FINDING INFORMED TRADERS IN FUTURES AND THEIR UNDERLYING ASSETS IN INTRADAY TRADING a Lydmila A Gli b, Oleg L Kisi c, Toms Polyechnic Univesiy, Rssia Absac We popose a mahemaical pocede fo finding infomed ades in la-high feqency ading We woe i as Veco ARMA and fond condiion of is saionaiy Fo he pice expose complied wih ARMA(,) we poved ha ndelying asse pice diffeence can be deived as ARMA(,) pocess Fo validaion of he model, we es an inflence of infomed ades in EUR/USD, GBP/USD, USD/RUB pais and fes, in gold and fes pices, in Rssian Tade Sysem shae index (RTS) and fes ading We fond some evidence of sch inflence in gold and cency pai USD/RUB picing, in RTS index in he peiod fom Dec 6 ill Dec 0, 03 and fom Jan 8 ill Jan 30 Keywods: infomed ades, inaday la-high feqency ading, ARMA consisency, fes, ndelying asses, pice disclose, mixed saegy JEL classificaion: G3, G4, G5, D8 Inodcion Idenifying of inside ades, defined hee as lage insiional invesos (sch as pension o hedge fnds, mae maes, deales and ec), is an acal and complex poblem They play an impoan ole in mainaining he opeaing pefomance of he soc mae by poviding i wih a high liqidiy, by eeping p some level of pices and ading volmes of financial insmens and by smoohing a significan pice volailiy Besides he special fncions, hey se pivileges which ae no accessible o individal invesos and speclaos (Schols e al (04); Lepone and Yang (03); Dey and Radhaishna (03)): hey may obain infomaion abo impoan macoeconomic indicaos fase, hey may also possess nonpblic infomaion abo fims befoe i a This wo was financially sppoed by Rssian Scienific Fnd b Toms Polyechnic Univesiy, 36 Lenin Ave, Toms, Toms eg, Rssia, 634050 c Coesponding aho Toms Polyechnic Univesiy, 30 Lenin Ave, Toms, Toms eg, Rssia, 634050 Tel:+738 4893 Fax: +738 59658 E-mail addess: olegol@p
is officially pblished in he qaely o annal financial epos Fo example, Schols e al (04) deemine he saisical significance of en changes and show an incease in ading aciviy befoe he official annoncemen ime of sch impoan economic indicaos as Chicago PMI and UMich Senimen I appeas ha sbscibes eceive infomaion 3 and 5 mines ealie han ohes And, a he ime of he annoncemen pblished daa is aleady inclded in he pice and significan spies disappea We inenionally did no deemine he impac of insides on he ading aciviy Fis, we assme ha he nmbe of insides is low in compaison o lage ades Second, hei aciviy is eglaed, fo example, by Seciies Exchange Ac (USA) o by Fedeal Law no 4-FZ (Rssia) Thid, he inside may benefi fom he disclose of pivae infomaion o infomed ades (see, eg, Gégoie and Hang (0); Li and Zhang (0)), becase i faciliaes he incease of mae aciviy and soc pices, heefoe pofi of he inside inceases oo The lieae on he deecion of inside and infomed ades is lage Even so, special aenion is devoed o he classic pape of Kyle (985) I employs basic ideas and an oiginal wopeiod Kyle model fo inside ading sing a linea pice disclose fncion and exisence of he eqilibim saegy wih no pblic disclose, consideing he mae efficiency and pofi maximiaion by he monopolisic inside Lae, he appoach was commonly acceped and developed in many wos (Gégoie and Hang (0); Li and Zhang (0); Wang e al (009); Dahe e al (0)) So, Gégoie and Hang (0); Li and Zhang (0) developed mahemaical models of ineacion beween one inside, N insiional invesos, a nmbe of individal ( noise ) ades and one mae mae In Dahe e al (0) ahos implied he Cono compeiion (dopoly) in he Kyle model and, by analogy wih Wang e al (009), examined he Sacelbeg compeiion whee insides ae he owne of he company and op manage sbodinaed o him Ideas of Kyle inflenced he papes of Deb e al (04); Zho (0); Viale (0); Piccione and Spiegle (04); Yang and Li (04)) So, Deb e al (04) examines he compeiion among infomed ades and a mae mae in he pesence of a noise ade The ahos esablish a heepeiod aional expecaions eqilibim (REE) model whee infomed ades eceive and veify a noisy signal, and ade by hei own In Zho (0) he oiginal wo-peiod Kyle model is genealied fo he case of a single inside, who has some confidence degee, mliple mae maes and mliple noise ades Ahos find he opimal ading saegies fo sch inside, based on he infomaion available o him and his belief level (confiden o pessimisic) Using he same iniial assmpions Viale (0) pesmes ha sch inside is is-avese, implying a mli-seciy vesion of Kyle s model wih Maovian linea seqenial eqilibim
Lasly, papes of Piccione and Spiegle (04); Yang and Li (04)) sgges a ading model wih inveso senimen ha exends he oiginal Kyle model In his model, hee ae an infomed aional inveso, who maximies his expeced pofis, and ninfomed noise senimen speclao, who ades on senimen shocs Ahos deive an analyical solion o he senimen eqilibim pices and descibe a dynamic pice pah Thee exiss a significan disadvanage in all he foegoing papes hey employ he lineaiy of he isy asse pice expose, which in o opinion, limis he scope of hei applicabiliy The pape of Pa and Lee (00) pesens a nonlinea model of he dynamics of isy asse ens in he pesence of inside ading The ahos disclose he dependence of isy asse ens on he amon of inside ansacions and denoe i in he fom of an ARMA(,) model Fhemoe, hey obain he deecion cieia of inside ading which poved o be closely elaed wih sabiliy condiions of he ARMA(,) pocess Along wih he idenificaion of insides and infomed ades only by changes in ndelying asse pices hee exis mehods ha involve is deivaives, noably opions (Popesc and Kma (03); H (03); Mavyev e al (03)) Ths, Popesc and Kma (03) veify he p-call paiy fo Ameican opions wih wo diffeen sies fo diffeen mae agens and compe he pobabiliy of infomed ading (PIN) And, H (03) fond an ode imbalance in ades of he ndelying asse and is hee opions, ie in-he-money (ITM), a-he-money (ATM) и o-of-hemoney (OTM) opions, ha enables o compe he pobabiliy of infomed ades Mavyev e al (03) combine hose wo appoaches The possibiliy of addessing fes pices fo deecion of infomed ades was fis noed in Yi-Tsng (03), whee i is shown ha he enhancemen of he ading aciviy in he fes mae anicipaes an inceased aciviy in he spo-mae, b in mos cases he diecion of ade (o sell o o by) emains nclea, even if sing he non-pblic infomaion The ppose of his sdy is o develop he mehodology fo idenificaion of he impac of infomed ades on he ading aciviy consideed in Pa and Lee (00) Hence, we pesen a Veco ARMA model fo ic pices of fes and is ndelying asse and esimae limis of is insabiliy Fhemoe, we fomlae elevan decisive cieia The compaional algoihm is applied fo he analysis of high feqency daa fo he peiod ha pecedes annoncemens of impoan macoeconomic infomaion abo phasing o he pogam of "qaniaive easing (QE3) and US GDP gowh fo he hid qae of 03, as well as in he peiod following his news This pape is oganied as follows In Secion we consc a mixed mli-peiod model of infomed ading in ems of soc and fes en seies and invesigae is chaaceisics In Secion 3 we analye he effeciveness of deecion cieia hogh a simlaion and apply i o FX 3
pais, spo gold pices, developing cony shae index and hei fes in ime of QE3 ending annoncemens Finally, Secion 4 pesens o conclsions Model Le s assme ha nmbe of all playes on he soc mae, ading an ndelying asse and is fes conac, ae divided ino infomed ades and odinay noise ades Le a macoeconomic annoncemen affecing he pice, be pblicly nown a a fe ime T, while he infomed ade has obained he daa a ime <T We assme ha he decides o by (sell) he ndelying asse o fes in eqal insallmens a egla inevals, ie a ime, (+),, T Then he effec of changes in he ndelying asse pice cold be defined as whee N0, X v, ~ addiion o he pice, offeed by ninfomed ades, pice ha an infomed ade is willing o pay Le v obey he elaion v, v schage o he whee β coefficien of popoionaliy, vale of ading ansacion of infomed ade We sppose ha saisfies AR() model, which is explained by he desie of he infomed ade o hide his aciviy and, fo insance, o edce his conibion v a low levels of mae aciviy:, () whee aveage vale of ading ansacion pice pe ime ni, N0, pice noise ~ Le S be a qoe of he ndelying asse a ime Since a ade bys a lage qaniy of he ndelying asse, we assme ha S will vay popoionally o he change of pices: whee cov, X D X v v mae deph vaiaion coefficien S S X, () I follows fom eqaion () ha he coefficien defines a pice expose wih espec o all mae paicipans Moeove in o case i is easy o veify ha, If noise pocesses, ae independen of one anohe 4
Using an analyical epesenaion of be wien as an ARMA (,) model fom Pa and Lee (00): X and sbsiing defined by (), eqaion () can S, (3) S whee ~ N0, is a noise pocess,, S S T 0 T, Repesenaion of eqaion () in he fom of (3) allows s o enail he following condiions fom Pa and Lee (00): ) if ρ<0, hen 0<δ<-ρ; ) if ρ>0, hen -<δ<-ρ We cold, heefoe, fomlae he following cieion: Cieion: coefficiens of he AR() and MA() pas of model (3) (ρ and δ, especively) ms have opposie signs If 0, hen based on he sabiliy condiions, If 0, hen Le S, 0,,, T, be a daa se ha is available fo analysis Le m<t be a ime window S m 0 lengh, which allows s o calclae he iniial esimaes of coefficiens and wih qoes S, nil we each ime T, by nown S m 0, S, S, Sm in model (3) Moving he ime window o he igh pe ni S, s, S s,, Sms we esimae s s and s, s,,, T m 0 Fhemoe, we se empiical vales of he coefficiens fond o fomlae a decision le Accodingly, we wie he cieion: Decisive cieion: sbjec o non-eo pice movemens 0,,,, T m 0, we assme ha, he infomed ansacion is deeced if one of he following ineqaliies holds: а) <0, 0, ; б) <0, 0, Fhe, le F be a fes pice of he ndelying asse piced a hee exiss a elaion (Alexande and Babosa (008)): 5 S I is well nown ha F S exp T, (4) whee is-fee inees ae, T expiy ime fo a fes conac, cen ime, one can wie he analoge of eqaion (3) fo ens F Now we sae o main esls of his pape Theoem Le s sppose A e e S exp T 0, ~ exp T is a Gassian noise pocess, C e e exp T Then,
F ~ ~ A e F C S j (5) j The poof of heoem is lised in Appendix A Theoem Sysem of eqaliies (3) and (5) can be wien in he fom of he Veco ARMA model: whee X F S, ; maices ; The poof of Theoem is obvios X ~ ~ ~, (6) ~ ; ~ A X B X jc ; j ~ A vecos, A B ~ e 0 C, ~ 0 0 C sqae C 0 We noe ha epesening he pocess in he fom of (6) allow s o deemine he condiions of is saionaiy (see, eg, Wei (006) fo geing condiions and esimaion of he saionaiy of Veco ARMA pocesses) Fom he esls we can fomlae Theoem 3: Theoem 3 Pocess X in eqaion (6) is saionay, if The poof of heoem 3 is lised in Appendix A Theoem 3 enables s o wie he necessay genealied cieion of he pesence of infomed ades when ading fes conacs and he ndelying asse on hem: Genealied cieion: ) if -<ρ<0, hen 0<δ<-ρ; ) if >ρ>0, hen -<δ<-ρ The decisive cieion will baely change and can be ewien easily A he end of his secion we noice ha if nlie eqaion () we choose he pice expose pocess as ARMA(,), ie, (7) hen eqaion (3) fo ndelying asse pice shold be ewien nde he following heoem 4 Theoem 4 In case an infomed ade implemens a mixed saegy () wih as 4 he infomaion expose saegy in a mli-peiod model, ndelying asse pice diffeence follows he ARMA(,) pocess below S, (8) S 6
whee ~ N0,, 4 S T S 0, T, The poof is lised in he Appendix A 3 Nmeical simlaion esls 3 Daa We se la-high feqency ic daa fo EUR/USD, GBR/USD and USD/RUB cency pais and spo gold pices, hei Mach, 04 fes, min daa fo Rssian Tade Sysem shae index (RTS) and is fes (ice RIH4) in he peiod Dec 7 Dec 0, 03 and Jan 8 Jan 30, 04 The daa wee obained fom FINAM holding (wwwfinam) and CME Gop The choice of financial insmens fo analysis is de o macoeconomic saisics, is infomaion is disclosed in ceain peiods of ime: i is news abo phasing o he US moneay simls, ie QE3, and final daa on US GDP fo he III qae of 03, and peliminay - fo he IV qae of 03, fom which he eminaion ime of QE3 was depended on 3 Resls While hee incenive pogams wee fncioning, he fis one was lanched in Mach, 009, he ole of egional cencies (Asalian and New Zealand dolla, Bailian and Mexican peso, Chinese yan, Soh Afican and, Rssian ble, Tish lia and Indonesian piah) significanly inceased (Tiennial Cenal Ban Svey Repo (03)): fo example, he pecenage shae of oble in ne-ne nove in he FX mae inceased fom 0,9% o,6% fo las hee yeas And his siaion is no niqe: he shae of RMB inceased ove he same peiod fom 09% o %, he Mexican peso - fom 3% o 5%, he Tish lia - fom 07% o 3 % These facs indicae ha hee was a fee cash flow fom developed conies o developing ones ove he pas hee yeas On he one hand, i simlaed hei economies and senghened egional cencies p o a ceain poin of ime On he ohe hand, imbalances inceased and oveheaing of economies occed a he fis hea of collapse of he incenive pogams, which led o a shap devalaion of he local cency and he soc mae cashes All of hese help o idenify lage infomed ades and fix hei aciviy, fo example, in he Rssian o any ohe emeging maes The possible exisence of elaionship beween FX mae and gold pices ding he cisis is discssed in he pape by Phanhong and Roll (0), whee song posiive coelaions beween gold pices and Dolla, Eo, Yen and Pond wee fond and invesigaed Theefoe, we invesigae he aciviy of ades in ading of gold fes and examine he gold spo pices 7
Le s define he impac of infomed ades in inaday ading of cency pais EUR/USD, GBR/USD, USD/RUB and Mach, 04 fes The esls of calclaions wih he ime window lengh m= ho, ae pesened in Table, Panel A C [Table is hee] Accoding o he esls of calclaions, given in Table, Panel A-C we conclde ha hee is no significan impac of infomed ades in ading of highly liqid cency pais EUR/USD and GBR/USD, while fo emeging mae cencies USD/RUB we aced i on Janay 9, 04, de o he obseved capial fligh fom emeging o developed maes while phasing o QE3 Becase of he elaionship of FX mae and gold pices discssed in Phanhong and Roll (0), i is ineesing o invesigae he aciviy of ades in he gold ade a he beginning of he global scal changes We analye he ic eail pice of gold and fes on i I is nown ha hese pices ae closely associaed wih capial inflows o developing conies and affec hei foeign exchange aes (Apegis (04)), inflaion and FX eseves The esls of calclaions wih he widh of he ime window m = h pesen in Tables The esls of calclaions wih he ime window lengh m= ho, ae pesened in Table [Table is hee] Accoding o he esls of calclaions, given in Table we fond he impac of infomed ades in gold ading in days following annoncemens of phasing o he pogam QE3 I is pedicable since he eminaion of QE3 has a diec impac on expecaions of lage playes abo he edcion of spply of dolla in he wold and, as a conseqence, he decease of pecios meal pices In o opinion, sch eason is based on he dop of indices in developing conies We show i on he example of an emeging soc mae, sch as Rssia We analye -mine daa of Mach, 04 fes on RTS index (ice RIH4) piced in oble and -mine daa of RTS index piced in dolla These index asses have a oble-dolla nae and he qoes depend diecly on EUR/USD ae associaed wih pocesses of capial fligh The esls of calclaions wih he ime window lengh m= ho, ae pesened in Table 3 [Table 3 is hee] 8
Ths, o calclaions idenify wo diffeen sages afe he annoncemen of he eminaion of QE3 A he fis sage (Dec 8 - Dec 0, 03) infomed ades showed high aciviy in gold ading and fes on i, b close o he end of he sage hey swiched o index asses of emeging maes ha o calclaions evealed A he second sage (Jan 8 - Jan 30, 04) opeaions wih cencies of developing conies (eg, RUB) wee added o he ading aciviy ha is coelaed o he capial fligh o developed maes A he same ime sspicios ansacions wih highly liqid pais EUR/USD, GBR/USD wee no deeced in he FX mae, despie he high volailiy of hei pices hogho he fis sage 4 Conclsion O analysis shows ha he poposed genealied and decisive cieia allow o idenify he aciviy of infomed ades in inaday ading in global maes Fhe, i is shown ha sch ades while ae nable o even in he sho em o se hei movemen ajecoy pices on all soc maes, ie pinciples of fai and hones ading ae flfilled Fhe, we eveal he cen inabiliy of sch ades o deemine pice ajecoies in all soc maes, ie pinciples of fai and hones ading ae flfilled A he same ime, infomed ading in he emeging mae of Rssia is deeced easie while sing a wide ange of financial insmens APPENDIX A Poofs To pove Theoem, we fis sae and pove an axiliay Lemma Lemma : If F holds eqaliy (4), hen S F F e S Poof By (4), F S exp T, F S exp T Hence, F S ln F S ln ln e Poof of Theoem Accoding o (3), S S, o, in ems of pices, S S S Then, We apply his expession o he esls in he poof of Lemma S S F F e S, o S F e S S F Le s se Lemma once again: S S F e F S S F e F So 9
F F e, S e F F F o, by (4), e F F exp T F e F, ie F exp T F e e F Le s fom he diffeence F in he lef side of he eqaion, hen we sbac and add e F : now, hen F exp T e F e e F We poceed similaly wih he las em on he igh side of he eqaion: e F F e F e e F, exp T e e F e F Le s ansfom F sbsiing he pice eqaion in (4) wih S S S S j S0, whee S 0 nown iniial pice of he j S S S ndelying asse, and dividing boh sides of he eqaion by e, consideing noions of he heoem we obain eqaion (5) Poof of Theoem 3 Accoding o he geneal heoy of saionay of Veco ARMA pocesses (Wei (006)), X is saionay if and only if all eigenvales of B ~ and C ~ in (6) lie inside he ni cicle in he complex plane Clealy, maix B ~ has wo eal eigenvales: as V j, so V 0 and V can be easily comped as follows: 0 e and ρ, and maix C ~ eo eigenvale of mlipliciy Since e by condiion of he heoem, hen X is saionay Poof of Theoem 4 Afe doble sbsiion of eqaion ino eqaion wih diffeen we obain We modify (A) as S, (A) S (A) S S (A3) We denoe he aocovaiance of some axilia expession S S
V, (A4) 0 V (A5) 0 If we compe simila aocovaiances of (A3) diecly and eqae hem o (A4) and (A5), we can find nnown and So, i is poved ha The sysem of sch eqaions is as wien below:, 4 These coefficiens, obviosly, define o axilia expession in he fom (8) needed,
Refeences Alexande, C, Babosa, A, 008 Hedging index exchange aded fnds Jonal of Baning & Finance 3 (), 36-337 Apegis, N, 04 Can gold pices foecas he Asalian dolla movemens? Inenaional Review of Economics & Finance 9, 75-8 Dahe, W, Kaam, F, Miman, LJ, 0 Inside ading wih diffeen mae sces Inenaional Review of Economics & Finance 4, 43-54 Deb, P, Koo, B, Li, Z, 04 Compeiion, pemae ading and excess volailiy Jonal of Baning & Finance 4, 78 93 Dey, MK, Radhaishna, B, 03 Infomed ading, insiional ading, and spead Jonal of Economics and Finance, -0 Gégoie, P, Hang, H, 0 Infomaion disclose wih leaages Economic Modelling 9 (5), 005-00 H, J, 04 Does opion ading convey soc pice infomaion? Jonal of Financial Economics (3), 65 645 Kyle, AS, 985 Coninos Acions and Inside Tading Economeica 53 (6), 35-335 Lepone, A, Yang, JY, 03 Infomaional ole of mae maes: The case of exchange aded CFDs Jonal of Empiical Finance 3, 84-9 Li, H, Zhang, Z, 0 Inside ading wih pblic and shaed infomaion Economic Modelling 8 (4), 756-76 Mavyev, D, Peason, ND, Bossad, JP, 03 Is hee pice discovey in eqiy opions? Jonal of Financial Economics 07(), 59-83 Pa, YS, Lee, J, 00 Deecing inside ading: The heoy and validaion in Koea Exchange Jonal of Baning & Finance 34 (9), 0-0 Piccione, M, Spiegle, R, 04 Maniplaing mae senimen Economics Lees, (), 370-373 Popesc, M, Kma, R, 03 The implied ina-day pobabiliy of infomed ading Review of Qaniaive Finance and Acconing, -5 Phanhong, K, Roll, R, 0 Gold and he Dolla (and he Eo, Pond, and Yen) Jonal of Baning & Finance 35 (8), 070-083 Schols, M, Dic, van Dij, Fijns, B, 04 Speed, algoihmic ading, and mae qaliy aond macoeconomic news annoncemens Jonal of Baning & Finance 38, 89-05 Tiennial Cenal Ban Svey Repo on Global Foeign Exchange, 03 Ban fo Inenaional Selemens Commnicaions, Swieland, Basel, 74 p
Viale, P, 0 Ris-avese inside ading in mli-asse seqenial acion maes Economics Lees 7 (3), 673-675 Wang, LFS, Wang, YC, Ren, S, 009 Sacelbeg financial leade in inside ading model Inenaional Review of Economics and Finance 8, 3 3 William WS, Wei, 006 Time Seies Analysis: Univaiae and Mlivaiae Mehods Peason Edcaion Inc nd ediion, 64 p Yang, C, Li, J, 04 Two-peiod ading senimen asse picing model wih infomaion Economic Modelling 36, -7 Yi-Tsng, Lee, Wei-Shao, W, Yang, YH, 03 Infomed Fes Tading and Pice Discovey: Evidence fom Taiwan Fes and Soc Maes Asia-Pacific Financial Maes 0 (3), 9-4 Zho, D, 0 Oveconfidence, pblic disclose and long-lived infomaion Economics Lees 6 (3), 66-630 3
Table Impac of infomed ades on ading pocess in he analysis of EUR/USD, GBR/USD, USD/RUB and hei Mach, 04 fes ic pices a diffeen daes Panel A EUR/USD Dae Undelying asse Fes Pesence of impac 703 0,76 0,37 0,68 0,77 declined 803 0,769 0,836 0,309 0,679 declined 903 0,344 0,443 0,869 0,908 declined 003 0,44 0,350-0,639-0,667 declined 8004 0,008 0,9 0,507 0,559 declined 9004-0,079 0,08 0,058 0,5 declined 30004 0,788 0,848-0,894-0,866 declined Panel B GBR/USD 703 0,740 0,769-0,09-0,96 declined 803 0,034 0,099 0,78 0,374 declined 903-0,007 0,089-0,643-0,689 declined 003-0,457-0,403 0,347 0,86 declined 8004 0,78 0,808 0,36 0,73 declined 9004 0,057 0,06 0,36 0,66 declined 30004 0,598 0,656-0,090-0,08 declined Panel C USD/RUB 703-0,0 0,746-0, -0,93 declined 803 0,090 0,700 0,380 0,394 declined 903-0,00 0,78-0,503-0,69 declined 003-0,065 0789 0,47 0,95 declined 8004-0,04 0,58-0, -0,3 declined 9004-0,696 0,96-0,58 0,75 acceped 30004-0,3 0,43-0,0 0,33 declined Impac of infomed ades on ading pocess in he analysis of ic spo gold pices and Mach, 04 fes ic pices a diffeen daes Table Dae Gold Fes Pesence of impac 4
703-0,5 0,3-0,055 0,38 declined 803-0,35 0,66-0,98 0,06 acceped 903-0,077 0,89-0,086 0,33 declined 003-0,087 0,44-0,03 0,0 declined 8004-0,034 0,79 0,46 0,78 declined 9004-0,5 0,050 0,334 0,709 acceped 30004 0,44 0,99 0,454 0,763 declined Table 3 Impac of infomed ades on ading pocess in he analysis of -mine daa of RTS index and pices of RIH4 fes a diffeen daes Dae Fes on RTS RTS Index Index Pesence of impac 703-0,655-0,695 0,5 0,35 declined 803-0,853-0,756 0,78 0,99 declined 903-0,633-0,688-0,4-0,039 declined 003 0,808 0,773-0,46 0,07 acceped 8004 0,874 0,845-0,306-0,95 declined 9004 0,05 0,043 0,769 0,74 declined 30004 0,58 0,046-0,43-0,439 declined 5