Working Paper Series 301 (ISSN )

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1 INFORMATION ASYMMETRY, SHARE MISPRICING AND THE COORDINATION PROBLEM: INVESTOR PORTFOLIO CHOICE IN CZECH VOUCHER PRIVATIZATION Elena Yusupová CERGE-EI Chales Unvesty Cente fo Economc Reseach and Gaduate Educaton Academy of Scences of the Czech Republc Economcs Insttute WORKING PAPER SERIES (ISSN -398) Electonc Veson 30

2 Wokng Pape Sees 30 (ISSN -398) Infomaton Asymmety, Shae Mspcng and the Coodnaton Poblem: Investo Potfolo Choce n Czech Vouche Pvatzaton Elena Yusupová CERGE-EI Pague, July 006

3 ISBN (Unvezta Kalova. Centum po ekonomcký výzkum a doktoské studum) ISBN (Akademe věd České epublky. Náodohospodářský ústav)

4 Infomaton Asymmety, Shae Mspcng and the Coodnaton Poblem: Investo Potfolo Choce n Czech Vouche Pvatzaton * Elena Yusupová CERGE-EI** Abstact Vouche pvatzaton n the Czech Republc pesented a natual expement of the ablty of nvestos to constuct the potfolos unde condtons of asymmetc nfomaton and the absence of stock maket pces. Ths pape povdes a theoetcal model of an optmal potfolo choce made by the nvestos maxmzng the expected etun and at the same tme solvng a coodnaton poblem n a non-coopeatve game wth othe nvestos. The pecepton of shae msvaluaton and pvate nfomaton ae endogenzed. The model offes an ntepetaton and theoetcal justfcaton of eale empcal fndngs and explans the cucal ole of the auctonee, dffeent optmal stateges fo dffeent types of nvestos and the edundancy of legal lmts constanng owneshp stakes n fms. The esults povde mplcatons fo the desgn of vouche pvatzaton, whch should lead to moe effcent shae dstbuton and pce settng. Abstakt Kupónová pvatzace v České epublce představuje přozený expement schopností nvestoů sestavt potfólo v podmínkách asymetckých nfomací a absence tžních cen akcí. Tento článek poskytuje teoetcký model optmálního potfóla sestaveného nvestoy maxmalzujícím očekávaný výnos a současně řešícím poblém koodnace v nekoopeatvní hře s dalším nvestoy. Vnímaní nespávného ohodnocení akcí a soukomé nfomace jsou endogenní. Model umožňuje ntepetace a teoetcké zdůvodnění předcházejících empckých výsledků, vysvětluje ozhodující ol oganzátoa aukce, ozlšuje optmální statege po jednotlvé typy nvestoů a ukazuje nadbytečnost pávního lmtu omezujícího vlastncký podíl nvestoů ve fmách. Výsledky mají mplkace po nastavení kupónové pvatzace, kteá by vedla k efektvnější dstbuc akcí a stanovování cen. Keywods: vouche pvatzaton, asymmetc nfomaton, potfolo and stategc nvestos, potfolo choce, mspcng JEL Classfcaton: D8, D8, G * I am gateful to Randall Fle, Jan Hanousek, Evžen Kočenda, Jan Švejna, Tmu Yusupov and Pete Zemčík fo useful comments, suggeston and constuctve ctque. The gant suppot fom GAČR No.40/05/08 s hghly appecated. The autho would also lke to thank Rchad Stock fo Englsh edtng. E-mal: Elena.Yusupova@cege-e.cz. Addess fo coespondence: CERGE-EI, P.O. BOX 88, Poltckých věznu 7, Pague, Czech Republc **CERGE-EI s a jont wokplace of the Cente fo Economc Reseach and Gaduate Educaton, Chales Unvesty, and the Economcs Insttute of the Academy of Scences of the Czech Republc, CERGE-EI, P.O. Box 88, Poltckých vězňů 7, Pague,, Czech Republc.

5 . Intoducton The pvatzaton of state-owned entepses (SOEs) was a cucal pont n the tansfomaton of Cental and Easten Euopean countes (CEECs) nto maket economes at the begnnng of the 990s. In spte of many poltcal, socal and economc ssues elated to pvatzaton, thee s a unvesal consensus among economsts that pvatzaton mpoves effcency (Rees, 988). Howeve, pvatzng n countes wth unde-developed o nonexstent domestc fnancal makets, suffeng fom a shotage of pvate captal fo nvestment and a lack of useful asset-pcng sgnals, s a challenge. Consequently, the queston ases whch method of pvatzaton s feasble and the most effcent when a lage numbe of fms need to be pvatzed and the value s not known. A natual outcome was the choce of vouche pvatzaton n seveal CEECs and Russa. It has a numbe of advantages, such as () elatve tanspaency, whch mostly pevents coupton and helps poltcal legtmacy (Tříska, 00), () equalty, snce t s avalable to all ctzens ove 8, () t gves a lage coss-secton of the populaton a sense of owneshp n the economy and helps to ovecome the dual legaces of communsm (Hllon and Young, 996), (v) the ablty to handle a huge numbe of SOEs n a elatvely shot tme (Takla, 994), (v) t ntates captal maket development (Bzca, 996), and (v) govenments can lagely sdestep the valuaton poblems that plague pvatzaton n tanston economes. The pvatzed entepses dd not have a maket tack ecod on whch valuaton could be based and thee wee no expet nsttutons to fulfll ths task. In vouche pvatzaton, as Hllon and Young (996) o Mejstřík et al. (997) ague, nvestos need to assess only the entepses elatve values,.e. the values wth espect to one anothe, athe than havng to expess each n monetay tems. In addton, Bennett et al. (004) analyzed the mpact of vaous pvatzaton methods on economc gowth and found that mass pvatzaton s the only method wth a sgnfcantly postve effect. Govenments n tanston countes had moe objectves than a mee tansfe of assets fom publc to pvate owneshp. Fst, a patten of owneshp that would ensue the effcent pefomance of fms was of nteest. Second, a moe concentated owneshp was, wth nonfunctonng captal makets, a bette guaantee of effectve copoate govenance. Vouche pvatzaton, whch all ctzens would take pat n, pesented a sk that the esultng owneshp stuctue would be so wdely dspesed that t would mpede the development of effectve copoate govenance and hampe mpovement n economc pefomance. In

6 addton, t was often ctczed fo ts nablty to povde fms wth eal ownes who could mpove pefomance. Fea of too-dspesed owneshp, whch mght lead to consdeable agency costs, low nvesto patcpaton n fm contol and a lack of pofessonal management of nvestments wee the man easons why authotes suppoted the patcpaton of nvestment funds n the mass pvatzaton n seveal CEECs, such as the Czech Republc, Poland and Bulgaa. The Czech Republc was the fst county n the egon that ntated a wdespead mass pvatzaton pogam. The popety value of pvatzed SOEs was substantally hghe than the cumulated pce of the vouche ponts assgned to the ctzens: each got 000 ponts fo appoxmately 30 USD. The pvatzaton thus seemed to be a lucatve nvestment oppotunty and ths fact motvated the se of Investment Pvatzaton Funds (IPFs). Vouche holdes could entust the vouche ponts (o some of them) to IPFs, whch nvested on the behalf. These enttes thus became the pedecessos of late pofessonal nsttutonal nvestos and mutual funds. Lack of nvestment expeence among ctzens and lage maketng campagns enabled IPFs to collect a majoty of the total vouche ponts. The patcpaton of IPFs was suppoted, as the ntal eseach shows, also n academc ccles. As Švejna (993) agued, IPFs enabled ctzens to get equal popotons of the pvatzed popety and at the same tme educed ctzens exposue to sk. Hyclak and Kng (993) concluded that the IPFs had the pupose to establsh a model of a dvesfed potfolo of pvatzed fms and to ase conscousness about pesonal fnancal nvestng n maket economes. Bzca (996) also poposed that IPFs would contbute to developng fnancal makets and pomotng collectve nvestment. In contast to Poland, the ndvdual nvestos and IPFs n the Czech Republc selected the potfolos based on the knowledge, expeence and belefs about the futue pefomance of avalable secutes. Howeve, the poblems IPFs faced dung the potfolo choce, whch esembled a pce-settng, multound teatve aucton, wee sgnfcantly dffeent. Pces wee set by the govenment, thee was a lmted supply of shaes, no altenatve use of the vouche ponts that seved as a means of payment fo the shaes, and thee was lttle o no expeence wth nvestng n and contollng fms. Snce the md-990s ths phenomenon has been the focus of theoetcal and especally empcal eseach. Investo stateges, detemnants of shae demand, dffeences between Fo evdence on the fea of too-dspesed owneshp weakenng the shaeholde montong actvty and stengthenng the management see e.g. Caln and Maye (99), Boycko et al. (994), Takla (994), Kazbeg (999). 3

7 ndvdual nvestos and IPFs and between the pvatzaton desgns n ndvdual CEE countes and, moe geneally, the effcency of the bddng pocess wee of lage concen to eseaches. The man am of govenments was to sell all shaes and to have all ponts allocated (Tříska, 00; Hanousek and Fle, 00; Kazbeg, 999). Ths seemed to be n conflct wth fndng optmal shae pces and motvated a numbe of eseach questons such as: Dd popety go to those nvestos who valued t most? Was the bddng pocess optmal as a pce dscovey mechansm? Though empcal studes povded nteestng nsghts nto the pvatzaton pocess, they wee mostly not based on any theoetcal foundatons. Švejna and Snge (994) found the exstence of systematc factos n the vouche bddng system. They stessed that an empcal nvestgaton of the detemnants of bddng behavo and pce settng s complcated by the lack of well-establshed theoy. Ths comes as no supse takng nto account the complex natue of pvatzaton and the bddng pocess, n patcula the nconsstent behavo of some nvestos and the heteogenety leadng to dvese objectve functons. Ou man objectve s to fll ths gap n the eseach and to buld a model that enables studyng ths ssue and tes to explan the detemnants of the expected-etun-maxmzng nvestos shae demand. The model s based on the cuent knowledge of the bddng pocess. The study ams to dentfy nvestos ntentons, the pecepton of fms msvaluaton and the atonalty by lookng at the nvestment stateges. Povdng nsght nto nvestos motves and the level of peceved mspcng would allow polcy-makes to set pces moe pecsely and, n geneal, to dstngush dffeent goups of nvestos and egulate the actvtes. The model can assst n futue pvatzaton effots. The analyss of dffeences n the decson-makng of dffeent types of bddes n an envonment chaactezed by nfomaton asymmety and n the absence of maket pces should also contbute to the banch of economc lteatue focused on tadng and auctonng mechansms. Theoetcal analyss of the model shows how dffeent ncentves of nvestos affect the shae demand. In patcula, the IPFs mght pefe to play the ole of potfolo nvestos and, as classcal mutual funds, bd fo the most undevalued fms to beneft fom an ncease n the maket value afte the pvatzaton and fom the management fee. On the othe hand, they mght wsh to be actvely nvolved n management and undetake fm estuctung, attact foegn nvestos o n othe actve ways ncease a fm s value. 4

8 The pape poceeds as follows. In Secton, we evew the elated studes, statng wth the geneal lteatue on mult-unt auctons and poceedng wth an ovevew of studes modelng dffeent aspects of the Czech pvatzaton pocess. In Secton 3, based on the cuent level of knowledge we constuct a model and deve the equatons of the optmal shae demand. In Secton 4, the shae demand and the weght of elevant factos ae analyzed fo potfolo nvestos and the nvestos ntendng to patcpate n fm management, and the mpact of changes n elevant factos ae outlned. The analyses also show how shotages n pce-settng dstot the nvestos decsons and lead to an neffcent outcome. In Secton 5, we dscuss the fndngs. We conclude and deve some polcy-makng mplcatons n Secton 6.. Lteatue Revew Although many empcal studes wee undetaken n the aea of mass pvatzaton n the Cental and Easten Euopean countes, the bddng pocess as an aucton wth a specfc nsttutonal stuctue has not eceved much attenton. Ths secton s dvded nto two subsectons. Fst, we evew the up-to-date eseach on auctons and the elevance fo the bddng pocess that took place dung vouche pvatzaton; second we look at the theoetcal studes of the bddng pocess n the Czech Republc. We stess mpotant questons and conclusons of the eseach, whch lead to the foundatons of ou model pesented n Secton 3.. The elated aucton theoy lteatue Mass pvatzaton s often compaed to an auctonng mechansm, whch effcently dstbutes shaes and dves the pces to the equlbum value. Theefoe, befoe lookng at the eseach effots to model the pvatzaton pocess, t s useful to have a look at geneal aucton theoy and to assess how much nsght t actually bngs fo the desgn of mass pvatzaton. 3 The objectve of an aucton s to elct enough nfomaton about a bdde s pefeences to ealze an effcent o appoxmately effcent allocaton. Auctons have ecently come nto the spotlght because of the use n deegulaton, pvatzaton and on the In ths secton we ae pmaly nteested n explong the natue of the bddng pocess fom the theoetcal pont of vew. 3 As the aucton theoy lteatue s vast and goes fa beyond the scope of ou eseach, we lmt ouselves to the studes elated to multple-tem multple-unt bddng. 5

9 Intenet. They have the convenent popety of aggegatng nfomaton. Even f no nfomaton on bddes valuatons of an tem s avalable, the auctonee can acheve the sale of the tem to the bdde who values t most. When multple tems ae fo sale, ths task becomes moe complex. In esponse to ths poblem, combnatoal auctons emeged n the academc lteatue. Rassent et al. (98) and Banks et al. (989) ae the ealest woks on the topc. Combnatoal auctons ae smultaneous multple-tem auctons that allow the submsson of combnatons of the tems beng sold. Bds on combnatons of tems ae mpotant to bddes whose value fo combnatons s geate than the sum of the values fo the ndvdual tems. Ths can be the esult of cost savngs n pocuement and syneges between assets o when wnnng altenatve tems can meet the same need (Pekeč and Rothkopf, 003). The dstnctve featues of these auctons ae: the complexty of wnne detemnaton as ndvdual bddes ae bddng fo dffeent combnatons of tems and the hghest bds ae not guaanteed to wn and the coopeatve flavo of bddng stemmng fom the way aucton wnnes ae detemned. Bykowsk et al. (995) pesent examples n whch allowng combnatoal bds nceases both evenue and effcency. Hastad and Rothkopf (995) suppot the effcency agument. Kshna and Tanaes (00), though admttng the hghe effcency of combnatoal bddng, fnd that when thee s a suffcent numbe of bddes, full bundlng wth a wnne-take-all fomat bngs less evenue. Next to potental gans, thee ae also dsadvantages connected wth allowng combnatoal bds. The fst s the dffculty of fndng the best evenue maxmzng set of wnnng bds gven by two man factos. Computatonal complexty, whch apdly nceases wth the numbe of tems, s a cental eason fo dffcultes n desgnng such auctons. Thee wee a numbe of ways poposed to deal wth ths ssue, such as algothmc appoaches suveyed by de Ves and Voha (003), lmtng bddable combnatons dscussed by Pak and Rothkopf (00) o lmtng the use of combnatoal bds to educe the ntesectng stuctue of all bddable combnatons (FCC, 000). 4 Some stuctues of combnatoal bds that ae computatonally manageable ae dscussed n Rothkopf et al. (998). Also, as Pekeč and Rothkopf (003) ague, the detemnaton of the aucton wnne may be also opaque. Tanspaency s theefoe mpotant n auctons snce t smplfes bddes' undestandng of 4 Sometmes, lmtng the use of combnatoal bds can nteact favoably wth concens about bddes ncentves. 6

10 the stuaton and nceases the tust n the aucton pocess. Geneally, thee s no clea-cut way to deal wth the complexty of wnne detemnaton and the tade-off between some unwanted consequences depends on the choce of the aucton desgne. The second s the "theshold" o "fee-de" poblem dscussed n Mlgom and Wlson (993), when the dseconomes of scale domnate and the bds on combnatons exceed hghe bds fo ndvdual unts. The poblem s magnfed when many tems ae beng sold and lage combnatons ae sought. The combnatoal auctons can be conducted as sngle ound sealed bd auctons, pogessve auctons, Vckey-Clake-Gowe mechansm, unfom pce mechansm 5 o teatve combnatoal auctons. Each has advantages and dawbacks, and the fnal choce s detemned by the most optmal outcome gven the pedefned potes of the aucton. Snce the teatve combnatoal auctons best eflect the vouche pvatzaton bddng pocess, we wll elaboate moe on ths topc. Ths type of auctons ae pedomnant n e-busness (Pekeč and Rothkopf, 003). They come n two vaetes. In the fst type, quantty settng, bddes submt pces on vaous allocatons n each ound. The auctonee makes a povsonal allocaton of the tems that depends on the submtted pces. Bddes ae allowed to adjust the pce offes fom the pevous ounds and the aucton contnues. The am s to ensue apd pogess and encouage competton. In the second type, pce settng, the auctonee sets the pce and bddes announce whch bundles they want at the posted pces. The auctonee obseves the equests and adjusts the pces, govened by the need to balance demand wth supply. The pactcal use of quantty settng pevals ove pce settng, also due to the feedom gven to the bddes. Compaed to othe fomats, fo example sealed bd auctons, teatve combnatoal auctons have a numbe of advantages that ae lsted n de Ves and Voha (003): () It saves bddes fom specfyng the bds fo evey possble combnaton, so the bd submsson buden s sgnfcantly lowe. () Such methods can be adapted to dynamc envonments whee bddes and objects ave and depat at dffeent tmes. () It allows nfomaton to be evealed (the pospectve patcpants can lean about the vals evaluatons though the bddng pocess) and ceates a space fo collusve behavo. Though the total bd pepaaton pocess mght be lengthy and budensome and many shotages of sngle ound combnatoal auctons ae not elmnated, ths s the most popula combnatoal aucton fomat n pactce. 5 Fo moe detals on the lsted auctonng mechansm see Robnson (985), Kshna and Tanaes (00), Hastad and Rothkopf (000), Vkey (96), Clake (97), Goves (973), Rothkopf et al. (990), Yokoo et al. (004), Paks (00), Ausubel and Mlgom (00), de Ves and Voha (003). 7

11 Thee ae some poblems elated to combnatoal auctons, especally to the teatve auctonng mechansm. The exposue poblem nvolves the sk of bddes wnnng unwanted tems. Fo example f the bdde wants to wn {a} o {b}, but not both, the bdde mght be eluctant to submt compettve bds fo both. Allowng (o mposng) budget o capacty constants (e.g. Hohne et al. 003) on bds o both (e.g. Elmaghaby and Kesknocak, 003) can mtgate ths poblem. Tes n auctons lead to abtay allocatons. Thee ae some ways to deal wth ths, howeve, no one way s fully satsfactoy. Combnatoal auctons usually place a much hghe nfomaton and communcaton buden on both bddes and the auctonee. Bddes can evaluate and bd on all combnatons; the auctonee pocesses the bds, detemnes the wnnng allocatons and pces and povdes feedback afte each bddng ound. Based on ths, the bddes pocess the new nfomaton and submt new bds. The complexty flows fom many combnatons and the coopeatve aspect of combnatoal bddng. Even the multound fomat mght not be able to ovecome these ssues. Nssan and Segal (00) consde the communcaton bottleneck even moe sevee than the computatonal one, snce t becomes an ssue aleady wth a smalle numbe of tems when the computatonal complexty s stll manageable and cannot be sdestepped by tansfeng t to the bddes themselves. Nssan and Segal (00) and Rothkopf et al. (998) popose some techncal pocedues to mtgate ths poblem. Fo example, the stuctue of bddable combnatons can be lmted o the auctonee should povde some tools that help bddes n bd pepaaton.. Pevous wok n the theoetcal modelng of pvatzaton Though aucton theoy povdes a lot of nsghtful nfomaton and ntuton fo the desgn of the mass pvatzaton, the aucton lteatue does not offe a model esemblng the unque chaacte of mass pvatzaton. Czech vouche pvatzaton can be descbed as an teatve combnatoal pce-settng auctonng mechansm conducted n a multound fomat, whee bddes choces ae lmted by the budget constants and estctons on bds. Howeve, n some espects t ctcally dffes fom the descbed auctonng mechansms. Fst, egadng the man ctea of the aucton assessment, the govenment dd not stve fo evenue maxmzaton. The am was possbly just a fa dstbuton of shaes of pvatzed fms to the ctzens. 8

12 Second, the auctonee adjusted pces afte evey ound to dstbute all shaes and the bddes made effots to allocate all the vouche ponts. The allocatve effcency n the classcal sense to sell the shaes to the bddes wth hghest pvate values was lmted. Ths was because all bddes wth a esevaton pce exceedng the vouche pce could bd and eceve the shaes and also the pces mght not eflect the value peceved by the bddes due to () dffeent pvate valuatons of dffeent types of bddes and the nteests and () an auctonee who mght not adjust pces effcently. Thd, whle n classcal combnatoal auctons, multple ndvsble tems ae dstbuted, evey tem n the vouche pvatzaton (shaes of one fm) conssted of multple unts (n the context of aucton theoy one can speak about dvsble objects). As a esult, eseaches mostly chose the own appoaches to the theoetcal modelng of the bddng pocess. Bada (99) and Hllon and Young (996) looked fo an analogy between the vouche scheme and a esouce allocaton mechansm smla to the one poposed by Walas, whee bddng fo goods o fnancal nstuments would eventually convege to a set of pces that would equate supply and demand. Howeve as Bada (99) and Fle and Hanousek (00) ponted out, the pocess dffeed fom Walas tatonnement n the asymmety of the dstbuton pocess. In the Walas pocedue the goods ae not delveed untl the pce s found, when supply equaled demand. Hllon and Young (996) also do not consde pce dscovey as a man motve of the auctonee. Theefoe Bada (99) poposed the concept of an asymmetc dstbuton of shaes, whch s suppoted by bddes dffeent value dstbutons of the same shaes and leads to nvestos stategc behavo. Bada (99) ntepets stateges accodng to the Counot and Stackelbeg model, whee the playes who ae maxmzng the pofts o some fom of utlty functon, ae not coopeatng and have equal powe n a compettve game (Stackelbeg, 95). Howeve, ths solves statc models, wheeas the vouche pvatzaton was a sequental bddng mechansm, whee the past ound s stateges and bddng behavo can have a dect nfluence on the cuent bddng oppotunty and behavo. 6 Ma (994) dew on the theoetcal lteatue and hs dssetaton pesents the fst pofound theoetcal analyss of the dynamcs of the vouche pocess. Ma (994) focused on 6 Besdes, as Wendelová and Bukáč (993) ndcated thee mght be some level of coopeaton among IPFs. Theefoe the models of Pescott (973) and Kydland (977), who assume that the playes detemne the best decsons on the cuent state of the system and the decsons of the othe playes, mght be bette ponts of depatue. 9

13 the assessment of pce development. He also made nfeences about IPFs objectves fo the acquston of vouche ponts fom actual behavo and stateges n the bddng system usng a game-theoetc analyss, n patcula two models: a smultaneous bddng and sequental bddng model wth Makov stateges, whee behavo s chaactezed by the lkelhood of a bdde s wnnng of shaes. The smulatons suggested that the behavo and stateges wee consstent wth the second model. Compang the bddng of fms and ndvduals, he concluded that () IPFs had a lot of powe n detemnng the esults of the aucton; () IPFs wee sk-avese (wheeas ndvduals wee moe sk-takes) and () IPFs wanted actve nvolvement n management decsons. So the nvestments wee motvated by hghe owneshp stakes, low shae pce and postve futue pospects. The shotage of the model s that the nvesto maxmzes only the numbe of shaes won, egadless of the pce. The subjectve pobablty of ovesubscpton, whch s a functon of the msvalued pce, s an unknown paamete. Bzca (996) and Hllon and Young (996) expessed the vew that one of the attactve featues of vouche pvatzaton was the fact that nvestos needed to assess only fms elatve values, nstead of expessng the absolute value n monetay tems. Ratonal nvestos would bd on elatvely undevalued shaes and avod elatvely ovevalued shaes. Tříska (00) dd not beleve that nvestos had a clea vew of fm qualty, howeve Hngoan et al. (997) as well as Fle and Hanousek (00) showed a postve elatonshp between the fst-ound demand and late stock maket pces, whch suppots the use of shae demand to measue elatve shae values. Ths led Hngoan et al. (997) to the concluson that nvestos behavo was poft-maxmzng. Though the man am of the govenment was the fast tansfe of owneshp, the man nteest of eseaches concened the effcency of the pocess. Dd the bddng mechansm assgn the hghest stakes n the fms to the nvestos who valued them most? Katz and Owen (997) combned the unque featues of vouche pvatzaton and deved ts Nash soluton. It mples that n equlbum, IPFs should acque moe owneshp n those fms n whch the elatve sklls ae hghe unde the assumpton that the ponts ae exogenously assgned to the IPFs. The man esult s that the futue maket pefomance of the fm s endogenous and cannot be pedcted by the nvestos. Accodng to Katz and Owen (997), effcent pvatzaton eques the most sklled and cedble IPFs to extact the most vouche ponts of 0

14 ndvduals, whch was n the Czech case hadly possble. 7 Ths led them to the concluson that the desgn of the Czech pvatzaton was flawed. 8 Smlaly, Boycko et al. (994) found out that n an envonment wth sgnfcant wealth constants, assets mght not end up n the hands of the hghest-value uses. In esponse to ths poblem Maskn (000) constucted an aucton whee budget-constaned nvestos wth pvate values wn the shaes that they value most. But, as Fle and Hanousek (00) coectly agued, the pce was set at a supposed appoxmaton of the tue equlbum athe than a pce hghe than the esevaton pce; a bdde wth the hghest value was theefoe not necessaly a wnne. Ths leads to the queston how effcent the Czech vouche pvatzaton was and consequently how mght ts effcency have been mpoved. The next queston elates to the effcency of the bddng pocess as a pce dscovey mechansm. Fle and Hanousek (00) undetook an empcal study whee they nvestgated whethe pces n a lmted numbe of adjustments based on excess demand and supply ae able to fully eflect all avalable nfomaton. Though the esults ae postve, the auctonee mght stll nappopately pocess the coect sgnals sent by nvestos. Ths holds manly fo small fms. Kazbeg (999) showed neffcency n pce dscovey, whch mght have a dstotve mpact on the allocaton of esouces n the economy. Ths agument s futhe stengthened by the pmay am of the govenment to sell all the shaes and absob all the avalable vouche ponts, whch led to a mspcng bas (Hngoan et al., 997). Hllon and Young (996, p. -3) stessed ths pont statng, n late ounds, bddng behavo can be best descbed as the seach fo mspced secutes. The pces obtaned n the aucton theefoe, wee unlkely to be elable sgnals of elatve value, theeby questonng the usefulness of the aucton as a pce-dscovey mechansm. One should also keep n mnd that nvestos mght modfy the nfomaton set dependng on othes evealed nfomaton. Fnally, f one wants to assess effcency, t s necessay to know the objectve functon of nvestos. As Andeson (994) agues, the objectve functon vaes accodng to the desable functons of the fund. Ths has futhe mplcatons fo the optmal potfolo choce. Macnčn and Shemetlo (995) asseted that the ntal stuctue of the nvesto s potfolo eflected the wllngness to monto the entepse. In othe wods, potfolo nvestos have dffeent motvatons to nvest than nvestos who want to be nvolved n management and 7 The man eason s that the ctzens wee often attacted by the dffeent maketng measue of the IPFs backed by a stong fnancal o non-fnancal nsttuton. The fnancal stength was howeve not always coelated wth the sklls as etun-maxmzng nvestos. 8 In the next pape, Katz and Owen (00) show that even unde full nfomaton thee s no guaantee that the dstbuton of vouche ponts between funds of dffeent sklls wll be poft-maxmzng fo pvatzed fms.

15 theefoe the nvestment stateges should dffe. Ths was howeve dstoted by some neffcences, as Egee (996) ponted out, the ntatve of IPFs to contol the fms seemed to be detemned by the sze of the stake they managed to get. In addton, as Kazbeg (999) agued, neffcency was patally due to the vey shot nvestment hozon of cash-poo nvestos, who wee maxmzng the fst offcal maket value of funds to obtan a lage popotonal management fee. The evewed wok helps us to clafy the basc assumptons and constants of the model. Effcent nvestos wth a longe-tem hozon maxmze the futue expected value of the fms bddng fo the most undevalued fms. The devatons fom ths stategy wee caused by the asymmetc knowledge of nvestos, by dffeent ntended functons of the IPFs as Andeson (994) poposed and dstotons n pce-settng (Kazbeg, 999). We wll nclude n ou model all these factos. The am s to nfe the IPFs objectve fo the acquston of vouche ponts and the extent of leanng fom the behavo and stateges n the bddng pocess. 3. Model The model daws on the cuent knowledge pesented n the lteatue evew. The man taget of the model s to show how the heteogenety of nvestos detemned the vaety of nvestment stateges. Though ou am s to model the pvatzaton pocess as geneally as possble, defnng the bddng ules and constants on whch the model s based, we depat fom the desgn of Czech vouche pvatzaton. Theefoe, as a fst step, we poceed wth a bef llustaton of the bddng mechansm. The vouche pvatzaton was oganzed n two waves and each had seveal pvatzaton ounds. In the fst ound pces wee unfom, p = p vouche ponts pe shae n the both waves. In the second and all consequent ounds, the shae pce of fm was adjusted accodng to the ato of the aggegate demand of all nvestos n a gven ound, sd = sd, and shae supply ss. The shae demand was handled n the followng j manne:

16 If sd / <, the demand was satsfed at a pce vald n a gven ound and the pce of ss the unsold shaes was loweed f thee was a lot of shaes left o nceased f only few shaes stood out. 9 If sd / =, the demand was satsfed and the fm was completely sold out. ss If sd / (,. 5 ss, the demand of ndvdual nvestos was fully satsfed at the pce vald n the gven ound and the shae demand of IPFs was popotonally atoned. If sd / >. 5, the shaes wee not dstbuted but offeed n the next ound at a hghe ss pce, whch was a functon of excessve demand. Afte evey ound the Cente fo Coupon Pvatzaton (CCP) pocessed the bddng nfomaton fo each ound and publshed the esults, but a specal wokng goup apponted by a deputy mnste n the Mnsty of Fnance, the Pce Commttee, pefomed the epcng task accodng to the excess demand fo shaes n the pevous ound weghted by the last pce, shaes unsold and ponts left. Ths goup wll be efeed to as the auctonee. The numbe and pce of shaes fo each fm wee announced. As the ponts could be used only fo buyng shaes n the vouche pvatzaton, eveybody made an effot to allocate ponts completely and no altenatve use based the pocess. Ths mechansm was supposed to dve pces to the equlbum values. Howeve, t had some lmts, n patcula, the numbe of shaes to sell and the numbe of vouche ponts left so the pces had to be adjusted n such a manne to decease the pobablty of epeated ovebddng and to dvde the avalable ponts among the avalable shaes. Afte becomng famla wth the man featues of the pvatzaton pocess, we can poceed wth constuctng the model. We focus on bg nvestment companes and fo smplcty we efe to them below as nvestos. Thee ae N fms to be pvatzed, {,..., N}, and M nvestos, j {,..., M }. The stake whch nvesto j has n fm s denoted q j. The bddng pocess takes place dung a numbe of pvatzaton ounds {,..., R}. 0 In each ound each nvesto j chooses hs/he potfolo of shaes. Hs/he decsons ae based on two assumptons: Assumpton : All nvestos maxmze the expected utlty, usng all the avalable pvate and publc nfomaton and knowledge they have at the dsposal subject to budget and legal constants. 9 Fo detals on the pce-settng mechansm see Tříska (00) o Kčmář (99). 0 Investos dd not know the exact numbe of ounds R at the begnnng of the bddng pocess. Ths foced them to maxmze the expected etun n evey ound and gve a bgge weght to the negatve mpact of ovebddng. 3

17 Assumpton : The potfolo choce has the chaacte of a non-coopeatve game. The nvestos ncopoate nto the decsons only the expected stateges of othe nvestos. Ths gves se to a coodnaton poblem among nvestos. Thee constants lmt nvestos maxmzng behavo. The budget constant: the amount of ponts allocated to fms n ndvdual ounds b j must be smalle o equal to all ponts the nvesto has at he o hs dsposal B j. The stake of nvesto j n fm, q j, must not exceed the legal lmt l mposed on nvestment companes. The nvestos ae not allowed to shot-sell the shaes, whch mples that shae demand sd must be equal to o hghe than 0. The maxmzaton poblem of evey nvesto j can be specfed as follows (snce the poblem s specfed fo one nvesto, we can skp the subscpt j): Max R N = = E( Ω ) () U subject to R N = = b B (a) R = q l n evey {,..., N} sd 0 n evey {,..., R} (b) and evey {,..., N}, (d) whee E Ω ) s the nvesto s expected utlty fom nvestng n selected fms, ( U accodng to he o hs pvate nfomaton on fms, publc nfomaton and nfomaton eceved dung the pevous ounds fom the behavo of othe nvestos, whch ae pat of the nvesto's nfomaton set Ω. The fst constant specfes that the sum of all the ponts allocated n ndvdual fms and ounds, b, fo evey nvesto cannot exceed hs/he budget consstng of B ponts. 3 The The fst assumpton s based on the geneal consensus eached n pevous empcal studes and the second s a easonable smplfcaton of the poblem takng nto account the numbe of fms and nvestos. Thee wee moe legal lmts constanng nvestment stakes of nvestos n fms (see Act No. 9/99 and No. 48/99 Collecton fo detal). Howeve, two of them ae elevant fo ou model: fst, the lmt on the stake of the nvestment company n a fm and second, the lmt on the popoton of the nvesto s entusted ponts nvested n one fm. Fo smplfcaton, we consde lage nvestos, so only the fst lmt s bndng. Ths legal lmt was n the fst ound 0% and n the second ound 0%. 3 We should also menton the constant that n each ound ss p. B + I fo =, R, whee j= = j= B j s the numbe of ponts of a patcula nvesto n ound and I s the sum of the ponts held by ndvduals. 4 M N J j

18 second constant (b) stpulates that the popoton of shaes held by any nvesto n any fm q cannot exceed the legally allowed lmt l. Fnally, the constant (d) pohbts shotsellng,.e. the bds can be hghe than o equal to 0. The queston then follows what n the gven ccumstances detemnes the nvesto s utlty functon. Ma (994) assumed n hs model that nvestos maxmzed the numbe of shaes they ae able to get. Howeve, fo a atonal, etun-maxmzng nvesto, not only the quantty of shaes matte but also the qualty,.e. the potental to geneate poft. Fle and Hanousek (00) found that dung the fst ound of bddng almost all pofessonal bddes knew whch shaes wee undevalued at gven vouche pces. Denotng the stock value of fm fo nvesto j n a gven ound as E V ) and the vouche pce of the fm s stock n j ( a gven ound as p, atonal nvestos pefe fms wth a hghe expected goss etun n a gven ound compaed to anothe fm k n the potfolo: E j ( V ) E j ( Vk ). () p p k As the nequalty shows, the ato can dffe acoss nvestos and ounds accodng to the futue pce expectaton E V ), whch can be based on new nfomaton, and accodng j ( to the pce development. Ths explans the vayng nteest of ndvdual nvestos wth dffeent nfomaton sets n patcula fms. Howeve, nvestos can possess some pvate nfomaton, whch enables them to daw pvate benefts. These can flow fom seveal souces: the nvesto wants to be nvolved n the management of the fm and ts decsonmakng; the atcles of assocaton whch detemne the dvson of powe n the fm between the executve boad and the supevsoy boad and specfes the stuctues, the nvesto can sell a block of shaes of a fm wth good pospects fo a pce that s hghe than the pce would be n the case when the nvesto has only a small stake. Theefoe hs expected etun exceeds the one expected by potfolo nvestos beneftng solely fom a pce ncease and dvdends. 4 Theefoe the auctonee must take nto account the numbe of unsold shaes and the numbe of ponts left. Ths lmts shae pces beng fully adjusted to the demand/supply ato n the pevous ound. As ths constant s ncopoated nto the shae pces t s exogenous fo the nvesto. 4 We have n mnd mostly fms wth gowth potental but bad govenance. Ths dvson has futhe mpacts on the second constant. In vouche pvatzaton, the legal constant was 0% n the fst wave and 0% n the 5

19 We ncopoate ths possblty nto the model though the paamete c whch accounts fo the possble benefts fom hghe concentaton o actve patcpaton n a patcula fm. The paamete affects the expected shae value E V ), whch becomes j V c j ( E ( ) and enables us to dstngush two types of nvestment nteests. Fst, f the nvesto pefes solely fnancal potfolo management, hs stakes n fms ae smalle than 0% and he does not ntend to ntevene n fm govenance; paamete c =. We efe to these nvestos as potfolo nvestos. Second, f the nvesto wants to be nvolved n the fm management, and consequently stves fo stakes equal to o bgge than 0% of the fm, the paamete c > nceases the shae value fo nvesto j, and thus nceases the expected etun above the value fo potfolo nvestos. We efe to the second goup as stategc nvestos. Ths paamete seves as an addtonal facto explanng the dffeences n nvestos nteest n patcula fms. 5 Howeve, gven the budget constant and sk of ovebddng, one has to keep n mnd that nvestos have mostly dual nteests: stategc nteests n some fms and potfolo nteests n the est of the eceved fms. Theefoe when we speak about stategc nvestos, we efe to those tyng to eceve bgge stakes n moe fms and accodng to the success to actvely pefom the owneshp ghts. The expected etun s expessed pe shae, so fo evey fm, t has to be multpled by the numbe of shaes demanded sd. Gven Assumpton that nvestos do not collude and the possblty that the nfomaton can be to some extent symmetc,.e. moe nvestos ae awae of undevalued fms, a fxed lmted numbe of shaes n ndvdual fms mght lead to a stuaton whee shae demand consdeably exceeds shae supply. Based on the descpton of the pvatzaton pocess, these shaes ae not allocated but offeed n the next ound at a hghe pce. Ths stuaton s called n the lteatue ovebddng o ovesubscpton and ts extent detemnes the pce fo the next ound. 6 Ratonal nvestos ae esponsve to the descbed lost oppotunty costs: gong fo the most lucatve the fst best nvestment oppotunty, they can face ovebddng, the ponts ae not allocated and second wave. Gven that stategc nvestos need hghe stakes fo effectve contol, the legal lmts amountng to 0% and 0% wee bndng n both waves, manly n the second one. 5 In addton, showng an nteest n a bgge shae n the fm can sgnal to the maket actve montong, whch mght futhe ncease ts maket value. Though Katz and Owen (997) agued that the value of the fm s endogenous, detemned by the nvestos and volume of the stakes, we assume hee that the fm value s based on the belefs of the elevant nvestos concenng ts futue value. 6 If the extent of ovebddng s smalle than 5%, the bds of nvestment companes ae popotonately cut and the shaes ae dstbuted. Theefoe when we speak about the pobablty of ovebddng, we efe to ovebddng exceedng 5% of suppled shaes when the shaes ae offeed agan n the next ound. Fo detals on the ules of bddng see the lteatue evew and cted efeences. 6

20 the second best fms mght have been sold out n the same ound. Theefoe, nvestos dvesfy the bddng and choose a numbe of shaes n a patcula fm n each ound to balance the maxmzng of the expected etun and the mnmzng of the sk of ovebddng. Ths behavoal featue s captued by the paamete sd µ, whch appoxmates the pobablty, gven by the subjectve belefs of nvesto j, that ovebddng wll not take place and shaes wll be dstbuted. So the numbe of demanded shaes s adjusted by the pobablty that the shaes wll be won. Addtonally, we assume (consstent wth the ules of the bddng pocess) that the nvestos dd not know at the begnnng how many ounds the bddng pocess wll consst of. Ths ule should pevent the stategc behavo of bg nvestos and potect small nvestos. As a esult, n evey ound nvestos make a smultaneous decson whch fms to nvest n and how many shaes to bd on to maxmze the expected utlty subject to the constants based on the publcly avalable nfomaton, pvate knowledge and pesonal belefs and expectatons. Consequently, nvesto j solves n evey ound the same maxmzaton poblem. 7 N = E( U Ω ) = N = sd µ E ( V ) p c n evey {,..., R} (3) subject to N t= = b t B (3a) t= q t l n evey {,..., N} sd 0 n evey {,..., R} (3b) and evey {,..., N}. (3c) The man dsadvantage of ths specfcaton s the pesence of unobseved factos. Expected maket value and the subjectve pobablty of ovebddng theaten the feasblty of empcal vefcaton and futhe analyss of the model. Theefoe we eplace them wth the paametes. Fst, the expected maket value of the fm shaes s not obseved. Howeve, nvestos mostly had expectatons on whch they based the nvestment decsons (see nequalty ()). We can dstngush thee possble cases: the shaes ae peceved by nvesto j as undevalued 7 In tems of constants we stll need to take nto account the pevous ounds. The bddng mechansm had an ntemedate allocaton of shaes afte evey ound, whch means that the budget and legal constants wee nfluenced by the pefomance n pevous ounds. 7

21 E c c j ( V ) > p, ovevalued E j V ) < p (, o accuately valued E j ( V ) = p. We can dop the unobseved vaable the expected value of the fm and at the same tme account fo the mspcng of the fm s shaes though the paamete v eplacng E j ( V ) / p by p c / p = p c. The extent of ovevaluaton (undevaluaton) s eflected n v (0 < v < ) whch deceases (nceases) the expected etun fom the shae of the fm >. 8 Fo a coectly pced fm, v =, assumng that c =, the expected goss etun would be equal to. In addton, when the shae s ovevalued o undevalued, c p wll be, n the case of shae ovevaluaton, educed to a lage extent fo moe expensve shaes than fo cheape shaes and, n the case of undevaluaton, on the contay, the tem wll gow faste fo moe expensve shaes than fo cheape shaes at the same level of undevaluaton. Second, the pobablty that shaes mght be ovesubscbed and tansfeed to the next ound as a consequence of the coodnaton poblem matteed fo nvestment decsons. Ma (994) agued that IPFs wee sk-avese n the bddng behavo, whch contbuted to the stablty of the system. Geneally, the moe substantal the undevaluaton of fm, the hghe the pobablty that the shaes wll be ovesubscbed and the smalle the chance of gettng them at a gven pce. Ths mples a decease n µ. In addton, as Hllon and Young (996) ague, the valuaton of the fm elatve to othe fms matteed n the vouche pvatzaton moe than ts absolute value. We can apply the agument to ou poblem. Undevaluaton does not automatcally mean a hghe sk of ovebddng. One would nstead expect that nvestos ae compang a msvaluaton of a patcula fm wth a msvaluaton of the esdual shaes n the potfolo and based on ths they assess the elatve sk of ovebddng. Denote the msvaluaton paamete of othe shaes n the potfolo v = N ss p =, p p v N ss p =, p suppled shaes n the fms p {,..., } { +,..., N } p, whee ss p denotes the amount of. The pobablty that nvesto j wns the shaes, µ, s expessed as a functon of the ato of the elatve msvaluaton of the shaes the nvesto s consdeng buyng,, to the aveage msvaluaton of esdual shaes n the potfolo µ = f v ), such that the pobablty of ecevng the shaes declnes as ( 8 We assume, n lne wth the eal development, that the shae pce of each fm n evey ound s equal to o bgge than. 8

22 the elatve undevaluaton of fm deepens,.e. µ / ( v ) > 0. Theefoe we expess the pobablty that the shaes wll be dstbuted usng a logstc functon as µ = /( + exp( v )). (4) We can see that n exteme cases, when v conveges to 0, µ 0, whch mples a close to null pobablty of ecevng vey stongly elatvely undevalued shaes. When the value of v tends to plus nfnty,.e. the shaes of fm ae elatvely ovevalued, µ. It can also be obseved that a decease n utlty esultng fom a hgh pobablty of ovebddng elatvely nceases wth the sze of the bd sd. 9 Ths leads us to a moe pecse specfcaton of the maxmzaton poblem of evey nvesto j whch he o she solves n evey ound : / [ + exp( v p )] ( c ) max sd p (5a) { sd } N = subject to I ) sat. pt + N N ( sd. p B (5b) = t= = j whee I( ) t= sa S t + sd l, whee I ( ) sa t < ls (5c), fo all {,..., N} sd 0 fo all {,..., N}, (5d) S denotes the numbe of shaes of fm and t= sa denotes the shaes of fm eceved by nvesto j n the ound. 0 f = I () s the ndex functon such that I () =. f > As one cannot ex ante dentfy whch constants (5b)-(5d) wll be bndng fo whch nvestos, ou poblem contans nequalty constants. Fo the pupose of coectly solvng the maxmzaton poblem contanng nequalty constants and dentfyng possble egulates on the boundaes of the feasble set we use Kuhn-Tucke condtons (KT condtons). The 9 Fo modfyng the pce and the numbe of shaes to account fo the expected utlty and the pobablty that the shaes wll be eceved, we choose the exponental fom, as we assume that the nvestos ae moe senstve to moe exteme values of msvaluaton. Fo example the elatonshp between the extent of msvaluaton and the expected pobablty of ovebddng s not lnea, nstead the expectaton that ovebddng occus becomes stonge as elatve msvaluaton nceases. A smla agument holds fo expessng the unobseved expected shae value to account fo the expected goss etuns. The detemnaton wth whch nfomed nvestos make effots to avod ovevalued shaes s much stonge than the detemnaton to buy undevalued shaes. 9

23 Necessty Theoem stpulates that the KT condtons ae necessay condtons fo a local optmum f the constant qualfcaton s satsfed. Ths s always the case f all constants ae lnea (Vnogadov, 999, p. 50). Denotng the objectve functon of nvesto j n ound as f sd, sd,..., sd ), the patal devatve f sd ) / sd j ( fo {,..., N} j ( N evaluated at sd = 0 s not defned, theefoe KT condtons do not apply n ths case and we specfy them only fo sd > 0,.e. when the thd constant s not bndng. 0 Comng back to ou poblem (5a)-(5d), we wte the Lagangan fo nvesto j n ound as follows: L j N /(+ exp( v p )) c = sd p λ ( I( ) sat. pt + sd = N N = t= =. p B) N =, ( I( ) sat + sd ) / S l) t= λ n evey {,..., R} and deve FOC and complementay slackness condtons L j sd = µ sd µ p c λ p λ / S 0,, (6) L j µ c sd 0 and sd = sd ( µ sd p λ p λ / S ) = 0 sd fo all {,..., N}. (7a) L λ j = ( I( ) N sa. p + N t t = t= = sd. p B) 0, N N λ 0 and λ ( I( ) sat. pt + sd. p B) = 0 (7b) = t= = ( ) + I sat sd L j t= = ( l) 0 λ S = I( ) sat + sd t λ 0 and ( l) = 0 S λ fo all {,..., N}. (7c) 0 We have to keep n mnd that thee ae two possble easons why the shae demand falls to 0. Fst, the shaes ae lagely ovevalued and the nvestos expect a pce declne, howeve, as the non-negatvty constant apples, shot postons cannot be taken and the shae demand s smply 0. Second, the nvestos possbltes ae lmted by wealth and the legal constant, and thee s no space fo futhe nvestment n fm, and sd = 0 even though the non-negatvty constant s not bndng. 0

24 If λ 0 and 0 λ fo any {,..., N} and {,..., R}, we get bndng constant condtons. In the opposte cases when λ 0 and/o λ 0, the constant does not have to = hold. The specfcaton (7a)-(7c) takes cae of all cases. = In evey sngle ound, we solve fo the vecto {,...,, λ, λ λ } sd sd N,..., N, howeve as the devatons ae analogous, we pesent the possble solutons fo a epesentatve shae demand sd of nvesto j, fm and ound. Fo evey combnaton {, } we deved fou possble solutons. The esults ae pesented n the Appendx. Howeve, befoe devng the optmal demand functons when ndvdual constants ae o ae not bndng, we fst have to make sue that KT condtons ae ' * * suffcent condtons fo f sd ( sd,..., sd N ) = 0 to be a local maxmum at sd * fo all { N},...,. The Suffcency Theoem stpulates that KT condtons ae suffcent condtons fo * x to be a local optmum of a maxmzaton pogam f the followng assumptons ae satsfed: the objectve functon s dffeentable and quas-concave, each constant s dffeentable and quas-convex (Vnogadov, 999, p. 5). The twce-dffeentable functon s concave f and only f ts second devatve s eveywhee negatve semdefnte (Vnogadov, 999, p.39). Ou functon fulfls ths condton (ths statement s poven n the Appendx). As all ou constants ae lnea functons, they automatcally fulfll the second condton. We can conclude that ' * sd, fo whch f ( ) = 0 holds, s a local maxmum of * sd sd ou maxmzaton poblem. Now we can poceed wth devng the optmal shae demand equatons fo consequent theoetcal analyses and empcal testng. Keepng n mnd that the esult of evey ound fo evey nvesto s a vecto of shaed demand n all fms {,..., N}, { sd,..., } sd N, we pont out and analyze fou possble stuatons wth dffeent combnatons of bndng constants. Ths s elevant fo futhe theoetcal analyss, whee we dscuss how the constants affected shae demand factos and fo the empcal testng that helps us to dentfy the pevalng nvesto type and the heteogenety of nvesto stateges. Fo detals on devatons see the Appendx.

25 Fst, snce the objectve functon s stctly nceasng n each agument, when nethe the budget constant no the legal constant fo the shae demand of fm n ound needs to be bndng, the only soluton consstent wth the equatons n (7a) s sd = 0. As a zeo vecto cannot be a soluton, at least one constant othe than the non-negatvty one must be bndng. Theefoe the stuaton λ 0 and λ 0 s not possble. = = Second, only the legal constant s bndng ( λ 0); n the case of the budget constant ( λ 0 ), ths does not need to hold. Ths stuaton s chaactestc fo nvestos = who ae n possesson of a lage amount of ponts and make effots to allocate them to the geatest extent possble. The shae demand can be specfed as sd = ls I( ) sa jt. t= Howeve, fo the pupose of empcal testng, we do not deve. Instead, we maxmze (6) wth espect to demand equaton of nvesto j s the followng: ln sd * µ = ln( µ λ λ sd and make ts logathmc tansfomaton. The optmal shae c ) ln p ( µ ) ln S. (8a) µ As µ = /( + exp( v ) < 0, the sze of the fm has a postve mpact on the shae demand and at the same tme the pce elastcty s modeate (postve f c / > ); t v s dffcult to assess f the legal constant s bndng due to vouche pont abundance o the contol nteests of the nvesto. Thd, only the budget constant s bndng, ( λ 0) ; fo the legal constant ths s not necessaly the case ( λ = 0). Ths stuaton s chaactestc fo nvestos focused on a dvesfed allocaton of all the ponts, but snce the legal constant s not bndng, they ae also wthout obvous contol nteests. The shae demand can be expessed, usng the budget constant, as sd = B j I( ) sat. pt N = t= k =, k N ( sd. p ) / p,.e. only the budget constant s bndng. We deve the optmal shae demand n ths stuaton as a functon of pce ln sd * µ c = ln( ) ln p µ λ ( µ ) k k. (8b) Compaed wth (8a), the sze of the fm s not mpotant any moe fo potfolo nvestos, who ae on the othe hand moe senstve to pces.