EVALUATION OF THE FIXING TRADING SYSTEM IN THE SPANISH MARKET*


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1 EVALUATION OF THE FIXING TRADING SYSTEM IN THE SPANISH MARKET* Davd Abad and Anono Ruba** WPEC 997 Correspondenca a: Davd Abad: UNIVERSIDAD DE ALICANTE, Deparameno de Economía Fnancera, Campus de San Vcene del Raspeg, 0307 ALICANTE, emal: Edor: Insuo Valencano de Invesgacones Económcas, S.A. Prmera Edcón Dcembre 999. IVIE workngpapers offer n advance e resuls of economc researc under way n order o encourage a dscusson process before sendng em o scenfc ournals for er fnal publcaon. * Te auors would lke o express er graude o Juan Carlos Gómez Sala, Angel León, Jorge Izagurre, Mkel Tapa and Gonzalo Rubo for er valuable commens and suggesons. We are also endebed o Juan España for s compung asssance. Suppor from IVIE s graefully acknowledged. ** D Abad and A. Ruba: Unversy of Alcane.
2 EVALUATION OF THE FIXING TRADING SYSTEM IN THE SPANISH MARKET Davd Abad and Anono Ruba ABSTRACT In 998 e Fxng radng sysem was mplemened n e Spans Sock Marke. I s consdered an alernave o e radonal sysem of connuous negoaon, applcable o ose socks a ave a seres of basc caracerscs n common. I represens an mporan nnovaon, e fundamenal purpose of wc s o reduce e volaly of socks and us mprove er lqudy. Te man move of s sudy s o verfy weer e mprovemens a e advocaes of e new radng sysem ave been predcng ave acually aken place, as we beleve a any nnovaon a s nroduced no e marke sould be subeced o emprcal evaluaon. To do so, e effec a s nnovaon as ad on e ndcaors of lqudy, reurns and volaly of e socks nvolved s examned, usng paramerc and nonparamerc ess and employng a meodology based on e ecnque of e even sudy. We concluded a e evdence observed seems o conradc e very expecaons a movaed e mposon of e new negoang sysem, snce a sgnfcan worsenng was observed n lqudy and reurns, wereas, on e oer and, no apparen decrease s observed n volaly. Key Words: Fxng, Lqudy, Reurns, Volaly, Tn Tradng. JEL Classfcaon: G0, G9 RESUMEN Durane 998 se mplanó en el mercado español el ssema de conraacón de valores con precos úncos en cada perodo de ause, más conocdo como ssema de negocacón fxng. Ese ssema represena una fórmula alernava al ssema radconal de negocacón connua, aplcable a aquellos valores que reúnen una sere de deermnadas caraceríscas. A su vez, consuye una mporane nnovacón cuya fnaldad es, fundamenalmene, reducr la volaldad de los íulos y meorar su lqudez. La movacón fundamenal del presene rabao consse en conrasar s se an producdo las meoras que vacnaban los mpulsores del nuevo ssema de conraacón, en la creenca de que cualquer nnovacón llevada a cabo en el mercado debe ser someda a evaluacón. Para ello, se esuda el efeco sobre ndcadores de lqudez, rendmeno y volaldad medos de los íulos a los que esa nnovacón afecó, ulzando pruebas paramércas y no paramércas y meodología basada en la écnca del even sudy. La conclusón a la que se llega en ese esudo es que la evdenca observada parece ser conrara a las expecavas que movaron la mplanacón del nuevo ssema de conraacón, pues se observa un empeorameno sgnfcavo en los nveles de lqudez y renabldad y, en cambo, no se observa dsmnucón aparene en el nvel de volaldad. Palabras Clave: Fxng, lqudez, volaldad, rendmeno, negocacón nfrecuene.
3 . INTRODUCTION A e nernaonal level, weer n developng markes or n ose a are already well esablsed, mporan nvesmens and nnovaons are akng place n marke mcrosrucure, enforcng e mplemenaon and evaluaon of new negoang sysems. W suc a vew, e Spans Sock Marke as recenly oulned new operaonal norms for e sock radng, n an effor o mprove s compeveness n e lg of e emergng European sngle marke. Tese reforms ave focused fundamenally on mprovng lqudy by ncreasng e ransparency and qualy n e execuon of e ransacons. In dong so, s oped a e negoang of ceran asses wll be faclaed, makng em more accessble o a wder range of nvesors. To s am, wo noveles were nroduced no our marke durng 998. Frs, a block marke was developed for wo dfferen caegores of sares, one, a agreed prces, for socks regsered n e IBEX35 ndex. Anoer one, by prces, for all sares raded on e connuous marke. Te reason for creang suc a marke was o faclae e conracng of large volumes. Ts s a grea mprovemen for bg companes and nsuonal nvesors. Secondly, e Fxng sysem, wc s e focal pon of s sudy, was nroduced. Ts new conracng mecansm was desgned o ncrease e lqudy of e less frequenly raded socks. I could be envsoned as an effor on e par of e Spans Sock Marke o faclae e radng of small and medumszed socks. Te sysem s nended o mprove on prces formaon for less aracve values, by concenrang e conracng a us wo momens durng e sesson. I sould erefore be of grea neres, no only o fnancal economss bu o anyone wo parcpaes n marke acves, o verfy weer s ype of nvesmen n e mprovemen of radng sysems really yelds posve resuls. Includng e socks negoaed n e Fxng sysem. 3
4 Amud and Mendelson (997 argue a for e marke mcrosrucural mprovemens o be consdered valuable, e prces of e asses raded n e new sysem sould ncrease. In fac, any cange or novely nroduced no e marke sould be subeced o an emprcal evaluaon o deermne us ow effecve s and weer was really wor mplemenng a all. Terefore, f any grea dvergence from e predced oucome s observed, measures sould be aken o correc e msguded course. Te am of e presen sudy s o analyze e beavor of e sares raded n e Fxng sysem and measure e exen o wc e desred mprovemens ave been aceved. To do so, e effec a s nnovaon as ad on e ndcaors of lqudy, reurns and volaly of e socks a were ncluded n e Fxng sysem s analyzed. Ts sudy sould be consdered as an addon o e exensve emprcal researc wc analyzes e effecs a e announcemen and subsequen cange o an alernave radng sysem as on e sares nvolved. Among oers, Cooper e al. (985; McCowell and Sanger (986; Bandar e al. (989, and Crse and Huang (994, sand ou for er work on asses raded on e sock excange a ad prevously raded OTC. Baker and Edelman (99 analyze e case of socks ransferred from NASDAQ o NASDAQ/NMS. Amud and Mendelson (997 sudy canges n e TelAvv Sock Excange radng sysems and Ko and Lee (997 do e same n e case of asses raded n A and B sysems of e Korean Sock Marke. On e oer and, e move o e Fxng sysem supposes a cange of e negoang sysem from one of connuous aucon o one of call aucon. So, s sudy could also be classfed among e leraure devoed o e eorecal and emprcal analyss of e advanages and nconvenences of ese wo sysems for Ts effec on e prce concdes w e fndngs of Amud and Mendelson (986, Amud and Mendelson (99 and Brennan and Subramanyam (996, wo fnd negave correlaons beween e levels of lqudy and e expeced reurns (afer akng a seres of oer facors no accoun. 4
5 orderdrven markes. Te man conclusons and resuls obaned from prevous sudes are summarzed n e followng epgrap. Te paper s organzed as follows: In e nex secon we descrbe ow e Fxng sysem funcons n e Spans marke. In secon ree we explan e meodology and e daa used n e sudy. In e four and ff secons, e man resuls obaned for e ndcaors of lqudy, reurns and volaly are sown. Fnally, n e sx secon, e evdence obaned n e analyss s summarzed and e man conclusons are arrved a.. THE FIXING SYSTEM From July s 998, e Spans marke as been operang w a new conracng model: Ssema de facón de precos úncos para cada perodo de ause, beer known as e Fxng Tradng Sysem. Aloug s sysem s a novely o our marke, as s precedens n oer European markes, lke Germany and France, for example. Te move bend suc a cange s o ncrease e lqudy of ose less frequenly raded socks. Perodcally, ceran asses are assgned o s negoang sysem, based on e levels of er acvy and lqudy among oer caracerscs. Tey no longer rade connuously rougou e day, bu raer, are raded exclusvely a wo fxed momens durng e day. In oer words, ere s a cange from a sysem of connuous aucon o one of call aucon. Now, from a raer general pon of vew, we sould lke o commen on e man advanages and nconvenences of e wo dfferen sysems nvolved, as glged n e leraure. Aferwards, we sall descrbe n more deal, ow e Fxng sysem funcons n e Spans marke, e approac employed for e selecon of e socks a sould be ncorporaed no e new sysem and e man prospecs olds. 5
6 Call Aucon vs. Connuous Aucon Under e call aucon sysem, orders accumulae for predeermned perods of me durng e radng sesson. A e end of eac of ese adusmen perods, orders are baced for execuon a a sngle prce o maxmze e number of sares negoaed. In conras, under e connuous aucon meod, orders are execued wenever submed bds and offers cross durng a radng sesson. Ts meod generaes a sngle prce for eac cross. Several eorecal and emprcal sudes ave analysed e advanages and nconvenences of e wo dfferen conracng models. Prce sably s, peraps, e mos mporan advanage of e call aucon meod over e connuous aucon. Ts greaer sably s aceved because bacng orders over me elmnaes prce flucuaons caused by e bdask bounce and reduces prce volaly nduced by e random sequence n wc orders and nformaon arrve. Lkewse, as radng orders accumulae over a fxed me nerval, e mpac of a sngle large order becomes less severe (Coen and Scwarz, 989. Te sysem also represens an effecve mecansm for dealng w asymmerc nformaon problems beween nformed and unnformed lqudy raders (Soll, 985. Te mposon of delays forces e nformed agens o reveal, by e locaon of er orders, e exsence of nformaon, wc, n urn, elps o reduce prce volaly 3. However, s acclamed reducon of volaly s aceved a e expense of prce dsconnuy and e lack of nformaon (Madavan, 99 wc all ranslaes no a lower level of lqudy. In conras o e call meod, e mos frequenly menoned advanage of e connuous aucon sysem s e supply of mmedacy o buyers and sellers. By allowng e mmedae execuon of ransacons, a ger degree of marke lqudy may be expeced. I would seem, erefore, a ere s a ceran volalylqudy radeoff n e coce beween ese wo sysems. 3 Te nformed agens ad e opon of nroducng e orders a few momens before e execuon of orders. 6
7 We sould pon ou a e call aucon sysem concdes w a of connuous aucon wen e nervals for accumulang orders ends owards zero, or, wc s e same ng, wen e number of negoaon momens ends owards nfny. Te wd of e nerval (or smlarly, e predeermned number of momens a wc orders are baced proves o be a fundamenal varable by wc o quanfy e range of e neracon beween volaly and lqudy. Tese wo negoaon sysems can be used only and, n fac, some markes allow bo meods for e same asses, aloug a dfferen momens of e day. So, n many cases call aucons are used exclusvely o deermne e socks openng prces, and en cangng o connuous aucon durng e remander of e radng sesson. Moreover, e wo sysems may be used smulaneously for dfferen socks. I s e case analyzed n s paper, e Spans Fxng radng sysem proposes a knd of call aucon meod for ceran socks w pecular caracerscs n common. Descrpon of e Fxng Sysem n e Spans marke Te new radng meod allows e admsson of orders from 9:00 ours o 6:00 ours. Te peculary s us a sares are raded a a sngle prce a wo specfc momens durng e radng sesson. Prces are frs se a :00 noon, and en agan a 6:00 ours. Ts fnal prce beng aken as e closng prce. Apar from seng e prce a maxmzes e number of sares a can be raded, e conracng uns a correspond o eac case are assgned. Te algorm and e sysem of dsrbung sares used for s purpose, are exacly e same as ose used from 989 n e openng up of e marke o all socks. Te sock selecon s done by e Comsón de Conraacón y Supervsón de la Socedad de Bolsas, S.A. (Commsson for e Recrung and Supervson of e Sock Marke, S.A. by observng e levels of acvy and lqudy of e asses 7
8 durng e sx prevous mons 4. Te followng varables are employed for s purpose 5 :  Daly volume n ordnary operaons.  Number of crossed operaons per day.  Average spread beween bes bd prce and bes ask prce.  Annual roaon rae: e number of conraced uns raded n ordnary operaons dvded by e number of sares admed on e marke.  Tradng frequency: Percenage of sessons durng wc e sock as been negoaed. In addon o e foregong, oer parameers a may be requred o esabls e degree of lqudy of eac asse can also be used. In e case of socks a are ncorporaed no e marke for frs me, er assgnmen o e sysem depends on er dmensons, er dffuson and oer dsngusng caracerscs, as well as on e companes marke expecaons. Te sock selecon decson s made every sx mons, excep n e case of new ncorporaons or n crcumsances n wc e marke s condons ndcae e need for an exraordnary revson. Te precursors o e Fxng sysem sugges a... s s e sysem a adaps bes o e condons of e seleced sock s lqudy and marke acvy, (Revsa de la Bolsa de Madrd, nº 67 June 998. W e new sysem a concenraon of orders s effeced a gven momens durng e radng sesson, ereby ncreasng er radng acvy and er lqudy, as well as reducng e g volaly (Revsa de la Bolsa de Madrd, nº63, February 998. Ts sysem 4 Excep n e case of e frs group of socks, for wc only e ree prevous mons were used. 5 In several sudes, e decson o cange radng sysem s volunary and s erefore aken exclusvely by e companys. Ts mples an prevous opmzaon program and prvae nformaon. Ts could cause auoselecon bas (Amud and Mendelson, 997. In s case a neress us, e decson s exogenous and s ype of bas does no exs. 8
9 accumulaes purcase and sellng orders for gven momens, ereby acevng equy prces beween offer and demand w lower volaly (no only nraday volaly, bu closng prce volaly, oo, w somewa lower ransacon coss and w less mpac on e prces of e orders nroduced an wen ey are negoaed n on e open marke for 7 ours a day (Revsa de la Bolsa de Madrd nº 67, June of 998. Te new sysem res o concenrae e operaors aenon a.00 ours and 6.00 ours durng eac radng sesson and so reduce e spread beween bd and ask prces, ereby reducng er volaly and ncreasng e volume of negoaon n socks nvolved. Tese obecves are muc more dffcul for ceran asses o aceve n a connuous marke of 7 ours of radng (Anuaro de la Bolsa, 998. As we can see, e promoers rus e new conracng sysem as an effecve way of elmnang e radng problems for e socks concerned, on e grounds a connuous conracng generaes g prce volaly and makes s knd of socks less aracve. So, e fac a orders and e aenon of e nvesors are concenraed on us wo momens durng e sesson, sould creae more effcen and less volale prces. I sould, n urn, generae greaer and more economc negoaon. 3. DATA AND METHODOLOGY So far, wo groups of asses ave been ransferred o e Fxng sysem, and e nex nclusons are programmed for July s, 999. Te frs group of 5 socks were announced n e Sock Marke s Operang Insrucon nº 9/998 on e 0 of June 998, and began radng n e new sysem on July s, 998. Te second group, composed of 4 asses (e mos of wc are e same a ose of e frs group was announced n e Operang Insrucon nº 30/998 on e 7 December 998. Tese socks began radng on January 4, 999. In Table, e evoluon of e frs wo seres of socks negoaed under e new radng model s dealed. 9
10 Table : Evoluon of e socks raded n e Fxng sysem Te followng able presens e groups of socks a canged o e Fxng sysem s GROUP SITUATION ( nd GROUP ( CONTINUE DO NOT CONTINUE NEW ( Bco. Andalucía (AND ( AND AFR Aforasa (AFR Bco. Alánco (ATL ATL Bco. Andalucía (AND Bco. Caslla (CAS (  CAS* Bco. Alánco (ATL Bco. Galca (GAL ( GAL Bco. Galca (GAL Bco. Vascona (VAS ( VAS Bco. Herrero (HRR Bco. Herrero (HRR HRR Bco. Vascona (VAS Bco. Smeón (SIM  SIM** Bayer (BAY Bayer (BAY ( BAY Bco de Crédo Balear (CBL Inbesós (BES ( BES CUN Ca. Vnícola Nore España (CUN Croen Hspana (CIT  CIT** Elecra de Vesgo (VGO Commerzbank (CBK  CBK** Esaconamenos Suberráneos (HES Bco. de Crédo Balear (CBL CBL FYM Fnancera y Mnera (FYM Dmeal (DMT DMT FNZ Fnanzauo (FNZ Esaconamenos ANY HES Suberráneos (HES Grupo Anaya (ANY E.p.p..c. (EPC  EPC** Dmeal (DMT Hornos Ibércos Alba (HSB HSB Hornos Ibércos Alba (HSB Iberpsas (IBP  IBP* Inbesós (BES Indo Inernaconal (IDO  IDO* La Corporacón Baneso (LCB La Corporacón Baneso LCB (LCB Lafarge (LFG Lafarge (LFG LFG LGT Lngoes Especales (LGT Salos del Nansa (NAN NAN La Papelera Española (PAP La Papelera Española (PAP PAP Salos del Nansa (NAN Urbanzacones y Transpores (UBS  UBS** UND Unland Cemenera (UND Elecra de Vesgo (VGO VGO Volkswagen (VWG Volkswagen (VWG VWG * Wen back o e connuous marke. ** Sopped radng. ( Socks a ave undergone spls afer /7/998 and before 3// 998 Te daabase used for s sudy was compled from nformaon aken exclusvely from e frs of group of socks raded n Fxng sysem. As from e begnnng of e year 999, all socks are raded n Euros, e ncluson n e sample of e second group would ave caused a possble dsoron. Te currency cange, 0
11 e mnmum varaons n e prces of e asses and oer facors lnked o e new currency, could ave generaed bases and nerferences a would ave made very dffcul o solae e effecs a we ave soug o analyze. Ceran socks from e frs group of e 5 nal asses were also elmnaed (see Table. PAP, EPC and DMT were fnally excluded from e sample as ey evenually wen no lqudaon. Te SIM sock was also elmnaed, as ad prevously been radng on e oucry marke and no on e connuous marke. Fnally, CIT, CBK and UBS sopped radng n e Fxng sysem before e end of e year, so a e daa avalable was no suffcenly complee o allow e comparson of bo sysems. Te sudy, erefore, s concenraed exclusvely on ose socks a ad prevously been raded on e connuous marke, were canged o e Fxng sysem and raded unl e end of 998. For e 8 cerfcaes fnally seleced, we ave consdered a sample of daly reurns (calculaed w closng prces and correced for spls, dvdends and capal ncreases beween Ocober 997 and December Based on s daa, afer modelng e reurn and e volaly, an analyss s done on e repercussons a e cange of negoaon sysem as ad on ese varables. For a sorer perod (from Aprl s o Sepember 30, 998 we employed e daly seres of e negoaed volumes (n peseas, and e number of daly ransacons. W s daa, and by paramerc and nonparamerc ess, we suded e effec a e new sysem as ad on lqudy. All e daa was aken from Servco de Informacón Bursál de la Bolsa de Madrd (Servce for Marke Informaon of e Madrd Sock Excange. 4. REPERCUSSIONS ON STOCK LIQUIDITY In s secon, we examne e effec a e new negoang sysem as ad on e lqudy of e sock nvolved. As Kyle (985 pons ou, e lqudy of a marke s oo wde a concep for a sngle clear defnon, as s composed of
12 mulple dmensons. Decdng weer a ceran even produces a sgnfcan cange on a sock lqudy or no, erefore, s a raer rsky ask, snce an unequvocal mprovemen or worsenng of s varable merely mples a s mulple dmensons vary n a ceran drecon. In s sudy, we concenered exclusvely on e radng acvy of e socks, measured by e daly volume (expressed n moneary uns and e number of daly ransacons. Anoer commonly used dmenson for measurng a marke s lqudy s e ransacon coss, measured by e spread. Even oug, we could no consder s dmenson snce e cange of sysem causes a seres of problems n e calculaon of e spread, makng a drec and relable comparson of e wo conracng sysems praccally mpossble. Te man problem s a e spreads for e Fxng Sysem socks are abnormally low. Te sandard meod employed o calculae e spread n e daabase, consss of averagng e bes bd and ask prces a eac momen, so a spreads of e sares raded n e Fxng sysem are zero mos of e me. Terefore, e spread calculaed for ose asses s an nconssen and unrelable measure of e acual ransacon coss. Concenrang exclusvely on e negoang acvy of a marke, s obvous a e ger e level of acvy, e greaer e probably of fndng a buyer/seller for e nvesors, and erefore, less me for execuon. Te advocaes of e new sysem erald an ncrease n e acvy of e socks ransferred o e Fxng sysem as a resul of a more effecve formaon of er prces and e reducon of e volaly an ey prevously ad n e connuous sysem. Te lack of relable models for esablsng e normal beavor of e varables under sudy ere (and especally for nfrequenly raded socks ndcaes e need for an adequae descrpve meodology, suppored by paramerc and nonparamerc ess. Suc ess conss of deermnng weer sgnfcan dfferences ake place n e average values of e varables beween e momen prevous o and e followng e sysem cange. To do so, dfferen equdsan perods o e even dae were used. Specfcally, e wndows employed were days 5, 0, 5, 0, 30, 40,
13 50 and 60 before and afer e dae of e cange 6. By consderng e perods s way, we could deec no only mmedae effecs bu e sorerm and longerm effecs as well. On e oer and, we observed a seven of e egeen socks a compose e sample carred ou spls sorly afer ncorporaon no e Fxng sysem. Te spl s a pracce a produces sgnfcan aleraons n e level of lqudy around e dae a s done, as Gómez Sala (999 pons ou. Ts auor fnds n s sudy of spls n e Spans marke, a raer sgnfcan ncrease n e number of a sock s ransacons on e daes mmedaely followng s spl. He fnds an rregular, oug no sgnfcan cange, n e volume on ese same daes as well. For s reason, we ave consdered bo e enre sample and a subsample of socks a dd no carry ou spls. I allows o gve greaer robusness o e analyss of e effec on e negoang acvy. Frs, we ave compared e number of ransacons and e volume negoaed for e ndvdual asses, for e aggregae of e 8 cerfcaes and for e asses a dd no carry ou spls. Eac of ese observaons was en normalzed, by dvdng em by e daly equvalen of e marke. In s way, e endency of e marke s consdered as e normal endency n e beavor of e varables. Te procedure also avods e possbly a any sor of seasonal beavor could bas e resuls. (Durng e Summer mons, for example, e negoang acvy decreases. Afer compleng s operaon, we compared our resuls o see f sgnfcan dfferences exsed beween average and medan for e dfferen wndows proposed. Te resuls for e varables, e relave number of ransacons and e relave volume negoaed are presened n ables.,. and 3., 3.. respecvely. 6 Te even day s aken as e frs day of e followng perods. 3
14 Table.. Relave number of ransacons for e sample of 8 asses In e followng able, e cange n e average and e medan n e relave number of ransacons are sown for dfferen wndows. Eac wndow s cenered on e even dae and as e duraon a appears n e frs column. Te second and rd column sow e average/medan before and afer e even dae, gven eac duraon. For e average, e dfference s sown n 4 column and s sgnfcance s evaluaed (5 column by a es (pvalue n brackes. Fnally, e 6ª and 7ª columns sow, respecvely, e number of companes a experenced decreases/ ncreases n er relave number of ransacons, w respec o e average. For e medan, e sgnfcance of e dfference beween e prevous and laer perods s measured by e nonparamerc ess of Wlcoxon, medan and KruskalWalls. In brackes, e pvalue are sown. Fnally, e number of companes a experenced decreases and ncreases n e number of ransacons relave o er medan are gven. SAMPLE OF 8 ASSETS Wndow Before Afer Dff. ±5 days ±0 days ±5 days ±0 days ±30 days ±40 days ±50 days ±60 days AVERAGE es [pvalue] [0.97] 0.7 [0.865] .4 [0.59].76 [0.083].59 [0.0].04 [0.044].6 [0.48] Falls Rses Before Afer Dff MEDIAN Wlcoxon Medan Tes Tes [0.0] [0.00] [0.733] [.000] [0.340] [0.73] [0.036] [0.058] [0.569] [0.606] [0.30] [0.37] [0.876] [0.43] [0.073] [0.08] KW Tes 6.8 [0.009] 0.4 [0.705] 0.95 [0.39] 4.45 [0.034] 0.3 [0.564].04 [0.307] 0.0 [0.874] 3.0 [0.073] Falls Rses
15 Table.. Relave number of ransacons for e sample of companes. In e followng able, e cange n e average and e medan n e relave number of ransacons are sown for dfferen wndows. Eac wndow s cenered on e even dae and as e duraon a appears n e frs column. Te second and rd column sow e average/medan before and afer e even dae, gven eac duraon. For e average, e dfference s sown n 4 column and s sgnfcance s evaluaed (5 column by a es (pvalue n brackes. Fnally, e 6ª and 7ª columns sow, respecvely, e number of companes a experenced decreases/ ncreases n er relave number of ransacons, w respec o e average. For e medan, e sgnfcance of e dfference beween e prevous and laer perods s measured by e nonparamerc ess of Wlcoxon, medan and KruskalWalls. In brackes, e pvalue are sown. Fnally, e number of companes a experenced decreases and ncreases n e number of ransacons relave o er medan are gven. SAMPLE OF ASSETS Wndow Before Afer Dff. ±5 days ±0 days ±5 days ±0 days ±30 days ±40 days ±50 days ±60 days AVERAGE es [pvalue] Falls Rses Before Afer Dff MEDIUM Wlcoxon Medan Tes Tes [0.0] [0.00] KW Tes 6.8 [0.009] Falls Rses
16 Table 3.. Relave negoaed volume for e enre sample. In e followng able, e cange n e average and e medan n e relave negoaed volume are sown for dfferen wndows. Eac wndow s cenered on e even dae and as e duraon a appears n e frs column. Te second and rd column sow e average/medan before and afer e even dae, gven eac duraon. For e average, e dfference s sown n 4 column and s sgnfcance s evaluaed (5 column by a es (pvalue n brackes. Fnally, e 6ª and 7ª columns sow, respecvely, e number of companes a experenced decreases/ ncreases n er relave number of ransacons, w respec o e average. For e medan, e sgnfcance of e dfference beween e prevous and laer perods s measured by e nonparamerc ess of Wlcoxon, medan and Kruskal Walls. In brackes, e pvalue are sown. Fnally, e number of companes a experenced decreases and ncreases n e number of ransacons relave o er medan are gven. SAMPLE OF 8 ASSETS AVERAGE Wndow Before Afer Dff. es [pvalor] ±5 days [0.056] ±0 days [0.453] ±5 days [0.406] ±0 days [0.40] ±30 days [0.53] ±40 days [0.48] ±50 days [0.456] ±60 days [0.666] Falls Rses Before Afer Dff MEDIAN Wlcoxon Medan Tes Tes [0.036] [0.057] [0.473] [.000] [0.507] [0.75] [0.39] [0.57] [0.45] [0.605] [0.3] [0.79] [0.009] [0.045] [0.005] [0.00] KW Tes 4.8 [0.08] 0.57 [0.449] 0.47 [0.493].4 [0.34].4 [0.43].5 [0.] 6.75 [0.009] 7.73 [0.005] Falls Rses
17 Table 3.. Relave negoaed volume for e subsample. In e followng able, e cange n e average and e medan n e relave negoaed volume are sown for dfferen wndows. Eac wndow s cenered on e even dae and as e duraon a appears n e frs column. Te second and rd column sow e average/medan before and afer e even dae, gven eac duraon. For e average, e dfference s sown n 4 column and s sgnfcance s evaluaed (5 column by a es (pvalue n brackes. Fnally, e 6ª and 7ª columns sow, respecvely, e number of companes a experenced decreases/ ncreases n er relave number of ransacons, w respec o e average. For e medan, e sgnfcance of e dfference beween e prevous and laer perods s measured by e nonparamerc ess of Wlcoxon, medan and Kruskal Walls. In brackes, e pvalue are sown. Fnally, e number of companes a experenced decreases and ncreases n e number of ransacons relave o er medan are gven. SAMPLE OF ASSETS Wndow Before Afer Dff. ±5 days ±0 days ±5 days ±0 days ±30 days ±40 days ±50 days ±60 days AVERAGE es [pvalor] [0.] [0.00] 6. [0.30] [0.396] 9.8 [0.55] [0.00] 3.9 [0.304] 3.9 [0.543] Falls Rses Before Afer Dff Wlcoxon Tes.08 [0.036].4 [0.].74 [0.08].85 [0.064] MEDIAN Medan Tes 3.60 [0.057] 0.80 [0.37].0 [0.73] 3.60 [0.057] KW Tes 4.8 [0.08].65 [0.98] 3.0 [0.078] 3.48 [0.06] Falls Rses
18 In ese ables, e resuls for e average and medan for e wo samples, are presened separaely. Te frs and second columns sow e mean values (average or medan of e aggregae (8 or asses for e dfferen perods, before and afer e cange over, respecvely. In e rd column, e dfference beween e frs wo columns s presened. Te four column sows e sgnfcance of s dfference; for e average, a es s used and for e medan, ree nonparamerc ess were employed: e Wlcoxon (U MannWney es, e Csquared es for e medan and e KruskalWalls es. Fnally, e las wo columns sow e number of socks a ave experenced eer a rse or a fall n er relave number of ransacons or relave volume negoaed for eac perod. For e sample of 8 socks, we observe n e number of relave ransacons a very dfferen knd of beavor beween e average and e medan. Te wo measuremens only agree wen ey ndcae a sgnfcan reducon n e number of ransacons n e wndow a corresponds o e 5 days precedng and e 5 days followng e enry of e socks no e Fxng sysem. From s perod on, mporan dfferences begn o appear beween e wo measures. Parcularly n e larger wndows, n wc ere s a cange, from sgnfcan ncreases n e number of ransacons for e average, o nonsgnfcan decreases n s varable for e medan, (excep for e 60day wndow, wc sows a sgnfcan decrease. Te dfferen beavor of ese wo measures could be due o exreme values on ceran radng days. Tese exreme values could be e resul of e spls carred ou by some of e companes n e sample. Te resuls found n e subsample of asses a dd no spl er sares, seem o confrm s evdence. In s subsample, e dfference observed beween e average and e medan s que smlar. Tere s a sgnfcan reducon n e number of ransacons n every perod consdered. Ts resul suppors e evdence presened by Gómez Sala (999 n s sudy of spls n e Spans marke. To be more specfc, n comparng e wo samples, we noce a among e companes a ave eer ncreased or decreased er ransacons n any gven perod, e frms wc ncrease er number of ransacons, are generally ose a ad spl er sares. 8
19 W regard o e relave negoang volume, we also noe a dfferen sor of beavor beween average and medan values. In general, e averages ave muc greaer values an e medan, wc could ndcae e presence of exreme values. Te nonnormaly observed n s varable, manfes n e lepokuross of e dsrbuon, (n oer words, cker als an ose of e normal dsrbuon, as been exensvely debaed n e leraure. Ts fac can no be drecly arbued o e spls, wc e smlar beavor observed beween e wo samples confrms. Once agan, s resul suppors e fndngs of Gómez Sala (999, n wc no sgnfcan canges were seen n e radng volume of e asses a ad been spl. For e sample of 8 socks, e average volume negoaed only reduces sgnfcanly n e 5day wndow. For e remanng perods, nonsgnfcan reducons of s varable are observed. On e oer and, e medan sows sgnfcan decreases n e wndows of 5, 50 and 60 days. Te sample of asses presens smlar, f no more exreme resuls. Reducons are observed n e average volume n every sngle perod, aloug none of em s sgnfcan. W regard o e medan, e reducons become sgnfcan n almos all e wndows (excep n ose of 0 and 5 days. To renforce e accuracy of e resuls obaned a second es s done. Te new evaluaon ncluded wo nnovaons. Frs, e logarmc ransformaon was used for e varables examned n e sudy. Ts ransformaon as been wdely promoed for e analyss of e negoang acvy, snce smooens e beavor of e varables, as Ankya and Jan, (989, among oers, subsanae. Furermore, s second es measures e sgnfcance of e dfferences beween perods, n crosssecon, wc allows us o focus on e problem from oer meodologcal perspecve. Te es s based on e followng expresson, calculaed for eac asse: 9
20 D V V V ln M V ln ( before M afer 5,0,5,0,30,40,50,60 days. were, D, dfferenaes beween e wo perods, before and afer e cange n e varable under sudy (relave number of ransacons or relave negoang volume for e asse ; V s e mean value of e varable under sudy, for e days mmedaely precedng or followng e even, for e asse ; V M s e mean value of e varable under sudy for e days precedng or followng e even, for e marke. Once s dfference as been calculaed for eac asse and for every perod, e sgnfcance of s average and s medan s suded, n crosssecon, for e wo samples under consderaon. In Tables 4. and 4.. we presen e resuls for e relave number of ransacons and e relave volume negoaed, respecvely, for e sample and subsample. Te frs wo columns conan e number of companes a experence eer a rse or a fall n acvy beween e former and e laer perods. Te followng four columns presen e average and e medan of e dfferences of e socks and er sgnfcance (measured w a es for e average and e Wlcoxon es for e medan. Te resuls are very smlar o ose obaned w e frs es. For e number of ransacons, and for e sample of 8 asses, we agan observe a grea dfference n beavour beween e average and e medan. On s aspec, bo measuremens sow a sgnfcan reducon n e number of ransacons n e 5day wndow. For e sample of asses, a smlar beavor s observed beween average and medan. Once agan, sgnfcan reducons are observed n e number of ransacons for all e wndows. Apar from a few excepons, e companes wose negoang levels ncrease or decrease n s es are precsely e same ones a dd so n e prevous es. 0
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