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 October 5, 017 Most Recent Verson: Here 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 have prvate nformaton wth heterogeneous precson and ther values depend on a common and dosyncratc component. A trader s ncentve to choose an OTC market depends on the beneft of learnng the asset value and the potental 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. Market structures are endogenously determned by traders ndvdual market choces. Ths paper provdes comparatve statcs of endogenous market structures. When traders are asymmetrc, the OTC and centralzed markets can coexst. Furthermore, the OTC market decreases nformaton effcency by beng conducve to trade only between nformed traders. Keywords: Noncompettve tradng, Over-the-counter markets, Exchanges, Prce mpact, Lqudty, Effcency 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 1 Introducton Over-the-counter markets have been an mportant alternatve tradng venue for many assets, goods, commodtes, fnancal dervatves, and securtes. In over-the-counter markets, buyers and sellers are pared and prvately choose 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 the resultng market structure s endogenously formed by traders choces. Certan types of assets appear to be traded mostly n over-the-counter markets, whereas others have been traded n centralzed exchanges. Corporate bonds, nterest rate swaps, ndex dervatves, and many lqud fnancal products are mostly traded n over-the-counter markets, even wth ther standardzed structures and hgh volumes of trade. For some assets, the overthe-counter and centralzed markets coexst. For nstance, foregn exchange s traded n both over-the-counter spot markets and centralzed futures markets. A good porton of over-thecounter FOREX tradng s n fast venues, such as Currenex, EBS, and Reuters, n whch the foregn exchange spot prce s generally the same as the prce n centralzed futures markets. Ths paper examnes traders ncentves to choose over-the-counter markets and whether ths type of tradng venue can harm the effcency of the economy. Ths paper characterzes the endogenous market structure n whch traders play a Bayesan Nash equlbrum n the over-the-counter and centralzed tradng venues. In the frst perod t = 0, each trader chooses to enter ether a centralzed market or an over-the-counter market that opens at t = 1. In the centralzed market, all traders demand and supply schedules determne the sngle market prce. In the over-the-counter market, a par of traders are matched to be parwse stable; and then they trade blaterally at a par-specfc prce. Enterng nto the over-the-counter market, a trader observes types of others the correlaton between hs and ther asset valuatons (buyers and sellers) and ther nformaton precson (nformed and unnformed). In both the centralzed market and over-the-counter blateral trades, trade takes place n the unform-prce double aucton, n whch all traders smultaneously submt ther (net) demand schedules q (p) :p R, and the trades clear at prce p such that q (p ) = 0. Traders are uncertan about the value of a rsky asset and receve a prvate sgnal about the value before any market opens. Sgnal precson can be heterogeneous among traders. Ther asset 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 component captures the asset return or a future prce n the dynamc market. In turn, the dosyncratc value component captures an ndvdual portfolo return that s correlated to the asset traded. If traders portfolos are correlated (e.g., they

3 contan the same assets), then the trader s dosyncratc values are also correlated. Ths tradng mechansm s the canoncal model for non-compettve markets for dvsble goods (e.g., Kyle (1989), Vves (011), and Rostek and Weretka (01)). The unform-prce double aucton allows an explct treatment of prce mpacts, whch are the key equlbrum objects that determne traders tradng behavors, as well as, the market choces. The lterature based on the unform-prce mechansm so far has mantaned a jont symmetry assumptons on traders rsk aversons, the correlaton n traders asset values, and varance of values and uncertanty. Rostek and Yoon (017) dspense wth any symmetry restrctons to allow heterogenety n all characterstcs and prmtves. One message n ths paper s that heterogenety n trader and asset characterstcs matter for understandng traders ncentves to choose a market and endogenous market structure. Heterogenety n characterstcs affects lqudty and learnng for traders. Lqudty s measured by the prce mpact, whch s endogenously defned as the change of prce as a trader s demand ncreases by one unt n equlbrum. 1 Larger prce mpacts,.e. lower lqudty, reduce traders demands and lower ther utltes. Allowng traders to condton ther prvate nformaton and prces, the demand schedule ncorporates nference about values. Hence, prce mpact and nference are nterdependent. Heterogeneous correlatons and nformaton precsons affect the lqudty and learnng separately and determne the ncentves for traders to choose an over-the-counter market. The frst result shows that when the dosyncratc component domnates the common value, n the sense that f the dsperson of correlatons s larger than the average level of correlatons, over-the-counter markets are more attractve to traders n terms of both learnng and lqudty. Equlbrum prce s a weghted average of traders sgnals and thus aggregates out dosyncratc components n centralzed markets. When a trader s value reles more on the dosyncratc value, he learns more about ths component n an over-the-counter market. On the other hand, the lqudty ncentve s ndependent of whether the common or dosyncratc component domnates. An over-the-counter market allows a trader to choose a counterparty who would more lkely have opposte tradng needs (.e., more negatvely correlated asset values), so that the trader has a lower prce mpact, whle the centralzed prce mtgates the dfference between values of buyers and sellers. Ths effect s stronger when traders asset values are nterdependent through the dosyncratc values rather than the common component. The lterature has studed varous traders ncentves to trade n over-the-counter markets or alternatve tradng venues. Traders can beneft n over-the-counter trades by searchng better 1 Other frctons consdered n the lterature (e.g. search costs, a chance that blateral trades fal, bd-ask spreads by dealers, etc.) can ncrease traders ncentves to choose centralzed markets over over-the-counter markets, but the results n ths paper stll hold quanttatvely. 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 correlatons represents the common component. See Secton. 3

4 prces n an over-the-counter market (e.g., Vayanos and Wang (007), Vayanos and Well (008), and Zhu (013)) or by clearng ther large tradng needs that cannot be fully exhausted n the centralzed market (e.g., Bessembnder and Venkataraman (014), Ready (014), and Degryse, Jon, and Kervel (015)). In ths paper, even when there s no dfference n prces between an over-the-counter trade and centralzed market, the over-the-counter market can open by traders choces. Ths s because, for certan trader and asset characterstcs, tradng over-the-counter offers the beneft of mprovng learnng and lowerng prce mpact. Moreover, traders choose the over-the-counter market when the centralzed exchange s compettve. These results show that the heterogeneous asset values of traders from large dosyncratc value components are the new ncentve of over-the-counter tradng that ths paper contrbutes to the lterature. Second, ths paper shows that the ncentves to choose over-the-counter versus centralzed markets dffer between nformed and unnformed traders. Traders wth low nformaton precson (.e., unnformed traders) beneft from an over-the-counter market because t helps them learn counterpartes nformaton. On the other hand, the over-the-counter market dscourages those whose asset values are less dosyncratc or those wth hgh nformaton precson (.e., nformed traders) 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 of nformaton precson. If a trader s nformaton precson s hgher than the cutoff level, the lqudty ncentve domnates and he chooses to trade n the centralzed market. Lkewse, wth a precson lower than the cutoff, the learnng ncentve domnates and traders choose the over-the-counter market. Takng nto account that the market choce are ndvdual, the over-the-counter market wll attract unnformed traders or both nformed and unnformed traders. In the over-the-counter matchng, there are two structures of over-the-counter markets dependng on a domnant ncentve: When the learnng ncentve domnates for all traders, all prefer to trade wth nformed counterpartes. An unnformed trader cannot be matched wth hs preferred counterparty, and thus, he chooses another unnformed counterparty nstead. It creates a same-type (.e., postve assortatve) matchng. On the other hand, f the domnant ncentve dffers between nformed and unnformed, a cross-type (.e., negatve assortatve) matchng occurs. Wth an avalable centralzed market, however, the cross-type matchng does not occur n equlbrum. When an nformed trader values low prce mpact more than mprovng learnng, he s better off tradng n the centralzed market 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. Moreover, ths paper shows that asymmetry n traders s necessary for the two tradng venues to coexst n equlbrum. When traders asset values are nterdependent wth the same 4

5 profle of correlatons 3 and ther nformaton precsons are the same, the tradng strateges and ncentves n the market choces are symmetrc for all traders. Wth these symmetrc ncentves, the endogenous dstrbuton of traders n two tradng venues has a corner soluton, n the sense that ether all traders choose the centralzed market or all choose the over-thecounter market. Wth asymmetrc traders, endogenzng market structure creates a fxed pont problem between traders ncentves n market choces and the dstrbuton of traders n two tradng venues. Takng nto account that the learnng and lqudty ncentves are functons of endogenzed market structures, ths paper dentfes the types of traders tradng n the overthe-counter market n equlbrum. The over-the-counter tradng occurs between traders who have relatvely smaller dosyncratc value components or lower nformaton precsons. Lastly, ths paper develops an algorthm to construct a parwse stable over-the-counter matchng when the asset characterstc s asymmetrc across traders and shows that a stable matchng exsts wth any arbtrary nterdependence n traders asset values. Although the exstence of a stable equlbrum n one-sded matchng s not trval, traders preference on counterpartes followng the rankng of negatve correlatons ensures that a parwse stable over-the-counter matchng exsts. The stable matchng may not be unque f some traders are ndfferent between two or more counterpartes, but t does not affect the qualtatve results on the endogenous market structure and the denttes of traders who are n each market. The results n ths paper help explan whch traders choose the over-the-counter or centralzed markets, whch assets are traded n ether type of tradng venues, and when centralzed and over-the-counter markets can coexst. Bas and Green (007) show that transacton costs and lqudty are key determnants on why most trades for bonds are held n over-the-counter markets, whle Attanas, Centorrno, and Moscat (016) explore the effects of lack of nformaton n the over-the-counter market on effcency. Ths s consstent wth ths paper s predcton. 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. When these products are held by traders untl, or close to, the maturty, t suggests that the purpose of tradng can be hedgng of traders outsde portfolos so that they are dosyncratcally valued. On the other hand, centralzed markets attract assets traded mostly by arbtrageurs or short-term nvestors, such as stocks or bonds wth short maturty, whch are valued by future prces that are common to all traders. Hgh-yeld bonds that have low credt rankng are often traded n the over-the-counter markets (e.g., Hendershott and Madhavan (015)). Low past tradng volume and volatle return prevent the traders access to qualty nformaton,.e., low nformaton precson. Moreover, t s possble to ncrease the nformaton asymmetry between nsders and other traders. 3 Rostek and Weretka (01) defne a symmetrc nterdependence n traders asset valuaton by an equcommonal model, 1 I 1 j Corr( θ, θ j )= ρ for all. The symmetry condton n ths paper s stronger than the equcommonal model. The profles of correlatons {Corr( θ, θ j )} j are the same for all traders. However, the symmetrc model ncorporates the heterogeneous correlatons Corr( θ, θ j ) across pars of traders (, j). 5

6 Related Lterature: Lterature has developed theoretcal frameworks for over-thecounter markets for a fxed market structure. How lqudty affects traders behavor and effcency are studed n the lterature (e.g., Duffe, Garleanu, and Pedersen (005), Vayanos and Well (008), Well (008), Atkeson, Esfeldt, and Well (014)). Other studes show how prvate nformaton s aggregated n over-the-counter markets (e.g., Duffe, Malamud, and Manso (014), Maurn (015), Babus and Kondor (016), Back, Lu, and Tegua (016)). In addton to these papers focusng on over-the-counter markets, several papers compare these two tradng venues n terms of welfare or ndvdual proft. Observng that an over-the-counter markets can domnate centralzed markets n welfare terms, several authors examne determnants that favor ether market: such as default, search frcton, prce mpacts, or nformaton asymmetry between sellers and buyers (e.g., Acharya and Bsn (010), Malamud and Rostek (014), Duffe and Wang (016), and Glode and Opp (017)). Praz (015) and Zhu (014) studes how the presence of an alternatng tradng venue affect equlbrum n centralzed markets. Another strand of the lterature endogenzes the over-the-counter structure tself by studyng ncentves to choose a counterparty n over-the-counter markets (e.g., Duffe, Carleanu, and Pedersen (005), Golosov, Lorenzon, and Tsyvnsk (014), Farbood (015)). Golosov, Lorenzon, and Tsyvnsk (014) consder a dynamc ncentve of unnformed traders to learn nformaton at a cost of low lqudty n tradng wth an nformed counterparty. In ths paper, the jont effect (not necessarly a trade-off) of learnng and prce mpact s the man determnant of counterparty choce. The learnng and lqudty effects exst n the statc tradng due to the heterogenety n precson (nformed and unnformed traders) and correlaton (asset characterstcs). On the other hand, wth heterogeneous preferences, traders search for a counterparty who can provde a better surplus (Chang and Zhang (016)) or a better prce (n Zhu (01)). Ths paper shows that traders can strctly prefer one market to the other market or a counterparty to others even though equlbrum prces are the same across. Hence, the role of heterogenety n determnants of counterparty choce s new n the endogenous market structure that ths paper contrbutes to the lterature. The model n Babus and Parlatore (017) s close to ths paper. The authors examne over-the-counter dealer networks when tradng s based on a unform-prce double aucton as n ths paper. In ther paper, the endogenous choce of a segmented market (or the choce of a dealer) s determned by a trade-off between the prce mpact and the level of uncertanty n asset values. The contrbuton of ths paper, compared to Babus and Parlatore (017), s ntroducng a heterogeneous learnng effect n endogenous over-the-counter matchng and also n endogenous market choce. The objectve of ths paper s to understand endogenous market structures when centralzed and over-the-counter markets are both avalable. The choce between centralzed and overthe-counter markets has been explored by several authors. Up to my knowledge, ths paper s frst to consder the market formaton by all traders. Krlenko (000) and Vswanathan and 6

7 Wang (00) 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 (015) 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. Endogenzng the market choces of all traders lets the advantage of over-the-counter markets to be functons of endogenzed partcpaton and dstrbuton of heterogeneous traders n two markets, rather than functons of fxed market structures. Furthermore, no trader has an ncentve to change hs market choce gven chances n equlbrum wth all traders market choces, whch provdes a noton of the market stablty. Model Ths paper consders a statc economy where 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 (t = 0), traders can choose whch market they would trade n. If a trader chooses the over-the-counter market, then he also chooses a counterparty he would lke to trade wth. The market choce and blateral matchng occur at the end of perod t = 0. Traders can trade only once, n one market and wth one counterparty f they are n the over-the-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, () nformaton, (3) markets, (4) strateges, and (5) equlbrum. Strategc Traders: There are I< strategc traders. Each of trader has a constant absolute rsk-averson (CARA) utlty on quantty tradng q net of payment pq,whereps the prce n the market he partcpates n. The ex-post utlty s defne as ( ) u (q,p)= exp μ( θ q pq ). Here, μ>0 s the rsk-averson 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 ],σθ ). The condtonal expected utlty s equvalent to the mean-varance utlty: ( E[u (q,p) ] = exp μ ( E[ θ ]q pq μ Var( θ ) ) )q. (1) 7

8 Fgure.1: Tmng of the economy. q (p) s hs quantty demand at a market prce p. Trader has a prvate nformaton s before tradng, and ther ndvdual asset value θ s realzed at the end of economy and so does the utlty u based on the realzaton of θ and equlbrum outcomes q,p. In the CARA-Gaussan settngs, 4 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 (q,p) 1 μ log( E[u (q ) ]) = E[ θ ]q pq μ Var( θ )q. 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. The nterdependence of (θ ) s nterpreted as a combnaton of a common value component, whch s attrbuted to the future asset return n the market, and an dosyncratc value component, whch comes from ndvdual portfolo return consstng of other assets that are correlated to the tradng 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. 5 The decomposton of asset value θ s formalzed as 4 The CARA-normal settngs s the standard of the non-compettve market lterature. See Kyle (1989), Vves (011), and Rostek and Weretka (01). The non-compettve tradng lterature so far has focused on the cases when traders are symmetrc n terms of asset valuatons, nterdependency, and/or nformaton precson. One contrbuton of ths paper s ncorporatng the heterogenety n both nterdependent asset valuaton and nformaton precson. 5 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 8

9 follows: θ = θ + δ, I, where θ s the common value component and δ s the dosyncratc value component of trader. The common and dosyncratc value components are ndependent and drawn from normal dstrbuton, θ N(E[θ],σcv) and(δ ) N(0,σvΣ). The dosyncratc values (δ ) are nterdependent by a correlaton matrx, 1 ρ 1 ρ 1I Σ= ( Corr(δ,δ j ) ) = ρ 1 1 ρ I,j ρ 1I ρ I 1 The correlatons ρ j are heterogeneous across pars of traders (, j). I mpose an assumpton, wthout loss of generalty, that the sum of correlatons n a row j ρ j s normalzed to zero for all. Ths s for keepng the heterogenety from beng addtonal source of common value, so that for makng a clear separaton of nformaton aggregaton. Example 1 shows how the common value and dosyncratc value components determne Σ n a smplest and ntutve settng. Example 1 (Symmetrc Interdependence n Asset Values) There are two groups of strategc traders buyers and sellers wth equal group szes. 6 Each trader has ndvdual asset value that s decomposed nto two ndependent random varables: { θ + δ f s a buyer, θ = θ + δ = θ δ f s a seller. Suppose that Var(θ) =σcv and Var(δ) =σv. Then, the correlaton matrx of dosyncratc values (δ ) s [ ] 1 1 Σ=, 1 1 where each block represents ( I I ) matrx. From the dstrbutons of common and dosyncratc components, the correlaton matrx of total asset values ( θ ) s Σ = 1 σ cv + σ v [ σ cv + σ v σ cv σ v σ cv σ v σ cv + σ v 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. 6 Buyers and sellers are not explctly determned n ths model. ]. 9

10 The nterdependence of traders asset values s symmetrc n ths example, n the sense that the profle of correlaton n each row s the same, {ρ k } k = {ρ jk } k j for any j. However, the correlatons (ρ j ),j are stll heterogeneous across pars of traders (, j). I wll consder ths example for further analyss n Secton 4, and wll show the effects of the heterogeneous correlatons across pars and asymmetrc nterdependence across traders on endogenous market structures. Informaton: Each strategc trader gets a prvate nformaton (sgnal) on hs own valuaton, s = θ + ε wth an ndependent nose ε N(0,σ,ε). The nformaton precson φ 1/σ,ε can dffer across traders. The prvate sgnal s s realzed at the begnnng of tradng perod t = 1 and prvately observed by trader. The realzatons of other traders sgnals (s j ) j and prces n all markets are observed after all trades are done at the end of tradng perod t =1. Heterogenety across traders, whch s the key component n the model, s n both the correlaton structure Σ and nformaton precson (φ ). Throughout ths paper, I call ths par of asset and trader characterstcs a type. Each trader s type represents hs dentty, such as buyers or sellers n Example 1. It s worth to remark that the type defned n ths paper does not represent the realzaton of prvate sgnal s. Ths defnton of type s dfferent from the conventonal defnton n games wth ncomplete nformaton. Traders types and pror dstrbuton of asset values and sgnals are common knowledge..1 Centralzed Market (CM) Mechansm The centralzed market s a large market where many buyers and sellers trade at a sngle prce. I desgn the centralzed market as a unform-prce double aucton that s a canoncal model n markets wth dvsble goods. A strategc trader who enters the centralzed exchange submts hs net demand schedule q (p) :R R (or a combnaton of lmt and market orders) as a contnuous functon of prce. { max v (q,p)=max E[ θ s,p]q pq μ } q ( ) q ( ) Var( θ s,p)q, p R. () Addtonal L traders, called lqudty traders, are ntroduced n the centralzed market who are not gven a choce to enter the over-the-counter market. Ther presence ensures that the centralzed market always functon even when none of I strategc traders choose the centralzed market. 7 The lqudty traders can be those who could not meet a requrement to enter the OTC, for example, not enough depost or credblty. In a later secton, I also show that lqudty 7 Wthout ths assumpton on the presence of lqudty traders, there always exsts a trval equlbrum n whch all strategc traders are n the over-the-counter market, ndependently of asset or trader characterstcs. Two or more lqudty traders n the centralzed market allows a strategc trader I who s currently n the over-the-counter market to consder an ndvdual devaton to the centralzed market. 10

11 traders can be those who do not observe other traders types so that they optmally choose to stay n the centralzed exchange. Each lqudty trader submts ther demand schedule q lq (p) based on hs own prvate nformaton. The precson of prvate nformaton for lqudty traders are homogeneous and equal to the least nformed traders: σlq,ɛ =max I σ,ε. Also, ther asset values θ lq are equal to the common value θ wthout any dosyncratc value component. These assumptons on lqudty traders are to ensure that ther presence does not affect the market choce of strategc traders I. After all demands are submtted, the centralzed market s cleared at a prce of whch the total demand of I strategc traders and L lqudty traders s equal to zero; p such that I q (p )+ j L q lq,j(p ) = 0. The equlbrum allocaton s determned by the demand schedule traders submtted, q = q (p ) for any (I L).. Over-the-Counter Market (OTC) Mechansm An over-the-counter market s an off-exchange tradng venue n whch blateral trades occur between large nsttutons. Each trader who s n the over-the-counter market chooses a desred counterparty based on ther types, nformaton precson, and correlaton. The choce should be mutual for two traders to be matched, n the sense that the over-the-counter matchng s parwse stable. 8 Each trader has an ndvdual rankng on other traders, and based on the rankng, the matchng wll be determned by the algorthm of Irvng (1985). If two traders are matched, they trade and leave the market. If the counterparty choce s not mutual, the matchng fals and the trader searches for another counterparty untl he succeeds at matchng. I assume that the search cost s zero to focus on the dfference of endogenous ncentves n two tradng venues. The over-the-counter market ends when all traders partcpate n exactly one blateral trade or when only a sngle trader s left. Once the matchng occurs, each blateral trade s operated by the same mechansm as n the centralzed market: the unform prce double aucton. Two traders smultaneously submt ther demand schedules q (p) asfunctonsofprcep by solvng the optmzaton problem (). The equlbrum prce p j s determned by the market clearng condton: q (p j )+q j (p j )=0. The prce p j s par-specfc n the over-the-counter market. If an equlbrum prce does not exst, then there s no trade and the over-the-counter market ends wthout any further trade. The utlty of traders n such case are set to be the autarky utlty v (q =0)=0. 8 The equvalence s due to the fact that traders prvate sgnals are realzed after ther choce of the counterparty, and thus, the over-the-counter matchng s determned by traders ex-ante utlty n the trade wth each potental counterparty. 11

12 .3 Market Choce and Tradng Based on the tradng mechansms n two markets descrbed n Secton.1 and., the strateges of traders and equlbrum are determned. Strateges: At t = 0, each strategc trader I chooses a market where he enters, m {OTC, CM} and a type of counterparty τ upon hs enterng to the over-the-counter exchange m = OTC. 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 )nmarket (m,τ ). Therefore, the strategy profle of trader s {(m,τ ),q ( : m,τ )}. A lqudty trader 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 three condtons for equlbrum: () Bayesan Nash equlbrum n the double aucton n each market, () no ncentve to devate from the over-thecounter market to the centralzed market, and () parwse stable over-the-counter matchng ncludng a parwse devaton from the centralzed to over-the-counter market. For each trader I, E[u (m,τ )] denotes the expected utlty wth (m,τ ) for gven equlbrum dstrbuton of traders n both markets. Defnton 1 (Equlbrum) An equlbrum s defned by {(m,τ ),q ( : m,τ )} (I L) such that () traders optmal bd schedules {q ( : m,τ )} solvng the optmzaton problem () characterze a Bayesan Nash equlbrum n each market; () no trader n the over-the-counter market has a strctly postve ncentve to devate to the centralzed market:.e., f (m,τ )=(OTC, τ ) for trader, then E[u (m,τ )] E[u (CM, )], I; and () the over-the-counter matchng s parwse stable:.e., there exsts no par of traders (, j) who are not matched such that both traders and j strctly beneft from breakng ther respectve matchngs and creatng a new matchng between them. E[u (m,τ )] E[u (OTC, j)] or E[u j (m j,τj )] E[u j (OTC, )], j I. The nequaltes n Defnton 1 () nclude the case where ether trader or j (or both) choose the centralzed market, m = CM or m j = CM, n equlbrum. Ths equlbrum condton ensures that the over-the-counter matchng s mmune to an entry of a trader from the centralzed market as well as wthn the over-the-counter counterparty choce. Furthermore, 1

13 wth ths parwse devaton from the over-the-counter to centralzed market, a market structure where all traders choosng the centralzed market (.e. m = CM for all ) s a trval equlbrum, ndependently of asset or trader characterstcs. 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 develop comparatve statcs on traders expected utltes over the market, asset, or traders characterstcs. Secton 4 and 5 show endogenous market structures that are formed by traders market and counterparty choce - part () and () - and analyze nfluences of the characterstcs n traders market choces and thus n endogenous market structures. 3 Equlbrum n Double Auctons Ths secton shows traders bddng strateges n a gven market. Equlbrum characterzaton n a market provdes traders equlbrum utlty and ts dependence on market, asset, or trader characterstcs. Suppose that there are N traders n a market wth a correlaton structure of asset values Σ and nformaton precson {φ }. Each trader maxmzes hs expected utlty as n equaton (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, (3) where λ p/ q s the 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 leads to a further ncrease n equlbrum prce so that the trader s demand s reduced by hgher prce mpact. Ths demand reducton due to the prce mpact represents market llqudty that s endogenously determned by the traders strateges. A compettve market wth nfntely many traders s perfectly lqud and the prce mpact s zero. In terms of 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 (3), 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 observed the prce. Therefore, even n the statc model, traders make nference about ther asset values by the schedule bddng. Proposton 1 states three equlbrum condtons for a gven market wth N 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); () 13

14 the consstency condton for equlbrum prce mpact; and () the nference coeffcents by equlbrum prce dstrbuton. 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 () 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 μv ar( θ s,p)+λ = c θ,e[θ ]+c s,s (1 c p,)p μv ar( θ s,p)+λ, j q j ( ) ) 1 ( = p j 1 c p,j μ Var( θ j s j,p)+λ j ) 1 0,, (4) () nference coeffcents {c θ,,c s,,c p, } n E[ θ s,p] and condtonal varance Var( 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 Var( θ s,p). Ex-ante utlty of trader n a gve market s [ ( E[u ]=E exp μv ar( θ s,p)+λ )] μ( (E[ θ s,p] p) ). (μv ar( θ s,p)+λ ) The Gaussan structure of { θ,s } generates the dfference n ndvdual expected asset value from equlbrum prce, (E[ θ s,p] p), follows a normal dstrbuton. Thus, the expectaton on the rght hand sde of the above equaton s n the form of the moment generatng functon for χ k dstrbuton. It provdes an explct formula for the ex-ante ndrect utlty: ( E[u ]= λ (1 + λ ) }{{ } lqudty effect Var(E[ θ s,p] p) ) 1/, Var( θ s,p) }{{}. (5) 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 ] can be decom- 14

15 posed nto two parts: the value of lqudty and learnng. The beneft of lqudty s captured bytheterm(1+ λ )/(1 + λ ) =1 ( λ /(1 + λ )). 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 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, ncreases as the normalzed prce mpact λ ncreases. On the other hand, the utlty (5) contans the term Var(E[ θ s,p] p)/v ar( θ s,p)thatcapturesthe beneft of learnng from prce and prvate nformaton. Equlbrum prce aggregates all market partcpants prvate nformaton on asset values. Traders learn the aggregated nformaton from condtonng on prce. It decreases the rsk n uncertanty of the trader s own value θ and thus ncreases hs expected utlty through the term Var( θ s,p). In addton, the prce determnes the net surplus E[ θ s,p] p of buyng a unt of asset. Such nformaton on the future surplus nfluences the trader s utlty through Var(E[ θ s,p] p). The total beneft of learnng the trader s own and others valuaton, called learnng effect, s ncorporated n a form of rato n the expected utlty (5). q (p), 3.1 Equlbrum Utltes: Learnng and Prce Impact Now, ths secton characterzes the man objects of an equlbrum. Three characterstcs can be consdered n ths model: market sze (market characterstc), nterdependence of traders asset values (asset), and precson of prvate nformaton (traders). Each characterstc affects learnng and lqudty n traders utltes. Ths secton examnes these effects of the three characterstcs n a model wth symmetrc nterdependent asset values and symmetrc nformaton precsons across traders. Defnton (Symmetrc Traders) Traders are symmetrc, f () the profle of correlatons {ρ j } j s the same for all ; and () the nformaton precson φ = φ s the same for all. Wth the symmetrc traders defned n Defnton, traders submt symmetrc strateges n each market, but the correlaton of asset values s stll heterogeneous across pars, Corr( θ, θ j )= ρ j can dffer for each par (, j), whch s the key heterogenety n traders market choce. Asymmetrc traders wth asymmetrc correlatons and nformaton precson wll be consdered 15

16 n Secton 5. 9 Example and Proposton show how the three key characterstcs affect the ex-ante utlty of each trader n symmetrc markets. Example (Symmetrc Interdependence and Precson) Consder a market wth N traders. All traders have a symmetrc nformaton precson φ =1/σ,ε φ and a symmetrc average correlaton to the resdual market ρ = 1 I 1 j ρ j ρ for all. 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 by the prce mpact and condtonal varances: λ = λ μv ar( θ s,p) = (1+(I 1) ρ)(1 + σ ρ) (I )(1 + σ )+((I 1) +1 (I 1)(1 + σ )) ρ (I 1)(I ) ρ, Var( θ s,p)= (1 + σ )+(I ) ρ (I 1) ρ (1 + σ +(I 1) ρ)(1 + σ ρ) σ ε; Var(E[ θ s,p] p) = Trader gets the ex-ante utlty E[u ]= (1 + ξ ) where ξ = 1+ λ Var(E[ θ s,p] p) (1 + λ. ) Var( θ s,p) (1 ρ) 1+σ ρ I 1 σ I θ. The lqudty effect on utlty s captured by the term 1+ λ. Wth ths closed-form soluton (1+ λ ) of nference parameters and prce mpact, 1+ λ ( (1 + λ ) =1 ( λ ) (1 + σ ρ)(1+(i 1) ρ) ). =1 1+ λ (I 1)(1 ρ)(1 + σ +(I 1) ρ) The lqudty term ncreases 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 ncreases, the endogenous lqudty of the market ncreases f ρ >0, and decreases f ρ <0. 9 In asymmetrc markets, n the sense that the profles of correlatons {ρ j } j are heterogeneous across traders, as well as, across pars (, j) and/or that nformaton precson φ are heterogeneous, traders optmal tradng strateges are asymmetrc. The effects of characterstcs n traders behavor and utltes n ths secton and the comparatve statcs on endogenous market structures n Secton 4 can also be appled to asymmetrc markets. Ths secton focuses on the symmetrc market, n order to avod techncal complextes. 16

17 The effect of learnng from the prce on utlty s measured by Var(E[ θ s,p] p) Var( θ s,p) = I 1 I (1 ρ) (1 + σ +(I 1) ρ) σ ((1 + σ )+(I ) ρ (I 1) ρ ), whch s ncreasng n nformaton precson φ =1/σ. The effect of average correlaton ρ s ambguous. The utlty component due to learnng s decreasng wth respect to ρ, f and only f, (1 + σ )+(I 3)(1 + σ ) ρ +(I 3)(I 1) ρ (I 1) ρ 3 > 0. Proposton characterzes the effects of each characterstc - market sze, correlatons, and nformaton precson - on traders expected utltes through learnng and lqudty, when the other characterstcs are fxed. Proposton (Lqudty and Learnng Effects) For a gven market, the equlbrum utlty of a trader ncreases as () the number of traders n market N s larger; or () asset values are more negatvely correlated to prce,.e., corr( θ,p) are more negatve. The equlbrum utlty s non-monotone n the average nformaton precson,.e., () nformaton precson φ (0, ] of other traders maxmzes trader s utlty. 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, prce mpact can be small n large markets, when other characterstcs are fxed (See Rostek and Weretka (01)). Proposton (), however, suggests that the benefts of large markets n learnng and lqudty are not necessarly true f traders n each market, large or small, have heterogeneous asset valuatons. Suppose that the equlbrum prce n a small market exhbts greater negatve correlatons wth trader s asset valuaton. 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 n 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 the resdual supply curve, λ = ( j q j( )/ p ) 1, that s an nverse of the aggregate reacton of other traders when prce ncreases. Wth more negatve correlatons, trader j would rely more on the prce for hs nference, n the sense that c p,j s more negatve. Ths makes hs demand more elastc to prce change and thus trader s prce mpact s smaller. Hence, hs equlbrum utlty ncreases due to both learnng and lqudty as the correlaton between hs asset values and prce s more negatve. From the arguments, more negatve correlatons between traders asset values and/or 17

18 more traders n the market are benefcal to both learnng and lqudty. These condtons of two characterstcs jontly determne traders ncentves to choose a market, whch wll be examned n the next Secton 4. In addton to the jont condton of market sze and nterdependent asset valuaton, the last characterstc that affects equlbrum s the precson of traders prvate nformaton. Informaton precson has an ambguous nfluence on traders expected utltes. The value of learnng ncreases when the trader s own nformaton precson s lower or when the (weghted) average of other traders nformaton precson s hgher. At the same tme, the prce mpact ncreases, and thus, the lqudty decreases. It creates a trade-off between learnng and lqudty when the precson of nformaton from the prce changes. The trade-off between learnng and lqudty over traders nformaton precson s shown n Fgure 3.1. As a result, trader s utlty s non-monotone wth respect to the other other traders nformaton precson. If hs precson s suffcently low, the learnng effect domnates the lqudty effect, so that hs utlty s monotoncally ncreasng n others precson. Fgure 3.1: Lqudty and learnng effects wth respect to other traders nformaton precson 1/σ. Atrader has a nformaton precson φ 1 =1/σ1 =1/0.5 = 4. The lqudty effect and the learnng effect n hs expected utlty (5) are shown n each graph respectvely. Two effects are monotone over the other traders nformaton precson φ =1/σ avg(1/σj ) j 1. The comparatve statcs show the types of traders who would enter an over-the-counter market based on the nterdependence of asset values and the precson of ther nformaton. The ambguty n the nfluence of nformaton precson on traders utltes wll be consdered as a key determnant of traders market and counterparty choces. 4 Endogenous Market Structure Traders ndvdual choce for markets and counterpartes forms a dstrbuton of traders types n centralzed and over-the-counter markets and also an over-the-counter matchng. Ths s called a market structure. Ths secton characterzes endogenous market structures by usng the comparatve statcs developed n the prevous secton. There are three types of market 18

19 structure: only centralzed market opens, only the over-the-counter market opens, and both markets co-exst. Example wth a compettve centralzed market (.e. perfectly lqud market wth λ =0forall) provdes some ntuton on endogenous market structures. The compettve centralzed market maxmzes the dfference n market szes. The example shows that traders can stll be attracted to the over-the-counter market wth certan condton for asset and trader characterstcs. Example 1 & - Cont d Equaton (5) provdes the explct formula of expected utlty when there are N symmetrc traders. The utlty from the centralzed tradng s derved by takng N to nfnty, whle the utlty from a blateral trades n the over-the-counter market s by settng N =. Wth these ex-ante utltes n two exchanges, trader chooses whch exchange he wants to partcpate n. 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 OTC ] 1 ρ CM < σ ρ OTC 1+σ + ρ OTC 1 {ρot C <0}. where 1 { } s the ndcator functon. Here, ρ CM = σ cv s the average correlaton n the σcv+σ v centralzed market and ρ OTC = σ cv σv ρ s the correlaton between two traders who are matched σcv+σ v n the over-the-counter market, whch are suffcent statstcs on Corr( θ,p) n two markets. Consder the followng canoncal assumptons on traders asset valuaton: Independent Prvate Value: σcv = 0,σv = 1, and ρ = 0. Wth ndependent prvate (dosyncratc) value, traders get no gan-to-trade n the over-the-counter market,.e., ρ OT C 1+σ +ρ OT C 1 ρot C <0 =0, whle they get strctly postve equlbrum utlty 1/σ. Therefore, all traders choose the centralzed market, and the over-the-counter market does not open. Independent prvate value structure mples that the market has no valuable nformaton to any trader (no learnng occurs), so all traders choose the centralzed market to beneft from the lqudty. Fundamental Value (Vves (011)): σcv =1 a, σv = a wth a constant a (0, 1), and ρ =0. Takng a 0, the fundamental value model ncludes the common value: θ = θ for all. Wth the fundamental value model, the over-the-counter trade provdes no gan-totrade snce ρ OTC > 0. On the other hand, traders get strctly postve equlbrum utlty ɛ/σ, and thus, all traders choose the centralzed market. The over-the-counter market does not exst. Fundamental value model does not ncorporate heterogeneous correlatons across pars of traders, n the sense that Corr( θ, θ j )= σ cv for any par (, j). Hence, σcv +σ v t concludes that the heterogeneous correlaton s necessary for a trader to choose the over-the-counter market. Two-Sded Market wth Buyers and Sellers (Example 1): σ cv =1 a, σ v = a, and ρ = ±1. 19

20 Traders choose the over-the-counter market f and only f a σ < 4a a + σ a> 3σ + ( + 3σ ) 8σ > 1 a(1 a) and <σ. }{{ 4 }} 3a {{} v s suffcently large precson s suffcently low (6) Traders prefer to trade n the over-the-counter market f the dosyncratc value component n asset values s suffcently large and the nformaton precson s suffcently small. When the centralzed exchange s compettve, the lqudty ncentve strongly derves traders to avod hgher prce mpacts n over-the-counter blateral trades. Hence, partcpaton to the overthe-counter market occurs only when the 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. The predctons from the above example hold generally n the model wth a non-compettve centralzed market and/or wth asymmetrc traders. () Traders choose the over-the-counter market over the centralzed market f the dosyncratc value component n asset values s suffcently large and the nformaton precson s suffcently small; () The over-the-counter market does not exst f there s no heterogenety across traders asset valuaton. Proposton showed that equlbrum utlty of a trader ncreases as the number of traders who are partcpatng n the market ncreases or as the correlaton between hs asset value and the market prce s more negatve. Wth the presence of L lqudty traders n the centralzed market the number of traders (hereafter, market sze) s larger n the centralzed market and ts effect encourages traders to enter nto the centralzed market. However, the effect of correlaton between asset value and prce s the opposte. In the over-the-counter market, a trader can target a counterparty that has the most negatve correlaton, whle the correlaton wth the CM prce s determned by the average correlaton over all partcpants. Hence, the effect of correlaton Corr( θ,p) supports traders choosng the over-the-counter market. It s worth emphaszng that from the comparatve statcs n Proposton, the correlaton effect reduces the prce mpact, as well as, mproves learnng. Hence, the beneft of more negatve correlaton n the over-the-counter market s not only from better learnng but also from low prce mpact. The effects of market sze and correlaton create a trade-off n the traders choce of market. Theorem 1 examnes when the correlaton effect would domnate and provdes a suffcent and necessary condton such that the trader prefers to trade n the over-the-counter market and endogenous market structure followng the traders ndvdual market choces. 0