Centralized versus Over-The-Counter Markets

Transcription

1 Centralzed versus Over-The-Counter Markets Vral Acharya NYU-Stern, CEPR and NBER Alberto Bsn NYU and NBER March 16, 2010 We are grateful to Rob Engle for nsghtful dscussons. We also thank comments from Erc Ghysels, Martn Oehmke, Marco Pagano (dscussant) and semnar partcpants at the Federal Reserve Bank of New York and Econometrc Socety Meetngs n Atlanta (2010). 1

2 Centralzed versus Over-The-Counter Markets Abstract The opacty of over-the-counter (OTC) markets n whch a large number of fnancal products ncludng credt dervatves trade appears to have played a central role n the ongong fnancal crss. We model such OTC markets for rsk-sharng n a general equlbrum setup where agents have ncentves to default and ther fnancal postons are not mutually observable. We show that n ths settng, there s excess leverage n that partes n OTC contracts take on short postons that lead to levels of default rsk that are hgher than Pareto-effcent ones. In partcular, OTC markets feature a counterparty rsk externalty that we show can lead to ex-ante productve neffcency. Ths externalty s absent when tradng s organzed va a centralzed clearng mechansm that provdes transparency of trade postons, or centralzed counterparty such as an exchange that observes all trades and sets prces. J.E.L.: G14, G2, G33, D52, D53, D62 Keywords: OTC markets, leverage, counterparty rsk, externalty, transparency, centralzed clearng, exchange

3 1 Introducton and motvaton An mportant rsk that needs to be evaluated at the tme of fnancal contractng s the rsk that the counterparty wll not fulfll ts future oblgatons. Ths counterparty rsk s dffcult to evaluate because the exposure of the counterparty to varous rsks s generally not publc nformaton. Contractual terms such as prces, nterest rates and collateral that affect the terms of trade can be talored to mtgate counterparty rsk, but the extent to whch ths can be acheved, and how effcently so, depends n general on how contracts are traded. One possble tradng nfrastructure s an over-the-counter (OTC) market n whch each party trades wth another, subject to a bankruptcy code that determnes how counterparty defaults wll be resolved. 1 A key feature of OTC markets s ther opacty. In partcular, even wthn a set of specfc contracts, for example, credt default swaps (CDS), no tradng party has full knowledge of postons of others. We show theoretcally n ths paper that such opacty of exposures n OTC markets leads to an mportant rsk spllover a counterparty rsk externalty 2 that leads to excessve leverage n the form of short postons that collect premum upfront but default ex post and result n neffcent levels of rsk-sharng and/or deadweght costs of bankruptcy. Counterparty rsk externalty s the effect that the default rsk on one contract wll be ncreased f the counterparty agrees to the same contract wth another agent because the second contract ncreases the probablty that the counterparty wll be unable to perform on the frst one. Put smply, the default rsk on one deal depends on what else s done. The ntuton for our result concernng the neffcency of OTC markets s that n OTC markets t s not at all transparent what else s beng done. Hence, counterpartes cannot charge prce schedules that effectvely penalze the creaton of counterparty rsk. Ths makes t lkely that excessvely large short postons wll be bult by some nsttutons wthout the full knowledge of other market partcpants. In general, when such nsttutons were to default, ther counterpartes would also ncur sgnfcant losses, creatng systemc rsk n the economy or more formally, neffcent ex-ante rsk-sharng. 1 The bankruptcy code may be specfed n the contract or adhere to a unformly applcable corporate bankruptcy code. 2 The term counterparty rsk externalty s as employed by Acharya and Engle (2009). A part of the dscusson below, especally related to A.I.G. s also based on that artcle. 3

4 For example, n September 2008, t became known that A.I.G. s lqudty poston was nadequate gven that t had wrtten credt default swaps (bespoke CDS) for many nvestors guaranteeng protecton aganst default on mortgage-backed products. Each nvestor realzed that the value of A.I.G. s protecton was dramatcally reduced on ts ndvdual guarantee. Investors demanded ncreased collateral essentally postng of extra cash whch A.I.G. was unable to provde and the Treasury had to take over A.I.G. The counterparty rsks were so wdespread globally that a default would probably have spurred many other defaults generatng a downward spral. The A.I.G. example llustrates well the cost that large OTC exposures can mpose on the system when a large nsttuton operatng n OTC markets defaults on ts oblgatons. But, more mportantly, t also rases the queston of whether A.I.G. s true rsk as a counterparty was reflected by nvestors n prces and rsk controls for protectons they purchased from A.I.G. We argue that the opacty of the OTC markets n whch these credt dervatves trade was prmarly responsble for allowng the buld-up of such large exposures n the frst place. Whle a number of fnancal nnovatons n fxed ncome and credt markets have traded untl now n OTC markets, many products lnked to commodty and equtes have traded successfully on centralzed exchanges. A dstngushng feature of centralzed exchange relatve to OTC tradng s that even though ndvdual agents stll do not see each others trades, there s a centralzed counterparty the exchange that sees all trades (at least on all products traded on that partcular exchange). Crucally, ths enables the exchange to offer ndvdual partes prcng schedules (e.g., collateral arrangements) for trades that are contngent not just on observable or publc characterstcs (e.g., credt ratngs) but also on ts own knowledge of other trades (e.g., net postons n CDS contracts). However, exchanges are often vewed as detrmental to ease of search facltated by blateral markets, especally for customzed or non-standardzed fnancal products. Indeed, even f trades are not ntermedated by a centralzed exchange, a centralzed clearng mechansm can be arranged to provde the transparency of trades precluded n OTC markets. We show formally that when tradng s organzed n the form of a centralzed clearng mechansm, resultng transparency enables market partcpants to condton contract terms for each counterparty based on ts overall postons. In turn, such condtonng s suffcent to get that party to nternalze the counterparty rsk externalty of ts trades. In other words, the moral hazard that a party wants to take 4

5 on excessvely short postons collect cash today and default tomorrow s counteracted by the fact that they face a steeper prce schedule by so dong. Effectvely, centralzed clearng mechansms s suffcent to acheve the effcent rsk-sharng outcome. A compettve centralzed exchange also would nduce effcent rsk-sharng, but n practce, ths would be at the cost of restrctng all trades, ncludng those nvolvng of non-standardzed fnancal assets, through a sngle ntermedary. 1.1 Model and results We derve these results n a compettve general equlbrum (GE) model wth two perods but allowng for the possblty of default (Geanakoplos, 1997, Geanakoplos and Zame, 1998, Dubey, Geanakoplos and Shubk, 2005). There s a sngle fnancal asset, whch can be nterpreted as a contngent clam on future states of the world, and agents can take long or short postons n the asset. Trades are collateralzed by agents endowments. When an agent has short postons that cannot be met by the pledgeable fracton of endowment, there s default. The possblty of default (the opton to exercse lmted lablty, to be precse) mples that long and short postons do not yeld the same payoff and ndeed that there s counterparty rsk n tradng. We assume a natural bankruptcy rule that llustrates why counterparty rsk potentally arses n such a settng. In partcular, n any gven state of the world, the payoff to long postons s determned pro-rata across postons based on delvery from short postons. 3. Ths ratonng of payments mples that each trade mposes a payoff externalty on other trades. We call ths spllover a counterparty rsk externalty. In ths setup, we consder varous tradng structures and ask whether a counterparty rsk externalty leads to neffcent rsk-sharng. A centralzed clearng mechansm guarantees that all trades are observable and agents can set prcng schedules that are condtonal on ths knowledge. A centralzed exchange s a centralzed counterparty that observes all trades and can set prcng schedules based on ths knowledge. We show that compettve equlbra n economes wth a centralzed clearng mechansm or a centralzed exchange are constraned Pareto effcent. 3 In partcular, n case of a centralzed bankruptcy mechansm, delvery from short postons s the sum total of full payments from non-defaultng partes and partal payments from defaultng partes; whereas n case of a blateral bankruptcy mechansm, delvery on short postons s just the partal payment from the defaultng counterparty 5

6 In economes wth OTC markets, on the contrary, trades are not mutually observed and thus prcng schedules faced by agents are not condtonal on ther other trades (even though they mght be condtoned on publc nformaton about ther type, e.g., ther endowment level or equvalently ther credt ratng). We show that compettve equlbra n economes wth OTC markets are robustly constraned neffcent. We study two dfferent cases, one n whch OTC markets operate wth a blateral nettng mechansm and one wthout blateral nettng. We show that OTC markets are robustly constraned neffcent n both cases. 4 Ths makes t precse that t s the opacty or lack of transparency of postons n the OTC markets (rather than dfferences wth centralzed tradng n how bankruptcy s resolved) that leads to ex-ante neffcency. The neffcency n the OTC settng manfests as excessvely large short postons as agents do not nternalze the default rsk these postons mpose on other trades n the economy. Intutvely, as long as there s a rsk premum on the nsurance contract (e.g., because the rsk beng nsured s aggregate n nature) and/or the costs of defaultng are not excessvely large, the nsurer perceves a beneft from buldng up short postons and defaultng ex post. We nterpret ths outcome as characterzng excessve leverage from an ex-ante standpont. Interestngly, ths mples a lower cost of nsurance per unt of promsed nsurance payoff snce the realzed nsurance payoff s smaller when nsurer s more lkely to default. In our model, we capture the resultng neffcency n the form of deadweght costs of bankruptcy, but more generally, t could also manfest as excessve systemc rsk from an ex-post standpont. Put together, these results mply that a centralzed clearng mechansm (or a compettve exchange) are an effcent regulatory response to the moral hazard that n the absence of perfect observablty of trades, agents have ncentves to take on short postons that allow them to consume today and default tomorrow. As an extenson, we allow agents to alter ther producton schedules. In ths case, the moral hazard of excessve leverage n the OTC case translates nto an addtonal neffcency n terms of excessve producton. Ths result clarfes that the neffcency of OTC markets extends beyond just neffcent 4 In other words, the counterparty rsk externalty s orthogonal to a nettng externalty that default decson of one party depends on the default decson of ts counterpartes. The nettng externalty also arses n OTC markets operatng wthout a blateral nettng mechansm. 6

7 rsk-sharng. An example of ths neffcency could be ex-ante systemc rsk. Suppose that there s nsurance beng provded on economy-wde mortgage default rates. Ths would carry a sgnfcant rsk premum, gvng rse to perverse nsurer ncentves to default. Thus, n equlbrum, the nsurer would take on large and nadequately-collateralzed short-sellng (of protecton) on pools of mortgages and the nsured would feed the excessve creaton of the housng stock backng such mortgages. 5 The remander of the paper s structured as follows. Secton 2 provdes a smple example of the counterparty rsk externalty and the nsurance provson wth default rsk. Secton 3 presents our basc equlbrum model, the varous tradng settngs we study, and the welfare analyss. Secton 4 dscusses several possble extensons of the model. Secton 5.3 consders the polcy mplcatons of our model for OTC versus centralzed clearng. Secton 6 relates our work to exstng lterature. Secton 7 concludes. 2 Example Consder a two-perod economy wth three types of agents. There are two states of the world at t = 1, denoted by Good (G) and Bad (B). The probabltes of these states are p and (1 p), respectvely. Agents endowments n the two states are denoted as w (s), = 1, 2, 3, and s = G, B. Ther ntal endowments are denoted w0. We assume throughout that ntal endowments are large enough that there are no default consderatons at t = 0. For smplcty, we also assume that and w 1 (G) > w 2 (G) > w 3 (G) = 0, w 1 (B) = w 2 (B) = 0 < w 3 (B). In other words, agents of type 1 and 2 have endowment n good state of the economy, but none n the bad state, whereas agents of type 3 are endowed n the bad state but not n the good state. The utlty of agents of each type satsfes the mean-varance representaton: E[u(x 0, x(s)] = x 0 + E(x(s)) γ 2 var(x(s)), 5 Ths may be a partal explanaton of the role played by credt default swap nsurances and A.I.G. n fuelng the credt boom precedng the crss of

8 where x 0 s the resdual endowment at t = 0, and x(s) s the realzed endowment at t = 1, takng account of trades structured at t = 0 and materalzed at t = 1. We assume that the only traded contract s an nsurance (or a credt default protecton) whch resembles a put opton on the bad state of the economy. The contractual payoff of the contract s R(G) = 0 and R(B) > 0. For smplcty, we wll refer to R(B) smply as R. Importantly, the economy wll allow for default so that the actual payoff on the contract need not concde wth R. The nsurance contract must be pad for at t = 0 and we denote ts prce as q. To hghlght our man pont, we consder agents 1 and 2 purchasng nsurance contract from agents 3. We denote the long postons of agents 1 and 2 as z 0, = 1, 2, and the short poston of agents 3 as z 3 0. Note that the only agents that can default gven our assumptons are agents 3. We assume that n case they default, they suffer a lnear non-pecunary penalty as a functon of the postons defaulted upon, whose pecunary equvalent n the bad state s gven by ɛz 3. Broadly speakng, ths penalty can be nterpreted as loss of contnuaton of franchse value n a mult-perod settng. 2.1 OTC markets Consder the case of over-the-counter (OTC) tradng: agents do not observe the sze of the trades put on by other agents and hence prces cannot be condtoned on these. In other words, all agents take the prce per unt of nsurance as a gven constant (and not a schedule dependng on total nsurance sold by agents 3 n the economy). Agents are fully ratonal, however, and antcpate correctly the lkelhood of default, and ts consequent effect on the realzed payoff on the nsurance contract (R + ) relatve to the promsed payoff (R). Suppose the realzed postons on the long postons n state B s R + R. Then, the t = 0 payoffs to the three agents are (x 1 0, x 2 0, x 3 0) = (w 1 0 z 1 q, w 2 0 z 2 q, w z 3 q), and t = 1 payoffs n good and bad states are gven respectvely as and [x 1 (G), x 2 (G), x 3 (G)] = [w 1 (G), w 2 (G), w 3 (G)], [x 1 (B), x 2 (B), x 3 (B)] = [R + z 1, R + z 2, w 3 (B) R + z 3 ɛz 3 1 D ], 8

9 where 1 D s an ndcator varable whch takes on value of one f there s default (R + < R) and zero otherwse. Then, equlbrum n the economy s characterzed by the tradng postons, the payoff on the nsurance contract (nvolvng the possblty of default) and the cost of nsurance: (z 1, z 2, z 3, R +, q), such that 1. Each agent maxmzes ts expected utlty by choosng ts trade postons (as we descrbe below); 2. Market for nsurance clears: z 3 = z 1 + z 2 ; and, 3. In case of default, (we assume that) there s pro-rata sharng of agents 3 s total endowment between the long postons of agents 1 and 2: R + = { w 3 (B) f 1 z 1 +z 2 D = 1 R else Now, consder agent 1 s maxmzaton problem: max z 1 w 1 0 z 1 q + pw 1 (G) + (1 p)r + z 1 γ 2 var(x1 (s)), where var(x 1 (s)) = p(1 p)[w 1 (G) R + z 1 ] 2. Then, the frst-order condton for agent 1 mples that z 1 (R +, q) = 1 [ w 1 (G) + ((1 ] p)r+ q). (1) R + γp(1 p)r + Smlarly, we obtan for agent 2 s long poston that: z 2 (R +, q) = 1 [ w 2 (G) + ((1 ] p)r+ q) R + γp(1 p)r + (2) In other words, all else equal, agents 1 and 2 purchase more nsurance f they have greater endowment n the good state and less so f the cost of nsurance rses. On the other hand, the more nsurance agent 3 sells the hgher are ts ncentves to default n state B. To clarfy agent 3 s choce wth regards to 9

10 default, consder frst the case n whch t cannot default. In ths case ts problem s max z 3 w z 3 q + (1 p)[w 3 (B) Rz 3 ] γ 2 p(1 p)[w3 (B) Rz 3 ] 2, whch yelds z 3 ND = 1 R [ w 3 (B) ] ((1 p)r q). (3) γp(1 p)r In the lmt when there are no default costs, that s, ɛ = 0, agent 3 wth poston znd 3 wll not default n equlbrum only f w 3 (B) Rz 3 ND, whch turns out to be equvalent to requrng that q (1 p)r. Ths condton has the ntutve nterpretaton that the nsurer has ncentves not to default ex post only f the prce of nsurance s smaller than or equal to the expected payoff on the nsurance, or n other words, that there s no rsk premum n the nsurance prce. Ths wll, however, not hold n equlbrum n general, whenever the nsurance s aganst a rsk that cannot be fully dversfed away. 6 More generally, consder then the problem of agent 3, the nsurer, when we explctly allow for default at proportonal cost of default ɛ > 0: max z 3 w z 3 q (1 p)ɛz 3 γ 2 p(1 p)(ɛz3 ) 2. Clearly, the nsurer pledges the entre endowment n the bad state at t = 1 n order to collect as much nsurance premum as possble at t = 0. 7 Thus, 6 Ths s an mportant pont. Snce default s nherently a macroeconomc phenomenon, t explans why there s the moral hazard of default on part of nsurers sellng credt default swaps (CDS): CDS nherently contan at least some porton of aggregate rsk (or n the case of A.I.G., almost all porton). In contrast, there s less rsk of such a moral hazard for tradtonal nsurance busnesses: Tradtonal nsurances are on rsks such as death, accdents, etc., whch are easly dversfed away across agents n the economy, so that nsurers smply earn the actuarally far premum and do not earn a sgnfcant rsk premum. 7 Note that the no-default condton now takes the form: w 3 (B) (R + ɛ)z 3. 10

11 from the frst-order condton, we obtan that z 3 = q (1 p)ɛ γp(1 p)ɛ 2. (4) Thus, the lower the cost of default ɛ and greater the prce of nsurance q, the greater s the quantty of nsurance suppled by the nsurers. Substtutng for (z 1, z 2, z 3 ) n the market-clearng and bankruptcy condtons of the equlbrum yelds two equatons n the realzed nsurance payoff R + and nsurance prce q whch can be solved to characterze the equlbrum: R + (q) = w3 (B)γp(1 p)ɛ 2, (5) q (1 p)ɛ w 3 (B) = w 1 (G) + w 2 (G) + 2 γp 2q γp(1 p)r +. (6) Solvng ths system, we obtan a quadratc equaton n the cost of nsurance q, whch we can solve numercally. 2.2 Numercal example We parametrze the above economy wth w 1 (G) = 10, w 2 (G) = 5, and w 3 (B) = 10. We set p = 0.9 and vary ɛ n the range [0.1, 1.0]. Fgures 1, 2 and 3 plot respectvely the equlbrum quantty of nsurance sold (z 3 ), ts realzed payoff (R + ), and ts prce (q), all as a functon of ɛ, the proportonal deadweght cost of default. There s a crtcal value of ɛ below whch defaults take place and ths value s around Above ths value, there s no default. Interestngly, for all ɛ smaller than ths threshold value, the equlbrum s effectvely the same as far as rsk-sharng s concerned. In partcular, agents 3 transfer all ther endowment n the bad state at t = 1 to agents 1 and 2. To be precse, the equlbrum utltes (relatve to t = 0 endowments) are (U 1, U 2, U 3 ) = ( 1.97, 0.84, 1.35) regardless of ɛ n the default range. However, ths s not true of equlbrum quantty of nsurance and ts prce. For example, when ɛ = 0.5, the quanttes traded are (z 1, z 2 ) = (8.22, 2.74) wth z 3 = z 1 + z 2 ; there s 9% default on the contract (R + = 0.91); and, nsurance prce s q = In contrast, wth ɛ = 0.01, the quanttes traded become much larger: (z 1, z 2 ) = (410.95, ); there s 98% default on the contract (R + = 0.02); and, nsurance prce s q =

12 In other words, as the default ncentves for agent 3 become stronger, there s greater quantty of nsurance sold. Thus, there s greater default and greater deadweght costs suffered by agents 3. In turn, the equlbrum nsurance prce s smaller too. Default by the nsurer lowers the prce of nsurance snce the payoff on the contract s ratonally antcpated by those purchasng nsurance to be smaller. Put smply, the qualty of nsurance has gone down gven default rsk of the nsurer. 2.3 Ineffcency of OTC markets The neffcency of the equlbrum n example above stems from excessve deadweght costs of agent 3 s bankruptcy. Ths can be seen n Fgure 4 whch plots the sum of utltes of all three agents and also separately of agents 3. In effect, regardless of the value of ɛ, we obtan full transfer of endowment n the bad state from agents 3 to the other two agents. However, when ɛ s small, ths occurs n equlbrum wth agents 3 sellng quanttes of nsurance that lead to ther default. Hence, agents 1 and 2 enjoy the same equlbrum utlty as ɛ vares; n contrast, for ɛ < 0.548, default leads to deadweght costs borne by agents 3 and ther equlbrum utlty s substantally lower compared to ɛ It s clear n ths case that the planner can mprove upon the OTC case when ɛ s smaller than Essentally, the planner needs to enforce a poston lmt that restrcts agents 3 from sellng a quantty of nsurance z 3 that s beyond ther endowment n bad state w 3 (B). One way n whch ths poston lmt can be mplemented s through a non-lnear prcng schedule: q(z 3 ) = 0 f z 3 > w 3 (B), and q(z 3 ) determned by the markets otherwse. Whle n our specfc example, t s effcent for nsurance to be fully collateralzed so that any default s ruled out n equlbrum, ths s n general not true. What s however true, and we wll show below, s that the OTC markets always feature greater lkelhood of default n equlbrum compared to ts (Pareto) effcent level. Also beyond ths example, the hgh quantty of nsurance sold n OTC markets may also be welfare-reducng f nsurance has a moral hazard effect on part of hedgers, n terms of ther changng productve nvestments towards aggregate rsky assets. We extend the example to ths case n Secton 4.2. But frst, we derve the result on neffcency of OTC markets n a setup that generalzes the above example. 12

13 3 The economy We now buld on the above example to construct a general model of an OTC market wth default rsk and compare ts propertes wth those of fnancal markets regulated by a centralzed clearng mechansm. Effectvely, we extend a two-perod General Equlbrum (GE) exchange economy wth default (Geanakoplos, 1997, Geanakoplos and Zame, 1998, Dubey, Geanakoplos and Shubk, 2005) to allow for dfferent mechansms for fnancal market tradng. Agents and endowments The economy s populated by = 1,..., I types of agents. Let x 0 be consumpton of agent at tme 0. Let s = 1,..., S denote the states of uncertanty n the economy, whch are realzed at tme 1. State s occurs wth probablty p s, and p s = 1. Let x 1 be agent s consumpton s at tme 1, a random varable over the state space S: x 1(s), for s S. Let w 0 be the endowment of agent at tme 0; and w 1(s) her endowment at tme 1 n state s. The utlty of agent over consumpton n state s s denoted as u (x 0, x 1(s)) and belongs to the von-neumann Morgenstern class of expected utlty functons. Fnancal markets and default We assume, for smplcty, that only one fnancal asset s traded n ths economy, an asset whose payoff s an exogenous non-negatve S-dmensonal vector R. We can magne t representng a dervatve contract, e.g., a credt default swap. Agents sellng the asset mght default on ther requred payments. In partcular, agent s short postons are collateralzed by the pledgeable fracton α of her endowment at tme 1. In other words, n the event of default, credtors (counterpartes holdng long postons on the asset wth the defaultng party) have recourse only to a fracton α [0, 1] of the debtor s endowment w1(s). Only a fracton of the debtor s endowment can be pledged as collateral, for nstance, because part of the endowment s agent-specfc. Other than the defaultng agent smply losng her collateral to counterpartes, default s assumed to have a drect deadweght cost εz that s proportonal on the poston defaulted upon. Deadweght costs of default wll serve the convenent purpose of provdng a bound to short postons on the asset. Agents trade blaterally n fnancal markets. Even though one sngle asset s traded ex ante, the asset pay-off ex post depends on the type of the agent shortng t, as default decsons n turn do. Let z j + be long postons of 13

14 agents of type sold by agents of type j. Let z+ = ( ) z j + denote the long j I portfolo vector of agents of type (wth z+ = 0, by constructon). Let z be the short poston of agents of type. As we wll explan shortly, all short postons are symmetrc for the agents shortng the asset, ndependently of the counterparty, so that there s no need to ndex short postons of an agent by the counterparty. 3.1 OTC markets Consder frst the case n whch tradng s ntermedated n over-the-counter (OTC) markets. We model OTC markets as standard compettve markets wth no centralzed clearng or centralzed counterparty (such as an exchange). We assume that no credtor has prvleged recourse to a debtor s collateral n case of default. Nonetheless, a bankruptcy mechansm operates to dstrbute the cash flow delvered on the short postons (full cash flow or endowment recovered n case of default) pro-rata amongst the long postons. To be precse, consder an agent of type shortng the asset. At equlbrum, the sum total of the repayment cash flow s dstrbuted pro-rata among the holders of long postons wth counterparty. 8 The default condton An agent of type wth (long, short) portfolo poston (z+, z ) wll default n perod 1 n state s ff her ncome after assets pay off s smaller than the non-pledgeable fracton of her endowment. Let R j (s) denote the payoff n state s of her long asset portfolo wth counterparty j I\{}. The payoff R j (s) s taken as gven by each agent, though t s endogenously determned, dependng on the equlbrum default rate of agents of type j n the economy (as shown later). Consder an agent wth a net short poston z > 0. She wll default on her short poston n state s ff: w 1(s) + j R j (s)z j + R(s)z < (1 α) w 1(s) εz. (7) Note that we allow for an agent to mantan at the same tme both short and long postons on the asset: z and z j + > 0, for some j. In other words, 8 In fact, n the model the bankruptcy mechansm wll pool all repayments of agents of type and redstrbute them pro-rata to the counterpartes. Ths s wthout loss of generalty, as we concentrate on symmetrc equlbra. 14

15 we assume that the clearng mechansm provded by OTC markets does not nclude blateral nettng. We shall study nettng later on n the secton. Let I d (z +, z ;, s) be an ndcator varable takng on value 1 f agent wth poston (z +, z ) wll default at equlbrum n state s, and zero otherwse. Fnally, let I nd (z +, z ;, s) = 1 I d (z +, z ;, s). Wthout loss of generalty, I d (z +, 0;, s) = 0. Equlbrum payoffs on long and short postons: Snce all long postons share pro-rata the payments from defaultng and non-defaultng short postons, the equlbrum payoff of the asset shorted by agent j, denoted R j (z+, j z ; j s), s gven by R j (z j +, z j ; s) = { αw j 1 (s) z j f I d (z j +, z j ; j, s) = 1 R(s) otherwse (8) where (z j +, z j ) s the portfolo of agents of type j at equlbrum. Opacty In OTC markets, there s no centralzed clearng and dsclosure, nor any centralzed counterparty that sees all trades. Thus, the trades of each agent, (z+, z ), are not observed n OTC markets by other agents. Prces and budget constrants Long and short blateral postons wll n general be traded at a prce q j, where the apex j denotes the type of the agent n the short poston. Importantly though, the prce does not depend on her portfolo, snce t s not observed. The budget constrants of agent n the OTC market are thus gven by: x 0 + j qj z j + { q z = w0, x 1(s) = max w1(s) + } j Rj (s)z j + R(s)z, (1 α) w1(s) εz (9) where z j +, z 0, for any j. The untary prce of a blateral asset trade z j + depends on the short agent s type j, as the type determnes the agent s endowment whch s publc knowledge and affects her probablty of default. The fact that the ask prce for agent j s nstead not condtoned on her trades, as we noted, s the prmary 15

16 dstncton between OTC and markets wth a centralzed clearng mechansm: contract terms (prces, nterest rates, collateral requrements, etc.) are not condtoned on agents trades n the case of OTC markets whereas they wll be n case of a centralzed clearng mechansm (Secton 3.3). At the compettve equlbrum, fnancal mar- Compettve equlbrum kets clear: z j + z j = 0, for any j. (10) Furthermore, at equlbrum, the payoff R j (s) must satsfy the consstency condton: R j (s) = R j (z j +, z j ; s) = { αw j 1 (s) z j f I d (z j +, z j ; j, s) = 1 R(s) otherwse (11) Let u (x m (s) = MRS x 0, x 1(s)) (s) p 1 s (12) u (x x 0, x 1(s)) 0 denote the margnal rate of substtuton between date 0 and state s at date 1 for agents of type at equlbrum. Equlbrum prces are then such that 3.2 OTC wth nettng q j = max E ( m R j), for any j. (13) In the OTC markets modeled n the prevous secton an agent s allowed to go both short and long on the asset, and n equlbrum t mght be that z > 0 and, at the same tme, z j + > 0 wth some counterparty j. In ths context, a mechansm for blateral (ex-post, that s, state-by-state) nettng mght have welfare consequences. Whle blateral nettng mght be dffcult to mplement n OTC markets, we nonetheless defne here an economy wth OTC markets and nettng so as to be able to better dstngush the welfare effects of varous dstnct components of OTC and centralzed market clearng mechansms. 16

17 We model blateral nettng by requrng that agents are wthout loss of generalty on one sde only of the market, that s, for an agent of type : z j +z = 0, for any j. (14) As a consequence, an agent of type wth a short poston z > 0 wll default n state s ff: w 1(s) R(s)z < (1 α) w 1(s) εz. (15) Let I d (z ;, s) be an ndcator varable takng on value 1 f agent wth short poston z wll default at equlbrum n state s, and zero otherwse. Short postons payoffs are now wrtten R j (z j ; s) = { αw j 1 (s) z j f I d (z j ; j, s) = 1 R(s) otherwse and budget constrants of agents are restrcted by z j +z = 0, for any j. Fnally, at a compettve equlbrum n an economy wth OTC markets and nettng, fnancal markets clear, the consstency condton R j (s) = R j (z j ; s) s satsfed, and equlbrum prces are 3.3 Centralzed clearng q j = max E ( m R j), for any j. In the prevous secton we formalzed the compettve equlbrum of an economy n whch fnancal market trades are ntermedated by an OTC market. In ths secton we model nstead the operaton of a centralzed clearng mechansm. We model centralzed clearng mechansms as composed of two fundamental functons: blateral nettng and transparency. Transparency s obtaned because a centralzed clearng mechansm aggregates centrally all the nformaton about trades and dssemnates t to market partcpants. 9 Regardng bankruptcy resoluton, we contnue to assume that no credtor has drect prvleged recourse to a debtor s collateral, n case of default; and that, at equlbrum, the sum total of cash flows s dstrbuted pro-rata among 9 We stress that a centralzed clearng mechansm need not centrally ntermedate the trades as, for nstance, a centralzed exchange would do. We study centralzed exchanges n Secton

18 the holders of long postons. Because of blateral nettng, as already noted, an agent wth a short poston z > 0 wll default n state s ff w 1(s) R(s)z < (1 α) w 1(s) εz ; and the equlbrum payoff of the asset shorted by agent j s thus gven by R j (z j ; s) = { αw j 1 (s) z j f I d (z j ; j, s) = 1 R(s) otherwse. Because of transparency, each agent n the economy has access to detaled nformaton about all trades and can condton contract terms on ths nformaton. We assume that prces are set n a compettve manner. Specfcally, agents are prce-takers. However, the payoff on the short poston of agent j depends on the poston tself, z, j and prces wll n general reflect such dependence. Dfferent agents wll face dfferent prces, reflectng the probablty of default mpled by ther characterstcs: ther type as well as ther tradng postons. Ths requres us to modfy the prce-takng assumpton for short postons n an mportant manner (that s smlar n sprt to modfcatons n Acharya and Bsn, 2008, and Bsn, Gottard and Ruta, 2009). Specfcally, an agent of type j wth short poston z j wll face an ask prce map q (z j ) j = max E ( m R j (z ) ) j. (16) In other words, an agent of type j understands that the prce he wll face for a short poston depends on the total short postons he sells, z. j Furthermore, an agent of type j understands that the prce he wll face for a short poston s equal to the hghest margnal valuaton across all agents of the payoff assocated to hs/her poston, R (z j ). j Prce takng s then represented by the fact that agents take the vector of prcng kernels ( m 1,..m,.., m I) as gven. On the other hand, regardng long postons, the payoff R j (s) s taken as gven by each agent, and so s the prce q j. The budget constrants of agent are thus gven by: x 0 + j qj z j + { q (z )z = w0, x 1(s) = max w1(s) + } j Rj (s)z j + R(s)z, (1 α) w1(s) εz (17) where z j +, z 0, z j +z = 0, for any j. 18

19 At compettve equlbrum, the portfolos demanded by all agents clear: z j + z j = 0, for any j, (18) and the prce maps and returns are ratonally antcpated by agents: q j = q (z j ) j = max E ( m R j (z ) ) j, (19) R j (s) = 3.4 Welfare { αw j 1 (s) z j f I d (z j ; j, s) = 1 R(s) otherwse, for any j. (20) How does the compettve equlbrum under OTC markets compare n terms of effcency propertes to the compettve equlbrum under centralzed exchange? To answer ths queston, we wrte down the constraned Pareto effcent outcome as the soluton to the followng problem: max λ E ( u (x 0, x 1) ) (x 0,x 1,zj +,z ),j s.t. x 0 w0 = 0, x 1(s) w1(s) = 0, for any s { x 1(s) = max R j (z j ; s) = { αw j 1 (s) z j w 1(s) + j R j (s)z j + R(s)z, (1 α) w 1(s) εz f I d (z j +, z j ; j, s) = 1 R(s) otherwse }, (21) (22) (23) where z+, j z 0, z+z j = 0, for any j. (24) where λ s the Pareto weght assocated to agents of type. Ths s the standard constraned effcency problem for a GE economy once t s assumed that default s not controlled by the planner. The constrant (21) serves two purposes: 19

20 () t restrcts the planner s allocatons to those that can be acheved wth the lmted fnancal nstruments avalable n the economy; and () t accounts for the fact that each agent can choose to default or not, n each state s: 10 consumpton n a default state s s (1 α) w 1(s) εz, the non-pleadgeable fracton of endowment net of the deadweght costs. 3.5 Results We can derve the followng results on the constraned effcency of the centralzed exchange economy and the (generc) constraned neffcency of the economy wth OTC markets: Proposton 1. Any compettve equlbrum of an economy wth a centralzed clearng mechansm s constraned Pareto optmal. The ntuton for effcency of the centralzed exchange economy s that each agent that s short on the asset faces a prce q (z j ) j = max E ( m R (z j ) ) j that s condtoned on her postons. Consequently, she nternalzes the effect of her default on the payoff of long postons on the asset R j (s). The observablty of all trades allows for condtonng of prces based on ths nformaton and hence n turn t enables the economy wth default rsk to get agents to nternalze any externalty ther default choces mpose (n terms of neffcent rsk-sharng) on other agents due to postons that lead to excessve defaults ex post. It s straghtforward to show, on the contrary, that equlbra n economes wth OTC markets are not n general constraned Pareto effcent. Frst of all consder an economy wth OTC markets wthout blateral nettng. As we noted, n ths case, an agent of type wth a short poston z > 0 wll default n state s ff: { } x 1(s) = max w 1(s) + j R j (s)z j + R(s)z, (1 α) w 1(s) εz. (26) 10 Formally, the constrant ncludes the ncentve compatblty constrant for each agent s choce of default: u (x 0, x 1(s)) u (x 0, (1 α) w 1(s) εz ). (25) 20

21 The default decson of an agent of type, therefore, depends on R j (s), that s, on agents j s default decsons, whch n turn depend on s default decsons, ntroducng a nettng externalty at equlbrum. It s the case then that, Compettve equlbra of economes wth OTC markets wthout nettng are robustly not Pareto effcent. The proof of ths statement, however, requres some complex dfferental computatons and s omtted. It s an adaptaton of that n Bsn, Geanakoplos, Gottard, Mnell, and Polemarchaks (2001). Wth nettng, on the other hand, an agent wth a short poston z > 0 wll default n state s ff: w 1(s) R(s)z < (1 α) w 1(s) εz. (27) No nettng externalty arses then n ths case. We shall show however that equlbra of an economy wth OTC markets and nettng are also typcally constraned neffcent. In other words, the transparency provded by centralzed clearng mechansm (and not by OTC market economes, wth or wthout nettng) s typcally requred for constraned effcency. Proposton 2. Compettve equlbra of economes wth a centralzed clearng mechansm cannot be robustly supported as equlbra n economes wth OTC markets, wth or wthout nettng. 11 More specfcally, any compettve equlbrum of the economy wth centralzed clearng mechansm n whch default occurs wth postve probablty cannot be supported n the economy wth OTC markets, wth or wthout nettng. The ntuton s that n OTC markets, wth or wthout nettng, each agent j that s short on the asset faces a prce q j that s not condtoned on her poston z j. Consequently, she does not nternalze the effect of her default on the payoff of long postons on the asset R j. Ths s a counterparty rsk externalty n addton to the nettng externalty. More generally, t s also the case that 11 Formally, by robustly we mean: for an open set of economes parametrzed by agents endowments and preferences. 21

22 Compettve equlbra of economes wth OTC markets and nettng are robustly not constraned Pareto effcent. 12 Fnally, let the leverage of agent j, L j, be defned as the value of her (promsed) debt dvded by the value of her endowment Then, L j E(mj Rz j ) E(m j w j 1). (28) Proposton 3. For deadweght costs ε small enough, compettve equlbra of economes wth OTC markets, wth or wthout nettng, are characterzed by weakly greater (and robustly by strctly greater) leverage and default wth respect to equlbra of the same economy wth a centralzed clearng mechansm. Snce ask prces n economes wth OTC markets, wth or wthout nettng, do not penalze the short postons for ther own ncentves to default, agents have ncentves to exceed the Pareto effcent short postons. Indeed, the proof of these man propostons n the Appendx shows that as long as prce on the short poston s postve, whch s robustly the case n equlbrum, there s ncentve to go excessvely short, collect the prema up front, and default ex post. Ths ncreases the equlbrum default rate and leads to neffcent rsk-sharng. 13 For effcent rsk-sharng, t s n general necessary to be able to commt to future payoffs on fnancal assets, but n OTC markets, such commtment s not enforced through prces and ncentves to go excessvely short and default dlute the clams of shortng agent s counterpartes. Opacty and counterparty rsk externalty When combned together, Propostons 1, 2, and 3 mply that a centralzed clearng mechansm s an effcent response to the moral hazard that n the absence of perfect observablty of trades, agents have ncentves to take on short postons that allow 12 We omt the proof of ths statement, once agan, to avod some complex dfferental computatons. 13 If ε = 0, z s unbounded and, strctly speakng, the economy has no equlbrum. Ths s just a extreme case, whch s of nterest to dentfy the force towards borrowng and default bult nto our model of OTC markets. Postve deadweght costs, ε > 0, guarantee exstence. 22

23 them to consume today and default tomorrow. Our analyss, especally n Propostons 2 and 3, makes t precse that t s the opacty or lack of transparency of the OTC markets that leads to ex ante neffcency n terms of excessvely large short postons or leverage. We call ths neffcency counterparty rsk externalty snce t stems from counterparty rsk, the rsk of default of the short party on long postons. Excessve level of such counterparty rsk lowers the payoff to all long postons n the economy, consttutng an mportant negatve externalty on economy-wde rsk sharng. In equlbrum, agents antcpate the lowerng of payoff on long postons and the prce of nsurance falls. However, ths s not suffcent to preclude the nsurers from sellng large quanttes of nsurance and defaultng ex post, resultng n neffcently large deadweght costs of bankruptcy. Whle the externalty s not fully nternalzed n OTC markets, t s nternalzed f there s a centralzed clearng mechansm that provdes dsclosure or transparency of agents postons. 4 Extensons 4.1 Centralzed exchange economy In ths secton we study an economy n whch all asset trades are operated by a compettve centralzed exchange. In essence, the exchange s a centralzed counterparty that observes all trades and condtons contract terms for ndvdual agents on these trades. We shall contnue to assume that no credtor has drect prvleged recourse to a debtor s collateral, n case of default. The centralzed exchange, on the other hand, has full recourse to the debtors pledgeable collateral. Furthermore, the exchange operates as a bankruptcy mechansm, by dstrbutng the cash flow of the short postons of the asset, pro-rata wth respect to the long postons. An agent, takng a long poston z j + > 0 wth short counterparty j, takes the return R j as well as the prce q j as gven. The equlbrum payoff of the asset shorted by agent j, denoted R j (z ; j s), contnues to be gven by R j (z ; s) = { αw 1 (s) z f I d (z +, z ;, s) = 1 R(s) otherwse (29) Consequently, an agent of type j wth short poston z wll face an ask prce 23

24 map q j (z j ) = max E ( m R j (z j ) ). (30) Prce ( takng s represented by the fact that agents take the prcng kernels m 1,.., m,.., m I) as gven. We turn next to the decson problem of the compettve centralzed exchange, whch controls the supply of the asset to agents. Let the supply offered by the exchange to agent for long and short postons be denoted (θ+, j θ, s.t. θ+θ j = 0),j. 14 Then, gven the supples, the exchange can compute the cash flow of the short postons of agents: R j (θ j ; s) = { αw j 1 (s) θ j f I d (θ j ; j, s) = 1 R(s) otherwse. (31) The exchange prces a untary short poston as max E ( m R j (θ ) ) j, takng as gven the stochastc dscount factor of the agent who values t the most at the margn, that s the agent who would acqure t f offered. To summarze, ( a compettve exchange takes as gven the stochastc dscount factors m 1,.., m,.., m I). Crucally, the exchange antcpates the compostonal effects on default rsk of portfolos of dfferent agent types, that s, t recognzes how each agent s ncentves to default are affected by ts postons (θ+, j θ ). Thus, the exchange solves the followng problem: s.t. max (θ j +,θ ) [ j max E ( m R j (θ j ) ) ( ) ] θ j + θ j (32) θ j + θ j = 0, for any j. (33) At compettve equlbrum, the portfolos demanded by the agents are offered by the compettve exchange and markets clear: 14 By constructon, θ + = 0. θ j + = z j +, θ = z,, j, (34) 24

25 and the prce maps and returns antcpated by agents are consstent wth those perceved by the exchange: q (z j ) j = max E ( m R j (z j ) ). (35) q j = q (z j ) j = max E ( m R j (z j ) ). (36) R j (s) = R j (z ; j s). (37) It s straghtforward to show that the compettve equlbrum allocatons of economes wth a centralzed exchange concde wth those of economes wth a centralzed clearng mechansm. Therefore, by Proposton 1, compettve equlbrum allocatons of economes wth a centralzed exchange are constraned effcent. Note however that a centralzed exchange whch ntermedates all fnancal market trades s a much more nvasve nsttuton than a centralzed clearng mechansm. 4.2 Producton rsk In our whole analyss the aggregate endowment of the economy, I w 0 at tme 0 and I w s n each state s S, has been kept constant. Consequently, the neffcency of OTC markets has only dstrbutonal effects: nsurers have ncentves to take on excessve leverage, asset prces ratonally reflect equlbrum leverage, and hence nsurance markets endogenously fal to serve ther purpose. Therefore, resources are ms-allocated n equlbrum. Nonetheless, no resources are lost or altered n the aggregate other than the deadweght costs of bankruptcy. Ths ceases to be the case f we allow for producton n the economy, as we proceed to show n ths secton. 15 Suppose each agent s endowed wth a producton functon f whch transforms consumpton goods at tme 0 nto consumpton goods at tme 1. More precsely, consder the followng technology. Let K = k 2 k 1 : denote a captal allocaton vector over A actvtes k A (e.g., projects), so that k 1 + k k A = k. The producton functon can then 15 Whle we restrct to an economy wth backyard producton on the part of agents, for smplcty, the analyss drectly extends to a frm-level producton economy. 25

26 be defned as the output n state s gven captal allocaton K: f(s, K), s. 16 Note that, by allowng for multple technologcal actvtes (A 2), ths formulaton allows for some control of the agents over the dstrbuton of captal across actvtes and hence over the probablty dstrbuton of outcomes, that s, over producton rsk. Wth ths technology n place the equlbrum analyss of centralzed clearng and OTC economes can be extended to producton. For nstance, the budget constrants n the economy wth a centralzed clearng mechansm become: x 0 + j qj z j + q (z )z = w 0 k { x 1(s) = max w1(s) + } j Rj z j + R(s)z + f(s, K ), (1 α) w1(s) εz (38) and agent chooses a non-negatve portfolo (z+, j z, s.t. z+z j = 0) as well as a non-negatve captal allocaton K. Budget constrants n the OTC economes are smlarly formulated. It s easy to show that, n the producton economy, 1. A centralzed clearng mechansm contnues to decentralze constraned Pareto effcent allocatons; and 2. The generc neffcency of OTC markets manfests tself as over-producton or n other words undertakng of excessve producton rsk. An example of ths neffcent rsk-takng s the possble effect of credt default swaps sold by A.I.G. to a large number of fnancal frms n the Unted States and the Europe, effectvely nsurng tal rsk of corporate bond and loan portfolos and mortgage-backed securtes. Ths s tantamount to sellng nsurance on economy-wde default rsk. Our model mples that n an OTC settng for sellng such nsurance, the nsurer would take on large and nadequately-collateralzed sellng of protecton on pools of default rsk; n turn, the nsured would feed the excessve creaton of the housng stock and corporate assets backng such pools of aggregate default rsk. To see ths n a transparent manner, we revst our example economy of Secton 2. Suppose that agents 1 have access to a producton technology, 16 We assume f s contnuously dfferentable, strongly ncreasng, and strctly quasconcave. 26

27 e.g., makng mortgages, that yelds per unt of nvestment f(g) n the good state and f(b) n the bad state, where the nvestment contans aggregate rsk n that f(g) > f(b). Then denotng the level of nvestment as k, agent 1 s maxmzaton problem s: max z 1,k w 1 0 k z 1 q+p [ w 1 (G) + f(g)k ] +(1 p) [ R + z 1 + f(b)k ] γ 2 var(x1 (s)), where var(x 1 (s)) = p(1 p)[w 1 (G) + f(g)k R + z 1 f(b)k] 2. Then, for a gven level of nsurance z 1, the frst-order condton for agent 1 s nvestment decson mples that k(z 1 ) = [pf(g) + (1 p)f(b) 1] γp(1 p) [f(g) f(b)] 2 [w1 (G) R + z 1 ] [f(g) f(b)]. Intutvely, the nvestment s more attractve the greater s ts net present value (pf(g) + (1 p)f(b) 1), and greater s the extent of nsurance and ts qualty (R + z 1 ) as nsurance lowers the attendant rsk of the nvestment. Now, assumng the nvestment s ndeed net present value, nsurance s desrable up to an extent. It reduces rsk of the producer (agent 1) and facltates greater nvestment n the economy. However, as s clear from the above maxmzaton, agent 1 does not take account of the fact that n case nsurance s assocated wth default of the nsurer (agent 3), there may be deadweght costs (ɛz 3 whenever z 3 > w 3 (B)) to facltatng producton n the economy. On the other sde, the nsurer s unable to commt not to default gven the attracton of collectng rsk premum upfront and defaultng on nsurance ex post. As explaned n last remarks of Secton 2, default could be restrcted (and f t be Pareto effcent, even elmnated) by requrng that nsurers sutably (possbly fully) collateralze nsurance sold. Dong so would restrct leverage n the economy and ensure productve effcency n that nvestments take account of deadweght costs of rsk transfers nvolved n managng the rsk of nvestments. We leave the detaled analyss of the full-blown producton economy, notng that centralzed clearng can n fact acheve the outcome that planner would produce even n decentralzed markets. 27

28 5 Dscusson 5.1 Interpretng default and bankruptcy costs A central feature of our modelng technology was the strategc nature of default sell nsurance today and default tomorrow and the ex-post costs assocated wth such default. It s useful to nterpret ths feature n vew of practcal settngs n whch fnancal frms trade. Agan, the example wth A.I.G. as the protagonst s useful. A.I.G. had traders (specfcally, at A.I.G. Fnancal Products) who were engaged n the busness of sellng nsurance through synthetc credt default swaps on portfolos of mortgages and corporate loans. Ther ncentve to sell a large quantty of such swaps s as n the model to collect premums upfront and get pad salares and bonuses based on these premums. The result was a hghly levered bet of A.I.G. on the tal rsk of the economy, that s, the lkelhood of default of A.I.G. n case aggregate rsk materalzed was rather large. Indeed, A.I.G. as an enterprse tself suffered substantal costs of the resultng default on these swaps. These costs can be nterpreted as the parameter ɛ n the model. However, due to lmted lablty, these costs were not borne by traders who sold the swaps but by rest of A.I.G. s busnesses (such as lfe and property nsurance) whose franchse value s at least n part beng deployed to pay off A.I.G. s (non baled-out) postons. In contrast to ths example, our modelng of default had the same agent sellng large quanttes of nsurance, defaultng ex post and sufferng the bankruptcy costs. However, as seen n our examples and formal analyss, when these costs (ε) were small, default moral hazard became a relevant concern, and n turn, nduced counterparty rsk externalty. Ths case s more n the sprt of the A.I.G. example where traders bore only a small cost n case default materalzed. It should be noted that whle we have focused on centralzed clearng and exchange as mechansms to elmnate the counterparty rsk externalty, another possble remedy s to drectly address the ssue of default moral hazard. Ths would requre the regulator to ncrease the bankruptcy costs suffered by defaultng fnancal frms, e.g., by mposng state-contngent penaltes. To the extent such penaltes are restrcted by lmted lablty, our analyss hghlghts that mprovng tradng nfrastructure through centralzed clearng can serve as an mportant part of regulatory desgn to contan systemc rsk and leverage. 28