Endogenous Market Structure: Over-the-Counter versus Exchange Trading

Transcription

1 Endogenous Market Structure: Over-the-Counter versus Exchange Tradng J Hee Yoon Job Market Paper September 8, 2017 Abstract For many assets, traders favor ether over-the-counter (OTC) or centralzed markets. Ths paper examnes how traders choce between these tradng venues depends on asset and trader characterstcs. Traders values depend on a common and dosyncratc component, whle traders have prvate nformaton wth heterogeneous precson. A trader s ncentve to choose an OTC market depends on the beneft of learnng the asset value and the cost due to prce mpact. Traders choose OTC markets over centralzed exchanges when the dosyncratc component domnates n asset values or ther prvate nformaton s suffcently naccurate, and thus, the beneft from learnng s hgh. Ths paper provdes comparatve statcs of equlbrum and effcency for centralzed and over-the-counter markets. Furthermore, when the common value component domnates n asset values, the OTC market decrease nformaton effcency by beng conducve to trade only between nformed traders. Keywords: Noncompettve tradng, Over-the-counter markets, Exchanges, Prce mpact, Lqudty, Effcency 1 Introducton Over-the-counter markets have been an mportant alternatve tradng venues for many assets, goods, commodtes, fnancal dervatves, and securtes. In over-the-counter markets, buyers and sellers are pared and prvately decde ther own tradng terms, whle publc exchanges use a centralzed tradng mechansm such as unform-prce auctons. Many commentators have rased concerns about the mplcatons of the varous market mechansms for ther role n facltatng nformaton aggregaton and effcency. The goal of ths paper s to examne these mplcatons when traders ndvdually choose a tradng venue and a market structure s endogenously formed by ther choce. Certan types of assets appear to be traded mostly n over-the-counter markets, whereas others have been traded n exchanges. Thus, the potental challenges for the tradtonal role of markets wll not affect all types of assets and goods equally. Ths paper asks what attracts traders to over-the-counter markets and whether ths type of tradng venue can harm the effcency of the economy. I gratefully acknowledges the fnancal support from the Leon Mears Graduate Fellowshps for ths paper under the ttle Incentves to Trade n Over-the-Counter Markets. Ph.D. Canddate, Unversty of Wsconsn - Madson, Economcs. Emal: jyoon43@wsc.edu 1

2 A framework ntroduced n ths paper allows characterzng Bayesan Nash equlbrum n both over-the-counter and centralzed tradng venues. Wthn the framework we can study the equlbrum ncentves of market partcpants dependng on ther types, namely, nsttutonal and retal, nformed and unnformed to choose varous tradng venues. An economy s modeled for two perods. In the frst perod t = 0, each trader chooses to enter ether a centralzed market or an over-the-counter market that open at t = 1; then trade takes place by traders bds submtted n each market. The centralzed market s desgned as a unform-prce double aucton, n whch all traders smultaneously submt ther (net) demand schedules q (p) : p R and trades clear at prce p such that q (p ) = 0. The over-the-counter market s desgned as blateral tradng based on the unform-prce aucton, wth trader pars determned by the traders choce of the counterparty. More precsely, upon the partcpaton n the over-the-counter market, traders observe types of others the correlaton between hs and ther asset valuatons (buyers and sellers) and ther nformaton precson (nformed and unnformed) and choose a counterparty to trade wth. The model accommodates the followng characterstcs, whch determne traders market choce: market sze (market characterstc), nterdependence of traders asset values (asset), and precson of prvate nformaton (traders). Each characterstcs affects learnng and lqudty of traders. Equlbrum prce aggregates all market partcpants prvate nformaton on asset values, and by condtonng on prce, traders learn the aggregated nformaton. The market lqudty s measured by endogenous prce mpact, the change of prce as a trader s demand ncreases by one unt. 1 Larger prce mpacts,.e. lower lqudty, reduce demands of traders and lower ther utltes. The effects of market sze on learnng and lqudty have been studed n lterature. Wth more traders partcpatng n the market, prce reveals more accurate nformaton. Moreover, n larger markets, prce mpact can be smaller when other characterstcs are fxed (See Rostek and Weretka (2012)). The beneft due to both learnng and mproved lqudty leads traders to the centralzed market because of ts larger sze. Unlke the market sze, the effect of nterdependence among asset values s ambguous. Ths paper shows that certan asset characterstcs can ncrease both benefts from learnng and lqudty to trade n the over-the-counter market. Traders are uncertan about the value of a rsky asset. Ther valuatons are nterdependent and have two components: a common component, whch s the same for all traders, and an dosyncratc component, whch can be correlated heterogeneously across traders. The common value captures the asset return or a future prce n dynamc market. In turn, the dosyncratc value component comes from an ndvdual portfolo return that s correlated to the asset traded n our economy. If the portfolos of traders are correlated (e.g., they contan the same assets), then the trader s dosyncratc values are also correlated. When the dosyncratc component domnates the common value, n the sense that the spread of correlatons are larger than the average level of correlatons, 2 over-the-counter markets are more attractve to traders n terms 1 Other frctons consdered n the lterature (e.g. search costs, a chance that blateral trades fal, bd-ask spreads by dealers, etc.) can ncreases ncentves of traders to choose centralzed markets over over-the-counter markets, but the results n ths paper stll hold quanttatvely. 2 Suppose that ρ,j denotes the correlaton between ndvdual asset values of two traders, j. A trader s value s correlated all other traders {ρ,j} j. The varance of these correlaton represents the dosyncratc component n trader s asset value, whle the average of them represents the common component. See Secton 2. 2

3 of both learnng and lqudty. Equlbrum prce aggregates traders prvate nformaton n a form of a weghted average of sgnals, whch mples that t aggregates out dosyncratc components n centralzed markets. When a trader s value reles more on the dosyncratc value (or the common value), he learns more on ths component n an over-the-counter market (n a centralzed market). On the other hand, lqudty ncentve s ndependent of domnant components. Over-the-counter market allows a trader to choose a counterparty who would more lkely have an opposte tradng needs (.e., more negatvely correlated asset values), so that he has a lower prce mpact, whle the centralzed prce mtgates the dfference between values of buyers and sellers. Ths effect s strengthened when traders asset values are nterdependent through the dosyncratc values rather than the common component. Each trader receves a prvate sgnal about value before any market opens. Sgnal precson can be heterogeneous among traders; thus, traders dffers n the learnng needs and value of nformaton. Traders wth low nformaton precson (.e. unnformed traders) beneft from an over-the-counter market because t helps them learn counterpartes nformaton. The beneft from learnng encourages any, nformed or unnformed, traders to partcpate n the over-the-counter market. On the other hand, the over-the-counter market dscourages traders wth large lqudty needs (.e., large endowments) to partcpate, snce t decreases the lkelhood of meetng a counterparty to trade wth and also may ncrease prce mpact. The trade-off between nformaton and lqudty ncentves n over-the-counter markets creates a cutoff level on nformaton precson. If a trader s nformaton precson s hgher than the cutoff level, the lqudty ncentve domnates and he chooses to trade n centralzed market. Wth a precson lower than the cutoff, the learnng ncentve domnates and traders choose the over-the-counter market. Ths result may seem contrary to the conventonal belef that nformed traders tend to trade n over-the-counter trades for keepng prvacy and for the beneft of nformaton advantage at later perods, but ths paper consders statc markets n whch the dynamc ncentve of keepng prvacy does not exst. The effects n ths paper are ndeed complementary to those n dynamc markets for nformed traders. In statc models, or wth short-lved nformaton n dynamc models, nformed traders choose the centralzed market where prvate nformaton can be aggregated out n equlbrum prce so that traders beneft from more precse nformaton n a perod. Ths paper dentfes market structures that are formed n equlbrum by traders choces between tradng venues: the centralzed market, an over-the-counter market, or both markets coexstng. I show that an over-the-counter market opens when the sze of centralzed market s small, the asset values are closer to dosyncratc than common, and prvate nformaton of traders s less precse. Many fnancal dervatves such as forwards contracts, nterest rate swaps, or equty or credt lnked securtes are traded n over-the-counter markets, even though ther tradng volumes (lqudty) are large. These products are often held by traders untl, or close to, the maturty, whch suggests that the purpose of tradng can be hedgng of traders outsde portfolos. Ths paper suggests that dosyncratcally valued assets tend to be traded n the over-the-counter markets. On the other hand, centralzed markets attract assets traded mostly by speculators, such as stocks or bonds wth short maturty, whch are valued by future prces that are common to all traders. 3

4 Hgh-yeld bonds that has low credt rankng are often traded n the over-the-counter markets (e.g., Hendershott and Madhavan (2015)). Low past tradng volume and volatle return prevents the traders access to qualty nformaton. Moreover, t s possble to ncrease the nformaton asymmetry between nsders and other traders. Ths s consstent wth ths paper s predcton that low nformaton precson encourages traders to choose over-the-counter markets. I examne whether traders ndvdual market choce leads to an equlbrum market structure that s effcent. For the smplcty of dscusson, ths paper analyzes markets wth two nformatonal types, nformed and unnformed, and symmetrc nterdependence of asset values.if no centralzed market s avalable for traders to enter, each trader faces a trade-off between learnng and lqudty n the choce of counterparty n the over-the-counter market. Namely, trades wth nformed counterpartes mprove learnng, whle trades wth unnformed counterpartes provde better lqudty. Dependng on whch ncentve domnates, one of two structures of over-the-counter markets s formed. When a same ncentve domnates for all traders, for example, when the learnng ncentve s stronger than the lqudty ncentve, all traders prefer to trade wth nformed counterpartes. Knowng that he cannot be matched wth nformed counterparty, unnformed traders choose to trade wth unnformed counterpartes (.e. same-type matchng). On the other hand, f the domnant ncentve s dfferent for dfferent types, nformed and unnformed traders choose to trade wth each other (.e. cross-type matchng). Wth an avalable centralzed market, however, a blateral trade between these two types does not occur n equlbrum. When the learnng ncentve domnates the lqudty ncentve for an nformed trader, he s better off tradng n the centralzed market that provdes an even lower prce mpact than n the over-the-counter tradng wth unnformed counterpartes. Wth only unnformed traders enterng n the over-the-counter market, nformaton s not transmtted between the nformed and unnformed traders and the over-the-counter market aggravates the nformaton asymmetry n the economy. Related Lterature: There s a growng lterature provdng theoretcal models wth overthe-counter markets. How lqudty affects traders behavor and effcency are studed n the lterature (e.g. Duffe, Garleanu, and Pedersen (2005), Vayanos and Well (2008), Well (2008), Atkeson, Esfeldt, and Well (2014)). Other studes show how prvate nformaton s aggregated n the over-the-counter markets (e.g. Duffe, Malamud, and Manso (2014), Maurn (2015), Babus and Kondor (2016), Back, Lu, and Tegua (2016)). In addton to these papers focusng on over-thecounter markets, several papers compare these two tradng venues n terms of welfare or ndvdual proft. Observng that the welfare domnance of over-the-counter markets or centralzed markets s ambguous, Acharya and Bsn (2010), Malamud and Rostek (2014), Duffe and Wang (2016), Glode and Opp (2017), and other studes consder determnants to favor ether over-the-counter or centralzed tradng: such as default, search frcton, prce mpacts, or nformaton asymmetry between sellers and buyers. Praz (2015) ntroduces a market structure n whch a centralzed (lqud) and over-the-counter (llqud) markets co-exst and characterzes tradng behavors and equlbrum prces. In hs model, traders are assumed to partcpate n both markets, whle ths paper consders traders entry problem, based on whch markets are domnant n ther ndvdual utltes. 4

5 My model s close to Babus and Parlatore (2017). The authors examne over-the-counter networks between dealers and nvestors, when tradng s based on a unform-prce double aucton, as n ths paper. Smlar to mne, ther paper show that the nterdependence of traders asset values s a key determnants n the comparson between over-the-counter and centralzed markets. Dealers prce mpacts create a trade-off between tradng n an nter-dealer market and a local market wth customers and determnes ether domnance of over-the-counter or centralzed markets n dealer s utltes. My contrbuton, compared to ther paper, s ntroducng a beneft of learnng from prce. An arbtrary correlaton structure for traders values allows mperfect nformaton aggregaton by equlbrum prce (see Vves (2011), Rostek and Weretka (2012), and Rostek and Yoon (2017)), whle ther paper focuses on ndependent values so that the learnng beneft s absent. Furthermore, Babus and Parlatore (2017) consder traders behavor for a gven over-the-counter market. Equlbrum market structures are endogenously formed by traders market choce between over-the-counter and centralzed markets n ths paper. Another strand of the lterature endogenzes the over-the-counter market structure. Some papers consder traders counterparty choce, who they want to trade wth, when an over-the-counter market s the only avalable market. Golosov, Lorenzon, and Tsyvnsk (2014) consder the jont effects of learnng and lqudty n the choce of counterpartes n over-the-counter markets. Chang and Zhang (2016) show that traders heterogeneous preferences endogenously form core-perphery networks n equlbrum and those who have low rsk exposure serve as ntermedares. The coreperphery networks are also derved n other papers (e.g. Farbood (2015), Farbood, Jarosch, and Shmer (2017), Hugonner, Lester, and Well (2016), Wang (2017)). In addton to these studes for the counterparty choces, Atkeson, Esfeldt, and Well (2014) and Babus and Hu (2016) consder entry and ext problems for over-the-counter markets. Smlar to these papers, over-the-counter markets are endogenously formed n ths paper. Traders heterogenety s the key determnant for the resultng over-the-counter structures, n ther nformaton precson (as n Golosov, Lorenzon, and Tsyvnsk (2014)) and n ther valuatons (as n Chang and Zhang (2016)). The objectve n ths paper s to understand endogenous market structures when centralzed and over-the-counter markets are both avalable. The choce between the centralzed and over-thecounter markets, when they can co-ext, has been explored by several authors. Krlenko (2000) and Vswanathan and Wang (2002) consder a choce between tradng venues for dealers by non-strategc agents (e.g. desgners, authortes, consumers) maxmzng proft or effcency of the market. Bolton, Santos, and Schenkman (2015) consder an entry problem of an nformed seller to ether market: a centralzed (organzed) market or an over-the-counter market wth unnformed dealers. In ths paper, all buyers and sellers, nformed and unnformed strategcally choose a tradng venue. Ths lets us explore the stablty of market structures: no trader has an ncentve to change hs market choce gven chances. Many emprcal studes (e.g. Bessembnder and Kaufman (1997), Conrad, Johnson, and Wahal (2003), Barclay, Hendershott, and McCormck (2003), Bas and Green (2007), Hendershott and Madhavan (2015), Attanas, Centorrno, Moscat (2016)) dentfy determnants that nfluence welfare n gven markets and forms of market structures. Bas and Green (2007) show that transacton 5

6 costs and lqudty are key determnants on why most trades for bonds are held n over-the-counter markets, whle Attanas, Centorrno, Moscat (2016) explores the effects of lack of nformaton n the over-the-counter market on effcency. 2 Model In a statc economy, two tradng venues open smultaneously: a centralzed market where all traders bds are executed at a sngle market prce and an over-the-counter market where a par of traders are matched and they trade blaterally at a par-specfc prce. Fgure 1 summarzes the economy. Before the markets are open (enterng perod t = 0), traders can choose whch market they would trade n. If a trader choose the over-the-counter market, then he also chooses a counterparty he would lke to trade wth. The market choce and blateral matchng are done at the end of perod t = 0. Traders can trade only once, n one market and wth one counterparty f they are n the overthe-counter market. At tradng perod t = 1, two assets a rsky asset (asset) and a rskfree asset (numerare) are traded n both markets. The assets are perfectly dvsble. Traders submt ther demands to the market they chose at the enterng perod, and each market cleared ndependently. I descrbe the detals below, ncludng (1) traders and payoffs, (2) nformaton, (3) structures of the markets, (4) strateges, and (5) equlbrum. Fgure 1: Tmng of the economy Strategc Traders: There are I < strategc traders. Each of them has ntal endowment (w 0, q 0 ), where w 0 and q 0 are the amounts of numerare and asset, respectvely. If a trader holds (w, q ) after tradng n the market he partcpates n, hs ex-post utlty s defne as ( ) u (w, q ) = exp µ(w + θ q ). Here, µ > 0 s a constant absolute rsk-averson (CARA) that s common for all traders, and θ s the ndvdual value of the rsky asset for trader that s randomly drawn from θ N (E[θ ], σ 2 θ ). 6

7 The condtonal expected utlty s equvalent to the mean-varance utlty: ( E[u (w, q ) ] = exp µ ( w + E[θ ]q µ 2 V ar(θ )q 2 ) ). (1) In CARA-Gaussan settngs, the condtonal varance V (θ ) s a non-random constant ndependent of q, w or any realzaton n the markets, whle the condtonal expectaton E[θ ] s a random varable that s determned by condtonng varables. Therefore, the expected utlty (1) s equvalent to a quadratc utlty wth the coeffcent on the frst order term beng random, whch represented traders expectaton on asset value. v (w, q ) 1 µ log( E[u (w, q ) ]) = w + E[θ ]q µ 2 V ar(θ )q 2. Traders values (θ ) I are nterdependent. The correlaton matrx for (θ ) s denoted by Σ = (ρ j ),j I wth ρ j Corr(θ, θ j ). The model allows any arbtrary Gaussan structure for traders asset values. 3 The nterdependence of (θ ) s nterpreted as a combnaton of a common value component, whch comes from the future asset return n the market, and an dosyncratc value component, whch comes from ndvdual portfolo return (e.g. securtes, assets, goods, producton whose returns are correlated to the asset n the market). The dosyncratc value component s assumed to be ndependent to the common value component, but t can be correlated to other traders dosyncratc value components. 4 Example 1 shows how the common value and dosyncratc value components determne Σ n a smplest but ntutve settng. Example 1 (Symmetrc Interdependence n Asset Values) There are two groups of strategc traders buyers and sellers wth equal group szes. Each trader has ndvdual asset value that s decomposed nto two ndependent random varables: for a gven common value v c and dosyncratc value v, a trader s asset value s θ = v c + v p,. Here, suppose that V ar(v c ) = ρ 0+ρ 2 σθ 2, V ar(v p,) = σθ 2 V ar(v c) = 2 (ρ 0+ρ) 2 σθ 2, and corr(v p,, v p,j ) = ρ 0 ρ 2 (ρ 0 ρ) f both and j are sellers or both are buyers, and corr(v p,, v p,j ) = ρ 0 ρ 2 (ρ 0 ρ) f one s buyer and the other s seller. Then, the correlaton matrx Σ = (corr(θ, θ j )) j s as follows: Σ = [ ρ 0 1 (I/2) (I/2) ρ1 (I/2) (I/2) ρ1 (I/2) (I/2) ρ 0 1 (I/2) (I/2) ] + (1 ρ 0 )Id. 3 Rostek and Yoon (2017) show the exstence and unqueness of equlbrum n markets wth arbtrary Gaussan structure. 4 Ths model wth arbtrary nterdependence of asset values can ncorporates varous nterpretatons and settngs. For nstance, as another nterpretaton of common and dosyncratc value components: Each trader gets a random ntal endowment before he enters the market, that can be correlated wth other traders endowments. Ths prvate endowment forms hs dosyncratc value component. When the market has more tradng rounds (τ > t = 1) after the rounds we are consderng n the model (t = 1), the asset value at t s determned by the margnal value functon, whch s a lnear combnaton of ndvdual asset return and future market prces. Hence, traders valuaton s nterpreted as a combnaton of dosyncratc value by holdng the asset and common value by sellng t at market prce. 7

8 If two traders have postvely correlated values, Corr( θ, θ j ) = ρ 0 > 0, then both of them want to ether buy or sell. If ther values are negatvely correlated, Corr( θ, θ j ) = ρ < 0, then they are wllng to hold opposte postons, one buyer and one seller. Wth ths parameterzaton, we say that traders valuaton are dependent more on the common value when ρ 0+ρ 2 s larger. Furthermore, traders dosyncratc value components are more correlated when consder ths example for further analyss n Secton 4. ρ 0 ρ 2 (ρ 0 +ρ) s larger. We wll Informaton: Each strategc trader gets a prvate nformaton (sgnal) on hs own valuaton, s = θ + ε wth an ndependent nose ε N (0, σ 2,ε ). The nformaton precson φ 1/σ 2,ε can dffer across traders, and t determnes the traders nformatonal type. Traders types and pror dstrbuton of asset values and sgnals are common knowledge. Centralzed Market (CM): The centralzed exchange s desgned as a unform-prce double aucton that s a canoncal model for markets. A strategc trader, who enters the centralzed exchange wth endowment (w 0, q 0 ), submts hs demand schedule q (p) : R R as a contnuous functon of prce. There exsts L traders, called lqudty traders, n the centralzed market who are not gven the market choce. Lqudty traders strategcally submt ther demand schedule q lq (p) as well as the traders who can choose a market, 5 based on ther own prvate nformaton. smplcty, precson of prvate nformaton for lqudty traders are homogeneous, σlq,ɛ 2 (0, ]. After all demands are collected, the centralzed market s cleared at a prce of whch the total demand s equal to zero; p such that I q (p ) + j L q lq,j(p ) = 0. For The equlbrum allocaton s determned by the demand schedule traders submtted, q = q 0 + q = q 0 + q (p ) and w = w 0 p q. Over-the-Counter Market (OTC): In the over-the-counter market, each trader chooses a counterparty based on ther types, nformaton precson and correlaton. If the choce s mutual between two traders, then they are matched as a par. If the counterparty choce s not mutual, then traders are not gven a tradng opportunty and the market ends. If there are more than one trader for the chosen type of counterparty, a trader of the type s randomly matched. In a matched par, two traders smultaneously submt ther demand schedules q (p) as functons of prce p. The equlbrum prce n ths blateral tradng s determned as same as n the centralzed market: the prce p solves the market clearng condton q (p ) + q j (p ) = 0. If an equlbrum prce does not exst, then there s no trade and the over-the-counter market ends wthout any further trade. There s no lqudty trader n the over-the-counter blateral trades. Strateges: At t = 0, each strategc trader I chooses a market where he enters, m {OT C, CM} and a type of counterparty τ who he would trade wth unpon enterng the over-thecounter exchange, m = OT C. When the market choce of a trader s m = CM, we wll notate τ = for the convenence. At t = 1, the trader chooses hs demand functon q ( : m, τ ) n market (m, τ ). Therefore, the strategy profle of trader s {(m, τ ), q ( : m, τ )}. A lqudty trader 5 The exstence of lqudty traders make the centralzed exchange more lqud than the over-the-counter market, ndependently of strategc traders market choce. In later secton, I show that lqudty traders are those who do not observe other traders types so that they optmally choose to stay n the centralzed exchange. 8

9 j L n the centralzed market has a strategy {(CM, ), q j ( ; CM, )} snce she cannot enter the over-the-counter market. Equlbrum: Defnton 1 provdes two condtons for equlbrum: Bayesan Nash equlbrum n each market and no ncentve to devate from market and counterparty choces. Defnton 1 (Equlbrum) For each trader I, () traders optmal bd schedules {q ( : m, τ )}, such that, max E[u (w 0 pq, q q 0 + q ) s, p] = max E[ exp ( µ(w + θ q ) ) s, p], p R, q characterze a Bayesan Nash equlbrum n each market. () No trader has a strctly postve ncentve to devate from the market and counterparty. When E[u (m, τ )] denotes the expected utlty wth (m, τ ) for gven equlbrum dstrbuton of traders n both markets, the optmal market and counterparty choce (m, τ ) satsfes E[u (m, τ )] E[u (m, τ )], (m, τ ) (m, τ ),. The followng sectons characterze equlbrum defned n Defnton 1: Equlbrum bd strateges and outcomes n Bayesan Nash equlbrum for a gven market - part () - s characterzed n Secton 3. The characterzaton allows us to develope comparatve statcs on traders expected utltes over market, asset, or traders characterstcs. Secton 4 shows equlbrum market structures that s endogenously formed by traders market and counterparty choce - part () - and analyze nfluences of the characterstcs n traders ncentves to choose over-the-counter markets and thus n market structure. Secton?? provdes effcency propertes n equlbrum. 3 Equlbrum n a Market: Learnng and Lqudty Incentves Ths secton shows traders bddng strateges n a gven market and for a gven dstrbuton on partcpants types. Equlbrum characterzaton n a market provdes traders expected utlty n equlbrum and how the utlty depends on the characterstcs of market, asset, or traders. Such comparatve statcs analyzes traders ncentves to choose one market over the other. Suppose that there are I traders n a market wth a correlaton structure of asset values Σ and a nformaton precson {φ = 1/σ,ɛ 2 }. Each trader optmzes hs expected utlty (1). The frst order condton s characterzed as follows: E[θ s, p] µv ar(θ s, p)q p λ q = 0, p R, (2) where λ p/ q s prce mpact that represents the change of prce when trader ncreases hs demand by one unt. A larger prce mpact mples that each unt of a trader s demand ncreases the equlbrum prce further so that a trader places a smaller demand wth hgher prce mpact. Such 9

10 demand reducton by prce mpact captures market llqudty that s endogenously determned by traders strateges. A compettve market wth nfntely many traders s perfectly lqud n that the prce mpact s zero. In prmtves, when there are fewer traders n the market or when traders are more senstve to prce changes due to nference or rsk-averson, the market becomes less lqud. In a trader frst-order condton (2), he takes an expectaton of asset value condtonng on the equlbrum prce p as well as hs own prvate nformaton. A trader chooses hs bd at each potental realzaton of prce, and thus, hs behavor ncorporates the nformaton revealed by the prce as f he observes the prce. Therefore, even n the statc model, traders learnng on ther asset values occurs mplctly by the schedule bddng. We do not mpose a value of such learnng or a value of mproved nformaton. The beneft or cost of learnng nformaton from the market s valued n terms of equlbrum utlty change. Endogenzng learnng and llqudty n ths model allows us to consder a market choce wthout any assumpton on exogenous frctons. Proposton 1 states three equlbrum condtons for a gven market wth I traders whose asset values are correlated by Σ and whose nformaton precsons are {φ } : a trader s strategy for a gven prce mpact (llqudty) and nference on asset values (learnng), the consstency condton for equlbrum prce mpact, and nference coeffcents by equlbrum prce dstrbuton. In general, there s no closed-form characterzaton for equlbrum, outsde of models wth symmetrc correlaton and symmetrc precson. A lnear Bayesan Nash equlbrum unquely exsts under condtons. Postve prce mpacts for all traders are mposed, whch s equvalent to the submtted bddng functon should be strctly decreasng n prce. Proposton 1 (Equlbrum Representaton n a Market) In a market, a profle of demand schedules {q ( )} s a lnear Bayesan Nash equlbrum (hereafter, equlbrum) f and only f () a demand schedule q ( : λ ) maxmzng trader s utlty s q = where E[θ s, p] = c θ, E[θ ] + c s, s + c p, p, () prce mpacts satsfy the consstency condton ( λ = E[θ s, p] p = c θ,e[θ ] + c s, s (1 c p, )p, µv ar(θ s, p) + λ µv ar(θ s, p) + λ j q j ( ) ) 1 ( = p j 1 c p,j µ V ar(θ j s j, p) + λ j ) 1,, (3) () nference coeffcents {c θ,, c s,, c p, } n E[θ s, p] and condtonal varance V ar(θ s, p) are determned by the Projecton Theorem, wth equlbrum prce dstrbuton followng p = ( 1 c p, µv ar(θ s, p) + λ ) 1 c θ, E[θ ] + c s, s µv ar(θ s, p) + λ. A trader ndrect utlty n equlbrum can be wrtten as a functon of hs prce mpact λ, expected asset value E[θ s, p] condtonng on (s, p), and condtonal varable V ar(θ s, p). Ex- 10

11 ante utlty of trader n a gve market s [ ( E[u ] = E exp µv ar(θ s, p) + 2λ )] µ( 2(µV ar(θ s, p) + λ ) 2 (E[θ s, p] p) 2 ). Consderng that the dfference of ndvdual expected asset value from equlbrum prce, (E[θ s, p] p), follows a normal dstrbuton that s generated by Gaussan structure of {θ, s }, the expectaton on the rght hand sde of the above equaton s n form of the moment generatng functon for χ 2 k dstrbuton. It provdes an explct formula for the ex-ante ndrect utlty: ( E[u ] = λ V ar(e[θ s, p] p) ) 1/2,. (4) (1 + λ ) }{{ 2 V ar(θ s, p) }}{{} lqudty effect learnng effect Here, λ (µv ar(θ s, p)) 1 λ s a normalzed prce mpact by the quadratc coeffcent µv ar(θ s, p) of trader s mean-varance utlty. Trader s ex-ante utlty E[u ], or a suffcent statstc τ (E[u ] 2 1), can be decomposed nto two parts: the value of lqudty and learnng. The beneft of lqudty s captured by the term (1 + 2 λ )/(1 + λ ) 2 = 1 ( λ /(1 + λ )) 2. Recall that trader s demand s reduced by a fracton λ /(1 + λ ). In that, q = ( λ ) E[θ s, p] p ( 1 µv ar(θ s, p) + λ µv ar(θ s, p) = 1 λ ) 1 + λ q (p), where q (p) s the demand of trader n a compettve market for a gven prce p. The demand reducton lowers utlty wth the same fracton. The lqudty beneft n utlty terms, called lqudty effect, s ncreasng n the normalzed prce mpact λ. On the other hand, the utlty (4) contans a term V ar(e[θ s, p] p)/v ar(θ s, p) that captures a beneft of learnng from prce and prvate nformaton. Equlbrum prce aggregates all market partcpants prvate nformaton on asset values. By condtonng on prce, traders learn the aggregated nformaton. It decreases the rsk n uncertanty of the trader s own value θ and thus ncreases hs expected utlty through the term V ar(θ s, p). In addton, the prce reveals nformaton on other traders asset values, that determnes net surplus of buyng a unt of asset, E[θ s, p] p. Such nformaton on the future surplus nfluences the trader s utlty through V ar(e[θ s, p] p). The total beneft of learnng trader s own and others valuaton, called learnng effect, s ncorporated n a form of rato n the expected utlty (4). What are the key determnants of traders utltes? Three characterstcs can be consders n ths model: market sze (market characterstc), nterdependence of traders asset values (asset), and precson of prvate nformaton (traders). Each characterstcs affects learnng and lqudty n traders utltes. Example 2 shows the nfluences of three characterstcs, wth symmetrc nterdependent asset values and symmetrc nformaton precsons across traders. Example 2 (Symmetrc Interdependence and Precson) Consder a market wth I traders. All traders has a symmetrc nformaton precson φ = 1/σ 2,ε φ and has a symmetrc average 11

12 correlaton to the resdual market ρ = 1 I 1 j ρ j ρ for all. 6 Each trader s optmal schedule and equlbrum prce are q = p = E[θ s, p] p µv ar(θ s, p) + λ = c θe[θ ] + c s s (1 c p )p,, µv ar(θ s, p) + λ 1 1 (c θ E[θ] + c s s ) = 1 (c θ E[θ] + c s s). 1 c p I 1 c p Here, the lqudty and learnng effects n trader s ex-ante utlty are characterzed wth the prce mpact and condtonal varances: λ = λ µv ar(θ s, p) = (1 + (I 1) ρ)(1 + σ 2 ρ) (I 2)(1 + σ 2 ) + ((I 1) (I 1)(1 + σ 2 )) ρ (I 1)(I 2) ρ 2, V ar(θ s, p) = (1 + σ2 ) + (I 2) ρ (I 1) ρ 2 (1 + σ 2 + (I 1) ρ)(1 + σ 2 ρ) σ2 ε; V ar(e[θ s, p] p) = Trader gets the ex-ante utlty E[u ] = (1 + τ ) 2 where τ = λ V ar(e[θ s, p] p) (1 + λ. ) 2 V ar(θ s, p) (1 ρ)2 1 + σ 2 ρ I 1 σθ 2 I. The lqudty effect on the utlty s captured by the term 1+2 λ. Wth ths closed-form soluton (1+ λ ) 2 of nference parameters and prce mpact, λ ( (1 + λ ) = 1 ( λ λ ) 2 (1 + σ 2 ρ)(1 + (I 1) ρ) ) 2. = 1 (I 1)(1 ρ)(1 + σ 2 + (I 1) ρ) The lqudty term s ncreasng as I ncreases or ρ decreases. Larger market sze and/or more negatve correlaton wth others on average results n more lqudty and thus hgher utlty for traders. When the nformaton precson φ = 1/σ 2 ncreases, the endogenous lqudty of the market ncreases f ρ > 0, and decreases f ρ < 0. The effect of learnng from the prce on utlty s measured by V ar(e[θ s, p] p) V ar(θ s, p) = I 1 I (1 ρ) 2 (1 + σ 2 + (I 1) ρ) σ 2 ((1 + σ 2 ) + (I 2) ρ (I 1) ρ 2 ), whch s ncreasng n the nformaton precson φ = 1/σ 2. The effect of average correlaton ρ s ambguous. If (1 + σ 2 ) + (2I 3)(1 + σ 2 ) ρ + (I 3)(I 1) ρ 2 (I 1) 2 ρ 3 > 0, the utlty component due to learnng s decreasng n ρ. Otherwse, t s ncreasng n the average correlaton ρ. The example shows how three key characterstcs affect the ex-ante utlty of each trader, through lqudty and learnng. The same ntuton can be appled to gemeral models wth asymmetrc nterdependent structure for asset values and asymmetrc nformaton precson. Proposton 2 states 6 Rostek and Weretka (2012) call ths correlaton structure an equcommonal model and derve a closed form characteraton of equlbrum. 12

13 effects of each of three characterstcs on traders expected utltes, when the other characterstcs are fxed. Proposton 2 (Benefts of Learnng and Lqudty) In a suffcently symmetrc market, subject to exstence, the ex-ante utlty of a trader ncreases as () asset values are more negatvely correlated to prce,.e. corr(θ, p) are more negatve; or () the number of traders n market s larger so that the prce mpact s smaller,.e. λ s smaller. The utlty s non-monotone n the average nformaton precson, such that () an nformaton precson φ (0, ] of other traders maxmzes trader s utlty. From Proposton 2 (), when equlbrum prce s more negatvely correlated to hs asset valuaton, traders utlty ncreases n terms of both learnng and lqudty. Prce provdes new nformaton that s not captured n trader s prvate nformaton, and wth larger correlaton n the absolute sense mples that the nformaton s more relevant to hs asset value. Ths learnng effect s captured by the decrease of condtonal varance V (θ s, p). The correlaton structure also affects the lqudty through the endogenous prce mpacts λ. The prce mpact s characterzed by the slope of resdual supply curve, λ = ( j q j( )/ p ) 1, that s an nverse of aggregate reacton of other traders when prce ncreases. Wth more negatve correlatons, trader j would reply on prce for hs nference, n the sense that c p,j s more negatve. It makes hs demands more elastc to prce change and thus trader s prce mpact smaller. The effects of the number of traders (part ()) on learnng and lqudty have been studed n lterature. In a suffcently symmetrc market, wth more traders partcpatng n the market, prce reveals more accurate nformaton. Moreover, n larger markets, prce mpact can be smaller when other characterstcs are fxed (See Rostek and Weretka (2012)). From the arguments, more negatve correlatons between traders asset values and/or more number of traders n the market are benefcal to both learnng and lqudty. Informaton precson has an ambguous nfluence on traders expected utltes. Frst, t s worth to remark that Proposton 2 () states the effect of other traders precson rather than a trader s own. Wth symmetrc nformaton precson, the effect of the traders own precson cannot be analyzed separately from the effect of other traders precson that s aggregated n equlbrum prce. The trader s own precson represents hs nnate needs for learnng. It determnes how much the trader values learnng from the market. Intutvely, f a trader has a more precse nformaton, hs needs for learnng new nformaton s smaller. Others precson measures how much the trader can learn from the market (.e. mproved nformaton by condtonng on prce). When we fx the correlaton between a trader s asset value and the aggregate value n the market (.e. fx cov(s, avg(s j ))), the value of learnng ncreases as the trader s own nformaton precson s lower or as the (weghted) average of other traders nformaton precson s hgher. On the other hand, the prce mpact ncreases, and thus, the lqudty decreases, as the value of learnng ncreases. It creates a trade-off between learnng and lqudty when the precson of nformaton from the prce changes. 13

14 Fgure 2: Change of lqudty and learnng wth respect to other traders nformaton precson The trade-off between learnng and lqudty over traders nformaton precson s shown n Fgure 2. Suppose that the average correlaton and the number of traders n the market are fxed. A trader has a nformaton precson φ = 1/σ1 2 = 1/0.25 = 4. The lqudty effect and the learnng effect n hs expected utlty (4) are shown n each graph n Fgure 2. Two effects are monotone over the other traders nformaton precson avg(φ j ) j = avg(1/σj 2) j, and show the trade-off. It results n the total effect of other traders nformaton precson on trader s utlty s non-monotone. The utlty s maxmzed at a certan precson φ avg(φ j ) j of other traders, and t can be at φ < or φ = dependng on trader s own precson φ. In that, f trader s own precson s hgh, then φ < because of the trade-off. If hs precson s suffcently low, the learnng effect domnates lqudty effect, so that hs utlty s monotoncally ncreasng n others precson. These comparatve statcs n a gve market provdes some predctons on traders market and counterparty choce: whch types of traders would enter an over-the-counter market dependng on the nterdependence of asset values and the precson of ther nformaton. The ambguty n nfluence of nformaton precson on traders utltes wll be consdered as a key determnants of traders market and counterparty choces. 4 Equlbrum Market Structure Traders ndvdual choce for markets and counterpartes forms a dstrbuton of traders types n centralzed and over-the-counter market and matchng n the over-the-counter market, whch s called a market structure. There are three types of market structure: only centralzed market opens, only over-the-counter market opens, and two markets co-exst. To gather some ntutons on endogenous market structures, I frst consder the symmetrc model n Example 2 wth a compettve centralzed market (.e. perfectly lqud market wth λ = 0 for all ). Assumng the compettve centralzed market maxmzes the dfference n market szes. The example shows that traders can be attracted to the over-the-counter market, even n such cases, dependng on asset and trader characterstcs. 14

15 Example 2 - Contnued Equaton (4) provdes the explct formula of expected utlty when there are I symmetrc traders. The utlty at the centralzed market s derved by takng I to nfnty, whle the utlty at a blateral trades n the over-the-counter market s by settng I = 2. Wth these ex-ante utltes n two exchanges, trader chooses whch exchange he wants to enter to. Under the equlbrum exstence, the necessary and suffcent condton for hm to enter the over-the-counter exchange s as follows: E[u CM ] < E[u OT C ] τ CM = 1 ρ CM σ 2 < τ OT C = 2ρ OT C 1 + σ 2 + ρ OT C where ρ CM s the average correlaton n the centralzed market and ρ OT C s the correlaton between two traders who are matched n the over-the-counter market (Example 1). ρ CM = 0, ρ OT C = 1 (no common value; correlated dosyncratc). The nequalty can be wrtten by 1 < 4. It s satsfed f and only f σ 2 > 2 σ 2 2+σ 2 3. It mples that, when the nterdependence of asset values are dosyncratc, traders who has low nformaton precson φ = 1/σ 2 < 3 2 enter the over-the-counter market even when the centralzed market s compettve. ρ CM = 0, ρ OT C = 0 (ndependent prvate value). The nequalty becomes 1 < 0, whch never σ 2 holds for any σ 2 0. Independent prvate value structure mples that the market has no valuable nformaton to any trader (no learnng occurs), so that traders choose the centralzed market for the beneft of lqudty. ρ CM = ɛ, ρ OT C = 1 + 2ɛ (wth both common and dosyncratc values). 1 ɛ 2(1 2ɛ) σ 2 < σ 2 + 2ɛ ɛ < 2 + 3σ2 (2 + 3σ 2 ) 2 8 ; or 4 2ɛ(1 ɛ) 1 3ɛ < σ 2 Traders prefer to trade n the over-the-counter market f the common value component n asset values s suffcently small or nformaton precson s suffcently low. When the centralzed exchange s compettve, the lqudty ncentve strongly derves traders to avod hgher prce mpacts n over-the-counter blateral trades. Hence, a partcpaton to over-the-counter market occurs only when beneft of learnng from the market s hgh enough to domnate the loss from llqudty. When the aggregated correlaton ρ CM = 1 I 1 j ρ j satsfes ρ CM < ρ, the prce nformatveness s hgher n the over-the-counter exchange and thus the beneft from learnng s hgher. We wll show that the over-the-counter market s more attractve to certan types of traders when nformaton accuracy s heterogeneous across traders n followng sectons. Secton 4.1 consders a subgame where traders who are n the over-the-counter market choose an nformatonal type of hs counterparty, and then, Secton 4.2 solves the whole problem and the endogenously determned market structure. 15

16 4.1 Choce of Counterparty n Over-the-Counter Market In the over-the-counter market, each trader s gven an opportunty to choose hs counterparty based on nformatonal type (nformed/unnformed) and tradng type (buyer/seller). The tradng wll occur only when the chosen counterparty also choose hs type. chooses the counterparty by trader, whle hs counterparty by trader j. We denote the trader who Consder when two traders and j can be successfully matched. Frst, no matter of nformaton accuracy, there s no matchng between two players who have postvely correlated asset values. In that, f Corr( θ, θ j ) = ρ 0 > 0, traders optmal bd functon becomes nelastc so that there s no trade. Therefore, no trader chooses the same tradng type as hs counterparty. On the other hand, the choce for counterparty s nformatonal type s not trval. In an analogous argument wth Proposton 2, Corollary 1 show the determnant of the expected utlty n a blateral trade, E[u ] = µ + 2λ 2(µ + λ ) 2 }{{} lqudty V ar (E[θ s, p] p) : }{{} nformaton effect the correlaton between two trader corr( θ, θ j ) = ρ < 0 and nformaton accuracy (σ, σ j ). Corollary 1 (Learnng and Lqudty n the OTC Market) Upon traders partcpaton n the over-the-counter market, as the counterparty s nformaton precson ncreases, () the lqudty ncentves decreases,.e. µ+λ 2(µ+λ ) 2 decreases n (1/σj 2 ); and () the learnng ncentve ncreases,.e. V ar (E[θ s, p ] p ) ncreases n (1/σ 2 j ). Lqudty ncentve domnates learnng ncentve, f and only f the trader s own accuracy (1/σ 2 ) s suffcently hgh. As we can see n Corollary 1, the unnformed trader s better off than the nformed trader n a blateral over-the-counter market. It s because the prce n blateral trade s fully revealng about the counterparty s prvate nformaton, so that t removes nformatonal advantage of nformed trader. Furthermore, learnng from the prce s more valuable for unnformed trader, whch leads hm to be more senstve to prce change. The trader who chooses an unnformed counterparty faces a hgher prce mpact. We conlude that a trader who has a suffcently accurate prvate nformaton prefers an unnformed counterparty n the beneft of smaller lqudty frcton, whle a trader who has less accurate prvate nformaton prefers an nformed counterparty for learnng beneft. The cutoff value of hs own accuracy wth whch a trader s ndfferent between nformed and unnformed counterpartes are dependent on the set of accuracy {σ k } k=i,u. Wth two nformatonal types, the over-the-counter matchng can be formed n two ways: sametype matchng where traders are matched wth a trader wth the same type, and cross-type matchng where nformed and unnformed traders are matched to each other. Fgure 3 presents regons of {σ I, σu 2 } for the same-type and cross-type matchng n equlbrum. Frst, let us consder the case where nformed trader has suffcently hgh accuracy (small σ I ) and unnformed trader has 16

17 Fgure 3: Equlbrum matchng n OTC subgame: σθ 2 = 1, ρ = 0.5 suffcently low accuracy (large σ U ). Both types of traders choose to trade wth the opposte type of counterparty, wth a dfferent ncentves: nformed traders get beneft from lqudty ncentve, and unnformed traders get from learnng nsentve. Hence, the cross-type matchng s equlbrum. Outsde of ths regon, equlbrum shows the same-type matchng. When the accuracy levels for both traders are hgh (small σ I and σ U ), lqudty ncentves domnates and all traders want to be matched wth an unnformed counterparty. It results n that some nformed traders may not be matched wth ther preferred counterparty. Snce there s no more chance of another match and trade, the nformed traders optmally shft ther counterparty choce to less preferred counterparty, nformed traders. Hence, the same-type matchng occurs n equlbrum. Lastly, when the accuracy s low for both types (large σ I and σ U ), all traders prefer to trade wth nformed counterparty for learnng ncentve. Wth the smlar argument wth the hgh accuracy case, unnformed traders should shft ther counterparty choce nto the second best, and equlbrum shows the same-type matchng. Proposton 4 n Appendx shows a suffcent and necessary condton for the cross-type matchng equlbrum, n terms of the set of nformaton accuracy (σ I, σ U ) and correlaton between buyers and sellers ρ. We emphasze the cross-type matchng, because t provdes nformaton transmsson from nformed to unnformed traders. The transmsson reduce the nformaton asymmetry across traders at the end of market. However, wth the same-type matchng, nformed traders share ther nformaton between themselves, not wth unnformed traders. It worsen the nformaton asymmetry. We wll dscuss the effcency n later sectons wth market choce. 4.2 Equlbrum wth Market Choce Based on the comparatve statcs on equlbrum utlty for a gven market n secton 3 and the counterparty choce n secton 4.1, we now characterze equlbrum for the whole problem consderng traders choce between over-the-counter market and centralzed market. We recall that a trader faces a counterparty n the over-the-counter market who has a more 17

18 strongly and negatvely correlated asset value than the aggregate resdual market n the centralzed market. It s because () he can chooses hs own counterpaty n the over-the-counter market based on ther correlaton and nformaton accuracy, and because () the aggregated asset value n the centralzed market ncludes both buyers and sellers, and both nformed and unnformed, so that ts correlaton to the trader s value s mtgated. A trader who chooses to enter the over-the-counter market gets suffcent beneft from ths nformaton ncentves, snce he faces hgher prce mpact n a blateral trade n over-the-counter market than n centralzed market (where suffcently many lqudty traders present). From Proposton 2, we know that these traders exsts when the asset valuatons are more relyng on the correlated prvate value rather than the common value, and ther prvate nformaton has suffcently naccurate. Proposton 3 (Informaton Sharng n OTC) Wth two nformatonal types {σ I < σ U } and wth postve common value (.e. (ρ 0 + ρ)/2 > 0), n equlbrum, the over-the-counter matchng between nformed and unnformed traders (.e. cross-type matchng) does not occur. Fgure 4 s an example of equlbrum market structure through traders market and counterparty choce. The fgure on left shows three types of equlbrum: all traders choose the centralzed market (when both σ I and σ U are small, and learnng s not suffcently valuable to nether of them); only unnformed traders choose to trade n the over-the-counter market (large σ U but small σ I ); and all traders choose the over the counter market (both types of traders has naccurate nformaton). Snce learnng ncentve s more lkely domnatng for unnformed traders, there s no equlbrum where only nformed traders enter the over-the-counter market. Fgure 4: Equlbrum Market Structure: σ 2 θ = 1, ρ = 0.5 Traders n the over-the-counter market always trade wth a same-type counterparty. The subgame equlbrum for over-the-counter matchng are shown n the fgure on rght. When an nformed trader has learnng ncentve domnated by lqudty ncentve, he would choose an unnformed counterparty f he s already n the over-the-counter market. However, wth hs own trade-off between two ncentves, t s more better off for hm to trade n the centralzed market, rather than the cross- 18

19 type blateral trade n over-the-counter market. Snce nformed traders do not enter, unnformed traders n the over-the-counter market are matched wth another unnformed. Non-exstence of matchng between nformed and unnformed s nterpreted as nformaon asymmetry worsenng by over-the-counter market. Wth a random match mechansm, nformaton can be transmtted from nformed to unnformed when they are met and thus nformaton asymmetry dsappears or dmnshes over tme. However, when traders choose ther own counterparty based on how accurate nformaton they have, nformed traders do not want to be matched wth unnformed traders. The nformaton s shared only wth each type, and the asymmetry between types ncreases after trades n our settng. It results n the nformatonal neffcency by allowng an over-the-counter market nto the economy. 5 Dscusson Connecton to Markets. I show that an over-the-counter market opens when the sze of centralzed market s small, the asset values are closer to dosyncratc than common, and prvate nformaton of traders s less precse. Many fnancal dervatves such as forwards contracts, nterest rate swaps, or equty or credt lnked securtes are traded n over-the-counter markets, even though ther tradng volumes (lqudty) are large. These products are often held by traders untl, or close to, the maturty, whch suggests that the purpose of tradng can be hedgng of traders outsde portfolos. Ths paper suggests that dosyncratcally valued assets tend to be traded n the overthe-counter markets. On the other hand, centralzed markets attract assets traded mostly by speculators, such as stocks or bonds wth short maturty, whch are valued by future prces that are common to all traders. Hgh-yeld bonds that has low credt rankng are often traded n the over-the-counter markets (e.g., Hendershott and Madhavan (2015)). Low past tradng volume and volatle return prevents the traders access to qualty nformaton. Moreover, t s possble to ncrease the nformaton asymmetry between nsders and other traders. Ths s consstent wth ths paper s predcton that low nformaton precson encourages traders to choose over-the-counter markets. Alternatve Over-the-Counter Desgns. Ths paper desgn over-the-counter markets by unform-prce double aucton, as well as centralzed markets. The beneft of desgnng centralzed markets and over-the-counter markets consstently wth the same mechansm s that the results on market choce s based on the characterstcs of market, asset, or traders, rather than the dfference between mechansms. When conventonal mechansms and/or frctons n lterature on over-the-counter markets are mposed, the results n ths paper do not change. For nstance, suppose that the over-the-counter market s operated by random matchng nstead of traders counterparty choce. Traders expected utltes n the over-the-counter market would strengthen the effect of asymmetrc nterdependence of traders asset values and heterogeneous nformaton precsons. Unnformed traders has a chance to meet an nformed traders and to learn more precse nformaton, whle nformed traders s lqudty can be mproved wth a hgher chance of meetng unnformed counterparty. It mples that mposng random matchng mechansm n the over-the- 19