Credit Default Swaps in General Equilibrium: Spillovers, Credit Spreads, and Endogenous Default

Transcription

1 Credt Default Swaps n General Equlbrum: Spllovers, Credt Spreads, and Endogenous Default R. Matthew Darst Ehraz Refayet June 2, 2016 Keywords: credt dervatves, spllovers, nvestment, default rsk. JEL Classfcaton: D52, D53, E44, G10, G12 Ths paper was formerly ttled: Credt Default Swaps and Frm Fnancng: Borrowng Costs, Spllovers, and Default Rsk. We are mmensely grateful to Ana Fostel for numerous dscussons, gudance, and mprovements. We also would lke to thank Jay Shambaugh, Pamela Labade, Davd Feldman, and Nel Ercsson for useful comments. We thank semnar partcpants at the 2014 NASM of the Econometrc Socety, 2014 Mssour Economcs Conference, 2013 Georgetown Center for Economc Research Conference, 2013 World Fnance Conference - Cyprus, and 2013 ESEM-EEA jont Summer meetng, and an anonymous referee. All errors are our own. The vews expressed n ths paper are those of the authors and do not necessarly represent those of the Federal Reserve Board of Governors or anyone n the Federal Reserve System, the Department of the Treasury, or the Offce of the Comptroller of the Currency. correspondng author: Federal Reserve Board of Governors: matt.darst@frb.gov, 1801 K St. NW, Washngton, D.C (202) Offce of the Comptroller of the Currency: ehraz.refayet@occ.treas.gov 1 Electronc copy avalable at:

2 Abstract Ths paper hghlghts two new effects of credt default swap markets (CDS) n a general equlbrum settng. Frst, when frms cash flows are correlated, CDSs mpact the cost of captal credt spreads and nvestment for all frms, even those that are not CDS reference enttes. Second, when frms nternalze the credt spread changes, the ncentve to ssue safe rather than rsky bonds s fundamentally altered. Issung safe debt requres equty holders to transfer profts from good states to bankruptcy states to ensure full repayment. Rsky bonds allow equty holders to ncrease good state profts as much as possble because of lmted lablty n default. Hgher credt spreads lead to more safe rather than rsky debt because equty value n good states, when debts are repad, falls. Symetrcally, lower credt spreads lead to more rsky rather than safe debt. CDS affect the credt spread at whch frms ssue rsky debt, and ultmately whether frms ssue defaultable securtes. The drecton of the tradeoff between credt spreads and frm default depends on whether CDS are used to speculate or hedge aganst credt rsk. 2 Electronc copy avalable at:

3 1 Introducton The global fnancal crss of underscored the need to better understand how fnancal market partcpants prce and take rsk. Credt default swaps (CDSs) are a partcular type of fnancal nstrument that market partcpants used wth ncreasng regularty n the buld-up to the crss. Accordng to the Bank for Internatonal Settlements (BIS) the notonal sze of the CDS market (value of all outstandng contracts) at ts peak before the market crash n 2007 was $57 trllon. Whle that number has abated manly as a result of the multlateral nettng of contracts, ts sze as of the frst half of 2015 was $15 trllon. Clearly the CDS market remans large and actve, and contnues to engender a varety of research efforts amng to better understand the effects of CDSs on captal markets. We nvestgate the general equlbrum mpact of CDS markets on credt spreads 1 and the endogenous nvestment and default decsons for multple frms, some of whom are CDS reference enttes and others are not. 2 We begn by allowng frms, whose expected cash flows dffer, to choose the amount of debt they wsh to ssue to debt fnancers. Specfcally, small amounts of debt can be repad n all states and bonds are equvalent to safe assets credt spreads wll be zero. Alternatvely, large amounts of debt cannot be honored n all states credt spreads wll be postve. Frm managers maxmze the equty value of the frm by choosng to ssue safe or rsky debt dependng on assocated credt spread. We then ntroduce a market for CDSs on frm debt. The CDS market gves frm credtors access to new securtes whose payouts are more algned wth ther subjectve belefs. The market prce of CDS contracts and the market prce of debt are lnked through a non-arbtrage relatonshp. CDSs affect the credt spread when frms ssue rsky debt, but not frms ssue rsk-free debt. Our model shows that the credt spreads of all frms, even those frms who are not CDS reference enttes, are mpacted by CDS tradng. More mportantly, we show that the CDS market alters frm ncentves to ssue rsky rather than safe bonds dependng on how CDSs affect equlbrum credt spreads. 1 Our model has an asset wth rsk-free rate normalzed to zero. The credt spread between a zero-coupon rsky bond and the rsk-free asset s the dfference between the assets yeld-to-maturty. The yeld-to-maturty of the rsk-free asset s equal to zero. Therefore, the credt spread s equvalent to the yeld-to-maturty on a rsky bond. 2 Usng data from ether Markt or the Depostory Trust and Clearng Corporaton (DTCC), there are only around 3000 frms for whch a CDS contract ever exsts. We do not attempt to endogenze CDS ssuance n ths paper; we smply take as gven that the market s actve only for a porton of the frms n the economy. 1

4 We buld on the work by by Fostel and Geanakoplos (2012) and subsequently by Che and Seth (2015), by showng that the collateral used to back CDS contracts re-allocates captal from the bond market to the CDS market, whch changes the demand for bonds and the equlbrum credt spread requred to ssue rsky debt. Thus, CDS tradng affects real outcomes n the economy. We use the re-allocaton channel to show that n equlbrum, when assets (frm producton n our model) have dfferent but correlated cash flows, an optmstc margnal buyer prces frm bonds so that the relatve expected returns to nvestng n ether bond wll be equal. The equvalent expected bond returns mply that when CDSs alter the demand for one type of bond, they also alter the demand for the other, resultng n credt spread changes for all frms seekng rsky-debt fnancng. Frms endogenously respond to lower (hgher) credt spreads by ncreasng (decreasng) the amount of debt they ssue. Thus, CDSs may ncrease or decrease the expected value of equty when frms ssue rsky-debt. The endogenous nvestment and credt spreads, n our model, lead to nterestng debt-fnancng decsons regardng the choce to ssue debt that s safe rather than rsky. Specfcally, as credt spreads fall, the beneft to equty holders of ssung rsky debt rses. Essentally, lmted lablty protects equty holders from default losses when cash-flows are low whle preservng ther return on equty when cash-flows are hgh and debts are repad. The commtment to repay debt n full, n all states, can only be acheved when rasng small amounts of debt, whch lmts producton. Shareholders alternatve to safe debt s to ssue rsky debt. The shareholders gnore the bankruptcy states because debt holders become the resdual clamants. Therefore, shareholders ssue as much debt as can be repad n states where cash flows are good, whch generates hgher producton and profts. The cost to the frm of ssung rsky debt s the credt spread. Credtors demand a postve credt spread n order to hold an asset that may default. CDS alter the credt spread that nvestors requre to hold rsky debt, and thereby alter the cost of ssung rsky rather than safe debt. We adopt a one-perod, statc, general equlbrum model wth two states characterzed by a commonly known aggregate productvty shock. The shock takes on hgh values n the up state and low values n the down state. For smplcty, we consder two frm types endowed wth dfferent producton technologes. The technology shock s common to both frms the producton technologes generate hgh cash flows n the up state and low cash flows n the down state. To produce, each 2

5 frm endogenously ssues non-contngent, collateralzed debt. The frms know the true probablty over the hgh and low cash-flow states, but ths s unobservable. 3 We assume a porton of the cash flows from producton are not pledgeable so that producton generates postve profts and control rents. Debt fnancng comes from nvestors wth heterogeneous belefs about the probablty of the future states. We frst solve the baselne model wthout CDSs for equlbrum bond prces, frm nvestment, and characterze the states n whch frms choose to ssue rsky or safe debt. Smlarly to Che and Seth (2015), we then extend the model to ncorporate CDS contracts, where CDS purchasers must also own the underlyng bond, whch we call covered CDS Economes. Ths restrcton on CDS ownershp s then removed so nvestors are free to purchase CDS wthout ownng the underlyng bond, n what we call naked CDS economes. 4 We begn by characterzng equlbrum based on whether the debt contracts are safe or rsky. Low values of the technology shock, resultng n low expected cash flows, always result n debt contracts that are rsky. Fnancng nvestment wth rsky debt allows the frm to produce much more and ncrease equty value n the hgh cash-flow state. Equty holders, by commttng to ssue safe debt, must take nto account the worst case cash-flow outcome, whch also lmts output n the hgh cash-flow state. The result of lower nvestment also lmts the resdual equty clams n the hgh cash-flow state. For ntermedate values of the technology shock, safe debt contracts are only possble when the lkelhood of generatng hgh cash-flow s suffcently low. The greater the probablty of the up-state and hgh cash-flow, the more equty holders wsh to move ther consumpton to the up state. Fnancng nvestment wth rsky debt allows equty holders to maxmze the value of equty n the up state by gnorng the down state. The remanng unnterestng case s when technology shocks are suffcently hgh that debt contracts are always safe because the cash flows n the down state are always suffcent to repay debt. We then ntroduce covered CDSs to study how credt spreads and the decson to 3 Alternatvely, one could assume that the state probabltes reveal a non-verfable or noncontractble sgnal about cash flows. 4 Norden and Radoeva (2013) document that there s clear frm heterogenety n the sze of the CDS market relatve to the sze of the underlyng bond market supportng the CDS contracts. One natural way to nterpret the covered CDS economy s as a CDS market that s small relatve to the sze of the underlyng bond market whereby a suffcent level of nvestor captal remans avalable to purchase bonds. Naked CDS economes n our framework would correspond to very large outstandng CDS markets relatve to the underlyng bond market supportng those trades. 3

6 ssue safe rather than rsky debt change. Frst, consstent wth Che and Seth (2015), covered CDSs rase bond prces and lower credt spreads. Optmstc nvestors can hold more credt rsk when usng ther cash as collateral to sell CDSs because of the mplct leverage embedded n CDSs. 5 The concentraton of credt rsk held by optmsts ncreases the remanng supply of captal that can then fnance other frm nvestment needs. Our analyss thus extends ths mechansm to show that even when CDSs trade only on one bond, both frms debt contracts are affected. 6 More nterestngly, because nvestment s endogenous to credt spreads, frms respond by ssung more rsky debt, and are more lkely to default. Wth fxed nvestment, frms default n fewer states as n Che and Seth (2015). The dfference between ther model and ours s that we consder not only the decson of how much debt to ssue, but also whether to ssue debt that s defaultable. CDSs do not trade f the frm ssues safe debt. Thus, for a gven technology shock n whch a frm s ndfferent between ssung safe or rsky debt n an economy wthout CDSs, the frm strctly prefers to ssue rsky debt at lower credt spreads n the economy wth covered CDSs. The restrcton that CDS buyers must own the underlyng bonds s then removed and naked CDS postons are the permtted. Naked CDSs also generate spllovers even when only one frm type serves as the CDS reference entty. Pessmsts ncrease the demand for CDSs, whch rases CDS prces. Hgher CDS prces reduce the amount of ther own captal CDS sellers have to post to sell CDSs. The lower collateral requrement ncreases the embedded leverage that optmst receve and attracts more captal nto dervatve markets from natural bond buyers. Less nvestor captal s then avalable to fund debt rrespectve of frm type. Consequently, credt spreads rse, whch makes ssung rsky debt less attractve compared to safe debt. The hgher credt spreads reduce nvestment and the equty value of the frm n hgh cash-flow states, brngng the value of equty more n lne wth ts value when producton s fnanced wth safe debt. The tradeoff between credt spreads and whether bonds contan credt rsk, agan, stands n contrast to Che and Seth (2015). Thus, both types of CDS contracts lead to a tradeoff between credt spreads and 5 As we later argue, the leverage n CDS s actually hgher than that whch can be obtaned va buyng bonds on margn due. The ntal margns requred to buy and sell CDS are substantally lower than the ntal margns requred to buy corporate bonds on margn or sell short. 6 We do not endogenze whch frm s the CDS reference entty. Oehmke and Zawadowsk (2016b) provde one ratonale for why CDS emerge on certan frms and not others, such as debt covenants and fragmentaton. We take ths fact as gven, and explore the general equlbrum fnancng mplcatons. The qualtatve results of our model hold regardless of whch frm serves as the CDS reference entty because the mechansm s symmetrc. 4

7 the probablty of default. Taken together, the model predcts that CDS markets have unntended consequences on corporate debt markets that are novel to the theoretcal CDS lterature. The best way to thnk about why a frm over certan parameters would ssue safe debt rather than rsky debt, and forgo the lmted lablty opton, s as follows. Equty holders consume n both hgh and low cash-flow states when bonds are safe, compared to consumng only n hgh cash-flow states when bonds are rsky. Moreover, the hgh cash-flow state consumpton level fnanced wth rsky debt must be greater than the hgh cash-flow state consumpton level fnanced wth safe debt. Otherwse, frms would always ssue safe debt. The cost of ssung safe debt s that equty holders must forgo consumpton n hgh cash-flow states n order to repay credtors n low cash-flow states. As the value of the technology shock rses, frms are more productve on the margn rrespectve of whether producton s fnanced wth rsky or safe debt. However, consumpton n low-cash flow states ncreases only when the frm ssues safe debt. Thus, as technology shocks reach a certan level, the ncremental consumpton gan n low cash-flow states that s assocated wth safe debt fnancng outweghs the ncremental consumpton gan n hgh-cash flow states that s assocated wth rsky debt fnancng. Addtonally, for any gven value of cash-flow n the down state, equty holders are more lkely to ssue rsky bonds as the probablty of the hgh cash-flow state ncreases precsely because rsky bonds do not requre shftng potental hgh cash-flow consumpton to the low cash-flow states to repay debts. The growng body of theoretcal CDS lterature examnes how CDSs affect bond, equty, and soveregn debt markets (see Augustn et. al (2014) for a complete and thorough survey on the broad lterature). Our work s most closely related to a class of heterogeneous agent models developed by Fostel and Geanakoplos (2012, 2016). Fostel and Geanokoplos (2012) show that n an endowment economy, fnancal nnovaton n credt dervatve markets alters asset collateral capactes, and asset prces. Fostel and Geanakoplos (2016) study the effect that credt dervatves have on whether agents engage n producton, showng that credt dervatves can lead to nvestment beneath the frst best level obtaned n an Arrow-Debreu economy and can robustly destroy equlbrum. Our model s dstngushable from ther models because producton n our model has dfferent expected cash-flow realzatons, and we consder the decson to ssue safe or rsky debt. These nnovatons allow us to 5

8 characterze spllovers and the tradeoff between credt spreads and default rsk. Che and Seth (2015) study how CDS affect borrowng costs for a representatve frm wth a random output draw that rases an exogenous amount of captal. Our model adds several relevant features by explctly modelng an endogenous producton envronment wth dfferent frm types. Our model also gves rse to a more n-depth dscusson of the nvestment and default decsons because of the general equlbrum settng. Oehmke and Zawadowsk (2015a) study the effects CDSs have on bond market prcng when nvestors have not only heterogeneous belefs, but also heterogeneous tradng frequences. Ther model s more suted to studyng the effect of CDSs on secondary bond market actvty. The authors do not consder nvestment n producton or default. Common to all of these models, however, s the underlyng mechansm through whch CDS generate effects on the real economy. Manly, the embedded leverage n the dervatve contracts alters nvestor use of collateral that would otherwse be used to purchase bonds. A dfferent strand of CDS lterature hghlghts the effect of CDS on the credtordebtor relatonshp. Bolton and Oehmke (2011) show how CDS lead to an empty credtor problem n a model wth lmted commtment. Lenders ncentves to rollover loans are reduced, leadng to ncreased bankruptcy and default rsk. Frms nternalze the dffculty of renegotaton ther debts when credtors are protected wth CDS, leadng to stronger ex ante frm commtment to repay debts. Parlour and Wnton (2013) show that CDS can reduce the ncentves to montor loans, thereby ncreasng default and credt rsk. Smlarly, Morrson (2005) shows that banks ablty to sell off the credt rsk of ther loan portfolo leads frms to substtute away from montored bank lendng and nto ssung rsky publc debt. Dans and Gamba (2015) study the trade-offs between hgher ex ante commtment to debt repayment and hgher ex post probablty of default n a dynamc model wth debt and equty ssuance. They calbrate the model to U.S. data and fnd the postve benefts of lower CDS spreads stemmng from hgher repayment commtment domnate and ncrease welfare. The mplct assumpton n all of these models s that CDS are used to hedge credt rsk, whch s equvalent to our covered CDS economy. All told, the ncreased default rsk when covered CDSs trade n our model s, thus, complementary. We propose a new mechansm, though. Qute smply, lower credt spreads and lmted lablty rase the ncentves to ssue rsky bonds. Ths s dstnct from the default rsk mplct n the empty credtor problem. Empty credtors may arse when frms face debt refnancng needs that are not met when credtors buy CDS contracts to nsure aganst default. 6

9 Thus there s a maturty-msmatch argument underlyng that story n whch debts that come due before all cash-flows are realzed may be renegotated. Our model s one perod wth no refnancng or maturty ms-match, and debt labltes and asset cash-flows are perfectly algned. We show that CDS may lead to hgher default because lower credt spreads reduce the cost of ssung defaultable bonds. Lastly, unlke our paper, none of debtor-credtor papers evaluate the effect on nvestment and default rsk when nvestors may take purely speculatve postons n the CDS market. Emprcally, Norden et. al (2014) fnd evdence of nterest rate spllovers n syndcated bank lendng markets. The authors attrbute these spllovers to more effectve portfolo rsk management. Our model suggests an alternatve explanaton operatng through how dervatves change the demand for bonds when frm cash-flows are correlated. L and Tang (2016) fnd that there are leverage and nvestment spllovers between CDS reference frms and ther supplers. They argue that the hgher the concentraton of CDS reference enttes s among a frm s customers, the lower suppler leverage ratos and nvestment levels are. The authors nterpret ther fndng as the CDS market provdng superor nformaton about the credt qualty of suppler frm customers (see Acharya and Johnson (2007) and Km et. al. (2014) for references on how nsder tradng of CDSs leads to nformaton transmsson). Our model provdes a complementary explanaton under the nterpretaton that frms n our model are n the same ndustry. Investor demand for debt at the ndustry level s altered when frms n the ndustry become named CDS reference enttes. Introducng CDSs changes the demand for bonds of other frms n the ndustry, alterng bond prces and nvestment levels. Our paper also provdes the followng new testable mplcaton: The effect on corporate default rsk of tradng CDS depends on whether the CDS buyer has an nsurable nterest n the underlyng reference entty. Current emprcal studes on the effect of CDSs on default rsk stem from the predctons of the empty credtor problem whch requre the effects to operate through hedgng credt rsk (see Subrahmanyam, Wang, and Tang (2014); Km (2013); and Shan, Tang, and Wnton (2015)). However, these studes cannot dstngush between covered and naked CDS postons. 7 Furthermore, our model s spllover mplcatons call nto queston the wdely employed method of propensty score matchng used to control for the 7 Ths s an ongong project we and co-authors are undertakng. 7

10 endogenety of CDS ssuance. Frm borrowng costs n matched samples wll not be exogenous to CDS ntroducton f CDS tradng alters the cost of captal for non-cds reference frms whose cash flows are correlated wth the CDS oblgors. The organzaton of the paper s as follows: In Secton 2, we descrbe frms, debt contracts and nvestors. We then solve the baselne economy wth no CDS contracts, and descrbe the relevant comparatve statcs. In Secton 3, we ntroduce covered CDSs. In secton 4 we allow for naked CDS tradng. In Secton 5 we close wth dscusson and concludng remarks. 2 Non-CDS economy 2.1 Model Tme and Uncertanty The model s a two-perod general equlbrum model, wth tme t = {0, 1}. Uncertanty s represented by a tree, S = {0, U, D}, wth a root, s = 0, at tme 0 and two states of nature, s = {U, D}, at tme 1. Wthout loss of generalty we assume there s no tme dscountng. There s one durable consumpton good rsk-free asset n ths economy that s also the numerare good. We wll refer to ths good as cash throughout the paper Agents Frms There are two frms, = {G, B}, n the economy where frm G s the good type and frm B s the bad type. Each frm s owned and operated by a manager wth access to a producton technology. The managers operate the frms and consume from frm profts. One could thnk of the postve profts earned n equlbrum as non-pledgeable control rents wth whch equty owners are compensated to nvest n producton. We use the terms control rents and profts nterchangeably. 8 only dfference between the two frms s the producton technology at the respectve managers dsposal. The frms use the durable consumpton good as an nput at tme 0 and produce more of ths good for consumpton at tme 1. The respectve frms have 8 We abstract away from any agency problem between equty holders and frm managers. Alternatvely, one could thnk of the managers as operatng the frm and beng pad through equty. The 8

11 standard, decreasng returns to scale, producton functons gven by f (I ; α, A s ) = A s I α wth the followng propertes: f > 0, f < 0. Frm G s more productve than frm B; that s, I αg > I α b, 0 < I < 1. The technology shock, A s, takes on bnary values at tme 1, wth A U > A D. The technology parameter s dentcal for both frms. Consequently, the only type of uncertanty n our model s aggregate. 9 Idosyncratc rsk would not have any mpact n a model wth two frms and two states, because agents would be able to perfectly nsure themselves. The only way dosyncratc rsk would have an effect s f we consdered more than two states (n whch case there would stll be non-aggregate rsk remanng even after agents trade wth each other). 10 For smplcty we normalze the technology shock, A U, to 1. Both frms have dentcal knowledge about the qualty of ther producton process, where each frm knows that s = U arrves wth probablty γ and s = D wth probablty (1 γ). Lastly, frms are compettve prce takers n the market for the durable consumpton good. Investors We consder a contnuum of rsk-neutral, heterogeneous nvestors, dstrbuted accordng to h H U (0, 1), who do not dscount the future. The absence of tme dscountng allows us to focus on credt spreads wthout loss of generalty. Investors are characterzed by lnear utlty for the sngle consumpton good, x s, at tme 1. Each nvestor s endowed wth one unt of the consumpton good, e h = 1, and assgns probablty h to the up state, U, and (1 h) to the down state, D. Thus, a hgher h denotes more optmsm. Agents agree to dsagree about ther subjectve state probabltes. The von Neumann Morgenstern expected utlty functon for nvestor h s gven by U h (x U, x D ) = hx U + (1 h)x D. (1) We assume a unform dstrbuton for tractablty. The results wll hold n general as long as the belefs are contnuous and monotonc n h. In terms of nvestor preferences, we assume rsk-neutralty, but the results are also qualtatvely preserved wth homogeneous belefs and state contngent endowments. 9 It may be natural to thnk of the model as one of ntra-ndustry debt fnancng n whch two frms n the same ndustry are equally affected by a ndustry specfc technology shock. 10 We leave ths to future research. 9

12 Fgure 1: Bond payout h 1 p 1 h d s q Frm fnancng We assume the frms use future output as collateral and optmally rase captal from nvestors by ssung debt. Our am s to better understand the effect of credt dervatves on the debt-ssuance decson. The effect of credt dervatves on a more general captal allocaton problem s an nterestng natural extenson of the model. At tme 0, frms ssue debt contracts that specfy a fxed repayment amount (bonds) and are collateralzed usng the pledgeable proceeds from output, whch we refer to as cash flows. The lender (nvestor) has the rght to seze the collateral up to the face value of debt, but no more. Ths enforcement mechansm ensures that the frm wll not smply default on ts commtment at tme 1. Each bond, prced p at tme 0, promses a face value of 1 upon maturty. The two frms ssue bonds denoted by q at tme 0. In the up state, each bond returns full face value. 11 In the down state, bonds pay credtors accordng to the delverable functon, d s = mn [1, As I α q ]. If debt oblgatons are not honored, credtors become the resdual clamants of the frm and consume from the cash flows generated from producton. Frm borrowng costs are denoted by r, and equal to the dfference n what the frm owes on maturty and the amount of captal they receve at the tme of ssuance, r = 1 p. Fgure 1 depcts the bond payouts. 11 We assume the bonds repay n full at s = U to make the model nterestng; otherwse, the frm does not nvest n producton. 10

13 2.1.4 Frm maxmzaton problem Each frm chooses an nvestment amount, I, gven the market prce of bonds to maxmze expected profts. Frms must ssue debt n order to produce snce they have no ntal endowment. Hence I = p q. Let π s profts. Frms solve the followng program: denote state-contngent frm max E [π ] Π = { γ [ ] [ A U I α q + (1 γ) A D I α q d D (q ) ]} I s.t. I = p q Investor Maxmzaton Problem We can now characterze each agents budget set. Gven bond prces p, each nvestor, h H, chooses cash holdngs, { x h 0}, and bond holdngs, { q h }, at tme 0 to maxmze utlty gven by (1) subject to the budget set defned by: (2) B h (p ) = { (x h 0, q h, x h s) R+ R + R + : x h 0 + ( x h s = p q h = e h, 1 p q h ) + d s q h }, s = {U, D}. Each nvestor consumes from two potental sources n ether state of nature: consumpton based on rsk-less cash holdngs and consumpton based on ther total bond portfolo. In the up state, consumpton from bond holdngs s equal to the quantty of bonds an nvestor owns n hs portfolo because each bond has a face value of 1. In the down state, frms may default on ther debt, n whch case nvestors take ownershp of the frm and consume from the frms avalable assets on a per-bond bass. We rule out short sales of bonds by assumng q R +. It s frequently argued that CDS are nherently redundant assets f one allows for assets to be perfectly leveraged and short short sales are not constraned. It s true that sellng a CDS and buyng a bond wth leverage span the same asset payoffs. Buyng a naked CDS and short sellng the asset also span the same asset payoffs. However, what ths argument does not consder s that takng a long poston on credt rsk by sellng a CDS allows an nvestor to take more leverage than buyng the bond on margn because the 11

14 ntal margn requrements are dfferent. 12 For example, accordng to the Fnancal Industry Regulator Authorty (FINRA), the ntal margn requrement for sellng a 5yr CDS wth a spread over LIBOR less than 100 bps s 4% of the notonal amount of the CDS contract. Conversely, the regulatory mnmum to purchase an nvestment grade bond on margn assumng that the spread over LIBOR for sad bond s also less than 100 bps s 10% of the market value of the purchase. 13 Thus, the return to every dollar of collateral posted aganst a CDS transacton s hgher than the return of a dollars worth of collateral posted as ntal margn n the bond market. The same logc holds for naked CDS purchases and short sales. Investors have to take a 2% harcut wth ther broker to borrow a corporate bond, n addton of the 50% margn requred by Regulaton T. 14 Accordng to FINRA, CDS purchasers are requred to post 50% of ntal margn requred of CDS sellers, whch s 2% n the example gven above Equlbrum An equlbrum n the non-cds economy s a collecton of bond prces, frm nvestment decsons, nvestor cash holdngs, bond holdngs and fnal consumpton decsons, p, I, (x 0, q, x s ) h H R + R + (R + R + R + ) such that the followng are 12 Ths s a dfferent argument than suggestng that tradng cost between the cash and synthetc markets are dfferent, whch tends to also be the case, as measured that bd-ask spreads (see Bswas, Nkolova, and Stahel (2015). 13 The FINRA ntal margns can be found here: man.html?rbd=2403&element d=8412. The corporate bond margns can be found here: 14 See Asquth et. al. (2013). 15 Furthermore, n the sprt of Banerjee and Gravelne (2014) dervatve prcng n our model contans no nose, as wll be clear n the followng secton, because the nvestors know technology fundamentals. Banerjee and Gravelne show n proposton 6 that mposng a short-sale ban wll have no effect on bond prces when nvestors can trade n dervatves wth no nose. 12

15 satsfed: ˆ I = x h 0dh + ˆ 1 0 ˆ 1 0 ˆ 1 0 q h d s dh + p q h dh p q h dh = π s = ˆ 1 0 e h dh 4. π (I ) π (Î), Î 0 for = {G, B} A s I α, s = {U, D} 5. ( x h 0, q h, x h s) B h (p ) U h (x) U h ( x h), h Condton (1) says that at tme 0 the ntal aggregate cash endowment s held by nvestors for consumpton or used to purchase bonds ssued by frms. Condton (2) says the goods market clears at tme 1 such that all frm output s consumed ether by frm managers va profts or by credtors va bond payments. Condton (3) corresponds to the bond market clearng condtons. Condton (4) says that frms choose nvestment to maxmze expected profts, and condton (5) states that nvestors choose optmal portfolos gven ther budget sets. 2.2 Equlbrum bond prcng We begn by characterzng equlbrum bond prcng and credt spreads. Ths characterzaton wll lay the foundaton for analyzng the borrowng cost spllover effects n subsequent sectons. We then analyze the frm nvestment decson that nvolves a choce between ssung a lmted number of safe bonds or rsky bonds that carry a postve credt spread. Ths then allows us to nvestgate how credt dervatves affect the frm debt ssuance decson. Equlbrum n heterogeneous belef models s characterzed by margnal nvestors prcng debt. In equlbrum, as a result of lnear utltes, the contnuty of utlty n h, and the connectedness of the set of agents, H = (0, 1), there wll be margnal buyers, h 1 > h 2, at state s = 0. Every agent h > h 1 wll buy bonds ssued by frm B, every agent h 2 < h < h 1 wll purchase type-g bonds, and every agent h < h 2 wll reman n cash. Ths regme s shown n fgure 2. The margnal buyer ndfferent between the payouts of the varous assets avalable n the economy wll be crucal n subsequent sectons for understandng why ntroducng dervatves affects the credt spread for all debt contracts n the economy, rrespectve of debt contracts 13

16 are referenced by CDS. Wth ths, we now characterze the relatonshp between the respectve frms bond prces. Proposton 1 In any equlbrum wthout dervatves where both frms ssue rsky debt wth postve credt spreads, type G bonds are prced hgher than type B bonds. Proof. See appendx A. The ntuton s that the producton value of the more productve frm s always hgher than the less productve frm. Debt holders wll therefore be wllng to pay a hgher prce for those bonds, ceters parbus, snce they are the resdual clamants of the frm output gven default. Snce both bonds have equal face value and pay n full at s = U, more optmstc nvestors wll prefer frm-b bonds, the cheaper of the two assets. The two margnal nvestor ndfference equatons can be wrtten as: h 1 + (1 h 1 ) d D g p g = h 1 + (1 h 1 ) d D b p b (3) h 2 + (1 h 2 ) d D g = p g. (4) Equaton (3) says that the more optmstc margnal buyer, h 1, wll be ndfferent between the expected payouts from type-b and -G bonds. Equaton (4) says that the less optmstc margnal buyer, h 2, wll be ndfferent between the cash flows on type-g bonds and cash. The bond market clearng condtons for type-b and -G bonds requre that the two bond prces be determned by the endowment avalable to the respectve sets of nvestors buyng the bonds. That s 1 h 1 p b = q b for type-b bonds and h 1 h 2 p g = q g for type-g bonds. Ths characterzaton clearly shows that bond prces are jontly determned based on how the margnal nvestors vew the respectve payouts. A change n the prce of one bond necessarly changes the yeld on the two assets. For example, an exogenous decrease n the prce of bond B makes t more attractve and means t wll become strctly preferred to the relatvely more expensve bond G unless there s a correspondng change n the bond G s cash flows. In equlbrum, as more captal moves to fnance bond B, bond G s prce must also fall and wll be prced by a less optmstc nvestor. 2.3 Debt Fnancng Regme We now turn to the ssue of when t s optmal for the frm, gven market prces, to ssue rsky debt wth postve credt spreads versus ssung safe debt. The frm 14

17 maxmzaton problem gven by (2) bols down to choosng an nvestment, I, that corresponds to ether full repayment or default at s = D. Bonds that fully repay n ether state have zero credt spread: p f = 1 where the super-scrpt f denotes default-free prcng. Rsky bonds wll carry a postve credt spread, p ρ < 1, where the super-scrpt ρ denotes a postve credt spread. Let the correspondng expected proft levels from each of these nvestment decsons be denoted by Π f and Π ρ (. The frm thus chooses I α, γ, A D) ] arg max Π f, Πρ. The frst-order condtons for the two nvestment levels are I [ I ρ I f : α I α 1 : α I α 1 = 1 p ρ = 1 p f (5) ( ) 1. (6) γ + (1 γ) A D These are the standard margnal products of captal that must equal the margnal costs of captal condtons. The default-free condton n (6) takes nto account that all debt s fully repad at s = U, D through the expected value of the technology shock, γ+(1 γ) A D. Usng (5) and I ρ d s (q ρ ), gven s = D can be wrtten as = p ρ q ρ, the rsky bond repayment functon, d D (q ) = AD α. (7) Intutvely, recoverable frm asset values are proportonal to the technology shock parameter, 0 < A D < 1, and the productvty parameter, 0 < α < 1. The recovery value also places a fundamental restrcton on the relatonshp between the two parameters. Specfcally, for A D < α frms wll ssue rsky debt n equlbrum. Snce α g < α b there are dfferent values of A D for whch there s fundamental default rsk for the two frms, 0 < A D G < α G < A D B < α B < 1. As we show n the subsequent dscusson, for a gven (α G, α B )-par, frms decson to ssue rsky or safe debt depends on the gven ( A D, γ ) -tuple. If frms always repay n all states, p f = 1, the credt spread s zero, and the optmal nvestment s gven by (6): I f = [ ( α )] 1 γ + (1 γ) A D (1 α ) = q f. Note that the default-free bond repayment ( ) [ ] functon, d s = mn 1, As (I f ) α = 1, mples that AD (I f ) α 1. Usng the q f q f optmal nvestment level and I f = q f gves a relatonshp between the good state probablty, γ, and the value of the technology shock, A D, for whch ssung defaultfree debt s possble even wth fundamental default rsk, α > A D. Formally, q f 15

18 Proposton 2 For any gven state probablty γ, there exsts a threshold value of the technology shock, A D (γ) where realzatons of A D greater than ths threshold can support safe debt fnancng. The threshold value of A D of γ. Proof. See appendx A. (γ) s an ncreasng functon The ntuton underlyng proposton 2 s that the cash flows from producton must be suffcently hgh n bad states (hgh A D ) for the frm to always honor ts debt oblgatons. The cost of ssung safe debt s that nvestment wll be lmted and the potental up state profts are reduced n order to promse credtors full repayment gven poor cash flow realzatons. The hgher are bad state cash flows, the less frms need to lmt debt-fnanced nvestment and potental returns n good states n order to ensure credtors are always repad, hence the cost of ssung safe debt s fallng as A D rses. Addtonally, the more lkely t s that good states wll arrve (hgh γ) the more frms nvest because dong so ncreases ther expected profts. Ths means that cash flows n the down state must be even hgher as γ ncreases f the frm s to fully honor ts debt oblgatons. Thus, A D (γ) s ncreasng n γ. We must stll determne what the optmal debt fnancng regme s for any set of ( parameters. Ths s done ( ) by solvng } for the equlbrum I α, γ, A D) based on (5) and (6) to max {Π f I f, Π ρ I (Iρ ). Pluggng q f = I f nto (2), we obtan the rsk free fnancng expected proft functon Π f = (1 α ) α ( q f A D (γ), γ ). As debt s always repad n default-free regme, expected profts are only affected by state probabltes, γ, through the affect on bond quanttes, q f. Moreover, by proposton 2, an equlbrum n whch default-free bond prcng exsts must be characterzed by A D > A D (γ). If A D < A D (γ), safe debt fnancng s not proft maxmzng for the frm. The expected profts from rsky debt fnancng are obtaned usng the optmalty condton (5) along wth (2): Π ρ = γ (1 α ) α ( q ) ρ A D. Note from (5) that good state probabltes, γ, do not nfluence rsky debt fnancng nvestment levels, I ρ, because of lmted lablty. The frms nvest as f γ = 1 because 16

19 they default at s = D; the good state probablty, γ, affects only the expected profts of the frms for a rsky-debt regme. Comparng the two expected proft functons, t( s clear that ) f the bond ssuances correspond to the same face value at maturty q f = q ρ, frms prefer safe debt fnancng because credt spreads are zero. However, rsky debt fnancng s prefered f the face value of rsky-debt s greater than the face value of safe debt, and the rato of the face values s less than the good state probablty, γ: γ > qf q ρ. Rsky debt fnancng allows equty holders to maxmze ther profts n the good state because, unlke safe debt fnancng, nothng must be conceeded to the down state to ensure repayment. Therefore, the hgher the good state probablty, the more equty holders prefer to shft all profts to the good state. Lastly, note that the only nterestng range of technology shocks for analyzng a tradeoff between the two dfferent debt ssuances s A D [ ) A D, α. All technology shocks below A D result n the rsky-debt regme, q = q ρ, and all shocks greater than α result n the default-free regme, q = q f. The followng proposton characterzes the parameter regons over whch frms ssue the two dfferent types of debt. Proposton 3 Frms ssue rsky bonds for A D < A D and safe bonds for A D α. For A D [ A D, α ) frms ssue safe bonds f and only f γ < γ. Ths result says that dependng on the parameter values, frms must optmally choose between the default-free regme and the rsky-debt regme. Low values of the bad state technology shock, A D < A D, correspond to rsky debt fnancng because safe debt fnancng requres reduced nvestment to guarentee credtors full repayment when cash flows turn out to be low. Lower nvestment also reduces profts when the technology shock turns out to be good. Hgh values of the bad state technology shock, A D A D, enable safe debt fnancng because the amount of debt that must be curtaled to fully repay debt n all states s decreasng. Thus the beneft of the hgher ncremental good state output assocated wth rsky debt fnancng s domnated by the ablty to borrow at the rsk free rate. Debt fnancng for ntermedate values of the bad state technology shock, A D [ A D, α ), depends also on the lkelhood of good cash flows, γ. Rsky debt fnancng allows for more consumpton n good cash flow states, whch means that hgher γ leads to rsky debt fnancng regmes. Example 1 { A D = 0.2, γ = 0.5, α G = 0.5, α B = 0.65 } Ths example gves results for credt spreads, margnal buyers, and the remander of the endogenous varables n the economy for the lsted parameters. Fgure 2 17

20 Fgure 2: Non-CDS economy h =1 Type B Bond Buyers h 1 =.8471 Type G Bond Buyers h 2 =.6831 Cash h = 0 Table 1: Equlbrum values: Non-CDS economy non-cds economy = G = B Prce: p Credt Spread: cs Quantty: q Investment: I Output: Y U Exp.Proft: E [π ] s the characterzaton of the margnal buyer n equlbrum and table 1 gves the values of the endogenous varables. The values of the technology thresholds for determnng whether default-free bonds may be ssued for γ = 0.5 are A D G =.3 3 and A D B =.4814, and clearly p < 1, = G, B. The comparatve statcs for bond prcng and nvestment are not partcular to the parameters chosen so long as A D < A D. Hgher values of the technology shock naturally rase bonds prces, nvestment and profts. However, ncreases n the technology shock above the respectve thresholds, A D, wll change the comparatve statcs snce the respectve bond prces wll be p = 1. 18

21 3 Covered CDS economy In ths secton, we ncorporate CDSs nto the baselne model. A CDS s a fnancal contract n whch the CDS seller compensates the buyer for losses to the value of an underlyng asset for a specfed credt event or default. The underlyng assets n ths economy are frm bonds. CDS contracts compensate buyers the dfference between a bond s face value at maturty and ts recovery value at the tme of the credt event. Thus, CDS allow nvestors to hedge aganst dosyncratc default rsk. 16 We frst consder covered CDSs, n whch buyers are requred to also hold the underlyng asset (that s, the bond correspondng to the CDS reference entty). We assume the seller must post enough collateral to cover the payment n the worst case scenaro, but no more, to rule out any counterparty credt rsk. Let qc h be the number of CDSs that nvestor h can sell, and let p c be the CDS prce. Therefore, the total cash that nvestor h holds to collateralze CDS contracts, ncludng payments receved for sellng CDSs, wll equal the maxmum possble CDS payout n the event of frm default, tmes the number of CDS contracts sold: 1 + p c q c = qc h (1 d s ). (8) Solvng for the total number of CDS contracts gves q h c = 1 1 d s p. (9) c Fgure 3 shows the payout to the CDS seller and buyer. At tme 0, a CDS seller must post a porton of hs own collateral, 1 d s p c, to nsure each CDS. At s = U, the CDS seller consumes the posted collateral, because the bond pays n full. At s = D, all of the posted collateral s used to pay the CDS buyer. Thus, sellng a CDS contract s equvalent to buyng an Arrow-Up securty because t pays out only when s = U CDS do not allow nvestors to nsure away aggregate rsk. 17 Sellng a CDS s cash-flow equvalent to leveragng the bond, but the ntal margn dfferences between the two transactons allows nvestors to take more leverage through the CDS market relatve to the bond market. 19

22 Fgure 3: Covered CDS payout CDS Seller Covered CDS Buyer 1 d s q 1 h h 1 d s q p c p + p c =1 1 h 0 1 h Investor maxmzaton problem Gven bond and CDS prces, (p, p c ), each nvestor h decdes on cash, bond, and CDS holdngs, { x h 0, q h, qc} h, to maxmze utlty (1) subject to the followng budget set: B h (p, p c ) = { (x h 0, q h, q h c, x h s) R+ R + R R + : x h 0 + p q h + p c q h c = e h, x h s = x h 0 p c qc h + max { } } 0, qc h q h. q h d s + q h c (1 d s ), s = {U, D} The frst two equatons are analogous to the nvestor budget set n the non-cds economy. The thrd equaton states that snce CDS buyers are requred to hold the underlyng asset, the maxmum number of CDS contracts that can be purchased cannot exceed the number of bonds owned. Note that there s no sgn restrcton on qc. h Sellng CDS mples that qc h < 0, whle qc h > 0 mples purchasng CDS. Short sellng of bonds s stll ruled out by the restrcton q R + as n the non-cds economy. 20

23 3.2 Equlbrum An equlbrum n the covered-cds economy s a collecton of bond prces, CDS prces, frm nvestment decsons, nvestor cash holdngs, bond holdngs, CDS holdngs and fnal consumpton decsons, p, I, (x 0, q, q c, x s ) h H R + R + (R + R + R R + ), such that the followng are satsfed: 1. ˆ ˆ I = x h 0dh + ˆ 1 0 q h c = 0 ˆ 1 0 ˆ 1 0 q h d dh + p q h dh 5. π (I ) π (Î), Î 0 p q h dh = π s = ˆ 1 0 e h dh A s I α, s = {U, D} 6. ( x h 0, q h, q h c, x h s) B h (p, p c ) = U h (x) U h ( x h), h Condton (1) states that all of the endowment s ether held by nvestors or used to purchase bonds. Condton (2) says the goods market clears where total frm output s consumed by frm managers va profts and used to repay bond holders. Condton (3) says that the CDS market s n zero net supply, whle (4) states that the bond market clears. Condton (5) says frms choose nvestment to maxmze profts. Lastly, (6) states that nvestors choose a portfolo that maxmzes ther utlty, gven ther budget set. We make use of the followng lemma to characterze equlbrum n the covered CDS economy. Lemma 1 If 0 < d D (q ) < 1, any rsky bond that s a CDS reference entty wll not be purchased wthout the correspondng CDS. Proof: See appendx B. The ntuton behnd lemma 1 s that any nvestor optmstc enough to buy a bond wthout a CDS wll be better off sellng CDSs on that bond. Addtonally, f the recovery value of the bond s zero, then CDSs and bonds have dentcal payouts 21

24 n ether state, thus makng CDSs redundant assets. Fnally, f the recovery value of the bond s 1, then bonds are rsk free and no CDSs wll trade n equlbrum. 3.3 Borrowng costs and spllovers We ntroduce CDSs only on one frm s debt to establsh the borrowng cost spllover result. For expostonal purposes, let nvestors ssue CDSs on frm-b debt. 18 As n the non-cds economy, there wll be margnal buyers, h 1 > h 2. In equlbrum, every agent h > h 1 wll sell CDSs on type-b debt, every agent h 2 < h < h 1 wll purchase type-g debt, and every agent h < h 2 s ndfferent to holdng covered CDS and cash. More specfcally, agents h < h 2 hold a portfolo of covered postons on type-b debt and CDS, and cash. 19 Compared wth the non-cds economy, covered CDSs lower borrowng costs for the frm on whch CDSs are traded frm B, because the dervatve allows the optmsts who beleve frms wll always repay ther debt to hold all of the credt rsk. Because CDS sellers only have to hold a porton of ther collateral to cover the expected loss gven default, whch s always less than the prce of the bond, each ndvdual CDS seller can hold more credt rsk than they could when just buyng bonds. The resultng margnal buyers are therefore more optmstc than n the economy wthout CDSs. The margnal buyer ndfference equatons are now h 1 ( 1 d D b ) 1 p bc d D b = h 1 + (1 h 1 ) d D g p g (10) h 2 + (1 h 2 ) d D g = p g. (11) The aggregate endowment CDS sellers have at ther dsposal to prce CDSs s now (1 h 1 ) 1 p bc d D b = q b. The avalable endowment of type-g bond buyers takes the same form as the non-cds economy: h 1 h 2 p g = q g, wth dfferent margnal buyers. Lastly, because some agents hold a portfolo of covered CDS and cash, a non-arbtrage prcng condton between the CDS and bond market lnks the prce of credt rsk n 18 The qualtatve results for borrowng cost spllovers and endogenous postve credt spreads are not partcular to the frm s debt from whch the CDSs derve ther value. Endogenzng CDS ssuance s an nterestng queston, but beyond the scope of ths paper. Work by Banerjee and Gravelne (2014), Bolton and Oehmke (2011), and Oehmke and Zawadowsk (2015b) provdes nterestng reference ponts for thnkng about why we see CDSs emerge on some frms and not others. 19 In equlbrum, every agent h < h 2 wll be ndfferent between cash and a covered poston and each agent wll hold a portfolo consstng of 30.43% n covered postons and the rest n cash, for the same parameters chosen n example 1. To compute ths portfolo allocaton we smply dvde the number of type B bonds nvestors hold by ther total cash endowment, q b h 2. 22

25 the CDS market wth the postve credt spread n the bond market: p bc + p b = 1. Consstent wth Che and Seth (2015), but wth an addtonal dmenson n terms of borrowng cost spllovers, we have the followng bond prcng mplcatons: Proposton 4 Covered CDSs rase bond prcng for the CDS reference entty. Proof. See appendx B. More nterestngly, because our model has an addtonal rsky asset wth a dfferent bond pay-out structure, there are general equlbrum borrowng cost mplcatons for frm G even though frm-g debt s not referenced by a CDS. Corollary 1 The credt spread for a non-cds reference entty s affected by CDSs tradng on other reference enttes wth correlated cash flows. Proof. See appendx B. Ths result follows drectly from proposton 4 because the margnal CDS seller who mplctly prces frm B debt s more optmstc than the correspondng margnal bond buyer n the non-cds economy. Ths s because each CDS seller uses hs endowment solely for the purpose of buyng credt rsk n the amount equal to the loss gven default of the underlyng bond contract. Thus a gven set of nvestors of sze (1 h 1 ) n the non-cds economy have ncreased ablty to purchase credt rsk n the covered CDS economy. Furthermore, the number of CDS that can be sold s restrcted to the number of outstandng frm B bonds. The combnaton of ncreased ablty to buy credt rsk and restrcton of buyng CDS means that the margnal buyer prcng Frm G debt s more optmstc than n the non-cds economy. Ths ncrease n the set of nvestors fnancng both frms debt ssuances also rases bond prces for frm G. The fact that cash flows are correlated across good and bad states s also mportant. Take the lmtng example n whch frm G s cash flows are hgh at s = D and low at s = U. The frm would then fnd t optmal to ssue debt to those nvestors most wllng to pay for an asset whose payouts are closely correlated wth ther subjectve belefs. Frm G would then prefer to ssue debt to pessmsts who would pay a hgher prce for an asset that pays more at s = D wth certanty than to optmsts who would pay hgh prces for hgh payouts n the opposng state. It s ths nterpretaton of the model that leads naturally to an ntra-ndustry or geographcally 23