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1 PSONAL VSION Ths s a so called personal verson auhors s anuscrp as acceped for publshng afer he revew process bu pror o fnal layou and copyedng of he arcle. Bu, H & Vrk, N S 204, ' Lqudy and asse prces: An eprcal nvesgaon fro he Nordc sock arkes ' UOPAN FINANIAL MANAGMNT., 0./UFM.204. eaders are kndly asked o use he offcal publcaon n references.

2 Lqudy and Asse prces: An prcal Invesgaon of he Nordc Sock Markes Hlal Anwar Bu Deparen of Fnance and Sascs, Hanken School conocs, Vasa, Fnland. Nader Shahzad Vrk Deparen of Fnance and Sascs, Hanken School conocs, Vasa, Fnland. -al: Forhcong uropean Fnancal Manageen Absrac Ths paper presens a splfed sngle perod asse-prcng odel adjused for lqudy and ess for he Nordc arkes. The dealed eprcal evdence s presened fro Fnnsh es case. prcal esng of sall ye developed arkes s ovaed by he ncreased relevance of he llqudy effec for llqud asses/arkes. The an evdence repors lqudy rsk akes suffcenly larger par of predced facor rsk preu han he arke rsk, conrary o coparable U.S. evdence. Ths hghlghs he ably of lqudy relaed odel beas n capurng he e varaon n expeced reurns across llqud Nordc arkes han arke bea. Keywords: Asse-prcng odel, llqudy effec, predced facor rsk preu, odel beas JL lassfcaons: G0, G2, G5.. Inroducon Sudes connecng lqudy o asse prcng have evolved over e and are currenly based on a wofold proposon ha he level of llqudy and llqudy rsk are prced and boh are uually renforcng. One of he nal sudes poneerng he forer aspec of lqudy s of Ahud and Mendelson 986, hey showed a posve relaonshp beween an asse s level of llqudy and expeced reurns. Then Pasor and Sabaugh 2003 elaboraed upon laer aspec of llqudy and deonsraed a lnk beween he asse reurns and lqudy rsk. Furherore, Ahud 2002 nvesgaed syseac llqudy rsk and proposed ha expeced arke llqudy s prced posvely, whle shocks o arke llqudy lower coneporaneous reurns. Ahud 2002 provded hs evdence for he U.S. arke whereas, Bakaer e al esed hese hypoheses for eergng arkes and broaden he evdence. *We are graeful o he anonyous referee and John Doukas, he edor of he journal, for her coens on earler verson of hs paper. The auhors also wsh o hank conference parcpans a he Hanken School of conocs, he IFABS, 202 conference, he SFA, 202 Annual Meengs and MFS conference, 203. Dscussons wh Johan Knf, Kenneh Höghol and Peer Nyberg are graefully acknowledged. We are also graeful o Waleed Ahad for help wh wrng codes for daa consrucon. The fnancal suppor of Hanken Foundaon and Wallenberg FI s grealy acknowledged. orrespondence: Hlal Anwar Bu.

3 Around hs general concluson ha lqudy rsk s prced; here s anoher assocaed aspec of lqudy rsk, ha s, s varous densons. Hsorcally, a flgh o lqudy/qualy rsk Ahud 2002, Pasor and Sabaugh 2003, Sadka 2006, Fujoo and Waanabe 2005 and ohers has been explored ore, n whch an pac of changng arke-wde lqudy s seen on dfferen asse classes. Anoher denson of llqudy rsk s coonaly n lqudy as proposed by horda e al. 2002, Hasbrouck and Sepp 200 aong ohers. Karoly e al. 202 exended hs evdence of coonaly n lqudy for he socks n 40 developed and eergng counres. All he above, along wh an addonal denson of syseac lqudy rsk depressed wealh effec, are nealy presened n he heorecal equlbru odel of Acharya and Pedersen Besdes, anoher denson of odelng syseac lqudy rsk follows Faa and French 993 ype consrucon of rsk ckng lqudy facor under he equlbru assupon of no arbrage Lu, We splfy he odel developed by Acharya and Pedersen 2005 by akng he lqudy adjusen n a sngle perod odel raher han usng an overlappng generaon odel OLG. The odel proposes ha a arke ndex, spanned fro a ean-varance effcen asse space ne of assespecfc lqudy coss, s a beer canddae o reduce he repored sprcng assocaed wh sandard ean-varance APM. The generalzaon of he odel allows for he deernaon of asse prces nsde he odel and accouns for he oal cos of rade raher han exogenously deerned prces and odel agens confronng he cos of sellng, as n Acharya and Pederson Iporanly, he adjused heorecal odel and s esed specfcaon n hs sudy boh are one perod, whereas n Acharya and Pedersen odel n each generaon agens are effecvely assued o have one perod uly axzaon for he specfcaon esng of he odel. As s generally acknowledged, llqudy effecs are pronounced for llqud asses/arkes. However, wh few excepons, os lqudy-relaed sudes are conduced for he U.S. arkes. Arguably, he U.S. arke s he os lqud equy arke Bakaer e al., 2007 and herefore ay no be as suable for eprcal esng as oher llqud arkes. The repored dnshng llqudy preu n he U.S. sock reurns over e Ben-ephael e al., 200 hen should coe as no surprse. We argue ha s ore approprae o es lqudy-relaed odels n arkes ha are suffcenly llqud o dagnose he level and srengh of bearng such rsks n coparson o oher pernen rsks, such as arke rsk even f hey are developed. L, Sun and Wang 20 repor lqudy rsks are prced over and above arke rsk for he 2 nd larges global equy arke Japan afer he equy arkes n he U.S. In order o sress he porance of llqud arkes for he relevance of lqudy preu, we es he adjused odel for four Nordc capal arkes naely, Denark, Fnland, Norway and Sweden. 3 The an es s he quanfcaon of preu relaed wh lqudy rsks when copared wh dnshng lqudy preu for US sock reurns. Furherore, we selec a represenave arke ha s, Fnland. The es case selecon s o ake generalzaons across Nordc llqud arkes: how lqudy evolves over e; 2 success of dfferen easures n capurng effec of lqudy and 3 porance of a parcular lqudy rsk across dfferen lqudy rsks. The Fnnsh sock arke s a sall, developed arke ha, over he course of a decade, ransfored fro an llqud o a lqud arke; ye, he prospec of fndng llqudy reans a possbly due o he pecular seng n whch he arke operaes. 4 The lqudy crses affec he llqud asse he os. 2 Sellng coss can only be deduced when daa for each rade, whch allows buy and sell orders o be dsngushed, s avalable, bu hs ehod requres subsanal crosrucure daa. However, even he dsncon beween buy orders and sell orders s a es obscured n low frequency daa. Thus no exac procedure exss o approxae he cos of sellng usng any llqudy easure. 3 We especally noe he suggesons fro he dor John A. Doukas n he developens n hs drecon. 4 The eprcal leraure on he Fnnsh arke sudyng he relaonshp beween sock reurns and dfferen llqudy proxes s exensve. For nsance, Swan and Weserhol 2002 found ha he level of llqudy has a posve and srong effec on he cross-secon of sock reurns fro Vahekosk 2009 esed for arke specfc and asse specfc lqudy rsks for a cross-secon of sx sze porfolos and found ha asse specfc rsk s no prced, whereas he porfolo rsk sensves reveal a fla relaonshp across he sze of he porfolos. In he laer sudy, he llqudy rsk was capured by one facor ha only accouns for Ahud s 2

4 The cross-secon of 25 es porfolos, based on fve dfferen hree lqudy and wo nonlqudy sock characerscs, ess he real srengh of he proposed odel, as suggesed n Lewellen e al Furherore, we calculae he easure of llqudy for he socks lsed n he Fnnsh arke n wo dsnc ways: he easures proposed n Lesond e al. 999 and Ahud Boh of hese llqudy easures are hghly correlaed wh fner spread and prce pac proxes esaed fro low frequency daa Goyenko e al., The prary purpose of easurng llqudy n dfferen ways s o repor whch llqudy proxy beer capures he unobserved llqudy effec ha explans he cross-seconal reurn dfferences. Fnally, we also check for e varaon n llqudy and es all of he odels, excludng he perods wh hgh llqudy, usng he reduced saple. The resuls show ha he llqudy porfolos reurns are ore relaed o he syseac llqudy rsks han he syseac arke rsk. The pac of hs relaonshp s subsanal; he percenage of he llqudy preu n he oal odeled rsk copensaon s approxaely 92 percen for a odel wh hghes 2 and resrcons on odel nercep. In coparson, only 7 percen of he oal rsk preu s arbued o llqudy rsks for U.S. sock reurns Acharya and Pederson,2005. The reander of he facor rsk preu s arbued o APM rsk n boh arkes. The sronger assocaon of odel-predced facor rsk prea wh lqudy rsks reans nac even durng caler perods ha s, 60 percen of he aggregae odel preu s he reward for bearng llqudy rsks. The an eprcal fndng confrs our hypohess ha lqudy effecs are ore pronounced for llqud asses/arkes. Therefore, he evdence suggess ha lqudy relaed heores should prorze llqud arkes over/along wh he usual exanaons of he U.S. arke. The reanng evdence fro he Fnnsh es case can be suarzed n hree levels. Frs, he wo easures of llqudy perfor equally well n reducng cross-seconal sprcng. However, he overall odel effec ay be drven by a dfferen odel rsk denson alogeher. Second, he llqudy effec s e varyng. The Ahud 2002 prce pac easure s ore responsve n capurng hese e varaons o he exen ha odel esaes usng a proxy prce pac easure are ore sable under he odel s assupons. Thrd, he lqudy-adjused odel perfors well relave o a sple APM, even when he asse space of es porfolos ncludes non-llqudy porfolos n odel esaes. For llqudy es porfolos, hs proveen s subsanal n he full saple raher han n he caler perod. However, he generalzaon ha boh he lqudy easures across he reanng arkes Denark, Norway and Sweden provde dsngushable reurn dsperson across llqudy porfolos s no as pronen as we have for he Fnnsh sock reurns. Gven he dfferences n arke crosrucure, we resor o a varan zero easure ha nersecs he sock zero reurn days wh zero reurn n a respecve arke currency rae arke agans US dollar, see Bu 203 for deals. The easure helps generalzng he evdence for lqudy effec as repored for he Fnnsh sock reurns: he agnude of lqudy rsk copensaon n he oal odel rsk preu s even hgher n he oal odel rsk preu han we repor for he Fnnsh arke. Oher repored eprcal generalzaons fro Fnnsh arke rean nac across reanng hree Nordc canddae llqud arkes. Ths paper s organzed as follows. Secon 2 descrbes he ehodology used n hs paper. Secon 3 dscusses he daa and consrucs and elaboraes he porfolo and dfferen easures of llqudy. Secon 4 provdes eprcal analyss, and Secon 5 concludes he sudy flgh o lqudy noon. As noed prevously, oher llqudy rsks, such as coonaly effec and depressed wealh effec on asse s llqudy, exs; herefore, he resuls conrbue suppleenal eprcal evdence for oher rsk ypes affecng he Fnnsh sock reurn varaons. 3

5 2. Mehodology The presence of he law of one prce LOP provdes a sochasc dscoun facor,, such ha all he asses are correcly prced plyng, M X P. quaon could also provde a represenaon of gross reurns f we dvde he equaly by he non-zero sock prce P, such ha M. s he perod reurn on asse, and f s he excess perod reurn over he rsk free rae, hen he relaonshp can also ake he for M 0. All subsequen equaons wll represen as he excess reurn for exposonal convenence. If he dscoun facor s a funcon of he ean-varance effcen arke facor reurn, equaon converges o he sandard APM. One shorcong of APM ncludes he odel s plcaon for socks wh slar expeced cash flows ha dffer only n her ably o be raded or ransaced quckly Pasor & Sabaugh, 2003; Sadka, The odel ples heorecally equal prces for such socks; however, we observe volaons o he odel s plcaons and LOP n he real world. Therefore, hese noed shorcongs deand ha llqudy-adjused APM be proposed under ore generalzed assupons, n whch asse reurns could be prced subjec o he overall effec of llqudy. Here, we derve a sple prcng equaon adjused for lqudy relaed coss followng he eanvarance opzaons dscussed n Lo e al. 2004, assung ha nvesors observe he ne asse reurns of he ransacon coss accrued n he nheren asse specfc llqudy consrans. 5 We use a proporonal ransacon cos easure such ha I. In he equaly, I represens expeced llqudy, s a consan of proporonaly ha should be posve, and s he expeced relave ransacon cos. Slarly, we can represen he relaonshp beween arke llqudy and ransacon cos o hold for all he asses n he arke as I. The expeced llqudy s a funcon of he acual ransacon coss. The expeced asse llqudy and expeced arke llqudy are equal o he respecve ransacon cos relave for, such ha heorecal coss are precsely denfed. The subsequen odel equaons o he ers and for clary. Therefore, an asse-prcng odel adjusng for he lqudy effec can be derved fro expeced excess ne reurns on socks such ha he prcng kernel s a funcon of ne excess arke reurn 6 : M 0. 2 quaon 2 accouns for he expeced level of sock llqudy, whch for an llqud asse s hgher han he level of llqudy of a lqud asse, such ha ILLIQ LIQ. Furherore, he effec of arke llqudy on pay-offs fro llqud asses s also hgher. Therefore, even f he expeced excess reurns on boh llqud asses and lqud asses are dencal, he observed prce of he llqud asse s ILLIQ LIQ lower, such ha P P for havng addonal exposure o llqudy. Ths follows fro he sple rsk-reurn relaonshp ha f wo asses have equal excess reurns bu one s lqudy- M T 5 s he oal cos of he rade n our odel, bu when we conver he prcng relaonshp, as n equaon T P 4, n ers of ne reurns; he coponen represens he relave cos of rade for sock, such ha T M M M P P and slarly follows for oal arke porfolos, such ha. 6 The ers lqudy and llqudy are used nerchangeably hroughou he paper for exaple: lqudy effec, rsks, or beas and llqudy effec, rsks, or beas. 4 T

6 adjused rsker, hen he llqud sock s prce s se o be lower han he lqud sock because nvesors deand addonal copensaon for bearng hgher rsk. onsequenly, prcng equaon 2 can gauge he relaonshp beween expeced reurns and aggregae rsks, for any proxy easure of lqudy, caerng all syseac densons of llqudy rsks. We argue ha agens hypohecally assgn equlbru prces o all socks whle havng hoogenous expecaons for condonal expeced ne reurns. 7 Therefore, n any perod, agens choose consupon and porfolos o axze expeced uly. Assung exogenously deerned llqudy relaed coss, ne reurns are denfed n each perod, provded ha all agens are prce akers and shor sellng s no allowed. The agens denfyng ne reurns deerne he new feasble se and he effcen asse cobnaons ha wll hold n equlbru. The ne reurn adjusen wll re-esablsh he capal arke lne angen, gven he poor eprcal perforance of he sandard APM, o he effcen froner a he poson of he ne arke rsk, reurn radeoff pon n he reduced ean-varance space. The agens wll ake long posons n he ne arke porfolo, slar o he agned APM econoy. Moreover, he ne reurn on he arke porfolo ay no be he agned APM econoy opal soluon because our proposed odel adjuss for he observed sprcng. 8 The proposed odel perceves lqudy rsk as ncludng he oal cos of rade, and hus s ore lberalzed han Acharya and Pederson s 2005 lqudy-adjused odel, alhough generaes a slar odel n ers of odel rsks. 9 The proposed generalzaon of he Acharya and Pederson 2005 lqudy-adjused APM, followng Lo e al. 2004, can provde beer real world predcons when prcng asses n leu of a ne ean-varance porfolo. Furherore, slar o APM heory, he expeced ne rae of reurn on he socks s syseacally relaed o he reurn on a welldversfed arke porfolo. The esable cross-seconal resrcon on he asses wll ply a sngle bea represenaon such ha:, 3 ne ov, where and. Var The proposed odel wll converge o APM: n he absence of llqudy relaed coss f he rank of an agned APM opporuny space gven he consrans s equal o he proposed odel rank; and f he reduced nvesen se s an effcen subse of he agned APM econoy and shares he sae soluon space. The splfed one-perod odel proves he Acharya and Pederson 2005 OLG odel for he endogenous deernaon of asse prces and he deernaon of oal rade cos. The soluon o hs prcng equaon exends he applcably of he Acharya and Pedersen 2005 heorecal odel for any easure of llqudy and anans a slar effec of he level of llqudy and uncondonal separaon aong odel rsks. The separaon aong odel rsks enables he deernaon of he relave pac of a parcular rsk on expeced reurns. The proposed odel should be consdered an abrdgen of APM heory desgned o aelorae s laons whle allowng for lqudy-relaed coss rsks. quvalenly, we can decopose no APM bea and hree llqudy relaed beas such ha he uncondonal represenaon of equaon 3 expands o: n e ne 7 We assue expeced ne reurns are jonly norally dsrbued. 8 The non-conforably follows f one asse exss ha s gven posve weghs under he agned APM econoy; such ncluson drves he opal soluon under he APM sub-opal n he reduced ne reurn nvesen se, owng o greaer radng cos. 9 However, he feasble soluon n her odel s also applcable o he agned APM econoy, provded prces are exogenously deerned. The oher noable assupon n her OLG odel s ha he llqudy dscoun ncurred by he ernal perod agens s revealed n he cos of sellng. They descrbed ha agens can P P buy a bu us sell a page 379, where s he cos of sellng an asse. 5

7 6. 4 quaon 4 shows ha expeced excess reurns are sensve o he expeced level of lqudy arke rsk and he hree lqudy bea rsks. We can also wre equaon 4 as:. 5 The purpor of equaon 5 s o adjus, he arke bea, wh he oher llqudy-relaed beas,, and such ha he excess reurns on lqud and llqud asses ach wha we observe n he arke. Arguably, he llqudy-relaed beas ncrease or decrease he exposure of he expeced reurns on llqud asses or lqud asses whle accounng for he syseac rsk of lqudy. The eprcal esaon of he odel s execued assung all ha nvesors have a oneonh radng horzon. The odel rsks can be esaed wh he consraned prce of rsk as pled n equaons 4 and 5 under resrcon, such ha The success of he proposed odel, n reducng equlbru sprcng, s esaed wh he followng specfcaon:. 6 In equaon 6, s a APM relaed bea, whereas he oher hree beas are lqudy relaed. All of hese beas sgnfy lqudy rsks ha have been suded exensvely n he leraure. The unconsraned esaon of equaon 6 enables us o analyze all of he lqudy rsks and he lqudy level under a sple odel. We refer o Acharya and Pederson 2005 for a dealed dscusson of he econoc nuon behnd he dfferen lqudy beas. The beas for esaon of cross-seconal analyss are calculaed usng followng equaon 7 o 0 usng respecve e seres: Daa The frs proble n hs sudy for esng he llqudy effec, across Nordc arkes n general and n parcular for he Fnnsh es case, s he led nuber of lsed socks copared o oher developed arkes see Bu and Vrk, 203 for deals. Ths laon consrans he sudy o a large cross-secon of porfolos wh respec o a parcular sock characersc. Therefore, based on pror perod sorng crera, for each onh we dvde he avalable socks no fve qunle porfolos usng fve dfferen sock characerscs. The asse characerscs relaed o llqudy are he zero easure Lesond e al., 999, sze, and prce nverse PI rao. The res are generaed usng pror year oenu reurns and book-o-arke BM raos. Frs, he avalably of 25 characersc porfolos enables he sudy o repor he relave role of llqudy n prcng llqudy and non-,,,, Var ov Var ov Var ov Var ov , Var ov, 2 Var ov, 3 Var ov, 4 Var ov

8 llqudy es porfolos. Second, provdes an adequae nuber of es porfolos for he sascal power of cross-seconal ess. Pror o consrucng of es porfolos, daa are rereved fro DaaSrea fro January 994 hrough May We prefer onhly nforaon sorng crera for rankng he characersc sock reurns. Ths ehod ncreases he nforaonal conen Vahekosk, 2004 and provdes a onhly paron of he daa for llqudy relaed and oher avalable sorng crera, such as oenu reurns. 0 Only he BM-rao porfolos are ranked on he year-end nforaon. The rereved sock prces are adjused for dvdends, spls, and oher cash payous. The frs fve porfolos are sored on he bass of he prevous onh s ncdences of zero reurns zero easure onwards for all avalable frs. The qunle porfolo ncreases n he zero easure; ha s, L- s he porfolo conanng he 20 percen of he paroned socks wh he lowes value for he percenage zero reurn days. Subsequenly, L-2, L-3, L-4, and L-5 are ncreasng n he relave llqudes. In a slar fashon, he sze and he sock s PI rao-based qunle porfolos are generaed based on he pror onh s fr capalzaons and PI raos, respecvely. The chronologcal order for he sze qunles s such ha S- represens he salles capalzed frs, and S-5 conans he frs wh he hghes capalzaon n he daa. The prce nverse porfolos are such ha PI- conans he hghes prced 20 percen of he socks, and PI-5 represens he lowes prced 20 percen of he socks. Subsequenly, we consruc he 0 non-llqudy-based porfolos. The fve oenu porfolos are consruced eployng he sandard pracce n he leraure. The prevous eleven-onh rollng average reurns excludng he os recen onhly reurn are esaed each onh across all socks and are hen used o creae fve oenu parons, eravely. The generaed porfolos ndcae ha each succeedng qunle conans he frs for whch he prevous eleven onh rollng average reurns are hgher han he precedng qunle; ha s, M- are he loser sock porfolos, and M-5 are he wnner sock porfolos. For he consrucon of he BM porfolos, we rank he nex year s sock reurns no fve porfolos, whch are ncreasng n he BM raos; ha s, BM- represens growh overprced socks, and BM-5 are value underprced socks. We use equal weghng for porfolo reurns and porfolo-specfc llqudy easures for he Fnnsh arke. Nuerous lqudy-relaed sudes have followed he equal weghng schee for he es porfolo. The selecon of equally-weghed porfolos s even ore relevan for he Fnnsh arke Bu & Vrk, 202, as he capalzed porfolos severely suffer n he presence of few large frs. Therefore, he eprcal analyss wh he value-weghed porfolos ay ss he lqudy effec alogeher, whch s usually pronounced for sall frs. 3.. The llqudy easures for he Fnnsh arke Generally, llqudy easures consruced fro he daly observable daa fall no wo caegores; eher he easure s a proxy for effecve spread or a proxy for prce pac. The frs easure of llqudy used n he sudy s he zero easure, whch was proposed by Lesond e al The prese of he zero easure s ha hgher ncdences of zero reurn days for any fr proxy for hgher llqudy. The consrucon of he zero easure s begun by recordng he frequency of he zero reurn days n a onh across all socks. Then, for each sock we ake a sple rao of he zero reurn days n a gven onh over he oal nuber of radng days n ha onh: Zero Measure = Nuber of days wh zero reurn / Toal nuber of radng days, 0 However, usng yearly sorng ay no change he overall resuls because llqudy s a perssen characersc, and an llqud asse s lkely o be llqud a onhly or yearly frequences. Brennan and Subraanya 996 assued one-year llqudy esaes o be consan for he hree subsequen years n her sudy. The sze and PI rao based es porfolos have been exensvely used n he leraure o proxy for llqudy relaed characerscs. Ahud 2002 use sze porfolos o deerne he llqudy preu. Whle he prce nverse rao s suggesed by Brennan and Subrahanya 996 because llqud socks generally have lower prces copared o lqud socks. 7

9 The underlyng splcy of he proposed easure enables us o consruc he longes possble llqudy seres for he Fnnsh arke. The zero easure accoodaes all of he asses n he saple, whch gh have been oed under soe oher proxy easure of llqudy because hey requre addonal requreen, such as raded volue and ype of rade. The second easure of llqudy s volue relaed and easures he response of absolue reurn o un raded uro volue for a parcular sock, as proposed by Ahud The easure s consruced provded ha he raded volue for a parcular sock s avalable. onsequenly, he absolue reurn on sock on day d of onh s dvded by he raded volue n euros for d he correspondng day VOLD n he sae onh such ha / VOLD. We esae he onhly easure such ha: D d where s he nuber of radng days for sock n any onh. D ILLIQ / D / VOLD, The calculaed average onhly llqudy AILLIQ s he average prce pac of he raded volue sensves across Fnnsh socks: d d d d AILLIQ / N N ILLIQ, 2 where N s he nuber of socks n a onh. Ahud 2002 placed few resrcons on he consrucon of he prce pac easure. For nsance, llqudy s calculaed for socks ha are raded on a leas 5 days n a onh. By posng slar consrucon consrans as Ahud 2002, hs easure reaned avalable for only 40 percen of he socks n he Fnnsh arke. To ncrease he nuber of asses for whch we could esae prce pac based llqudy, he resrcons are waved. We also esae onhly arke llqudy whle posng all of he resrcons n Ahud 2002 and fnd ha, copared o he unresrced easure, he resrced easure only provdes approxaons for he relavely lqud socks n he Fnnsh arke. In order o accoodae llqud socks n Ahud 2002 easure we also nclude hose socks whch are no raded for a leas 5 days. We raonalze her ncluson on wo accouns, frs f hese socks are no raded frequenly hen as per Lesond e al. 999, s owed o hgher ransacon cos nvolved n radng. Secondly we conjecure even f hose socks were raded hen her lkely prce pac o raded volue could have no been ha dfferen whch we had wh avalable volue. On hese wo accouns, herefore hese socks are canddae for ncluson n he Ahud 2002 prce pac easure and hus wavng 5 days o rade resrcons ay help o capure addonal llqudyrelaed nforaon wh he prce pac easure Illqudy of he Fnnsh arke Because llqudy s a prary characersc of any sall arke, undersandng how llqudy evolves over e n Fnland s poran. Fgure plos he seres of prce pac easures durng Perods of llqudy and lqudy are evden n he Fnnsh arke. The perods spannng and exhb clear paerns of ncreased llqudy such ha he absolue reurn pac of one uro raded s exaggeraedly hgher han he reanng cal perod n he saple. Oherwse, he arke s que lqud durng , when he arke absolue reurn shows an pac of only 0.02 for one uro raded, on average, whereas he prce pac esae ncreases o n he full saple, whch s nearly sx es hgher han he esae for he cal perod. The dfference conveys an presson of hgher llqudy for he oal saple perod. 8

10 When he arke s os lqud, we fnd ha, especally for Noka, he reurn pac of one uro raded s as low as 2.x0-7. Vahekosk 2009 also repored ha he bd-ask spread for Noka was 0.2 percen durng hs perod of sudy. The use of he zero easure hghlghs slar paerns n llqudy across saples bu n a less vgorous anner han he Ahud easure. We dvde he zero easure llqudy seres no hree subsaples on he bass suggesed by he resuls for he Ahud 2002 prce pac easure n Fgure. We repor ncreasng ncdences of zero reurn days durng Ahud Prce Ipac Measure Fgure. Ahud easure of llqudy for he Fnnsh arke Proporon of Zero eurns Fgure 2. Zero easure of llqudy for he Fnnsh arke and , as ndcaed by he seepness of he relevan rend lne. The ncreased ncdences of zero reurn days are a sgn of ncreasng llqudy. Furherore, o llusrae he pon ha he Fnnsh arke s ore llqud hen any large capalzed developed arkes, we rely on he llqudy esaes fro sudes on he U.S. arke. The repored prce pac easure for U.S. sock reurns n Ahud 2002 s 3.37x0-7 wh a sandard devaon of 5.2x Under slar crera for he Fnnsh arke, whch spulae ha a sock s raded a leas for 200 days n a year and has a prce above fve uro, generaes n an annual ean prce pac of 3.79x0-4 for all frs wh a sandard devaon of 5.69x0-4. The coparable saple prce pac easure for he U.S. arke s 6.3x0-6 wh a sandard devaon of 9.2x0-7, as provded n Goyenko e al The coparable esaes show ha he Ahud 2 See Table n Ahud 2002 for he U.S. arke prce pac easure descrpve sascs durng Table panel A and panel D n Goyenko e al provded dealed descrpve sascs for he prce pac easure and percenage zero easure for he U.S. arke for , respecvely. For he Fnnsh arke, he correspondng esaes of he prce pac easure and zero easure, n a slar perod o ha 9

11 2002 easure for he U.S. arkes s sgnfcanly lower han he correspondng Fnnsh arke esaes. Goyenko e al also calculaed he average zero easure for he U.S., whch s 4.3 percen wh a sandard devaon of 4.7 percen, whereas he correspondng zero easure for he Fnnsh arke s 33.5 percen wh a sandard devaon of 8.5 percen n he full perod. The average zero easure for he Fnnsh arke s coparable o he average zero easure for nneeen eergng arkes, as repored n Bekaer e al The repored zero easure for he eergng arkes s 30.8 percen wh a sandard devaon of 3.5 percen for he e perod rangng fro 987 o Ths resul ndcaes ha, regardng lqudy easures, he Fnnsh arke s oo llqud relave o he U.S. arke and s slar o eergng arkes n ers of he zero easure. The llqudy characerscs and he hybrd naure of he Fnnsh Nordc arke ake he eprcal conrbuon of he sudy ore neresng and relevan saons 4.. Tesng porfolos and nnovaon n reurn and llqudy seres We use nnovaons nsead of orgnal seres n our eprcal analyss because he leraure ndcaes ha lqudy s predcable; an llqud porfolo s expeced o be llqud for a consderable lengh of e. Moreover, eployng nnovaons also crcuvens he saonary ssues, gven he hgh perssence n he levels of llqudy seres. The nnovaons n llqudy are gahered by posng AMA srucures of varyng order n p, q, where p s he lag lengh for he auoregressve er, and q s he lag lengh of he ovng average er: L p q L c. 3 L s he expeced level of llqudy of each es porfolo and arke porfolo. The nnovaons n he asse-specfc llqudes are colleced for boh easures of llqudy. We also collec nnovaons n he aggregae arke llqudy and arke reurn seres. In posng he AMA srucure across all llqudy seres, we ensure ha no predcably reans n he respecve nnovaon seres. We rereve nnovaon n he arke reurn seres usng an A odel and Faa and French 993 facors, llqudy easures, and volue as explanaory varables. Subsequenly, he llqudy relaed beas are calculaed usng nnovaons n porfolo and arke llqudy seres Lqudy relaed beas over e We presen he descrpve sascs for he es porfolos and he key characerscs and esaed bea rsks n Table and Table 2 for he nal analyss usng he zero and prce pac easures, respecvely. Frs, as shown n Table, he llqudy-based es porfolos provde adequae resuls n ers of sharng key llqudy characerscs. The expeced porfolo llqudes esaed wh he zero and prce pac easures are gven under he headngs L and A, respecvely. The esaed llqudes are ncreasng n he odd nubered llqudy and PI porfolos and show pernence of llqudy across he porfolo reurns, whereas for sze relaed porfolos boh llqudy easures are eployed by Goyenko e al., are 3.84x0-4 wh a sandard devaon of 6.36x0-4 and 36 percen wh a sandard devaon of 4.3 percen, respecvely. 4 All he Nordc sock arkes are developed capal arkes ha are ncluded n he MSI global ndex. Ye all of he share he llqudy feaures of eergng arkes as esablshed n he Fnnsh case n secon

12 Table Properes of porfolos wh lqudy beas calculaed by zero easure Ths able repors he properes of 25 equally weghed porfolos fored onhly for he perod fro 994 o 2009 on he bass of dfferen characerscs. Frs fve porfolos are based on easure of llqudy consruced by nuber of zero reurns n a onh for a gven fr. ach succeedng porfolo consss of 20% of frs wh hgher nuber of zero reurns. Ths consrucon of porfolo for llqudy also gudes foraon of oher porfolos wh dfferen characerscs whch n he order of Table are as, L represens llqudy, S represens Sze, P represens prce nverse rao, M represens oenu and lasly BM represens book o arke rao porfolos. β s usual arke bea whereas, β 2, β 3 and β 4 llqudy based beas, hese beas are calculaed usng equaon 7, 8,9 and 0. L, A, TO are he expeced llqudy calculaed fro Lesond zero easure of llqudy, Ahud easure of prce pac, and urnover. Sze shows average arke capalzaon of each porfolo and e s average excess reurns. The saplng dsrbuon for he bea rsks s calculaed fro yearly bea rsks usng he forula T, where s he sandard devaon of he yearly seres of bea rsks. The -sascs based on he sandard errors are repored n. Porfolos β.00 β 2.00 β 3.00 β 4.00 L % A,000 TO % Sze Ml. L L L S S S P P P M M M BM BM BM

13 Table 2 Properes of porfolos wh lqudy beas calculaed by prce pac easure Ths able repors he properes of 25 equally weghed porfolos fored onhly for he perod fro 994 o 2009 on he bass of dfferen characerscs. Frs fve porfolos are based on easure of llqudy consruced by nuber of zero reurns n a onh for a gven fr. ach succeedng porfolo consss of 20% of frs wh hgher nuber of zero reurns. Ths consrucon of porfolo for llqudy also gudes foraon of oher porfolos wh dfferen characerscs whch s order of Table are as, L represens llqudy, S represens Sze, P represens prce nverse rao, M represens oenu and lasly BM represens book o arke rao porfolos. β s usual arke bea whereas, β 2, β 3 and β 4 llqudy based beas, hese beas are calculaed usng equaon 7, 8,9 and 0. L, A, TO are he expeced llqudy calculaed fro Lesond zero easure of llqudy, Ahud easure of prce pac, and urnover. Sze shows average arke capalzaon of each porfolo and e s average excess reurns. The saplng dsrbuon for he bea rsks s calculaed fro yearly bea rsks usng he forula T, where s he sandard devaon of he yearly seres of bea rsks. The -sascs based on he sandard errors are repored n. Porfolo s β.00 β 2.00 β 3.00 β 4.00 L % A.000 TO % Sze Ml. L L L S S S P P P M M M BM BM BM decreasng n he capalzaon of sze porfolos. 5 Moreover, he porfolo expeced urnovers, TO, decrease as he llqudy of he porfolos ncreases. The average llqud porfolo reurns are hgher han hose of he lqud porfolos. Iporanly, he prevous onh s zero easure sorng produces a wde spread n he exree porfolo reurns. The 5 The resuls also hold for even nubered porfolos, bu o conserve space he resuls are only presened for odd nubered porfolos. These resuls are also conssen wh he noon ha sze facor also proxy for ransacon cos Desez 968, oll 984, Lesond e al. 999 aong ohers 2

14 annual reurn dfferenal beween he os llqud porfolo L-5 and lqud porfolo L- s approxaely 5.37 percen. 6 Ths resul hghlghs he greaer llqudy effec n he Fnnsh arke. A slar reurn dfferenal for he odd nubered oenu porfolos s also presen, and he annual reurn dfference beween wnners M-5 and losers M- s approxaely 5.6 percen, alhough he average llqudy levels capured n coluns L, A, and TO are no precsely co-corresponden. The varyng llqudy characerscs ply ha he porfolos wh approxaely equal reurn dfferenals are no necessarly holdng slar frs such ha he proposed odel s no esaed wh redundan es porfolos. Larger per annu reurn dfferenals are noed for PI 26 percen and BM 8 percen porfolos. The lowes reurn dfferenal s observed for sze porfolos S- nus S-5, whch sll average a subsanal 2 percen per annu, poranly wh vsbly dfferen characersc paerns han he ohers. Ths resul renforces our ovaon for sorng porfolos based on fve sock characerscs, gven he laons of he Fnnsh sock arke, such ha he Lewellen e al. 200 crcs of he success of asse-prcng odels s ncorporaed o address nuerous relaed ssues. The repored sascs regardng he hree llqudy beas n Table show ha he bea rsks are a funcon of he porfolo s llqudy level and ncrease n porfolo llqudy. Furherore, he zero easure based llqudy beas n Table are onooncally lnked o he ean reurns of he llqudy porfolos, wh he excepon of he coonaly rsk. Noably, he llqudy porfolos exhb subsanal onoonc sensvy o. I ay be nferred ha he os poran llqudy rsk, n explanng cross-seconal varaons n he es porfolos, s capured by flgh o lqudy rsk Ahud, 2002 when quanfed for he Fnnsh arke. The os llqud L-5 porfolo has a bea sensvy of for, whereas for he os lqud porfolo L- he bea sensvy s The hgher negave exposure for llqud porfolo sgnfes a larger drop n her reurns when arke llqudy suddenly ncreases. The non-responsveness of he non-llqudy porfolos o lqudy rsks s also exhbed n Table. The llqudy-relaed beas for he oenu and BM porfolos do no have any onoonc sensvy owards llqudy bea rsks. Because hese reurn dfferenals are no a funcon of he level of llqudy, he lqudy-relaed beas are also no ncreasng. In Table 2, he analyses for odel rsks are repored wh he prce pac easure. The only dfferences fro Table are n he four odel bea rsks. The repored bea rsks show ha s no noceably ncreasng wh he ean reurns of he llqudy porfolos. However, and, n coparson o he zero easure based correspondng lqudy beas, are ncreasng n he ancpaed drecon across he llqudy porfolos. Anoher noable dfference s he onoonc relaonshp beween he prce pac based llqudy rsks and BM porfolo average reurns copared o wha we repored n Table. The onoonc ncreases across llqudy bea rsks are such ha value socks show he larges prce pac sensvy copared o all oher es porfolos. The prce pac sensvy for BM porfolos s also larger for BM- and BM-3 copared o he correspondng values for llqudy porfolos L- and L-3 repored n colun A of Tables and 2. We also esaed he bea rsks for he ranqul perod, ha s, he saple perod , o copare he perforance of llqudy-relaed beas and he arke bea durng dfferen lqudy perods. Moreover, n odel equaon 6 he reurns are shown o be funcon of level of lqudy and lqudy beas. I furher poses he resrcon ha he uncondonal prce of rsk assocaed wh all four bea rsks reans dencal. However, esablshng he heorecal separaon aong he odel explanaory varables n he eprcal esaon of he odel s a dffcul underakng. In Table In Acharya and Pedersen 2005, n Table colun r e,p, he yearly dfference beween he os llqud and lqud porfolos, s 7.44 percen porfolos are sored wh Ahud 2002 easure of llqudy, whch s approxaely half he sze f he correspondng value for he Fnnsh arke. Frs, hs resul ples ha lqudy copensaon s large wh respec o he severy of llqudy n he arke. Second, necessarly reurn dfferenals ay no be coparable whle sorng wh a parcular easure across arkes for generalzaon of lqudy effec. To, elucdae hs pon a reurn dsperson beween L-5 and L- for Denark s 2.98, for Norway s even -4.65, however for Sweden s

15 and 3A, we esaed correlaon srucure aong level of lqudy, separae beas and ne bea for 5 llqudy relaed porfolos usng boh easures 7. I s obvous he srong correlaon exs aong odel based varables. Ths eludes he eprcal obscury confroned n racng segregaed llqudy rsks and, herefore, n esng he plcaons of he proposed odel requrng uncorrelaed facor rsks n he regresson analyss. Table 3 orrelaon by zero easure of llqudy Ths able repors he correlaon aong L, β, β 2, β 3, β 4 and β ne, for 5 porfolos for a perod of Where L s expeced llqudy of soe porfolo and β, β 2, β 3, β 4 are odel based rsk and β ne, s calculaed as β ne, = β + β 2 - β 3 - β 4. L β β 2 β 3 β 4 β ne, L β β β β β ne,.000 Table 3A orrelaon by Ahud 2002 easure of llqudy Ths able repors he correlaon aong L, β, β 2, β 3, β 4 and β ne, for 5 porfolos for a perod of Where L s expeced llqudy of soe porfolo and β, β 2, β 3, β 4 are odel based rsk and β ne, s calculaed as β ne, = β + β 2 - β 3 - β 4. L β β 2 β 3 β 4 β ne, L β β β β β ne,.000 Noneheless, Acharya and Pederson 2005 esaed he unconsraned unequal prea o rack he heorecally segregaed pac of each rsk on he cross-seconal reurn varaons. They acknowledged ha he eprcal evdence s weak. There are wo possble scenaros o ge around he ssues of ul-collneary, frs s, o rely on he valdy of he odel 3 and esae an overall ne, effec of llqudy by esang llqudy rsk by and calbrae he coeffcen on expeced llqudy by akng an average of urnover across all he socks. 8 Second s, o gauge separae effec of each of llqudy relaed beas as can also be nerpreed as showng he overall effec of llqudy, whch n oherwse deal suaon of no collneary should be anfesed by level of llqudy and separae llqudy relaed rsks. Therefore we also explore nesed odel 7 We esaed hese correlaons for 25 porfolos and for a dfferen perod of as well and hese ables can be provded upon reques. However resuls are slar o he one repored. 8 Acharya and Pedersen 2005 followed hs approach n her paper. 4

16 specfcaons ha only consder a sngle bea rsk a a e, whch are no repored n Acharya and Pederson As we used wo dfferen easures of llqudy herefore, he relaed odel beas have dfferen correlaon paerns n Table 3 and 3A. Wh Table 3A, our resuls are very slar o he one provded n Acharya and Pedersen 2005, possbly because hese correlaons are calculaed for porfolos by esang her llqudy as per Ahud Obvously sees o be he os represenave and s correlaed he os across all odel rsks and also wh level of llqudy of he porfolos. Therefore s suggesve of anfesng overall effec of llqudy when llqudy s esaed by 3 Ahud In Table 3, sees o be he os correlaed across all odel rsk 20 and wh level 3 of llqudy. Arguably when llqudy s esaed by zero easure Lesond e al. 999, s seengly capable of depcng overall effec of llqudy Model esng We proceed wh he esaon of he proposed odels n equaon 3 o he equally esable odel equaon: ne,, 4 ne, where shows ha he ne bea s an overall arke rsk when llqudy rsk s ncorporaed. The odel n equaon 3 s expressed n ers of excess reurns, whch ples ha he consan should be zero. However, we esae equaon 4 by allowng a nonzero consan for robusness. The esaons usng he zero easure of llqudy n all 25 es porfolos are repored n Table 3 a panel A. The success of he odel specfcaons s gauged under a jon creron of hgher cross-seconal 2 and ably o suppress prcng errors cross-seconal nercep. Usng he level of llqudy alone, he cross-seconal regresson n lne yelds he expeced posve esae and nsgnfcan prcng errors. The lower adjused 2 could be argued o be due o he low varably n he zero easure based llqudy levels for he PI, oenu, and BM porfolos see Table under colun headng L. Noneheless, he sgnfcance of he level of llqudy shows ha he porfolo reurns are lnked o her llqudy levels. In lne 2, he ne bea specfcaon also has a posve and sgnfcan prce of rsk. However, he ne bea specfcaon yelds sgnfcanly large prcng errors. The nex specfcaon esaes level of llqudy and ne bea sulaneously. The esaon oupu shows nsgnfcan prcng errors wh only a relavely hgher 2 of 0.45 han he resuls repored n lnes and 2. The coeffcen on he expeced llqudy s sgnfcan a he 0 percen level, and he coeffcen on he ne bea s nsgnfcan, alhough reans he posve sgn. However, he resuls show, hrough lnes o 3, ha a jon creron of hgher 2 and nsgnfcan prcng errors s no e. The relavely poor perforance of he ne bea specfcaon deonsraes he eprcal dffcules of akng accurae odel-based predcons when he coponen bea rsks do no capure he 2 underlyng heorecal drecon for exaple, he coonaly effec for all porfolos; 4 depressed wealh effec for oenu M and book o arke BM porfolos see Table. Noneheless, he plausble coeffcen esaes on expeced llqudy levels are an proveen on Acharya and Pederson 2005, as he llqudy level, when allowed o have a free paraeer value, was ofen plausbly esaed n her work. ne, ne, 9 Lee 20 n hs sudy The world prce for lqudy rsk noes hs proble of ul-collneary for he Acharya and Pederson odel lqudy rsks and also es sngle bea specfcaons ncludng level of lqudy and arke rsk Lower correlaon wh s undersandable as hs parcular llqudy relaed bea s no ncreasng for llqud porfolos as per Table. 5

17 As argued prevously ha prce of rsk assocaed wh eher of he bea rsks can also be nerpreed as capurng he overall odel effec. The ndvdual bea rsk specfcaon ncorporaes he possbly of deernng whch bea s a ore relevan rsk n suppressng cross-seconal prcng errors. Therefore, gven he hghlghed esaon dffcules and he srong correlaon paerns aong bea rsks, we es he followng cross-seconal specfcaons and he nesed sngle bea represenaons for he descrbed analyss:. 5 In lne 4, a APM specfcaon s eployed, and he prce of rsk assocaed wh s posvely sgnfcan. The sgnfcan odel prcng errors over predc he average porfolo reurns by.20 percen per onh, whch s subsanally large. The prce of rsk for he coonaly effec s expeced o be posve. However, we fnd an nsgnfcanly negave coeffcen, whch agan hghlghs he nably of he coonaly effec o no accoun for he parcular coneporaneous assocaon beween dosyncrac and aggregae llqudy shocks. The specfcaon wh flgh o lqudy rsk produces nsgnfcanly sall prcng errors. I also yelds he hghes adjused 2 across specfcaons usng only one explanaory varable. The esaed prce of rsk for s nsgnfcanly plausble. Acharya and Pedersen 2005 repored ha he depressed wealh effec rsk has he larges and os sgnfcan copensaon across all llqudy rsks for U.S. sock reurns. The regresson n lne 8 agan fnds a srong pac of, as n lne 6, and s sgnfcan even n he presence of oher odel rsks. The coparson of he odels, under he esablshed crera, suggess ha he specfcaon usng only flgh o lqudy rsks perfors beer han he ohers. The 3 rsk can explan he larges varably n ean porfolo reurns whle ananng he odel s parsony wh a slar adjused 2 o lnes 8 and 9. In bref, when llqudy s easured usng he zero easure, llqudy rsk s bes capured hrough o proxy he overall llqudy effec n he Fnnsh arke. The resul sgnfes he pervasveness of llqudy rsk, whch s arbued o a flgh o lqudy, also repored n Vahekosk 2009 for he Fnnsh arke. The esaons usng prce pac easure based llqudy rsks are repored n panel A of Table 5. The resuls show ha he level of llqudy s sgnfcanly relaed o expeced reurns wh a larger odel 2 han he correspondng zero easure specfcaons. The ncreased explanaory power deonsraes he ncreased varably nforaon conen n he prce pac easured porfolo llqudy levels n conjuncon wh expeced porfolo reurns copared o he zero easure see colun headers L and A n Tables and 2. However, he specfcaon wh expeced llqudy has sgnfcan prcng errors and fals o ee he odel success crera. The ne bea specfcaon does no have a hgh 2, alhough has nsgnfcanly esaed sall prcng errors. Usng he level of llqudy n conjuncon wh he ne bea hapers he odel n ers of he sgnfcan cross-seconal prcng errors. 2 The has posve and sgnfcan coeffcens n he sngle bea rsk specfcaons. However, he coonaly rsk alone s no a suffcen rsk facor for sgnfcan prcng errors. The flgh o lqudy specfcaon canno replcae s perforance under he zero easure and s neher sgnfcan nor plausble. In lne 7, he las llqudy-relaed rsk also has a negave, sgnfcan esae of he prce of rsk. The perforance of he ne bea specfcaon, aong he oher sngle bea specfcaons, s relavely beer under he odel selecon creron for suppressng crossseconal sprcng. The odel esaons hghlgh he key dfferences n easurng llqudy beween zero easure and prce pac hrough he sgnfcance of alernang llqudy beas o explan expeced porfolo reurns, as hypoheszed above

18 Table 4 qually weghed porfolos usng zero easure of llqudy Ths able repors he esaes for he llqudy relaed beas and arke bea usng cross-seconal regresson analyss for he perod of In panel A we esae coeffcens for all 25 es porfolos usng dfferen varans of followng relaon beween excess reurns and explanaory facors ne, p where, he oal of nne odels fro above relaon are esaed.in panel B he cross-secon regressons are perfored for equally weghed 5 porfolos whch are ranked wh soe llqudy relaed characerscs. The -sascs s repored n parenheses and hese are wh correced sandard devaon usng Newey and Wes 987 ehod wh wo lags. 2 s obaned for each of he esaed odel and adjused 2 s repored n parenheses. onsan L β ne, β β 2 β 3 β 4 2 Panel A: equally weghed 25 porfolos: Panel B: equally weghed 5 llqudy relaed porfolos

19 Table 5 qually weghed porfolos usng Ahud 2002 prce pac Ths able repors he esaes for he llqudy relaed beas and arke bea usng cross-seconal regresson analyss for he perod of In panel A we esae coeffcens for all 25 es porfolos usng dfferen varans of followng relaon beween excess reurns and explanaory facors ne, p where, he oal of nne odels fro above relaon are esaed.in panel B he cross-secon regressons are perfored for equally weghed 5 porfolos whch are ranked wh soe llqudy relaed characerscs. The -Sascs s repored n parenheses and hese are wh correced sandard devaon usng Newey and Wes 987 ehod wh wo lags. 2 s obaned for each of he esaed odel and adjused 2 s repored n parenheses. onsan L β ne. β β 2 β 3 β 4 2 Panel A: equally weghed 25 porfolos: Panel B: equally weghed 5 llqudy relaed porfolos

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