Centralized versus Over-The-Counter Markets

Transcription

1 Centralzed versus Over-The-Counter Markets Vral Acharya London Busness School, NYU-Stern, CEPR and NBER Alberto Bsn NYU and NBER December 23, 2009 We are grateful to Rob Engle for nsghtful dscussons. We also thank comments from Erc Ghysels and semnar partcpants at the Federal Reserve Bank of New York. 1

2 Centralzed versus Over-The-Counter Markets Abstract The opacty of over-the-counter (OTC) markets n whch a large number of nancal products ncludng credt dervatves trade appears to have played a central role n the ongong nancal crss. We model such OTC markets n general equlbrum wth default as markets for rsk sharng where agents nancal postons are not mutually observable. In 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-e cent ones. Thus, OTC markets feature a counterparty rsk externalty that we show can lead to ex ante productve ne cency. Ths externalty s absent when tradng s organzed va a centralzed counterparty, e.g., an exchange observng all trades.

3 1 Introducton amd motvaton Most nancal contracts are arrangements between two partes to delver goods or cash n amounts and at tmes that depend upon uncertan future events. Desgned approprately, nancal contracts facltate rsk-sharng n the economy. There may be many rsks n such contracts, but one addtonal rsk to be evaluated at the tme of contractng s the rsk that the counterparty wll not ful ll ts future oblgatons. Ths counterparty rsk s d cult 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 a ect the terms of trade can be talored to mtgate counterparty rsk, but the extent to whch ths can be acheved, and how e cently 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 spec c contracts, for example, credt default swaps, 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 ne cent levels of rsk-sharng. Counterparty rsk externalty s the e ect 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 rst one. Put smply, the default rsk on one deal depends on what else s done. The ntuton for our result concernng the ne cency 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 e ectvely 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 1 The bankruptcy code may be spec ed 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 also ncur sgn cant losses, creatng systemc rsk n the economy or more formally, ne cent ex-ante rsk-sharng. 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 re ected 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 rst place. Whle a number of nancal nnovatons n xed 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 o er 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). We show formally that when tradng s organzed n the form of a centralzed exchange, the condtonng of contract terms for each party on ts overall postons s su cent 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 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. E ectvely, centralzed tradng creates an ntermedary for whom agents trades are not opaque and ths s su cent to acheve the e cent 4

5 rsk-sharng outcome. 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 nancal 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 payo 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 payo 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 payo externalty on other trades. We call ths spllover as counterparty rsk externalty." In ths setup, we consder two tradng structures and ask whether counterparty rsk externalty leads to ne cent rsk-sharng. For pedagogcal purposes, we start wth the centralzed exchange n whch a compettve central counterparty observes all trades and sets prcng schedules for agents that are condtonal on ths knowledge. We show that the compettve equlbrum n the economy wth a centralzed exchange s constraned Pareto e cent. Next, we consder the OTC settng n whch 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 study two d erent cases, one n whch a centralzed bankruptcy mechansm operates to dstrbute the cash ow delvered on the short postons of the asset pro-rata wth respect to the long postons and one n whch the bankruptcy mechansm s blateral. We show that, n ether case, 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 the compettve equlbrum n the OTC economy s genercally ne cent compared to constraned Pareto e cent outcome. The ne cency 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 bene t 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 payo snce the realzed nsurance payo s smaller when nsurer s more lkely to default. In our model, we capture the resultng ne cency 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 centralzed markets such as an exchange are an e cent 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. Our analyss also makes t precse that t s the opacty or lack of transparency of the OTC markets that leads to ex-ante ne cency n terms of excessvely large short postons or leverage. The ne cency of OTC n fact obtans wth a centralzed bankruptcy mechansm as well as wth a blateral bankruptcy resoluton mechansm. 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 ne cency n terms of excessve producton. Ths result clar es that the ne cency of OTC markets extends beyond just ne cent rsk-sharng. An example of ths ne cency could be ex-ante systemc rsk. Suppose that there s nsurance beng provded on economy-wde mortgage default rates. Ths would carry a sgn cant 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. 4 4 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

7 In future, we plan to consder blateral OTC markets n the presence of a large" ndvdual agent that e ectvely observes the trades of all others but whose trades are not seen by others. Such an agent would enjoy monopoly rents n the OTC settng, whch n turn would reduce prvate ncentves n the economy to coordnate on a centralzed tradng platform and acheve Pareto mprovement. Furthermore, nformal dscussons motvated by the model suggest extensons n whch excessve leverage and excessve producton can lead to a bubble" n the market for a collateral good (e.g., the housng stock), a subsequent crash upon realzaton of adverse shocks, and a breakdown of credt markets n those states. Fnally, our analyss suggests that the possblty of regulatory forbearance of too bg to fal" postons can result n ex-ante ne cences even wth centralzed exchange tradng. 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 GE model, the centralzed exchange case, the OTC case, the Pareto e cent case, and the welfare analyss. Secton 4 dscusses several possble extensons of the model. Secton 5 consders the polcy mplcatons of our model for OTC versus centralzed tradng. 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, and ther ntal endowments are denoted as 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. 7

8 The utlty of agents of each type sats es the mean-varance utlty structure: E[u(x 0 ; x(s)] = x 0 + E(x(s)) 2 var(x(s)); 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 payo 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 payo 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 su er a lnear non-pecunary penalty as a functon of the postons defaulted upon, whose pecunary equvalent n the bad state s gven by z 3. Broadly speakng, ths penalty can be nterpreted as loss of contnuaton of franchse value n a mult-perod settng. Suppose the realzed postons on the long postons n state B s R + R. Then, the t = 0 payo s 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 payo s 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); 0]; [x 1 (B); x 2 (B); x 3 (B)] = [R + z 1 ; R + z 2 ; w 3 (B) R + z 3 z 3 1 D ]; where 1 D s an ndcator varable whch takes on value of one f there s default (R + < R) and zero otherwse. We assume that tradng s over-the-counter (OTC) so that agents do not observe the sze of the trades put on by other agents and hence prces 8

9 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 e ect on the realzed payo on the nsurance contract (R + ) relatve to the promsed payo (R). Then, equlbrum n the economy s characterzed by the tradng postons, the payo 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 + = w3 (B) z 1 + z 2 : Now, consder agent 1 s maxmzaton problem: where max z 1 w 1 0 z 1 q + pw 1 (G) + (1 p)r + z 1 2 var(x1 (s)); var(x 1 (s)) = p(1 p)[w 1 (G) R + z 1 ] 2 : Then, the rst-order condton for agent 1 mples that z 1 (R + ; q) = 1 w 1 (G) + ((1 p)r+ q) : (1) R + p(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 + p(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. 9

10 On the other hand, the more nsurance agent 3 sells the hgher are ts ncentves to default n state B. To clarfy agent 3 choce wth regards to default, consder rst 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 ] whch yelds z 3 ND = 1 R w 3 (B) 2 p(1 p)[w3 (B) Rz 3 ] 2 ; ((1 p)r q) : (3) p(1 p)r In the lmt for no default costs, = 0; agent 3, holdng the poston z 3 ND wll n fact not default n equlbrum only f w 3 (B) Rz 3 ND; whch turns out 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 the expected payo 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 dvers ed away. 5 More generally, let s consder then the problem of agent 3; the nsurer, when we explctly allow for default at costs > 0: max z 3 w z 3 q (1 p)z 3 2 p(1 p)(z3 ) 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. 6 Thus, 5 Ths s potentally an mportant pont as t explans why there s the default moral hazard on part of nsurers for credt default swaps whch nvarably contan at least some porton of aggregate rsk (or n the case of A.I.G., almost all porton) snce default s nherently a macroeconomc phenomenon. 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 dvers ed away across agents n the economy, so that nsurers smply earn the actuarally far premum and do not earn a sgn cant rsk premum. 6 Note that the no-default condton now takes the form: w 3 (B) (R + )z 3 : 10

11 from the rst-order condton, z 3 = q (1 p) p(1 p) 2 : (4) 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 payo R + and nsurance prce q whch can be solved to characterze the equlbrum: R + (q) = w3 (B)p(1 p) 2 ; (5) q (1 p) w 3 (B) = w 1 (G) + w 2 (G) + 2 p 2q p(1 p)r + : (6) We obtan a quadratc equaton n the cost of nsurance q, whch we solve numercally. 2.1 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 n the range [0:1; 1:0]. Fgures 1, 2 and 3 plot respectvely the equlbrum quantty of nsurance sold (z 3 ), ts realzed payo (R + ), and ts prce (q), all as a functon of, the deadweght cost of default. There s a crtcal value of below whch defaults take place and ths value s around 0:548. Above ths value, there s no default. Interestngly, for all smaller than ths threshold value, the equlbrum s e ectvely 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 n the default range. However, ths s not true of equlbrum quantty of nsurance and ts prce. For example, when = 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 = 0:30. In contrast, wth = 0:01, the quanttes traded become much larger: (z 1 ; z 2 ) = (410:95; 136:98), there s 98% default on the contract (R + = 0:02), and nsurance prce s q = 0:01. 11

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 su ered by agents 3. In turn, the equlbrum nsurance prce s smaller too. Default by the nsurer lowers the prce of nsurance snce the payo 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. The potental ne cency of the equlbrum n example above stems from excessve deadweght costs of agent 3 s bankruptcy. More generally, the hgh quantty of nsurance sold may also be welfare-reducng f nsurance has a moral hazard e ect on part of agents 1 and 2, n terms of ther changng productve nvestments towards aggregate rsky assets. 3 The model We now formalze the above numercal example for an OTC market wth default rsk and explan why a centralzed exchange mproves upon t. To start wth, we develop a general equlbrum (GE) model wthout producton or ntermedaton, e ectvely, a two-perod GE model wth default (Geanakoplos, 1997, Geanakoplos and Zame, 1998, Dubey, Geanakoplos and Shubk, 2005). We then extend t to allow for the d erent nformaton structures of centralzed versus OTC markets, s enough to llustrate the man ssues. 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 ; P p s = 1. Let x 1 be agent s consumpton at s tme 1, a random varable over the state space S: x 1(s); for s 2 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 asset and tradng We assume, for smplcty, that only one nancal asset s traded n ths economy, an asset whose payo s R, a non- 12

13 negatve vector n S: The payo R s exogenous. We can magne t representng a dervatve contract, e.g., a credt default swap. Default rsk Let z + and z be the long and short postons, respectvely, of agent n nancal markets. Agents sellng the asset mght default on ther requred payments. In partcular, agent s short postons are collateralzed by the pledgeable fracton 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 2 [0; 1] of the debtor s endowment w 1(s): Only a fracton of the debtor s endowment can be pledged as collateral, for nstance because a part of the endowment s agent-spec c. Other than the defaultng agent smply losng her collateral to counterpartes, default s assumed to have a small drect deadweght cost "z 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. Note that the recovery for each long poston depends on the bankruptcy resoluton whch we wll specfy below. 3.1 Centralzed exchange economy We rst 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. Frst, we explan how the exchange resolves default, the default condton for each agent, and next, how the exchange condtons contract terms takng account of ncentves of agents to default. Bankruptcy resoluton We 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 ow of the short postons of the asset, pro-rata wth respect to the long postons. To be precse, there are short postons that delver on the contracts n a gven state of the world, and there are others that default. At equlbrum, the sum total of these cash ows s dstrbuted pro-rata among the holders of long postons. In other words, the exchange can be nterpreted as guaranteeng all trades but requrng that those members of the 13

14 exchange who bene t from the guarantee on any gven default make captal contrbutons to cover the exchange s cost of provdng the guarantee. The default condton An agent of type wth (long, short) portfolo poston (z+; z ) wll default n perod 1 n state s her ncome after assets pay o s smaller than the non-pledgeable fracton of her endowment. Let R + (s) denote the payo n state s of her long asset portfolo. The payo R + (s) s taken as gven by each agent, though t s endogenously determned at equlbrum, dependng on the default rate n the economy at equlbrum (as shown later). Then, agent defaults on ts short postons : w 1(s) + R + (s)z + R(s)z < (1 ) w 1(s) "z : (7) Let I d (z + ; z ; ; s) be an ndcator varable takng on value one f agent wth the portfolo (z + ; z ) wll default at equlbrum n state s, and zero otherwse. 7 1 f w I d (z + ; z ; ; s) = 1 (s) + R + (s)z + R(s)z < (1 ) w1(s) "z 0 otherwse (8) Fnally, let I nd (z + ; z ; ; s) = 1 I d (z + ; z ; ; s). Equlbrum payo s on long and short postons: Snce all long postons share pro-rata the payments from defaultng and non-defaultng short postons, the equlbrum payo of long postons n state s, depends upon (z + ; z ), the vectors of long and short postons of agents, respectvely. We denote the payo as R + (z + ; z ; s), and t s gven by R + (z + ; z ; s) = P w 1 (s) I d (z+; z ; ; s) + R(s)z P z + I nd (z +; z ; ; s) (9) Note that n case of autarky, that s, wth no tradng ( P z + = P z = 0), we assume that R + (z + ; z ; s) = R(s). 7 R + (s) 0 and hence any agent defaultng for some s must have z > 0, or n other words, have some short poston n the asset. In other words, I d (z + ; 0; ; s) = 0. : 14

15 Importantly, whle the payout on long poston s dentcal for all agents, ths s not the case for short poston of agents. In partcular, the equlbrum payout of any short poston by agent can be computed as follows: for agent wth tradng postons (z +; z ), the payo on short poston s: R (z +; z ; s) = ( w 1 (s) z f I d (z +; z ; ; s) = 1 R(s) otherwse (10) Prces We assume that prces are set n a compettve manner. Spec cally, agents are prce-takers and so s the exchange (for nstance because many could operate the same exchange or because there are many market-makers performng the role of the exchange). Snce the payo on the long postons s symmetrc across agents, the prcng for long postons s straghtforward to descrbe. Takng as gven the return on her long portfolo, R + (s); an agent faces a gven bd prce q +. However, the payo on the short postons s not symmetrc across agents. Ths requres us to modfy the prce-takng assumpton on short postons n an mportant manner (that s smlar n sprt to mod catons n Acharya and Bsn, 2008, and Bsn, Gottard and Ruta, 2009). Note that agents holdng short postons on the asset mght default on ther requred payments, and ther default condton depends on ther type (endowment) and on ther total tradng postons. Snce the exchange observes agents types and total tradng postons, t o ers a d erent ask prce to d erent agents, re ectng the probablty of default mpled by ther characterstcs, that s, ther endowment as well as ther tradng postons. Consequently, the exchange o ers and n turn the agents face the ask prce map q (z+; z ). Budget constrants The budget constrants of agent are then gven by the followng equatons for consumpton at date 0 and n states s 2 S at date 15

16 1: 8 x 0 + q + z + q (z +; z )z = w 0 x 1(s) = max w 1(s) + R + (s)z + R(s)z ; (1 ) w 1(s) "z (11) where z +; z 0: The agents demand functons for gong long and short on the asset, (z+; z ), are obtaned from ther optmzaton, takng the prce q + and the prce map q (z+; z ) as gven. Note that, typcally, agents wll have both long and short postons n ther portfolos, as the payo s of long and short postons are not perfectly collnear, because of the default opton embedded n short postons. The exchange s problem We turn next to the decson problem of the compettve centralzed exchange, whch controls the supply of the asset to agents. Let the supply o ered by the exchange to agent 0 for long 1 and short ::: postons be denoted ( +; ), and let ( + ; ) + ; A denote the ::: vector of the exchange s o ered supples. Then, gven the supples, the exchange can compute the cash ow of the long postons of agents: 9 R + ( + ; ; s) = P w 1 (s) I d ( +; ; ; s) + R(s) P + ::: ::: I nd ( +; ; ; s) (12) wth R + ( + ; ; s) = R(s) n case of autarky when there s no tradng ( P + = P = 0). Let m (s) = MRS u 0 (s) p 1(x 0; x 1(s)) s u 0 0(x 0; x 1(s)) : (13) 8 To avod encumberng the notaton, we assume here and n the rest of the paper that each agent of type wll, n equlbrum choose the same portfolo postons (z +; z ). In fact, exstence of an equlbrum mght requre allowng dentcal agents to choose d erent portfolos to guarantee enough contnuty to aggregate demand. 9 To avod an even more cumbersome notaton, we avod an explct dstncton between the ndvdual portfolo of an agent and the aggregate portfolo of the agents tradng wth the exchange, whch are the same at equlbrum (whch mplctly mposes symmetry). 16

17 denote the margnal rate of substtuton between date 0 and state s at date 1 for agents of type at equlbrum, where u 0 t s the rst dervatve of the utlty functon u (x 0; x 1) wth respect to consumpton at date t. For any long and short postons o ered, ( + ; ), the exchange prces a untary long poston as max E m R + ( + ; ), 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 o ered. Note that m s an S-dmensonal vector (formally de ned below whle settng up the compettve equlbrum). Smlarly, gven ( +; ), the exchange can compute the cash ow of the short poston of agent as: R ( +; ; s) = ( w 1 (s) f I d ( +; ; ; s) = 1 R(s) otherwse (14) Then, the exchange prces a untary short poston of agent as q ( +; ) = E m R ( +; ) (15) takng as gven the stochastc dscount factor m of the agent whom the poston s o ered to. Agan, note that m s an S-dmensonal vector (formally de ned below whle settng up the compettve equlbrum). To summarze, a compettve exchange takes as gven the stochastc dscount factors fm g whch prce respectvely at equlbrum, the long postons of the asset and the short postons of the asset of agent. Crucally, the exchange antcpates the compostonal e ects on default rsk of portfolos of d erent agent types, that s, t recognzes how each agent s ncentves to default are a ected by ts postons ( + ; ) and how that a ects the payo s on the long poston (R + ( + ; )) and the short postons of each agent (R ( +; )). Thus, the exchange solves the followng problem: s.t. X max E m R + ( + ; ) f + E m R ( +; ) (16) + ; g X + = 0: (17) 17

18 Compettve equlbrum At compettve equlbrum, the portfolos demanded by the agents are o ered by the compettve exchange and markets clear: + = z +; = z ; 8 ; (18) and the prce maps and returns antcpated by agents are consstent wth those perceved by the exchange: 3.2 OTC markets q + = max E m R + (z + ; z ) ; (19) q (z +; z ) = E m R (z +; z ) ; and (20) R + (s) = R + (z + ; z ; s): (21) Let us now assume that tradng does not occur on a centralzed exchange (or any exchange for that matter), but s nstead ntermedated n Over The Counter (OTC) markets. We model OTC markets as standard compettve markets wth no centralzed exchange. We consder n turn two d erent bankruptcy resoluton mechansms, a centralzed one and a blateral one. However, we rst derve welfare propertes of the OTC markets wth centralzed bankruptcy and compare them to centralzed exchange, and then ntroduce the blateral bankruptcy. Ths sequence s for pedagogcal reasons as well as to hghlght that t s not the blateral nature of OTC markets that s the drvng force behnd the welfare analyss OTC markets wth centralzed bankruptcy 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 ow delvered on the short postons of the asset (full cash ow or endowment recovered n case of default) pro-rata wth respect to the long postons. Thus, as far as bankruptcy resoluton s concerned, OTC markets wth centralzed bankruptcy are comparable to a centralzed exchange. Prces As before, let z + and z be the long and short postons, respectvely, of agent n the asset. The mportant pont s that OTC markets have no centralzed clearng mechansm (nor a centralzed regstry) and hence the 18

19 trades of each agent, (z+; z ), are not observed n OTC markets by other agents. Thus, from an ex-ante standpont, no agent n OTC markets can net" other agents postons or o er to an agent a prce schedule that re ects the default probablty mpled by her overall postons. Note that the bankruptcy mechansm allows for such nettng n case of default ex post, when t s assumed that all trades are revealed, but absent observaton of trades ex ante, such nettng cannot be condtoned on trades whle settng prces. However, long and short postons wll n general stll be assocated wth dstnct prces, q + and q respectvely. The ask prce depends on the agent s type ; as the type determnes agent s endowment whch s publc knowledge and a ects her probablty of default. Importantly though, the ask prce for agent s not condtoned on her trades. Ths s the prmary dstncton between OTC and centralzed markets: contract terms (prces, nterest rates, collateral requrements, etc.) are not condtoned on agents trades n the case of OTC markets whereas they are n case of a centralzed exchange. Budget constrants Any agent takes as gven the prce and return of her long postons n the asset. The budget constrants of agent are thus gven by: x 0 + q + z + q z = w 0 x 1(s) = max w 1(s) + R + (s)z + R(s)z ; (1 ) w 1(s) "z (22) where z+; z 0: Compettve equlbrum At the compettve equlbrum, nancal markets clear: X z+ z = 0: (23) Furthermore, at equlbrum, the payo R + (s) must satsfy the condton: R + (s) = R + (z + ; z ; s) = P w 1 (s) I d (z+; z ; ; s) + R(s)z 19 P z + I nd (z +; z ; ; s) (24) ; 8s

20 wth R + (s) = R(s) n case of autarky ( P z + = P z = 0). Equlbrum prces are such that q + = E (m + R + ) ; for m + = m + wth + 2 arg max E m R + (25) q = E m R (s) (26) wth R (s) = R (z +; z ; s) = ( w 1 (s) z f I d (z +; z ; ; s) = 1 R(s) otherwse (27) 3.3 Welfare How does the compettve equlbrum under OTC markets compare n terms of e cency propertes to the compettve equlbrum under centralzed exchange? To answer ths queston, we wrte down the constraned Pareto e cent outcome as the soluton to the followng problem: X max E u (x 0; x 1) (28) (x 0 ;x 1 ;z + ;z ) s:t: X x 0 w0 = 0 (29) X x 1 w1 = 0; (30) x 1(s) = max w 1(s) + R + (s)z + R(s)z ; (1 ) w 1(s) "z ; 8; s R + (s) = P w 1 (s) I d (; s) + R(s)z P z + I nd (; s) where s the Pareto weght assocated to agents of type, I d (; s) s the ndcator varable correspondng to default of agent n state s, as before I nd (; s) = 1 I d (; s), and R + (s) = R(s) f P z + = P z = 0. Ths s the standard constraned e cency problem for a GE economy once t s assumed that default s not controlled by the planner. The constrant x 1(s) = max w 1(s) + R + (s)z + R(s)z ; (1 ) w 1(s) "z ; 8; s (34) 20 (31) (32) (33)

21 serves two purposes: () t restrcts the planner s allocatons to those that can be acheved wth the lmted nancal nstruments avalable n the economy; and () t accounts for the fact that each agent can choose to default, n each state s: 10 consumpton n a default state s s (1 ) w 1(s) "z, the non-pleadgeable fracton of endowment net of the deadweght costs. 3.4 Results We can derve the followng results on the constraned e cency of the centralzed exchange economy and the (generc) constraned ne cency of the economy wth OTC markets: Proposton 1. Any compettve equlbrum economy s constraned Pareto optmal. of the centralzed exchange The ntuton for e cency of the centralzed exchange economy s that each agent that s short on the asset faces a prce q (z +; z ) that s condtoned on her postons. Consequently, she nternalzes the e ect of her default on the payo of long postons on the asset R + (s). The observablty of all trades by the exchange and ts condtonng of prces based on ths nformaton enables the economy wth default rsk to get agents to nternalze the costs they mpose (n terms of ne cent rsk-sharng) on other agents due to postons that lead to excessve" defaults ex post. In strkng contrast, Proposton 2. Compettve equlbra of the centralzed exchange economy cannot be robustly supported wth OTC markets. 11 More spec cally, any compettve equlbrum of the centralzed exchange economy n whch default occurs wth postve probablty cannot be supported wth OTC markets. The ntuton s that n OTC markets, each agent that s short on the asset faces a prce q that s not condtoned on her postons. Consequently, she 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 ) w 1(s)): (35) 11 Formally, by robustly we mean: for a open set of economes parametrzed by agents endowments and preferences. 21

22 does not nternalze the e ect of her default on the payo of long postons on the asset R +. Furthermore, let the leverage of agent ; L ; be de ned as the value of her (promsed) debt dvded by the value of her endowment Then, L = E(m Rz ) E(m w 1) : Proposton 3. For deadweght costs " small enough, any compettve equlbrum of the OTC markets economy s characterzed, by weakly greater (and robustly by strctly greater) leverage and default wth respect to centralzed exchange economes. Snce ask prces n OTC markets do not penalze the short postons for ther own ncentves to default, agents have ncentves to exceed the Pareto e cent 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 ne cent rsk-sharng. In partcular, for e cent rsk-sharng, t s n general necessary to be able to commt to future payo s on nancal 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. Remark. If " = 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, " > 0, guarantee exstence. Fnally, t s also the case that a compettve equlbrum of the OTC markets economy wth centralzed bankruptcy s robustly not constraned Pareto e cent. The proof of ths statement, however, requres some complex d erental computatons and s omtted. It s an adaptaton of that n Bsn, Geanakoplos, Gottard, Mnell, and Polemarchaks (2001). 22

23 Opacty and counterparty rsk externalty When combned together, Propostons 1, 2, and 3 mply that centralzed markets such as an exchange are an e cent 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. 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 ne cency n terms of excessvely large short postons or leverage. We call ths ne cency as counterparty rsk externalty" snce t stems from counterparty rsk, the rsk of default of the short party on long postons, and excessve level of such counterparty rsk lowers the payo to all long postons n the economy, consttutng an mportant negatve externalty on economy-wde rsk sharng. 3.5 OTC markets wth blateral bankruptcy In ths secton, we formalze that our results on constraned ne cency of OTC markets are robust to consderng a blateral bankruptcy resoluton. We contnue modelng blateral OTC markets as standard compettve markets wth no centralzed exchange where no credtor has prvleged recourse to a debtor s collateral n case of default, but a blateral bankruptcy mechansm operates to dstrbute the collateral-based recovery on each agent n default, pro-rata wth respect to the agent s credtors. Ths latter feature s d erent from a centralzed bankruptcy n whch recoveres on all defaultng short postons were assumed to be pooled and dstrbuted pro-rate to the long postons. Tradng and prces Agents enter nto blateral contracts. Let z j + be long postons of agents of type sold by agents of type j. Let z be short postons of agents of type (all short postons are symmetrc for the agents shortng the asset, ndependently of the counterparty). As before, the trades of each agent, (fz+g; j z ), are not observed n OTC markets by other agents. 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, whle the prce depends on the type of the shortng agent, t s not condtoned on agents other trades, whch are not observed. Budget constrants The budget constrants of agent are thus gven by: 23

24 x 0 + q P j j2infg n zj + q z = w0 x 1(s) = max w1(s) + P o j2infg Rj +(s)z j + R(s)z ; (1 ) w1(s) "z where z+; j z 0; 8j 2 Infg; (36) and R+(s) j s the payo to the long postons where the counterparty s agent j. Compettve equlbrum Each agent determnes the demands for long and short postons by maxmzng ther objectves, takng as gven the payo of long postons on the asset, R+; j for any possble counterparty j 2 Infg. At equlbrum, however, the payo R+, j for any j 2 I; must satsfy the consstency condton: where 8, R j +(s) = ( w j 1 (s) Pj 0 2Infjg zj0 j + I d (; s) = 1 w 1(s) + X ; f I d (j; s) = 1; R(s) otherwse j2infg 8s; j 0 2 Infjg: (37) R j +(s)z j + R(s)z < (1 ) w 1(s) (38) and where +; z are evaluated at equlbrum. j2infg At the compettve equlbrum, furthermore, nancal markets clear: z j X j2infg z j + z = 0: (39) Results We do not formally show the followng results, but the blateral nature of OTC markets consdered above does not qualtatvely a ect any of the welfare propertes of OTC markets relatve to centralzed exchanges. In partcular, compettve equlbrum of centralzed tradng cannot be supported as a compettve equlbrum of blateral OTC markets; and, for deadweght costs of default that are su cently small, blateral OTC markets feature excessve leverage and default relatve to centralzed tradng. 24

25 To summarze, t s the opacty of OTC markets whch gves rse to the moral hazard of agents wantng to take excessve leverage through short postons, rather than the blateral or centralzed nature of resoluton of bankruptcy. 4 Producton rsk In our whole analyss the aggregate endowment of the economy, P 2I w 0 at tme 0 and P 2I w s n each state s 2 S; has been kept constant. Consequently, the ne cency of the nsttuton of over-the-counter markets, has only dstrbutonal e ects: borrowers have ncentves to take on excessve leverage, asset prces ratonally re ect equlbrum leverage, and hence borrowng-lendng and nsurance markets endogenously fal to serve ther purpose. Therefore, resources are ms-allocated n equlbrum. Nonetheless, no resources are lost n the aggregate. Ths ceases to be the case f we allow for producton n the economy, as we proceed to show n ths secton. 12 Suppose each agent s endowed wth a producton functon f whch transforms consumpton goods at tme 0 nto consumpton goods 0 at tme 1 1: More precsely, consder the followng k 1 technology. Let K = B k 2 : A denote a captal allocaton vector over A k A actvtes (e.g., projects), so that k 1 +k 2 +:::k A = k: The producton functon can then be de ned as the output n state s gven captal allocaton K: f(s; K); 8s. 13 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 exchange and OTC economes s extended to producton. For nstance, the 12 Whle we restrct to an economy wth backyard producton" on the part of agents, for smplcty, the analyss drectly extends to a rm producton economy. 13 We assume f s contnuously d erentable, strongly ncreasng, and strctly quasconcave. 25

26 budget constrants n the economy wth a centralzed exchange become: x 0 + q + z + q (z +; z )z = w 0 k x 1(s) = max w 1(s) + R + (s)z + R(s)z + f(s; K ); (1 ) w 1(s) and agent chooses a non-negatve portfolo (z +; z ) 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 exchange contnues to decentralze constraned Pareto e cent allocatons; and 2. The generc ne cency of OTC markets manfests tself wth overproducton and excessve producton rsk takng. An example of ths ne cent rsk-takng mght have been the e ect of credt default swap nsurances sold by A.I.G. to a large number of nancal rms n the Unted States and the Europe on 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 such a settng, the nsurer would take on large and nadequately-collateralzed short-sellng (of protecton) on pools of default rsk and the nsured would feed the excessve creaton of the housng stock and corporate assets backng such pools of aggregate default rsk. 5 OTC markets and the crss We now consder the mplcatons of our model for the debates rased by the nancal crss of on the desrablty of over-the-counter versus centralzed tradng. In partcular, analyss of the role played by OTC markets n the ongong nancal crss has led to several reform proposals. 14 Our theoretcal analyss can help provde a normatve comparson of these proposals. For example, Acharya, Engle, Fglewsk, Lynch and Subrahmanyam (2009) dvde the proposals nto requrng a () centralzed regstry wth no dsclosure to market partcpants; () centralzed counterparty wth no dsclosure 14 See Stulz (2009) for a summary of the dmensons along whch OTC markets for credt dervatves lkely contrbuted, and dd not contrbute, to the crss. 26

27 (except aggregates) to market partcpants; and () exchange wth publc dsclosure of prces and volumes. Our theoretcal analyss makes t clear that a centralzed regstry by tself s not su cent as t only gves regulators expost access to trade-level nformaton but does not counteract the ex-ante moral hazard of nsttutons wantng to take on excessve leverage. Both centralzed counterparty and exchange su ce on ths ground but t s the centralzed counterparty that s crucal rather than an exchange; n other words, t s su cent that one party sees all trades and sets prce schedules and rsk controls condtonal on that nformaton, and t s not necessary to dsclose nformaton on all trades to ndvdual agents. Regulatory reforms announced n March 2009, and snce then approved by the House n the Unted States, nvolve sgn cant changes to the tradng nfrastructure of OTC markets, wth the objectve of reducng systemc rsk n the nancal sector. Under the proposed reforms, mature and standardzed credt dervatves such as the credt default swaps (CDS) and ndces lnked to the CDS wll be traded through a centralzed counterparty; there s no proposal yet to mandate that these be traded on an exchange. Regulators wll gan unfettered access to nformaton on prces, volumes and exposures from the centralzed counterpartes, but the proposals do not requre that such nformaton be made publc. Whle some aggregate nformaton wll be dssemnated to all market partcpants, such as the recent data publshed by the Depostory Trust and Clearng Corporaton (DTCC) on all lve postons n credt dervatves, full transparency s beng requred only for regulatory usage. Our results suggest that these proposed changes are lkely to be adequate except that many nancal products such as the customzed or bespoke" collateralzed debt and loan oblgatons (CDOs and CLOs) are not amenable to centralzed clearng. The OTC markets wll surely exst f only to trade these remanng contracts. It mght seem that these bespoke products can be gnored from a rsk pont of vew, however nearly all the problem legacy assets are of ths type and these we now know are extremely rsky systemcally. On these assets, our results suggest that further trade-level transparency among market partcpants wll lkely be requred n at least some form to mprove the assessment and prcng of counterparty rsk. 27

28 6 Related Lterature The blateral nature of contracts n the OTC markets has been stressed n the recent lterature on the subject. Du e, Garleanu and Pedersen (2005, 2007) focus on search frctons, dynamc barganng and valuaton n OTC markets; Caballero and Smsek (2009) analyze the role of complexty ntroduced by blateral connectons and ther role n causng nancal pancs and crses; and, Golosov, Lorenzon, and Tsyvnsk (2009) examne what knd of blateral contracts wll get formed when agents have prvate nformaton about ther endowment shocks. Spec cally n the context of nsurance provson through nancal contracts, the lterature (e.g., Du ee and Zhou, 2001, Acharya and Johnson, 2007, Parlour and Wnton, 2008) has largely focused on moral hazard on part of the nsured due to presence of nformaton frctons, rather than moral hazard on part of the nsurer, the latter beng the focus of our paper. On ths focus, our paper s more closely related to Allen and Carlett (2006), Thompson (2009) and Zawadowsk (2009). Allen and Carlett (2006) consder contagon from nsurance sector to the nancal sector when there s credt rsk transfer, but they do not consder agency-theoretc ssues. In contrast, we allow for default ncentves of the nsurer and model credt rsk transfer more generally as rsk-sharng through nancal contracts n a GE settng. Zawadowsk (2009) analyzes counterparty rsk n entangled nancal systems. The system s entangled because banks hedge rsks usng blateral OTC contracts but do not nternalze the cost of ther own falure on other banks (through counterparty rsk exposures). As a result of ths network externalty, banks purchase less nsurance aganst low probablty events. Thus, there s less nsurance n hs model whereas due to moral hazard on part of the nsurer, there s n fact excessve nsurance n our setup but t s of low qualty and entals default by the nsurer. Thompson (2009) consders the moral hazard of default on part of the nsurer when there s credt rsk transfer n the nancal sector. Hs focus s on analyzng how ths moral hazard provdes ncentves to the nsured partes to reveal nformaton about ther type, so that the two agency problems nteract and reduce each others adversty. More spec cally on the bene ts of OTC versus centralzed markets, our analyss dd not consder practcal ssues relatng to the extent of nettng of postons that s possble when markets are OTC versus when there s a centralzed exchange but only for a part of the space of nancal products. 28