average repone of he EU FX realzed reurn Average repone of he EU FX realzed volaly Average repone of he EU FX realzed kuro Average repone of he EU FX realzed kewne Fch S&P Moody' Fgure 5a: Average repone of he EU FX realzed momen o he hock n upward rang drf Average repone of he EU FX realzed reurn Average repone of he EU FX realzed volaly Average repone of he EU FX realzed kewne Average repone of he EU FX realzed kuro S&P Fch Moody' Fgure 5b: Average repone of he EU FX realzed momen o he hock n downward rang drf 32

33 Table -Tranon probably marce of overegn rang drf Tran Sandard and Poor Fch Moody' from ae Sable Upward Downward Sable Upward Downward Sable Upward Downward Sable Upward Downward Noe: Th able preen he ranon probably marce of he overegn rang drf conruced a n formula from overegn rang daa provded by Sandard and Poor, Fch and Moody. The drf are caegored no hree obervable ae, namely he Sable, Upward and Downward aemen of overegn cred qualy correpondng o zero, pove and negave value of he overegn rang drf. The repored ranon probable are he probable ha he ae noed n he row followed by he ae noed n he column of he able. 33

34 Table 2a-Drec mpac of overegn rang drf on he EU ock realzed reurn Counre Upward rang drf Downward rang drf S&P Fch Moody' S&P Fch Moody' Aura France *** Germany Greece ** *** Ireland Neherland *** ** Span *** 2.78*** The UK *** *** Hungary ** Romana * Noe: Th able preen he emae of he fr elemen of he vecor and aocaed -ac n parenhee. Thee emae are nerpreed a he mpac of upward and downward overegn rang drf on he EU ock realzed reurn a compued n formula 2. The overegn rang drf, whch repreen he aemen of he CRA on overall EU overegn cred qualy, are conruced a n formula from rang daa provded by Sandard and Poor S&P, Fch and Moody. *, ** and *** denoe gnfcance a he 0, 5 and % level, repecvely. 34