Counterparty risk externality: Centralized versus over-the-counter markets

Transcription

1 Counterparty rsk externalty: Centralzed versus over-the-counter markets Vral Acharya NYU-Stern, CEPR and NBER Alberto Bsn NYU and NBER Aprl 2011 We are grateful to Rob Engle for nsghtful dscussons. We also gratefully acknoledge comments from Erc Ghysels, Martn Oehmke, Marco Pagano (dscussant), and semnar partcpants at the Federal Reserve Bank of New York, Econometrc Socety Meetngs n Atlanta (2010), NYU-Stern Fnance brown bag semnar, Macroeconomcs Workshop at NYU Economcs, Unversty of Mchgan, Unversty of Brtsh Columba and Stanford Macroeconomcs. We receved excellent research assstance from Rustom Iran and Hanh Le.

2 Counterparty rsk externalty: Centralzed versus over-the-counter markets Abstract We model the opacty of over-the-counter (OTC) markets n a setup where agents share rsks, but have ncentves to default and ther fnancal postons are not mutually observable. We show that ths setup results n excess leverage n that partes take on short OTC 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 a centralzed counterparty (such as an exchange) that observes all trades and sets prces compettvely. Whle collateral requrements and subordnaton of OTC postons n bankruptcy can amelorate the counterparty rsk externalty, they are n general nadequate n addressng t fully. J.E.L.: G14, G2, G33, D52, D53, D62 Keywords: OTC markets, leverage, counterparty rsk, externalty, transparency, centralzed clearng, exchange, collateral, margn

3 To restran prvate people, t may be sad, from recevng n payment the promssory notes of a banker for any sum, whether great or small, when they themselves are wllng to receve them; or, to restran a banker from ssung such notes, when all hs neghbours are wllng to accept of them, s a manfest volaton of that natural lberty, whch t s the proper busness of law not to nfrnge, but to support. Such regulatons may, no doubt, be consdered as n some respects a volaton of natural lberty. But those exertons of the natural lberty of a few ndvduals, whch mght endanger the securty of the whole socety, are, and ought to be, restraned by the laws of all governments; of the most free, as well as of the most despotcal. The oblgaton of buldng party walls, n order to prevent the communcaton of fre, s a volaton of natural lberty, exactly of the same knd wth the regulatons of the bankng trade whch are here proposed. Adam Smth, The Wealth of Natons, Introducton and motvaton An mportant rsk that needs to be evaluated at the tme of fnancal contractng s the rsk that a 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 and collateral that affect a 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. 2 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 that such opacty of exposures 1 The paragraph cted appears on Vol. 1, p. 289, of the J.M. Dent & Sons Publsher edton, London, The contract may adhere to a unformly applcable corporate bankruptcy code, or when the contract s exempt from the code, the bankruptcy outcome may be specfed n the contract. 1

4 n OTC markets leads to an mportant rsk spllover a counterparty rsk externalty 3 that leads to excessve leverage n the form of short postons that collect premum upfront but default ex post. Such excessve leverage results n neffcent levels of rsk-sharng, deadweght costs of bankruptcy, and productve neffcency. 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 beng 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 other market partcpants beng able to dscourage them through prcng or rsk controls for these nsttutons. 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 the cost that large OTC exposures can mpose on the system when a large nsttuton defaults on ts oblgatons. But, more mportantly, t also rases the queston of whether A.I.G. s true rsk as a counterparty was subject to adequate rsk controls n protectons they sold. We argue that the opacty of the OTC markets n whch these credt dervatves traded was at least n part responsble for allowng the buld-up of such large exposures n the frst place. 4 3 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. 4 Tradtonally, n economcs, we have consdered the moral hazard problem of nsurance as beng wth respect to the hdden acton of the nsured party. In ths paper, and as the A.I.G. example llustrates, the problem s flpped and the moral hazard s wth respect to the hdden acton (trades, contracts, etc.) of the nsurer. 2

5 A number of fnancal nnovatons n fxed ncome, foregn exchange, and credt markets have traded untl now n OTC markets, the (gross) global notonal outstandng of such dervatves beng close to $500 trllon n December 2009, as per the Global Fnancal Stablty Report of the IMF (Aprl 2010). In contrast, many dervatve products lnked to commodty and equtes have traded successfully on centralzed tradng platforms such as exchanges. A dstngushng feature of an 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). Ths enables the exchange to offer ndvdual partes prcng schedules for trades (n practce, collateral arrangements and exposure lmts) 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 futures contracts). However, exchanges are often vewed as detrmental to the ease of search facltated by blateral OTC markets, especally for customzed or non-standardzed fnancal products. Hence, as an alternatve to ntermedatng trades on a centralzed platform or through a centralzed counterparty, a centralzed clearng mechansm has been proposed that regsters all trades n OTC markets and then serves as a data repostory provdng transparency of these trades. We show formally that when tradng s organzed n the form of a centralzed clearng mechansm, transparency can enable market partcpants to condton contract terms for each counterparty based on ts overall postons. Such condtonng s suffcent to get that party to nternalze the counterparty rsk externalty of ts trades acheve the effcent rsk-sharng outcome. In other words, the moral hazard that a party wants to take on excessve leverage through short postons collect premums today and default tomorrow s counteracted by the fact that they face a steeper prce schedule by so dong. We show that a compettve centralzed exchange or a centralzed counterparty also would nduce effcent rsk-sharng, but n practce, ths would be at the cost of restrctng all trades, ncludng those nvolvng non-standardzed fnancal assets, through a sngle ntermedary. 1.1 Model and results We derve these results n a compettve two-perod general equlbrum (GE) model whch allows for the possblty of default (Geanakoplos, 1997, Geanakoplos and Zame, 1998, Dubey, Geanakoplos and Shubk, 2005). There s a 3

6 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 backed by agents endowments. When an agent has short postons that cannot be met by the pledgeable fracton of endowment, there s default. Default results n deadweght costs whch are borne by the short poston and are ncreasng n the sze of short postons, e.g., due to a greater number of partes to deal wth n a bankruptcy proceedng. Such costs may arse also due to loss of customers or franchse value n fully dynamc setups. We do not model the structure of bankruptcy costs but smply postulate ther pecunary equvalent n reduced form. The possblty of default (the opton to exercse lmted lablty, to be precse) mples that long and short postons do not necessarly 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 based on delvery from short postons. Ths ratonng of payments mples that each trade mposes a payoff externalty on other trades. Ths spllover s precsely what we refer to as a counterparty rsk externalty. In ths setup, we consder varous tradng structures and ask whether they can nternalze the counterparty rsk externalty or whether they lead nstead to neffcent rsk-sharng. One structure, a centralzed clearng mechansm wth transparency, guarantees that all trades are observable and agents can set prcng schedules that are condtonal on ths knowledge. Another structure, a centralzed exchange or a centralzed counterparty, observes all trades and can set prcng schedules based on ths knowledge. In contrast, n economes wth OTC market structure, 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 level of endowment). Our frst result s that compettve equlbra n economes wth a transparent centralzed clearng mechansm or a centralzed exchange are constraned Pareto effcent. Ths s true even allowng for market ncompleteness so that the result s not smply a consequence of welfare theorems n case of complete markets. Our second result s that compettve equlbra n economes wth OTC markets are robustly constraned neffcent. 5 5 We study two dfferent cases, one n whch OTC markets operate wth a blateral 4

7 The neffcency n the OTC settng manfests as excessvely large short postons as counterpartes takng long postons do not nternalze the default rsk they mpose on other long postons. Intutvely, as long as there s a rsk premum on the underlyng contract (e.g., because the rsk beng nsured n the contract s aggregate n nature) and the costs of defaultng are not excessvely large, the short poston (the nsurer) perceves a beneft from collectng premums upfront and defaultng ex post. We nterpret ths outcome as characterzng excessve leverage. 6 Formally, we capture the resultng neffcency n the form of deadweght costs of bankruptcy. More generally, the neffcency could manfest as excessve systemc rsk due to spllover on to other counterpartes. Furthermore, n an extenson, we clarfy that the neffcency of OTC markets extends beyond just neffcent rsk-sharng. When we allow agents to alter ther producton schedules, the ablty to hedge the producton rsk through fnancal contracts creates addtonal demand for long postons and the ncentves to buld excessve leverage through short OTC postons markets translate nto a producton neffcency. 7 In another extenson, we consder the role of blateral collateral arrangements n addressng the counterparty rsk externalty. We show that snce blateral arrangements cannot be condtoned on nformaton about all other trades of counterpartes, n general, they do not delver constraned effcency of equlbrum outcomes. In partcular, there are economes n whch a suffcently tght collateral arrangement can preclude any default by a counterparty. Ths level of default rsk may or may not be optmal. But even nettng mechansm and one wthout blateral nettng. We show that OTC markets are robustly constraned neffcent n both cases. In other words, the counterparty rsk externalty s orthogonal to what could be called the nettng externalty that default decson of one party depends on the default decson of ts counterpartes. 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. 6 Interestngly, ths mples a lower unt cost of nsurance snce the realzed nsurance payoff s smaller when the nsurer s more lkely to default. 7 As an example, suppose that there s nsurance beng provded on economy-wde mortgage defaults. Ths would carry a sgnfcant hedgng premum due to demand from mortgage lenders, 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 lenders would feed the excessve creaton of the housng stock backng such mortgages. Ths may be a partal explanaton of the role played by credt default swaps, sold n large quanttes by A.I.G. on corporate loan and mortgage pools, n fuelng the credt boom precedng the crss of

8 when t s optmal, the requred collateral can alter productve effcency of the economy by resultng n over-nvestment n the collateral assets, or alternately, f the collateral asset s lmted n quantty, ensurng no default can nduce too lttle rsk-sharng. Fnally, we examne whether subordnatng OTC postons n bankruptcy relatve to centrally cleared ones (when both OTC and centralzed markets co-exst) can elmnate counterparty rsk externalty. We show that n general ths s not the case. On the one hand, condtoned on default, the sze of OTC postons does not affect the payoff on centrally cleared postons. Ths lmts the externalty from OTC postons to centrally cleared ones. On the other hand, counterparty rsk externalty n OTC markets remans unaddressed. As a result, there may now be default n states of the world where there would be none under centrally cleared markets. Due to deadweght costs of default, ths lowers the payoff on centrally cleared postons. The remander of the paper s structured as follows. Secton 2 provdes a smple example of the counterparty rsk externalty n OTC markets. Secton 3 presents the general model, the varous tradng structures (OTC and centralzed clearng wth transparency), and the welfare analyss of compettve equlbrum under these structures. Secton 4 dscusses extensons of the model. Secton 5 dscusses the relatonshp between the compettve equlbrum n our model and the market mcrostructure of OTC and centralzed tradng structures n practce. Ths secton also consders the polcy mplcatons of our model for OTC versus centralzed clearng. Secton 6 relates our work to exstng lterature. Secton 7 concludes. The analyss of tradng wth a centralzed exchange or counterparty structure s n the Appendx, whch also contans proofs. 2 Counterparty rsk externalty: An example Consder a two-perod (t = 0, 1) compettve economy wth three types of agents ( = 1, 2, 3). 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 that ntal endowments are large enough that there are no default consderatons at t = 0. For smplcty, we also assume that w 1 (G) > w 2 (G) > w 3 (G) = 0, 6

9 and w 1 (B) = w 2 (B) = 0 < w 3 (B). In other words, agents of type 1 and type 2 have endowment n the good state of the economy, but none n the bad state; agents of type 3 are endowed n the bad state but not n the good state. Agents of each type have a mean-varance utlty functon: E[u(x 0, x(s)] = x 0 + E(x(s)) γ 2 var(x(s)), where x 0 s the resdual endowment at t = 0, and x(s) s the realzed endowment at t = 1, both takng account of trades that are structured at t = 0 and materalze at t = 1. We assume that the only traded contract s an nsurance that 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 n the bad state may be less than 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. 8 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 (or franchse) value n a mult-perod settng. Hence, the equlbrum cash flow of agents 3 wll be negatve n the bad state f they default, reflectng ths deadweght cost. 2.1 OTC markets We 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 8 It would suffce to smply consder n ths example economy two types of agents. Nevertheless, for sake of clearer exposton of counterparty rsk externalty, we consder three types of agents. 7

10 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), wth 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 [x 1 (G), x 2 (G), x 3 (G)] = [w 1 (G), w 2 (G), w 3 (G)], and [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 ], where 1 D s an ndcator varable whch takes on the value of one f there s default (R + < R) and zero otherwse. Equvalently, we wll show below that x 3 (B) = max(w 3 (B) Rz 3, ɛz 3 ). 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, denoted as (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) (q (1 ] p)r+ ). (1) R + γp(1 p)r + 8

11 Smlarly, we obtan for agent 2 s long poston that: z 2 (R +, q) = 1 [ w 2 (G) (q (1 ] p)r+ ). (2) R + γp(1 p)r + 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. The crucal observaton s that even though the payoff R + s affected by each agent s long poston n equlbrum, agents are compettve and do not nternalze ths effect. Ths s the source of counterparty rsk externalty n the model. In a GE model wthout default, R + s guaranteed to be R so that the externalty would not arse. Next, we wll show that agents of type 3 have ncentves to default n state B whenever the parameter governng the deadweght cost of default, ε, s not too hgh. To clarfy agent 3 s choce wth regard to 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 [ w 3 (B) + ]. (3) znd 3 = 1 (q (1 p)r) R γp(1 p)r In the lmt where 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 s aggregate n nature and cannot be fully dversfed away, e.g., f w 1 (G) + w 2 (G) > w 3 (B). 9 9 A large component of default rsk s drven by macroeconomc rsks. Ths explans why there s the moral hazard of default on part of nsurers sellng credt default swaps (CDS): CDS effectvely nsure at least some porton of aggregate rsk contaned n the default rsk of the underlyng entty. In contrast, there s less rsk of such a moral hazard on the part of nsurers sellng tradtonal nsurance products such as polces on death, accdents, etc. These rsks are easly dversfed away across agents n the economy, so that nsurers smply earn the actuarally far premum, or n other words, do not earn a sgnfcant rsk premum. 9

12 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 = Thus, 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 To get ntuton, we defne as rsk premum : p = 2q γp(1 p)r +. (6) q (1 p), (7) R + whch s, the dfference between the rsk-neutral probablty of state B and ts actual or statstcal probablty. Then, solvng the system n p and R + yelds as the soluton: p = 1 2 γp(1 p) [ w 1 (G) + w 2 (G) w 3 (B) ], (8) mplyng there s a rsk premum whenever agents are rsk-averse (γ > 0), there s rsk (0 < p < 1), and ths rsk cannot be dversfed away across 10 Note that the no-default condton now takes the form: w 3 (B) (R ɛ)z 3. 10

13 agents (w 1 (G) + w 2 (G) > w 3 (B)), and R + = (1 p)ε + (1 p) 2 ε 2 + 4w 3 (B)γp(1 p) [ p + (1 p)] ε 2 2 [ p + (1 p)] (9) whch s ncreasng n ε. In other words, the hgher the bankruptcy costs, the lower s the equlbrum default rate on the contract. It follows then that the contract prce q = [ p + (1 p)] R + s also ncreasng n ε. In turn, there s default n equlbrum (R + < R) f and only f bankruptcy costs are suffcently small (ε smaller than some threshold level ε). 2.2 Numercal example We parametrze the above economy wth w 1 (G) = 10, w 2 (G) = 5, and w 3 (B) = 10 so that state B s aggregate rsky n nature. We set γ = 1, p = 0.9 and vary ɛ n the range [0.1, 1.0] (a subset of the entre possble range ɛ > 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: agents of type 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 the equlbrum quantty of nsurance contracts sold and the unt prce of nsurance. 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 turn, the rsk premum p equals 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 much lower at q = To summarze, as the default ncentves for agents of type 3 become stronger, there s greater quantty of nsurance sold, greater default, and greater deadweght costs suffered by these agents. In turn, the equlbrum nsurance prce s smaller too. Snce the payoff on the contract s ratonally 11

14 antcpated by those purchasng nsurance to be smaller: the qualty of nsurance has gone down gven the nsurer s default rsk. Interestngly, there s no effect of default rsk on the rsk premum, whch s constant and s gven by equaton (8). 2.3 Ineffcency of OTC markets The neffcency of equlbrum n the example above when ε < 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 of type 3. Agents 1 and 2 enjoy the same equlbrum utlty as ɛ vares. However, for ɛ < 0.548, default leads to deadweght costs borne by agents of type 3 and ther equlbrum utlty s substantally lower compared to the case where ɛ The result of counterparty rsk externalty s that there s too much demand for nsurance n equlbrum, whch gves nsurers the ncentve to default ex post, for whch they pay ex ante. It s clear then that n the example 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 of type 3 from sellng a quantty of nsurance z 3 that s beyond ther endowment n the 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 ths 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 show below, s that the OTC markets always feature (weakly) greater lkelhood of default n equlbrum compared to ts (Pareto) effcent level. 3 The general model We now buld on the above example to construct a general model of an OTC market wth default rsk. In partcular, we allow for an arbtrary number of agent types, wth arbtrary structure of endowments, and the possblty of each of the agents takng long and short postons wth each other (requrng us to also ntroduce some addtonal notaton). Wthout much further complcaton, we also allow only a part of each agent s endowment to be pledgeable n honorng ts short postons. Deadweght costs of bankruptcy 12

15 could be nterpreted as (partly) arsng from loss of the non-pledgeable endowment. For sake of smplcty, we contnue to restrct attenton to a sngle fnancal contract. After completng the analyss of OTC markets, we consder fnancal markets wth a centralzed clearng mechansm that provdes transparency and compare ts equlbrum outcome wth that under the OTC markets. Formally, we extend the 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. In the nterest of pedagogcal clarty, we state the optmzaton programs n each settng fully even though some parts are common across dfferent programs. 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 effectvely backed 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 agent s endowment w1(s). Other than the defaultng agent smply losng her pledgeable endowment to counterpartes, default s assumed to have a drect deadweght cost that s proportonal to the sze of the poston defaulted upon. Deadweght costs of default wll serve the formally convenent purpose of provdng a bound on short postons on the asset. 13

16 Agents are assumed to 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 that agent s default decson also depends on the type. Let z j + be long postons of agents of type sold by agents of type j. Let z + = ( ) z j + denote the long portfolo vector of agents of type j I (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. Then, n case of ts default, agent suffers a deadweght cost of default whose pecunary equvalent s assumed to be εz, wth ε > 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 endowment 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 total repayment cash flow from an agent of type s dstrbuted pro-rata among the holders of long postons aganst counterparty. 11 The default condton An agent of type wth (long, short) portfolo poston (z +, z ) wll default n perod 1 n state s f and only f her ncome after assets have pad off s smaller than the non-pledgeable fracton of her endowment net of the bankruptcy costs. Let R j (s) denote the payoff n state s of agent s long asset portfolo wth counterparty j I\{}. The payoff R j (s) s taken as gven by each agent, though t wll be endogenously determned, dependng on the equlbrum default rate of agents of type j n the economy. 11 Gven the compettve nature of the model, the bankruptcy mechansm pools all repayments of all agents of type and redstrbutes them pro-rata to all ther counterpartes. Ths s wthout loss of generalty, as we concentrate on symmetrc equlbra. 14

17 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. (10) Note that n general 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, we assume that the clearng mechansm provded by OTC markets does not necessarly 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). Clearly, 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 (11) 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 transparency, 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 untary prce q j, where the apex j denotes the type of the agent n the short poston. Note that the prce 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. Importantly though, the prce s not a schedule contngent on overall trades of agent j, that s, does not depend on her portfolo, snce t s not observed. The budget constrants of agent n the OTC market are thus gven by: 15

18 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 (12) where z j +, z 0, for any j. Compettve equlbrum In equlbrum, fnancal markets clear: z j + z j = 0, for any j. (13) Furthermore, the equlbrum payoffs R j (s) satsfy the condton: Let R j (s) = R j (z j +, z j ; s) (14) m (s) = MRS (s) p s u (x 0,x 1 (s)) x 1 u (x 0,x 1 (s)) (15) denote the margnal rate of substtuton between date 0 and state s at date 1 for agents of type at equlbrum; that s, the stochastc dscount factor of agents of type. The equlbrum prce of an asset s then smply equal to the dscounted value of asset payoffs, where the dscount rate s adjusted for rsk accordng to the stochastc dscount factor of any agent wth a long poston n the asset. More precsely, agents wth a long poston n the asset are those who have the hghest margnal valuaton for the asset s return, and hence at equlbrum, prces q j satsfy: x 0 q j = max E ( m R j), for any j. 12 (16) 3.2 OTC markets wth nettng 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 12 Alternatvely, but equvalently, the equlbrum prce for any j can be wrtten as follows: q j = E ( m R j), for any s.t. z j + > 0 and q j = max E ( m R j), f z j + = 0 for any. 16

19 z > 0 and, at the same tme, z j + > 0 wth some counterparty j. In ths context, an ex-post mechansm for state-by-state blateral nettng mght have welfare consequences. Hence, we also consder 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. We model blateral nettng by requrng that agents are (wthout loss of generalty) on only one sde of the market, that s, for an agent of type : z j +z = 0, for any j. (17) 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. (18) Therefore, wth blateral nettng, the default decson of any agent s ndependent of z +, whch s constraned to be equal to 0 whenever z > 0. Let the default ndcator of agents of type be now denoted as I d (z ;, s), takng on value 1 f agent wth short poston z wll default at equlbrum n state s, and zero otherwse. Agent j s short poston payoffs are now wrtten as R j (z j ; s) = { αw j 1 (s) z j f I d (z j ; j, s) = 1 R(s) otherwse (19) and budget constrants of agents are restrcted by z j +z = 0, for any j. Fnally, at a compettve equlbrum of 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 satsfy 3.3 Centralzed clearng q j = max E ( m R j), for any j. (20) 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 beng composed of two fundamental functons: blateral nettng and transparency. Transparency s obtaned because a centralzed clearng mechansm s assumed to aggregate 17

20 all the nformaton about trades and dssemnate t to market partcpants. Two ponts are n order before we proceed. One, n the model, transparency provded by centralzed clearng mechansm s concdent wth submsson and executon of trades. Our equlbrum setup cannot deal wth the tmng or market mcro-structure ssues assocated wth when trades are submtted and when they are made transparent. We dscuss ths ssue n some detal n Secton 5.2. Second, we stress that a centralzed clearng mechansm need not centrally ntermedate the trades as, for nstance, a centralzed exchange would do (whch we dscuss later). 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 receved by the debtor s dstrbuted pro-rata among the holders of long postons aganst the debtor. Because of blateral nettng, 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 ; (21) 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. (22) 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 (e.g., level of endowment) 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 j (z ) j = max E ( m R j (z j ) ). (23) That s, an agent of type j understands that the prce t wll face for a short poston depends on the total short postons t sells, z. j Furthermore, an 18

21 agent of type j understands that the prce t wll face for a short poston wll reflect a rsk adjustment accordng to the stochastc dscount factor of the agents who would hold such a short poston, that s, of those agents who share the hghest margnal valuaton for the payoff assocated to ts poston, R j (z j ). Prce takng s then represented by the fact that agents take the vector of stochastc dscount factors ( m 1,..., m,..., m I) as gven. 13 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 (24) where z j +, z 0, z j +z = 0, for any j. At compettve equlbrum, all markets clear: z j + z j = 0, for any j, (25) and the prce maps and returns are ratonally antcpated by agents: 3.4 Welfare q j = q j (z j ) = max E ( m R j (z j ) ), (26) R j (s) = R j (z j ; s). (27) How does the compettve equlbrum under OTC markets compare n terms of effcency propertes to the compettve equlbrum under centralzed clearng wth transparency? To answer ths queston, we wrte down the constraned Pareto effcent outcome as the soluton to the followng problem: 13 Our defnton of compettve prce maps can be thought of as capturng the same consstency condton requred by Perfect Nash equlbrum n strategc envronments: every agent understands that the ask prce she wll face for any (possbly out-of-equlbrum) short poston z j wll depend on the wllngness to pay of agents on the long sde of the market. In a compettve equlbrum, however, all devatons from equlbrum are necessarly small, and hence such wllngness to pay concdes wth the hghest margnal valuaton at equlbrum. 19

22 max (x 0,x 1,zj +,z ),j s.t. x 0 w0 = 0, λ E ( u (x 0, x 1) ) x 1(s) w1(s) = 0, for any s x 1(s) = max { w 1(s) + j R j (s)z j + R(s)z, (1 α) w 1(s) εz }, R j (z j ; s) = { αw j 1 (s) z j f I d (z j +, z j ; j, s) = 1 R(s) otherwse (28) (29) and where z j +, z 0, and 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 (28) serves two purposes: () 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: consumpton n default state s s (1 α) w 1(s) εz, the non-pleadgeable fracton of endowment net of the deadweght costs Results We can derve the followng results on the constraned effcency of the economy wth centralzed clearng and transparency, n contrast to the (generc) constraned neffcency of the economy wth OTC markets. 14 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 ). (30) 20

23 Proposton 1. Any compettve equlbrum of an economy wth a centralzed clearng mechansm s constraned Pareto optmal. The ntuton for effcency of the economy wth centralzed clearng and transparency s that each agent j that s short on the asset faces a prce q j (z j ) = max E ( m R j (z j ) ) that s condtoned on her postons. Consequently, she nternalzes the effect of her default on the payoff of long postons on the asset. The observablty of all trades allows for such condtonng of prces and nternalzaton of any externalty that tradng and default choces mpose on other agents. Importantly, note that an economy wth a centralzed clearng mechansm, as we have defned t, s characterzed by both a blateral nettng mechansm and transparency. Both these components are needed for effcency. We can show that the opacty of OTC markets nduces neffcences through the counterparty rsk externalty, ndependently of the nettng mechansm n place. Conversely, t can be shown that the lack of a blateral nettng mechansm s assocated wth an externalty that nduces neffcences n equlbrum even when transparency s guaranteed. 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: w 1(s) + j R j (s)z j + R(s)z < (1 α) w 1(s) εz. (31) 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. Then, t s the case 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). Next, n OTC markets wth blateral nettng, 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. (32) 21

24 No nettng externalty arses n ths case. Nevertheless, we shall show 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 (but not provded by OTC market economes, wth or wthout nettng) s necessary 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. 15 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. Ths s a counterparty rsk externalty. More generally, when the counterparty rsk externalty nteracts wth the nettng externalty, t s also the case that: Compettve equlbra of economes wth OTC markets and nettng are robustly not constraned Pareto effcent. 16 Fnally, let the leverage of agent j, L j, be defned as the value of her short postons contractual payoff (promsed debt payment) dvded by the value of her endowment (asset value). Then, L j E(mj Rz j ) E(m j w j 1). (33) Proposton 3. For deadweght costs ε that are 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 15 Formally, by robustly we mean: for an open set of economes parametrzed by agents endowments and preferences. 16 Once agan, we omt the proof of ths statement to avod some complex dfferental computatons. 22

25 default rsk compared 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 () the underlyng asset has some aggregate rsk, ts prce wll robustly carry a rsk premum that s postve (as explaned n the example economy of Secton 2), and () bankruptcy costs are not too hgh (ε s small), then agents wth endowments n the aggregate rsky states have an ncentve to go excessvely short. Ths ncreases the equlbrum default rate and leads to neffcent rsk-sharng. 17 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 cannot be ensured through prces. Opacty and counterparty rsk externalty When combned together, Propostons 1, 2, and 3 mply that a centralzed clearng mechansm wth transparency s an effcent response to counterparty rsk externalty. 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. In equlbrum, agents antcpate the lowerng of payoff on long postons due to counterparty rsk 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, as the rsk premums they earn (whch depend on the rato of prce to the payoff) reman unaffected. Centralzed exchange economy In the Appendx, 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. In practce, ths could be thought of as capturng a settng wth a specalst that sees all trades and sets prce schedules, or an exchange that sees all trades and 17 If ε = 0, z s unbounded and, strctly speakng, the economy has no equlbrum. Ths s just an extreme case, whch s of nterest to dentfy the force towards borrowng and default bult nto our model of opaque OTC markets. Postve deadweght costs, ε > 0, guarantee the exstence of equlbrum. 23

26 mposes exposure lmts on traders based on ther overall postons. It can be shown that the compettve equlbrum allocatons of economes wth such 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. 4 Extensons 4.1 Collateral constrants We have not yet analyzed the welfare propertes of a commonly employed rsk control and polcy nstrument, namely blateral collateral constrants. 18 Consder our example OTC economy of Secton 2 wth blateral nettng n whch sellng one unt of the asset short requres postng k unts of the date-0 commodty as collateral to the counterparty. We assume that, when posted as collateral, one unt of the date-0 commodty pays an exogenous constant return r. To start wth, we wll assume r s equal to one. The collateral s segregated for each counterparty n that t has prvleged access to ts collateral n case of default on the contract. Then, agents of type 3 do not default n state B provded whch can be expressed as w 3 (B) + kz 3 Rz 3 εz 3, kz 3 Rz 3 εz 3 w 3 (B), (34) a condton that provdes a lower bound on the requred collateral constrant to deter default. However, not all collateral constrants are feasble for postng by agents of type 3 at date 0. Ths date-0 budget constrant s w qz 3 kz 3, (35) whch yelds an upper bound on the feasble collateral constrant. Snce n our example economy, effcency s acheved when there s no default and RzND 3 = w3 (B), effcency can be attaned wth a collateral 18 IMF (Aprl 2010) shows that the top fve banks and broker dealers n the Unted States posted cash collateral on dervatves postons as of 1 December 2009, rangng from 15% of dervatves payables (n case of Goldman Sachs) to 50% (for Bank of Amerca). 24