Liquidity Effects of Listing Requirements

Transcription

1 Liquidity Effects of Listing Requirements Sara Draus 1 May 009 Abstract I propose a mode in wic a stock excange can improve its iquidity by tigtening its isting requirements. Because tese reduce information asymmetry, tey increase te utiity of investors and ead to a ig investor participation on te excange. However, te excange never sets te igest possibe eve of isting requirements because investors aso incur a risk due to more transparency. Teir utiity is concave in te eve of isting requirements. Tis property determines te optima decisions of an excange as we as te socia optimum. Te eve of isting requirements maximizing investor wefare depends on te sensitivity of te utiity of investors to canges in iquidity and varies wit te organization of isting and trading. A monopoist excange aways under-reguates if reguation is costy. Underreguation is exacerbated if oter trading venues free ride on te reguation and if te trading fee is determined by te eve of isting requirements. Wie investors are better off if trading is separated from isting and is a competitive industry, an excange as a iger profit wen it is a monopoist in isting and trading. Keywords: iquidity, competition, trading voume, reguation, stock excanges EFMA cassification codes: 360, 530, 540, Université Paris Daupine, Pace du Maréca de Lattre de Tassigny, Paris, France DRM Finance sara.draus@daupine.fr Te: + 33 (0) , Fax: + 33 (0) I am gratefu for many epfu comments from Tierry Foucaut, Denis Gromb and Terrence Hendersott. 1

2 Liquidity Effects of Listing Requirements 1. Introduction Recent canges in te industria organization of stock excanges ave given rise to a debate in te academic and professiona iterature about ow excanges soud be reguated. Excanges are increasingy turned into isted and profit maximizing entities. Tey aso compete wit oter trading venues for voume on te secondary market, wic decoupes istings from trading. If excanges reguate istings, competing trading patforms can free ride on tis reguatory activity wie offering more advantageous trading conditions. Tese deveopments in te stock market industry ave given rise to a debate upon weter stock markets soud continue to reguate istings or weter tey soud focus on offering a ceap and iquid trading venue wie oter institutions dea wit istings. Tis paper expores ow a separation of isting and trading affects te optima decisions upon trading fees and isting requirements by profit maximizing excanges, and te impact of suc a separation on investor wefare. It sows tat isting requirements ave an impact on iquidity troug ess information asymmetry and enanced investor participation. Tese iquidity effects are sown to determine te decisions of excanges in equiibrium, and te wefare effects of different trading and isting organizations. Te specific questions addressed in tis paper are: wat determines te profit and tus te equiibrium decisions of excanges, wat determines te sociay optima eve of isting requirements, wat drives possibe under-reguation? Investors benefit from a iger eve of isting requirements troug a better iquidity on te market. However, wat isting requirements maximize teir wefare depends on te sensitivity of teir utiity to canges in iquidity. Tis sensitivity is determined by te risk premium but aso by te trading fee. Te iger te trading fee is, te ess investors benefit from iger isting requirements and te smaer is te sociay optima eve of isting requirements. Trading fees are infuenced by te industria organization of trading and isting wic affects terefore aso te reguation maximizing investor wefare. Investors are best-off and require a ig eve of isting requirements wen te trading fee is te owest. As ong as an excange bears reguatory costs, it under-reguates regardess of ow isting and trading are organized. Te extent of under-reguation depends on te sensitivity of te excange s income to canges in te iquidity. Under-reguation is exacerbated by two Feckner (006), Macey and O Hara (005), Macey and O Hara (00), Kuan and Diamond (006), Lee (00), Stei (00), Centre for financia market integrity (007), OICV IOSCO Consutation Report (006)

3 factors. First, if te voume goes on anoter trading venue wic free rides on te reguatory activity of te excange, te atter as a smaer income and sets a smaer isting requirement. Second, if trading is organized by a monopoy, te trading fee increases wit te eve of isting requirements. Tis reduces te impact of improved iquidity on te excange s profit and induces te excange to set a ow isting requirement. Bot effects can be avoided by introducing competition in trading in wic case, te iquidity effects of isting requirements ave te igest impact on investor wefare. Te main eements of te mode are as foows. Investors can enter a stock excange and participate in te IPO of a firm. Tey do so if teir expected utiity exceeds opportunity costs wic differ across tem. Tose investors tat ave entered te excange can be it by a iquidity sock in wic case tey must se teir oding. Tey can ave te possibiity to switc to a trading patform wic offers a smaer trading fee. Te isted firm must discose information about its productivity. Te precision of tis information depends on te eve of isting requirements. Te sareoders of te firm ony observe te information reeased by te firm. However, tere are informed investors on te secondary market knowing perfecty te productivity of te firm. Teir existence gives rise to a spread. Te excange sets its trading fee as we as its isting requirements to maximize its expected profit. A bencmark case is deveoped in wic te monopoist excange ists te firm and organizes trading in te sares. Te resuts are compared to cases in wic isting is separated from trading. Te spread is determined by te probabiity of informed trading on te secondary market. Terefore it decreases not ony te smaer information asymmetry is, but aso te more uninformed investors enter te excange. A smaer information asymmetry increases te expected utiity from participating in te IPO wic attracts investors wit ig opportunity costs on te excange, reducing furter te spread. Two equiibria are possibe: If te excange sets a ig eve of isting requirements, investor participation is ig eading to a ig market capitaization, a ig voume and a good iquidity. If te eve of isting requirements is ow, market participation is sma eading to a sma voume and a bad iquidity. Mutipe equiibria due to investor participation externaities ave been extensivey anayzed in Dow (004) and Pagano (1989) in a sigty different context. In tese modes, uninformed investors trade on te stock market to edge endowment socks. Te more investors participate on te stock excange, te better is iquidity, eiter because informed trading is reduced (Dow 004) or because prices become ess sensitive to individua endowment socks (Pagano 1989). Wie teir modes focus on te entry decision of 3

4 investors and ignore te organization of te excange, tis paper puses te anaysis furter since it integrates insigts of Dow (004) into a context of excange competition. Te present paper aso contributes to tis iterature because it not ony states te possibiity of severa equiibria, but endogenises teir occurrence. It sows aso tat te existence of severa equiibria may incite te excange to impement an equiibrium wit a sma investor participation and a too ow eve of isting requirements compared to te one maximizing investor wefare, even if reguatory costs are sma. Investors utiity does not increase monotonicay in te eve of isting requirements on te excange. Investors may need to trade on te secondary market after information is reveaed and incur terefore a risk reated to te precision of information. Te more precise information is te iger is te uncertainty about te future price on te secondary market. If tis signa risk (Aes and Lundom 1993) is important, it may offset te benefit of smaer trading costs if te precision is ig. Tus utiity of investors is concave in te precision of information and can decrease for ig eves of precision. Tis imits te sociay optima eve of isting requirements wic decreases, te smaer te gains from a better iquidity are compared to te signa risk. Tis property of te utiity function is studied in Diamond (1985) wo sows tat as ong as more precise information reduces te number of investors searcing for costy information, a ig precision increases investor wefare by reducing information costs and making beiefs more omogenous. In te mode anayzed ere, te concave utiity is obtained wit identica preferences and omogeneous beiefs. It stems from te trade-off investors face between a better iquidity and a ig signa risk. Te concave utiity aso infuences te optima eve of isting requirements set by te excange. Te iger te information precision is, te smaer is te increase in te excanges income. Tis is because te voume as we as te market capitaization are determined by investors preferences. Tis prevents te excange from setting a ig enoug eve of isting requirements to maximize investor wefare. Tis resut compements findings in Cemmanur and Fugieri (006) and Huddart et a. (1999) wo sow tat a monopoistic excange optimay sets te igest possibe eve of isting requirements. In Huddart et a. in particuar, te isting requirements aim precisey at reducing informed trading as in te mode anayzed ere. However, in teir mode investors benefit aways from a more precise information and te signa risk stemming from te fact tat investors determine teir optima portfoio before information is reeased but expect to trade after information is reeased, does not exist. Tis risk, owever, is sown to infuence investor s preferences and beavior and tereby te trading conditions, in particuar te iquidity, in equiibrium. 4

5 If te excange is a monopoist, its income stems from a isting fee corresponding to te market capitaization of te isted firms and from te trading voume. Te optima trading fee increases te smaer te isting requirement is but tota trading costs diminis. Te excange impements te equiibrium in wic a investors enter if its income is sensitive enoug to canges in te iquidity. Oterwise, te excange sets a ow eve of isting requirement and excudes ig cost investors. Te excange under-reguates aways, but tis is ony due to te existence of reguatory costs. Aso, te existence of a trading fee owers te sensitivity of te income to canges in te iquidity wic increases te under-reguation probem. If isting is separate from trading and if trading is organized by anoter monopoist, te trading patform can free ride on te isting requirements set by te excange and offer a good iquidity. Tis, owever, induces te trading patform to set a ig trading fee. Te trading fee owers te market capitaization of te isted firms and tereby te profit of te excange. Te trading patform does not internaize te oss of te reguating excange due to te trading fee wic is terefore iger tan in te case of a singe monopoist excange. Te excange sets a ow eve of isting requirements not ony because it oses income from trading but aso because of te iger trading fee. In tis case, investors are worse-off and te under-reguation probem is more severe tan in te bencmark case. Te free riding probem is not te source of under-reguation but enforces it. As ong as te trading fee depends on te eve of isting requirements, it aways owers te effect of a better iquidity on investor wefare and increases under-reguation. If isting is separated from trading and te trading industry is competitive, tere is no free riding probem and no interdependence between te trading fee and te isting requirements. In tis case, investor wefare is te igest. However, te profit of te excange is smaer tan in te bencmark case. Te iger income from istings does not compensate te oss of income from trading. Tere is a divergence in interests since investors prefer separation wit a competitive trading industry wereas te excange prefers to be a monopoist in isting and trading. Listing requirements are sown to improve iquidity by diminising information asymmetry, as we as by entaiing more participation of investors. Bot of tese resuts grounding te anaysis of te mode find support in te empirica iterature. Frost et a. (00) sow tat te strengt of discosure systems is positivey associated wit market iquidity in a sampe of 50 stock excanges in te word. Ramadorai and Jenkinson (007), suggest tat tere are different cientees among investors wit respect to isting requirements. Wie investors may prefer a igy reguated excange for confidence reasons (a smaer 5

6 probabiity to be ceated by te firms, a iger average quaity and a smaer maximum risk of isted firms) 3, te anaysis ere inks investors participation to a smaer risk of adverse seection on te secondary market. It takes te perspective of Huddart et a. (1999), wo concude tat a profit maximizing monopoist excange sets a ig eve of isting requirements to attract te order fow of iquidity traders, but broadens te anaysis by introducing competition for voume by anoter trading venue in te sares isted on te excange 4 as we as eterogeneity among investors. Tese enargements aow a more reaistic approac concerning isting reguation and sow tat te optima resut in Huddart et a. (1999) is ony one among severa possibe equiibria and tigty inked to market conditions not taken into account in teir mode. Te artice is organized as foows. Section sets out te mode. Section 3 anayses te entry decision of investors. Section 4 presents te optima trading fee and isting requirement set by a monopoist excange. Section 5 discusses separation of isting and trading and section 7 concudes. Proofs are given in te appendix.. Mode Firm. Consider a firm wit a risk neutra manager and witout assets in pace. Te firm can reaize a project if it raises capita by isting on an excange and issuing K sares. If te firm does not ist, it cannot reaize te project and its vaue is zero. 5 Te project yieds a payoff of V 1 x per sare. Te productivity, x, is a random variabe distributed over four equay ikey states of te nature. In te two best states, te average productivity is te fina productivity can take te vaues x and x or x wit probabiity ½. In te two oter states, te average productivity is x, wit x x 0, and te fina productivity can take te vaues x and x wit probabiity ½. Average productivities represent te quaity of te firm. A good firm as a ig mean productivity. Te parameter represents te risk of te firm reated to its economic activity. Te difference in average productivities is assumed to be ig reative to te economic risk: x x. 3 See for instance Guiso et a. (008), and Easey and O Hara (007) 4 Huddart et a. (1999) determine te optima isting requirement by introducing competition in istings. Firms isting on an excange wit a sma eve of isting requirements ave ess iquid sares since investors face more informed trading. 5 If te firm coud reaise te project wit oter means, it woud suffer a positive opportunity cost if isting. Te firm ists as ong as tis opportunity cost is not arger tan te expected gain from isting. Since tis paper focuses on investors decisions and not isting decisions tis possibiity is omitted for simpicity. Adding it woud not cange te resut. 6

7 Figure 1: payoff of te asset ½ x x ½ x x ½ ½ x x ½ ½ x At te time of isting, te average productivity is unknown to a agents. Terefore, te isting decision aone does not convey information to te market about te quaity of te firm. 6 Te expected market vaue of te firm if it ists is positive and since te reservation vaue is zero, te firm aways ists. Te manager earns its type after isting. However, e cannot or is not wiing to crediby convey tis information to market participants. It remains is private information. Even toug, in reaity, firms vountariy discose information, and in particuar arge firms are foowed by anaysts and te media, tere is information asymmetry even about arge internationa firms. Tis mode reies on te existence of information asymmetry, and needs terefore tis ypotesis. If te manager coud discose crediby its type, a good manager woud aways do so. Since te market expects te good manager to discose, it infers tat a firm wic does not discose is bad and information asymmetry vanises. Besides tis teoretica argument, two practica reasons justify tis assumption. First, tis paper ignores competey competition on te product market. Literature in accounting 7 sows tat firms may suffer proprietary costs by discosing information to competitors. Tese may adjust teir strategies and compete more aggressivey on te product market, wic can ead to a ower profit of te firm considered if it discoses information about its type. Second, for medium size firms and firms wit weak media or anaysts coverage it may be difficut and costy to bring te information to a market participants witout an institutionaized procedure. Excange. Tere is an excange isting te firm and organizing trading in te sares. It is a monopoist in isting as we as in trading. Te excange carges a trading fee, c, per sare traded on te secondary market and a isting fee, F, paid by te firm. Te isting fee is a 6 In a simiar set up in wic te firm knows its type before it takes te decision to ist, Stougton et a. (001) sow te existence of separating equiibria in wic ony good firms ist and revea perfecty teir type. More generay, as ong as te isting decision eads to semi-separating equiibria, it reveas te distribution of te types of isted firms. Te resuts in tis paper rey on te existence of information asymmetry and woud aso od if isting was informative as ong as it is not perfecty reveaing. 7 Nicos and Street (007), Leuz (004), Verreccia (1983, 001) 7

8 fixed price corresponding to te market vaue of te firm. If te isting fee varied wit te amount of issued sares or wit te market vaue of te firm, te number of issued sares and te market vaue woud aways be smaer tan in te case of a fixed fee. Terefore, a variabe isting fee is not optima for te excange. Te excange aso sets isting requirements. Listing requirements are a set of rues to wic te isted firm must commit. Tese rues may contain accounting and reporting standards but aso corporate governance devices wic, if tey are in pace, may revea information about te quaity of te firm. Listing requirements ead to pubic information about te quaity of te firm once te atter as been reveaed to te manager. Tey constitute a noisy pubic signa, s, observed by a market participants. Since te type of te firm is unknown wen te firm ists and bot possibe quaities occur wit te same probabiity, te signa is expected to take eiter vaue, x or x, wit probabiity ½ wen te firm ists. Wit probabiity 0.5,1 p te observed signa corresponds to te true type of te firm; it corresponds to te wrong type oterwise. Te precision of te signa, p, represents te strictness of te isting requirements: te touger tey are, te iger is te probabiity tat te observed signa corresponds to te true type of te firm. Te excange bears reguatory costs reated to te enforcement of te isting requirements: C ( p) wit C ' 0 and C '' 0. Te firm does not bear compiance costs. Te set up of tis game is cose to Staugton et a (001) but differs aong two dimensions. First te timing of information reveation is different since in Staugton et a. te manager knows its type (wic is aso te average payoff) before e ists te firm (see footnote 8). Second te information content is not te same. In Staugton et a. te signa is noisy information about te fina payoff of te security, wie in te present mode te signa reveas information about te average payoff of te security. Bot types of information ead to ess adverse seection on te excange, but teir impact on te risk perceived by investors is different. Wie a signa on te fina payoff reduces te potentia variabiity of tis payoff once information as been reveaed, information about te average quaity of te firm reduces ony te uncertainty on te distribution mean of te payoff but not te ex post perceived risk of te economic activity of te firm. Tis distinction aows separating te effects of te risk of te economic activity and te effects of te uncertainty about te firms quaity, on te decisions of te excange. Te assumption about te information content of te signa seems aso consistent wit reaity since information reported by or about firms concerns items ike production procedures, economic acievements, panned investments or, troug te 8

9 appication of corporate governance devices, te ikeiood of private benefit extraction or non optima investment strategies in te perspective of investors (empire buiding ). Tis information aows assessing te quaity on average of firms. Te excange sets te trading fee, c, te isting fee, F, and te eve of isting requirements, p, to maximize its expected profit,. As excanges are increasingy turned into demutuaised and isted entities, tis objective seems te must accurate in te current context. 8 Investors. Tere are two types of investors on te excange: informed and uninformed. Te number of informed investors is N I. Tey know perfecty te quaity of te firm and trade ony on te secondary market in te case te isted firm is bad. Uninformed investors observe te signa, s. Tey are te ony investors participating in te IPO. Wen uninformed investors enter te stock market, tey bear opportunity costs: N among tem ave ow opportunity costs ( Oc ) and N ave ig opportunity costs ( Oc ), witoc Oc 0. 9 Opportunity costs may represent aternative investment opportunities. Tey may aso represent entry costs borne by investors suc as costs reated to information gatering and understanding. Cristiansen et a. (005), for exampe, find tat economists are more ikey to participate in te stock market tan persons wit any oter education. If uninformed investors ave entered te stock market and bougt sares of te firm, tey may be it by a iquidity sock: wit probabiity 0,1 t tey must se teir entire oding on te secondary market. Tis constitutes te trading voume of te excange. In te case of a iquidity sock, investors se teir oding to a risk neutra market maker. Informed traders may mimic uninformed ones if tey know tat te firm is bad. Te market maker as te same information as uninformed investors. Te price, at wic e is wiing to buy te sares, P, takes into account te possibiity tat te order comes from an informed investor. Tus te market maker sets a spread, S, due to information asymmetry. Uninformed investors are risk averse. Tey ave an initia weat, W 0, and determine teir demand of sares, D, by maximizing te mean-variance expected utiity of teir future weat, W ~ : Max D ~ b ~ Var ( W ) E W 8 According to te 006 cost and revenue study by te Word Federation of Excanges, 75% of members wic responded to te survey were for-profit organizations in Tis modeing device is aso used in Pagano (1989). 9

10 Investors enter te stock market if teir expected utiity is iger tan teir opportunity cost. Denote te number of uninformed investors entering te stock market by informed investors among a investors on te market is n N N N. I u I N u. Te fraction of Timing. Te game is organized in five periods. In te two first periods, te excange determines its organization: first it sets a eve of isting requirements (tis decision is considered as a ong term decision since it impies to set up particuar isting procedures as we as speciaized departments to enforce tese requirements), second te excange sets a trading fee. Te isting fee is te market capitaization of te firms and tus not determined separatey by te excange. However, it is impicity taken into account in te determination of p and c. In te tird period, investors decide weter to enter te stock market, and if tey do, tey buy te sares issued by te firm. Te firm determines ow many sares to issue. In te fourt period, te manager of te firm earns its type and te signa, s, is reveaed to te market due to compiance wit isting requirements. In te fift period, some uninformed investors are it by a iquidity sock and se teir oing to a market maker. Finay, in te ast period payoffs are reaized. Te mode is soved backwards, beginning wit te bid price set by te market maker in period 5 and ending wit te determination of te eve of isting requirements in period one. Figure dispays te different stages of te mode. 3. Investors entry decision Trading. Te foowing trading mode draws upon Gosten and Migrom (1985) and is a generaization of Dow (004) to a situation wit a pubic signa. Ony one side of te market is modeed to determine te bid price: te transaction between te seing investors and te market maker. Te spread is inferred from te difference between te bid price and te conditiona expected vaue of te asset. As in Dow (004), it corresponds to twice tis difference. Wen te market maker receives a se order, e determines te bid price, P, according to te signa, s, its precision, p, as we as te different types of investors on te market. Depending on te observed signa, te probabiity tat te order stems from an uninformed investor differs. If te market maker as observed s x, wit probabiity p te signa corresponds to te true type of te firm and te order comes from an uninformed investor since an informed one does not se te sares of a good firm. Wit probabiity (1-p) te signa is wrong and te probabiity tat te order comes from an uninformed investor is ( 1 n) t. Oterwise, te order 10

11 stems from an informed investor. Te market maker sets te bid price per sare conditiona on te good signa, Ps x, suc as to break even: P sx xx p 1 p)(1 n te V s x V ( ) V (1) xx wit EV s x p 1 x ) (1 p)(1 x ) (, te expected vaue of te asset conditiona on te signa is: V 1 x te vaue of te asset of a bad firm. Te corresponding spread s x and x x S EV s x P (1 p)(1 (1 n) t px s x sx ) () wit ( 1 p)(1 (1 n) t) te probabiity of an informed trade and p x te difference in vaue between te conditiona expectation and te ow quaity firm. If te market maker as observed s x, wit probabiity (1-p) te signa is wrong and te order comes from an uninformed investor. Wit probabiity p, te signa is correct and te order comes from an uninformed investor wit probabiity ( 1 n) t and from an informed investor oterwise. Te bid price set by te market maker given te bad signa, Ps x, is: P sx xx 1 p) p(1 n) te ( V s x V V ( ) (3) xx wit E V s x ) p(1 x ) (1 p)(1 x ), te expected vaue of te asset conditiona on te signa ( s x. Te corresponding spread is: S EV s x P p(1 (1 n) t)(1 p x s x sx ) (4) wit p( 1 (1 n) t) te probabiity of an informed trade and ( 1 p) x te difference in vaue between te conditiona expectation and te ow quaity firm. Atoug te probabiity of informed trading is smaer in te case of a good signa, te market maker reduces te bid price by a iger amount wic increases te spread. On te contrary, if te signa is bad, te amount by wic te price is reduced compared to te 11

12 expectation is smaer wic reduces te spread despite a iger probabiity of informed trading. Tese two effects offset eac oter. Te spread is te same regardess of weter te signa is good or bad: S sx Ss. x Investors determine teir oding in te tird period, before te signa is reeased. Because of te possibiity of informed trading, uninformed investors expect te market maker to set a spread and to se teir order at a discount reative to te unconditiona expected payoff. However, ony te bid price is a random variabe for investors. Te spread is twice te distance between te unconditiona expected vaue of te asset, EV.5( x x ) te expected bid price, E P: 0, and EP) (1 p) p(1 (1 n) t S ( E V ) x x (5) In te tird period, te bid price is a random variabe since it depends on te reaization of te signa and te resuting probabiity of informed trading. Tus, investors incur a risk wen buying te security wic is reated to ow te future reaization of te signa impacts te bid price. Information reveation sifts weat of investors eiter upwards or downwards (reative to prior expectation). Tis risk is abeed signa risk in Aes and Lundom (1993) 10 and is determined ere by te variance of P: 1 Var ( P) (1 p) x x (6) 4 Te more precise tis signa is, te smaer is te spread but te coser is te revised expectation to te true te two possibe vaues, x and x, wic creates more voatiity in te price. If investors se after a good signa, tey experience a utiity gain. If owever tey se after a bad signa, tey suffer a utiity oss. Te variabiity of te bid price increases te more precise te signa is. It is aso ampified by te difference in average productivities since te randomness of te bid price stems from te uncertainty about average quaity and not from te firms economic risk ( ). Te signa risk is ony induced by te eary partia resoution of uncertainty. Ceteris paribus, investors woud prefer te firm not to commit to discose information. In te case of a competey uninformative signa (p=0.5), te trading price and te spread are ony affected by te proportion of informed investors among a market 10 It is aso caed distributive risk by Hirseiffer (1971). 1

13 participants, wic is known. In tis case, tere is no uncertainty on te bid price ( Var ( P) 0 ), but te spread is te igest possibe (for a given number of investors), S 0.5(1 (1 n) t) x x. IPO. Investors participating in te IPO determine teir demand of te asset by maximizing te expected utiity of teir fina weat. Since te price on te secondary market is random, investors face six states of te word at tis stage. If tey keep teir oding unti te end of te game (wic occurs wit probabiity (1-t)), teir fina weat is determined by te four states described in figure 1. If investors must se teir oding before te end of te game (wic occurs wit probabiity t), tey face two additiona sates of te nature since te bid price can be eiter ig or ow, depending on te signa. Te fina weat differs depending on weter investors are it by a iquidity sock. In te case, tey keep teir oding unti te end of te game, investors receive te fina payoff ~ and teir fina weat is: W D ( V PIPO ) W0. If investors ave to se teir oding in te fourt period, teir fina weat depends on te bid price tey obtain: ~ W D ( P c PIPO ) W. Wen investors determine teir portfoio oding, tey take te 0 expectation over te period of oding and over te vaues of te asset: E W ~ W D ( EV ts c P ) (7) 0 IPO Ceteris paribus, te expected weat increases te more precise information is because it depends ony on te spread wic diminises wit p. Te effect of te precision of te signa on te variance of te fina weat is ambiguous. Te precision increases te voatiity of te price but decreases te spread, reducing tereby te weat oss due to trading. Te signa as no impact on te economic risk of te firm. Lemma 1 Investors face tree types of risks: (i) a fundamenta risk due to te variabiity of te expected payoff: ( 1 t) Var( V) (ii) a signa risk due to te uncertainty on te bid price: tvar (P) (iii) a orizon risk due to te uncertainty about ow ong investors can keep teir oding: E( S) LR c (1 t) t 13

14 Investors incur a fundamenta risk if tey keep te asset unti te payoff is reaized. Tis risk is not ony determined by te risk of te economic activity ( ), but aso by te uncertainty about te quaity of te firm. Since te investment decision is taken before te reaization of te signa, tis risk is not affected by its precision. However, after pubic information is reveaed, tis risk diminises since uncertainty on te firm s quaity is smaer. However, te price sifts togeter wit beiefs, wic are omogenous, so tat tere is no trading once te signa is observed and investors keep teir initia oding if tey are not it by a iquidity sock. In addition to te fundamenta and te signa risk, investors aso incur a risk reated to te uncertainty about ow ong tey can keep te asset since expected payoffs differ in a six states of te nature (orizon risk). Investors cannot insure against te iquidity sock. Teir orizon risk is not diversifiabe. Te signa risk and te orizon risk are affected in opposite ways by te precision of information. Te orizon risk is determined by te difference between te expected payoff of te security and te expected bid price. Tis difference corresponds to te trading costs wic diminis te iger te precision is, ceteris paribus, since te spread becomes smaer. Tus, wie te signa risk aways increases wit p, te orizon risk aways decreases wit p. Te reaization of an informative signa can increase as we as decrease investors utiity depending on wic of te two risks takes te overand. Investors determine te price tey are wiing to pay per sare by maximizing te utiity of teir fina weat. Tey discount te sare price, P IPO, wit respect to te tree types of risks tey face and te expected trading costs (te spread and te trading fee): b (1 t) Var( V ) tvar( P) LR PIPO E V t S c K. Tis represents a cost for te firm N u wic adjusts te amount of issued sares. Te firm issues te number of sares, K, maximizing its expected market vaue: sares is: Max P K IPO K. In equiibrium, te number of issued S N K u EV t c b(1 t) Var( V) tvar( P) LR (8) Weter te number of issued sares increases wit te precision of information depends on te effect of te atter on te investors risk. However, te firm aways benefits from a more orizon market since iquidity reduces te trading costs and tereby aso te iquidity risk of investors. Te more uninformed investors participate in te excange, te ess 14

15 te firms decision is affected by te risk of investors fina weat since te atter can be spread over a iger number of investors. In tis case, te amount of issued sares becomes more sensitive to canges in trading costs. Tus te iger te number of participating investors is, te more sares are issued for a given signa precision. Te resuting equiibrium sare price and individua demand of investors are as foows: 1 S P IPO EV t c (9) PIPO D b (1 t) Var( V ) tvar( P) LR (10) Te equiibrium price at te IPO does not depend on te risk premium of investors since te firm adjusts te size of te sare issue to it. Te IPO price increases monotonicay wit te precision of te signa because it depends ony on trading costs. Tus, te more precise pubic information in te future eads aways to iger sare prices, but not necessariy to iger number of issued sares in equiibrium. Te precision of information as two opposite effects on te demand of investors. On te one and, it decreases te spread and tereby investors trading cost as we as teir orizon risk. On te oter and, it increases teir signa risk. For sma precisions, te signa risk is sma and an increase in te precision of information aso increases te optima demand of investors. In tis case, investors benefit from a better iquidity. If, owever, te precision is ig, canges in te signa risk ave a iger impact on te equiibrium demand tan te better iquidity. In tis case, an increase in te precision reduces te equiibrium demand. 11 Proposition 1: Te expected utiity of investors is concave in te precision, p, in equiibrium. If te signa ~ risk faced by investors is arge enoug, EU [W ] decreases for ig eves of p. ~ PIPO EU[ W ] W0 (11) b (1 t) Var( V ) tvar( P) LR 11 Tere is a signa 0.5,1 p for wic D 0 D if te foowing condition ods: p 1 4x P IPO (1 t) Var ( V ) tvar ( P) LR (1 t) A. Te demand D increases in p if P IPO A and 1 (1 n) t decreases oterwise. Since P IPO A 0 and 0, te equiibrium demand is increasing for p p decreasing for p p D. p p D and 15

16 Simiary to te optima demand, te precision of te signa as opposite impacts on te equiibrium expected utiity. Weter te utiity of investors increases in p depends on ow important te signa risk is. Wen p is sma, te signa risk is sma but trading costs are ig. Tis keeps not ony te expected weat of investors sma, but owers aso teir utiity troug a ig orizon risk. An increasing precision owers trading costs and tus te iquidity risk, but increases te signa risk. Investors utiity is maximized for te eve of p at wic tese two effects exacty offset. Hig eves of precision tend to make investors worse off despite te better iquidity on te excange resuting in ess adverse seection and a smaer orizon risk, because tey exacerbate te uncertainty about te payoff in te case of a iquidity sock. Since a investors ave te same preferences and beiefs, more precise pubic information increases investor wefare up to a certain precision eve. Very informative information can be undesirabe for investors. Te fact tat more pubic information does not necessariy increase te ex ante wefare of investors as been stated in severa papers in te accounting iterature. Hakansson et a. (198) determine under wic conditions information is wefare improving. Diamond (1985) sows tat te ex ante utiity of investors is concave in te precision. His argument is reated to information production. A firm optimay reeases pubic information wit a ig enoug precision for investors not to engage in costy information production. Tis saves information costs and improves risk saring by making beiefs more omogenous. However Aes and Lundom (1993) sow tat tis resut is strongy inked to te assumption tat private signas are independent. Wie many papers in te mentioned iterature concude tat investors must eiter differ in preferences or ave eterogeneous beiefs for information to ave socia vaue, my mode assumes investors wit identica utiities and omogenous beiefs and yet teir utiity is concave in te precision. Tis is because te precision of pubic information affects te trading conditions on te market and tereby not ony te trading costs borne by investors but aso teir risk. 1 Not ony does te individua utiity of investors depend on te trading conditions on te excange, it depends aso on te number of investors on te market. Te more investors enter te excange, te smaer is te probabiity of informed trading eading to a smaer expected spread on te secondary market and ence aso to a smaer iquidity risk. Tus tere 1 See Hakansson et a. (1993) for a discussion about te necessity of eterogeneous preferences and beiefs for te socia vaue of information. 16

17 is a positive externaity due to te participation of investors, since an additiona investor contributes to reduce te trading cost and to increase te expected utiity of a investors. Tis participation externaity is aso driving te resuts in Dow (004) wo sows tat if investors differ in risk aversion, mutipe equiibria wit different investor participations and eves of iquidity are possibe: te more investors enter, te smaer is te spread. Pagano (1989) igigts anoter participation externaity on iquidity: te more investors enter te market, te ess te security prices are sensitive to individua endowment socks. Entry decision of investors. Investors participate in te IPO if teir expected utiity ~ from entering te excange exceeds teir opportunity costs: EU[ W] Oc. Since teir individua utiity can be concave in te signa precision, p, investors do not necessariy enter on a very transparent market. More generay te foowing ods for a given eve of opportunity costs (Oc). Lemma Assume tat a investors incur te same opportunity costs. (i) If te expected utiity of investors is increasing in p, a investors enter te excange up from a eve of p wic equaizes teir utiity to costs. (ii) If te expected utiity is decreasing in p, investors enter te excange up unti te eve p wic equaizes teir utiity to costs. (iii) If te expected utiity is maximized for a p ˆ 0.5,1, tere are two tresod eves for te signa precision, p T1 and p T, wit pt1 pt and p ˆ T1 p pt, suc tat p p T p. investors enter if and ony if 1, T Investors incur two different utiity osses reated to information precision. A sma precision eads to ig trading costs and a sma utiity. A ig precision eads to a ig signa risk and possiby aso to a sma utiity. Tus, investors may never enter an opaque as we as a very transparent excange if tey bear opportunity costs. Te concavity in te utiity function of investors and te resuting entry beavior is ony due to te signa risk. Tis risk occurs because a investors od teir portfoio uncanged unti te signa as been reveaed. Tis kind of risk may seem irreevant on a financia market on wic trading is continuous because investors can aways take position before information is reeased. However, te stock market is aso used for ong term investments and investors can ave different investment orizons. Tis mode considers ony investors wit a ong orizon (impicity teir objective is to wait unti te end of te game), 17

18 but wo can be it by an exogenous iquidity sock and tus be forced to se after information was reeased. Since investors bear different opportunity costs, tey do not necessariy enter te excange a togeter: if investors wit ow opportunity costs enter it is not necessariy worty for investors wit ig opportunity costs to enter te excange. Te entry decision of bot investor types depends on te effect of te eve of isting requirements on teir utiity. Proposition ~ Assume tat te expected utiity EU [W ] is maximized for p ˆ 0.5,1. Two outcomes are possibe: (i) Te number of ig cost investors is ig eading to an important participation externaity and a investors enter te market as ong as te precision is between two tresods:, p p T 1 pt wit p ˆ T1 p pt. (ii) Te number of ig cost investors is sma eading to a sma participation p T p externaity. If te excange is eiter opaque or transparent ( p, 1 T1 and p T p wit p p ), ony ow cost investors enter. p, T pt T1 p and 1 T T For intermediate eves of isting requirements a investors enter te excange. Because investors differ in opportunity costs, mutipe equiibria are possibe. Wit a ow eve of isting requirements, investors wit ig opportunity costs can be deterred from entering te market eading to a set of equiibria wit sma investor participation and a sma iquidity. Te iger te eve of isting requirements is, te smaer is te spread wic increases te expected utiity of a investors (provided tat teir signa risk is sma) and attracts, up from a particuar eve, investors wit ig opportunity costs on te excange. Tus, a iger eve of isting requirements eads to a set of equiibria wit ig investor participation and a good iquidity. In tis case, te spread is sma not ony because te isting requirement reduces information asymmetry, but aso because te ig number of participating uninformed investors reduces te probabiity of informed trading. However, as soon as a iger precision decreases te individua utiity of investors, investor participation becomes smaer since ig cost investors do not enter te excange for eves of p up from te tresod p T. In tis case, more precise pubic information as an ambiguous effect on te iquidity. On te one and, te market maker can assess more accuratey te expected payoff of te security wic reduces te spread. On te oter and, te number of uninformed investors becomes smaer wic increases informed trading and tus aso te spread. If te number of ig cost uninformed investors is ig, very precise pubic information may deteriorate iquidity because ony a sma number if uninformed investors enter te excange. 18

19 Te tresod eve of p, at wic ig cost investors enter, is smaer wit te participation externaity, tan it woud be witout. Weter suc an externaity eads to a singe set of equiibria depends on its magnitude, wic in turn depends on te number of ig cost investors in te economy ( N ). If teir number is ig, te effect of teir entry on teir utiity is so ig tat it is aways worty for tem to enter. In tis case, tere is a unique set of equiibria in wic a uninformed investors enter. Oterwise, mutipe sets of equiibria exist. 4. Optima organization of te excange Trading fee. Te excange sets te trading fee to maximize its income from trading and isting. Te trading fee as opposite effects on te excange s profit. It increases te income per traded sare but reduces te number of sares issued and terefore te voume. Since a iger trading fee reduces te utiity of investors, it can aso ead to a sma market participation reducing furter te voume. Te market capitaization of te firm decreases aso te iger te trading fee is, because te price investors are wiing to pay diminises in addition to te smaer number of issued sares. Te voume te excange expects depends not ony on te number of sares, but aso on te probabiity wit wic uninformed investors trade. If te firm is bad, informed investors aways mimic uninformed ones and voume aways occurs. If, owever, te firm is a good one, informed investors never trade and te voume depends on te probabiity wit wic uninformed investors are it by a iquidity sock, t. In te tird stage, te probabiity of trading is: 0.5(1 t). Te optima trading fee is determined by te foowing maximization probem: Max ( c) 0.5(1 t) K c K P C( p) (1) c IPO Te first term represents te income from trading, te second term represents te income from te isting fee and te ast term is te reguatory cost (wic does not depend on te trading fee). Te trading fee maximizing te profit of te excange is: c u E V t SN u (1 t) (13) t N 19

20 Te trading fee set in equiibrium increases te iger te precision of te signa is as ong as a iger p entais market participation. A iger precision eads to a smaer spread due to ess informed trading and possiby more market participation. Te smaer spread reduces te trading costs and te orizon risk of investors. Bot effects transate into a smaer cost of capita for te firm, wic issues more sares. Tis in turn increases te voume as we as te income from isting. In equiibrium, te excange expoits tis mecanism to increase its trading fee. If a investors are on te market, te increase in te trading fee wit te precision is weaker tan in te case in wic ony ow cost investors enter. Tis is because te iger number of uninformed investors reduces te sensitivity of te spread to canges in p. In te specific case in wic ig cost investors do not enter for ig eves of p, increasing p as an ambiguous effect on te spread and terefore aso on te trading fee. Atoug te trading fee increases amost aways in p, te tota trading costs decrease wit a more precise te signa. 13 Te excange never increases te optima trading fee to offset competey te smaer spread. Te optima trading fee decreases te iger te probabiity of a iquidity sock, t, is. Te more ikey investors are to se teir oding on te secondary market, te smaer is te probabiity of informed trading and tus te spread, but te more te utiity of investors is sensitive to trading costs and te iger is teir signa risk. Tese effects can reduce te number of issued sares and tereby te voume and te income from isting. To reduce te negative effects of a iger t, te excange diminises its trading fee. Since a iger trading fee reduces te income from isting, a monopoy excange offering bot services, isting and trading, sets a smaer trading fee tan a monopoist excange wic organizes ony trading. 14 Te utiity of investors increases te smaer te trading fee is because te trading cost and te orizon risk diminis. Tus, atoug wit a isting fee, te surpus of firms is zero, investors are better off tan if te excange does not carge a isting fee because te trading fee is smaer. Te smaer trading fee can aso ead to a iger market capitaization and a iger voume. An monopoy excange wit income from isting as we as trading is arger wit respect to bot, voume and market capitaization, tan an excange wit income ony from trading. 13 Tota expected trading costs are: S E( V ) S t c (1 t) t(1 t) TC. It foows tat TC t E( S) (1 t) 0 4 p 4 p 14 Te trading fee witout income from isting is: c EV u t S t N N u 0

21 Listing requirements. Once te trading fee is cosen, te excange sets te eve of isting requirements to maximize its profit. At tis stage, its profit depends on te spread, on te number of uninformed investors on te excange, and on te risk premium required by investors. Tese tree eements affect te utiity of investors and determine terefore te voume and te market capitaization. Te excange maximizes its profit to determine te optima precision. Its profit is: S( p) EV t (1 t) Nu ( p) ( p) C( p) (14) t 16b (1 t) Var( V ) tvar( P) LR An increase in p as two positive effects on te profit troug te spread and te number of investors, and two negative effects troug te signa risk and te reguatory costs. A iger precision reduces te spread and tereby te trading costs as we as te orizon risk. Tis increases te profit of te excange. A iger precision can aso ead to iger market participation (see proposition ). More investor participation increases te number of issued sares wic in turn eads to a iger isting fee and voume. However, te more investors enter te excange, te ess sensitive is te spread to canges in p wic reduces te gain of an increase in p for te excange. Finay, a iger precision increases te signa risk wic reduces te profit of te excange. Te ast effect makes te income of te excange concave in p, simiary to te utiity of investors. Te equiibrium eve of isting requirements depends on severa parameters. Te iger te number of uninformed investors on te market is, te iger is te optima precision (assuming tat a margina increase in p is not te source of te iger number of uninformed investors). Hig market participation not ony increases te voume and te market capitaization directy, but it aso contributes to reduce te spread and eads tus to smaer trading costs and to a smaer risk premium. Tis owers te negative effect of a iger precision on te utiity of investors troug te signa risk, and induces terefore te excange to set a ig precision in equiibrium. Tus, if te excange attracts ony ow cost investors on te market, te eve of isting is aways smaer tan if a uninformed investors enter te excange in equiibrium. Te excange never impements an equiibrium wit a ig transparency and sma investor participation. x x Te fundamenta risk of te firm wic increases wit te difference in productivities,, and te risk of te undertaken project,, reduce te importance of canges in te precision on te trading costs and te orizon risk. Terefore, te more risky te firm is, te 1

22 ower is te equiibrium precision. However, wie te risk of te project ony affects te fundamenta risk, a iger difference in productivities aso increases te spread. Tus diverging average productivities ead to iger trading costs and reduce furter te equiibrium eve of isting requirements. Te effect of te economic risk is smaer te more ikey a iquidity sock is. In tis case, owever, investors utiity becomes more sensitive to canges in te spread wic ampifies te effect of diverging productivities. Tus, an excange is particuary ikey to set a ow eve of isting requirements if te quaities of te isted firms are igy different Given an optima eve of isting requirements set by te excange, te expected utiity of investors is te foowing: U ( p, c ) (1 t) W 0 (1 t) Var( V ) tvar( P) LR S EV t (15) 3b Since te voume and te market capitaization depend on te number of issued sares wic are determined by te trading costs and te risk premium required by investors, te factors affecting te profit of te excange are te same as tose affecting te utiity of investors. Listing requirements are considered as a device to improve investor protection. Tus, tey soud increase te utiity investors obtain from entering te stock market. To compare te equiibrium eve of isting requirements set by a profit maximizing excange wit te one maximizing investor wefare, define te sum of investors utiities as te investor wefare function, Iw: ~ Iw EU [ W ] (16) N u Te utiity of investors is concave in p. According to proposition 1, te utiity can aso decrease for ig eves of p. Terefore, investor wefare is aso concave and can aso be decreasing in p. If te aggregated utiity is increasing in p for p 0.5,1, te optima precision from te point of view of investors is perfecty informative: p=1. However, te iger te precision is, te smaer is te utiity gain of investors. If te aggregated utiity of investors decreases for ig precision, te eve of p maximizing investor wefare is pˆ suc