Repo Collateral Fire Sales: The Effects of Exemption from Automatic Stay

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Repo Collateral Fire Sales: The Effects of Exemption from Automatic Stay Sebastian Infante 2013-83 NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Repo Collateral Fire Sales: The Effects of Exemption from Automatic Stay∗ Sebastian Infante Federal Reserve Board October 25, 2013 Abstract Whataretheconsequencesofapotentialfiresalestemmingfromtheexemptionofrepurchaseagreements (repos) from automatic stay? This paper shows that repo’s exemption from stay alters firms’ financing and investment decisions ex ante. Specifically, a stay exemption changes firms’ investment opportunity set, enabling them to purchase assets of defaulted firms at fire sale prices. Fire sales arise endogenously because of limited capital available to purchase collateral posted by insolvent firms, i.e., cash-in-the-market pricing. A fire sale effectively creates a premium for holding on to dry powder and concentratesassetownershipwithfirmsthathavepreferencestoholdhighlyleveragedpositionsandrisk default. The premium reduces the initial asset price, potentially inducing more firms to take on risky positions, increasing the fraction of defaulting firms in the economy. In contrast, when repo is subject to automatic stay secured lenders do not receive their collateral immediately, reducing the severity of a firesale and ex ante price distortions. ∗I would like to thank Anat Admati, Anne Beyer, Darrell Duffie, Travis Johnson, Kristoffer Laursen, Stefan Nagel, Paul Pfleiderer,MonikaPiazzesi,MartinSchneider,KennethSingleton,FelipeVaras,andJeffreyZwiebel. Iwouldalsoliketothank seminarparticipantsattheFederalReserveBoard,McGillUniversity,StanfordUniversity,UniversityofHouston,Universityof Rochester,andtheStanford-Berkeleystudentseminarforhelpfulcomments. Theviewsofthispaperaresolelytheresponsibility of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System orofanyotherpersonassociatedwiththeFederalReserveSystem. FederalReserveBoard,20thSt. andConstitutionAvenue, NW,Washington, DC,20551. Pleasesendcomments to: sebastian.infantebilbao@frb.gov. 1

1 Introduction The financial crisis of 2007–09 has spurred considerable debate over the role deregulation played in the instability of the financial system. One particular area of interest has been the treatment of derivatives and repurchase agreements (repos) in bankruptcy. For the most part, when firms in the United States file for bankruptcy, a temporary hold is placed on the their assets known as automatic stay. The logic behind this bankruptcy provision is to prohibit creditors from collecting payments in a disorderly fashion, maintaining the firm as a going concern.1 This provision does not exist for derivatives and repos, which are exempt from automatic stay. Counterparties to these contracts have, among other things, immediate access to any collateral posted by the defaulted party. This is particularly important for repo contracts, which in essence are secured loans backed by financial assets. The consequences of repo’s exemption from stay is a relatively broad research question, and this paper focuses on a particular aspect of the debate, namely the impact of fire sales stemming from repo’s special treatment on firms’ incentives ex ante. This paper addresses the issue by examining agents’ financing and investment decisions under two regulatory regimes: repo subject to, or exempt from, automatic stay. The model features a continuum of firms with limited capital that raise debt from a competitive lending sector to purchase a risky asset. In the stay regime, in case of a debtor’s default, secured lenders (i.e., repo lenders) must wait until the following period to receive their collateral. In the stay exemption regime, repo lenders have immediate access to the contract’s collateral and have incentives to sell it to surviving firms, causing a fire sale. Fire sales occur because ofsolventfirms’limited capacity to purchaseassets after a defaultevent— a cash-in-the-market style pricing. Thus, repo’s exemption from stay alters firms’ investment opportunity set, potentially giving them theopportunitytopurchaseassetsatdiscountedpricesinthefuture. Thisopportunitycreatesincentivesfor firms to hold on to their initial cash endowment (dry powder), placing a premium on liquidity and reducing demand for the risky asset. Specifically, in the stay exemption regime, firms’ incentives to exploit future fire sales attracts capital that would have otherwise participated in the market initially, thereby reducing initial asset demand and consequently its price before the fire sale. Firms’ incentives to use their liquidity in the future places more assets in the hands offirms with preferences to take large positions and risk default, which is assumedto be costly. Moreover,the initial price discount can be so severe, that even firms that do not have preferences to become large are motivated to choose high levels of debt, increasing the fraction of defaulting firms in the economy. This is not the case when repo is subject to automatic stay, since the lock-up of secured lenders’ collateral doesn’t allow its immediate sale after default, effectively eliminating any possibility of a fire sale. 1ForthehistoryofautomaticstaysinU.S.bankruptcy, seeSkeel(2001). 2

The base setup consists of a group of firms — interpreted as dealer banks, hedge funds, or commercial banks — endowed with a fixed initial capital stock that raise debt from a competitive lending sector — interpreted as money market funds and bond investors — to purchase a risky asset. Because of reasons outside the model, a fixed fraction of firms enjoy private benefits for holding large risky asset positions, inducing them to take on higher leverage. This modeling device captures the fact that many financial firms increase their asset size by taking on debt, and that there is heterogeneity in financial firms’ leverage.2 Therefore, the number of assets each firm can purchase depends on its initial endowment, the amount of debt it canraise,andits willingness to take ondefaultrisk. Awell-capitalizedlending marketoffers secured and unsecured loans to firms, where secured contracts set aside a fraction of the firm’s risky asset position as collateral (i.e., repo contract). Firms are constrained as to how much debt they can raise, either because of regulatory constraints or because the lending sector demands them to have some participation in their portfolio’s outcome. It is assumed that there are direct bankruptcy costs that must be paid from the firms’ assets, making default costly, which lenders price accordingly. The main difference between regimes is that when repo is exempt from stay, secured lenders have access to the asset and sell it immediately to the remaining solvent firms. This assumption is paramount to the modelbutiseasilymotivated. Currentlymanyofthelendersparticipatinginrepomarketscannotholdlongdated assets because of regulatory restrictions or lack of expertise (e.g., money market funds), giving them strong incentives to sell it in case of default. Moreover,conditional on having to sell, the lender has limited incentives to find a “good” trading price since once the repo lender is made whole, any additionalupside on the collateral is the property of the borrower.3 Thus, the lender’s upside is bounded by the face value of the loan, but its downside may be substantial. For simplicity, in the model I assumed that repo contracts are overcollateralizedto such anextent that the loan is absolutely safe.4 This particular contractingfeature eliminates anyincentive forthe lendertoholdthe assetafterthe borrowerdefaults,makingthe assetsupply insensitive to the fire sale. Therefore, in a default event, the asset’s market clearing price will depend on solvent firms’ ability to raise funds and defaulting firms’ initial asset holdings, potentially creating a price below the asset’s expected future payoff. An important element of the model is the lack of initial capital committed to the market. This lack is due to market segmentation that only allows a fixed set of firms with limited capital to participate in the market. Market segmentation can arise because of a specific expertise needed to trade in the risky asset market,whichonlyalimitednumberoffirmspossess. Thissegmentationalsoimpliesthatmorecapitaldoes not flood into the market after firms default, which could result from an unmodeled lemons problem that 2Adrianetal.(2012)andHeetal.(2010) presentevidence ofthisduringthe2007–09financial crisis. 3Thiscontracting featureispresentinstandardMasterRepurchaseAgreements. 4Thisassumptionisinlinewiththenotionthatrepoloansare“relativelysafe.” 3

outside investorssuffer by participating in a marketunfamiliar to them. Potentially because ofslow moving capital,ittakestimefornewinvestorstocomeintothemarket,leavingonlytheoriginalparticipantstotake advantage of the price discount.5 Because of firms’ incentives to wait for future price dislocations, the stay exemption regime produces higher default costs since more assets are in the hands of firms that risk default. This paper also explores potential policy prescriptions that, in the context of the model, would eliminate the fire sale in the stay exemption regime, namely an asset purchase program by the government or a contracting change to repo arrangements. A brief subsection is dedicated to an environment where agents do not internalize the future cash-in-the-market pricing, which increases uncertainty and the magnitude of the fire sale, and potentially puts more firms at risk of default. Since firms’ debt capacity depends on the value of their portfolio, unforeseen price reductions could hinder their ability to roll over their debt, putting their solvency into question. This paper is inspired by the events that unfolded during the 2007–09 financial crisis. During that time, policy makers were concerned that fire sales could arise in relatively illiquid markets, for example the mortgage-backed securities (MBS) market, having destabilizing effects. The paper provides anecdotal evidence pointing to the main mechanism of the model, namely the unwillingness of market participants to purchaseassetsinitiallyinanticipationoffurthermarketdisruptions. Thesedisruptionswereplausiblegiven the current regulatory regime that would have liberated illiquid repo collateral after a default event. The rest of the paper is structured as follows. The following section presents a literature review, with a brief overview of the current debate over derivatives’ and repos’ exemption from automatic stay. Section 3 introduces the model setup, detailing the main market frictions driving the results. Section 4 presents firms’ optimal strategies, and Section 5 characterizes the resulting equilibrium in both regulatory regimes. Having detailed the model’s mechanics, Section 6 goes back to the stay versus stay exemption debate to put the model into context with the existing literature, highlighting the types of markets that this paper is most relevant to and giving anecdotal evidence for the model’s main mechanism. Section 7 presents the cost–benefit analysis, some policy considerations, and extensions to the original model. The final section concludes. 2 Related Literature The question as to whether the exclusion of repos from normal bankruptcy proceedings can have an impact on the stability of the financial system has interested economic and law scholars alike. Skeel and Jackson 5SeeDuffie(2010). 4

(2012)providea detailedaccountofthe rationalebehind exempting repofromautomaticstay,whichwasto mitigate the possibility of a run given the contract’s easy resolution in bankruptcy. They argue that during the 2008 crisis repo’s exemption played a minor role in preventing runs, and in fact aggravated troubled firms situation by not providing the regular protections enjoyed under bankruptcy. More broadly, Duffie and Skeel (2012) provide a detailed discussion of the role of stay exemption and the main trade offs in the debate. A rigorous economic analysis of the ex ante effect of stay exemption is given by Bolton and Oehmke (2011) in the context of firms engaging in derivative contracts to hedge part of their operational risk. They show that stay exemption creates incentives for firms to shift risk from derivative counterparties to debt holders, and the desirability of automatic stay exemption depends on which one of these agents can bear default risk more efficiently. If it is more costly for debt holders to bear the risks associated with default, then the stay exemption is undesirable. In this paper, I study the ex ante effects of repo’s stay exemption as a funding vehicle and analyze how different bankruptcy regimes can change firms’ aggregate risk-taking, which has an effect on asset prices. Specifically, this paper studies a particular externality that could arise from a mass default event that wouldinduceanassetselloffandadramaticreductioninprices,i.e.,afiresale.6 Stein(2012)studies theex post effect of fire sales, which attract capital that could have been used more efficiently in other investment projects. Antinolfi et al. (2012) take this view in the context of repo stay exemption, where the optimal bankruptcy regime balances the reduction in capital to productive investment because of a fire sale, with lenders’preferenceforimmediacy. Acharyaetal.(2011)andDiamondandRajan(2011)studyamechanism similar to the one presented in this paper: future fire sales that create incentives to hoard liquidity ex ante. Though the focus of this paper is to study how the bankruptcy treatment of a specific lending contract affects firms’ investment decisions, which impact the severity of price dislocations, the level of leverage in the economy,and the amountof default risk in the economy. An extensionof the model will also explorean additional fire sale externality: the reduction of firms’ debt capacity that could propagate defaults.7 This paper is also related to the vast literature on capital constraints and their effects on prices, from the original paper by Kiyotaki and Moore (1997) where hard collateral constraints limit agents’ funding, to the more recent literature that studies how different manifestations of capital constraints can influence intermediaries decisions (for example, Gromb and Vayanos (2002), Brunnermeier and Pedersen (2009), He andKrishnamurthy(2012),andKrishnamurthy(2010)). Therecurringthemeishowparticularbalancesheet 6Onemechanismbehindfiresalesiswhenhigh-valuationagentsareforcedtosellassetstolow-valuationbuyers(forexample Shleiferand Vishny(1992), (1997)). In this paper, firesales arisebecause of market segmentation andagents’ limitedcapital toincreasedemand. ShleiferandVishny(2011) provideacompleteoverviewoftheexistingfiresaleliterature. 7SeeStein(2013)foradiscussiononhowfiresalescanhinderfirms’financing. 5

SH CH α S 0 β CLH 1−α SL 1−β CLL Figure 1: Risky asset process constraints affect the capacity of intermediaries to trade assets, limiting their ability to exploit arbitrage opportunities and allowing prices to deviate from fundamentals. This is related to the intuition introduced by Allen and Gale (1994), (1998), and (2005) referred to as “cash-in-the-market” pricing, which illustrates how limited demand cancause anasset’sprice to be lowerthanits fundamental. These mechanisms are key in this paper since firms face limits on the amount of debt they can raise that depend on the value of their portfolio, which ultimately affects their demand. 3 Model Set Up The model consists of three periods t ∈ {0,1,2}, where specialized firms raise one period debt from a competitive lending sectorto financetheir positioninasingleriskyasset. Firms avoiddefaultifthe amount ofcashthey receivefromthe asset,orfromadditionalfunding, issufficienttopayoffexisting creditors. The model is analyzedunder two distinct regulatoryregimes: repo subject to automatic stay (regime S) or repo exempt from automatic stay (regime SE). 3.1 Assets There is an initial fixed supply K of one risky asset, which produces three possible cash flows in the final period: {CH,CLH,CLL},withCH >CLH >CLL. Afterperiodzerowithprobabilityα,theassethasahigh outcomeandwillpayacashflowofCH forsureint=2. Withprobability1−α,theassethasalowoutcome and still has some residualuncertainty: With probability β, it will pay off CLH, andwith probability1−β, it will payoff CLL. Thus, after a low outcome, the expected future cash flow of the asset is denoted by CL =βCLH+(1−β)CLL. The initialexpected cashflow ofthe assetis denoted by C =αCH+(1−α)CL. The initialmarketclearingpriceforthe assetisdenotedbyS, andinperiod1the price isdenotedbySH or SL in the high and low state, respectively (see Figure 1). There is also a num´eraire safe asset called “cash” and a storage technology to deposit it in with a gross interest rate normalized to 1. 6

3.2 Agents There are a continuum of risk-neutral firms who have an initial cash endowment AI and raise funds from a competitive lending sector to finance their risky asset positionQ. Firms are the only agents in the economy that can buy and hold the risky asset. They are risk neutral, but a fraction θ also enjoy private benefits b proportional to the size of their initial risky asset position. Private benefits can be interpreted as perks that firm managers enjoy for holding large risky asset positions, an unmodeled convenience yield perceived bythese firmsproportionaltothe portfoliosize8 oroptimisminthe finalcashflowofthe asset.9 The nature of these private benefits is not important. In essence, it is a modeling device to ensure that some firms have incentives to increase their risky asset position by taking on risky debt that will be assumed to be costly.10 Firms that receive private benefits are referred to as “private benefit firms”. The aggregate demand of PB NPB private-benefit and non private benefit firms at time t are denoted by Q and Q , respectively. t t Lenders are risk neutral, and their role is to provide firms with cash to increase their portfolio size. They have unlimited access to funds but cannot invest in the risky asset directly. That is, they can only gain exposure to the risky asset by lending to firms (i.e., market segmentation). This segmentation can be motivated by a prior participationdecisionthat gavefirms the expertise to trade in said risky assetmarket. Lenders can invest in two possible debt contracts: secured and unsecured. Secured debt, interpreted as repos,earmarksa fractionofthe firms riskyportfolio ascollateral,which lendershave firstlienonin caseof default. Unsecured debt have a claim to the firm’s remaining assets.11 Note that market segmentation plays two important roles. First, it makes the market clearing price depend on firms’ ability to raise funds, inducing cash-in-the-market pricing. Second, when repo is exempt from automatic stay, market segmentation makes secured lenders’ supply of the asset insensitive to the market clearing price. This outcome is aggravatedfurther since conditional on wanting to sell, lenders have little incentive to react to a low trading price since any gain above and beyond the promised debt payment is property of the original borrower.12 3.3 Firm Liabilities Lendersuse one-periodsecuredandunsecureddebt tosatisfy firms’demandforfunds. Securedlending contractsareassumedtobeabsolutelysafe,thustheloanrepaymentmustbecoveredbytheworstpossibleout- 8Forexample,throughmarketmakingfortheriskyasset. 9Thesefirmsmaybelievethe highassetoutcome willbeCˆH withCˆH−CH = b,andagreetodisagreewithother agents α in the economy. In this setting, if the asset has a high payoff these firms update their beliefs, eliminating their optimism for thefinalperiod. 10Detailsondefaultcostsareinsubsection3.4. 11Detailsondebtcontracts areinsubsection3.3. 12Oehmke(2013) studiestheproblemfacedbyagents attempting toselldefaultedcollateralinanilliquidmarket. 7

comeoftheasset(i.e.,fully collateralized). Thisassumptionavoidshavingtodeterminethehaircut/interest ratetradeoff,simplifyingthetermsoftradebetweenrepolendersandborrowers.13 Alternatively,itcouldbe assumed that lenders purchasing secured contracts are relatively more risk averse and it’s in the borrower’s best interestto offer safe loans. Given a fire sale in the stay exemption regime,this assumptionimplies that the initial amount of secured funding a firm can raise will differ under the two regulatory regimes. The nature of firms’ default costs, elaborated in subsection 3.4, will make firms prefer secured funding before they take on any unsecured debt. Thus, to simplify firms’ liability structure, I assume an exogenous upper bound on the fraction of the risky asset portfolio that can be earmarkedto secured lenders ϕ.14 This eliminates the unrealisticoutcomeofhavingthe entireportfoliofinancedby repo. Labelingϕthe fractionof the portfolio earmarkedfor securedlending and Pi as the worst-caseoutcome per unit of risky asset (which depends on regime i∈{S,SE}), the initial secured loan amount and repayment are both ϕPiQ where Q is the total quantity of risky assets held by the firm. Unsecured lenders set their lending terms to break even each period, internalizing secured lenders’ priority on earmarked assets and any potential deadweight loss. This additional funding channel allows intermediaries to increase their debt capacity, taking on positions that could make them insolvent in the following period. Denoting Iu the initial loan amount of unsecured funding, Fu the promised payment in the next period, Di the per unit value of the firm’s risky portfolio in case of default, and 1−λ < 1 the deadweight loss from liquidating any remaining fraction of the firm’s endowment, lenders solve for Fu using Iu =P(no default)Fu+(1−P(no default)) DiQ+λA−ϕPiQ , (1) (cid:0) (cid:1) where A and Q are the amount of cash and risky assets held by the firm, respectively.15 Thus, given the firm’s choice of {Q,A,Iu,ϕ}, unsecured lenders choose Fu according to equation (1). Firms default if the amount of cash on hand — either by raising new funds from the lending sector or directly from their own holdings — is not enough to pay off existing creditors. 13Martinetal.(2012)adoptasimilarassumptionforrepotransactions,andintheframeworkofGeanakoplos(2010)thesafe debt contract isthe onlyonetraded inequilibrium. Fostel andGeanakoplos (2011) show general conditions inwhichthe safe contract arisesandhighlights theliteraturelinkingleverageand assetpricesthat assumes the useofthe safecontract. Inthe context ofrepos,Infante (2013) shows that borrowerswitharelativelylargeinitialendowment accept contracts withhaircuts thatmakelendingriskfree. Thisfindingisinlinewiththenotionthatrepoloansare“relatively”safeinvestments. 14Inamoregeneralsetup,whereafirm’sriskyportfolioismorediverse,theremaybemorereasonswhyfirmsmaynotwant tousealloftheirfinancialassetsasrepocollateral. Forexample,theexpectedfiresaleforsomeassetclassesmaybetoosevere inthestayexemptionregime,whichlimitsthedesiretouserepoaltogether. 15To ensure there is enough value in the firm’s portfolio to make secured creditors whole DiQ+λA−ϕPiQ must be nonnegative. Thisisnot arestrictivecondition sincePi isset tothe asset’s worstoutcome and ϕ<1. It ensures thereis always enoughvalueintheportfoliotopayoffrepolenders. 8

t=0 t=1 t=2 Raiseinitialfinancing Initialoutcomerealized Lowassetoutcomerealized Purchaseportfolio Refinanceexistingportfolio Cashflowsdistributed Defaultifamountraised<amountowed SolventfirmsinSE: purchasedefaultedassets Figure 2: Timeline under both regimes The model also incorporates capital constraints that limit the amount of leverage firms can adopt. This constraintcanbe interpreted as firms’ capitalrequirements,or an unmodeled “skin-in-the-game”constraint to ensure that firms behave in the lender’s best interests.16 Capital constraints eliminate the possibility for a firm to turn over its entire portfolio to lenders — that is, it restricts the issuance of equity contracts. If firms were able to raiseequity, the unconstrainedlending sector wouldbe able to provideenoughcapital for firms to eliminate any price deviation below fundamentals.17 In the model, capital requirements at time t take the form, Iu+ϕPiQ≤η(SiQ+A), (2) where η ∈ (0,1) is the capital requirement parameter and Si is the period t market clearing price, which depends on regime i. Restriction (2) forces firms’ equity to be at least 1−η the market value of the firms’ assets. Note that a lower asset price decreases the amount of financing firms can raise. 3.4 Stay vs. Stay Exemption: Timing & Defaults The strategies and timing of the three-period model depend on which regime is under consideration. The resolution of default in period 1 is the main difference between regimes. In the stay exemption regime, a market for defaulted collateralopens where secured lenders who receive collateralsell it to solvent firms. In the stay regime, securedlenders must waituntil the final period to receive their payment. The exact timing of the model under both regimes can be summarized in Figure 2. The nature of firms’ default costs are specifically related to direct costs of default. They represent the costs of litigation (experts, lawyers, etc.) to resolve disputes among claimants of a defaulted firm, which must be paid from the firms’ assets.18 It is important to characterize how these default costs affect firms under different regimes. In the stay exemption regime, collateralizedassets leave the firm immediately, thus 16Althoughthenatureofthisbadbehaviorisn’tspecified,thistypeoffrictionhasbeencommonlyusedintheliterature. For exampleseeAcharyaetal.(2011) andAcharyaandSkeie(2011). 17In fact, without the constraints firms that enjoy private benefits may have incentives to raisefunding beyond the default valueoftheportfolio,potentiallyincreasingtheinitialpricebeyondit’sfundamentalvalue. 18Theyarenotindirectcostsduetothesuboptimaluseofanassetbyathirdparty,noraretheycostsassociatedtothefirm asagoingconcern. Inthe model,thereisnoscopetorestructurethefirmsinceinthefinal periodalluncertainty isresolved, theassetmatures,andcashflowsaredistributed. 9

it can be argued that the cost to resolve these claims are relatively small.19 This outcome might not be the case for secured lenders in a stay regime, where disputes between various secured claimants as to which specific asset they are entitled to could arise. To simplify the comparison between regulatory regimes, I assumed that secured claims are resolvedat no cost across both of them.20 The consequence of this assumption is that secured funding will always be preferred in the stay regime sinceitinduceslowerdefaultcosts. ThiswillalsobetrueinthestayexemptionregimeaslongasSL ≥λCL, which creates a natural lower bound for the fire sale. In case the fire sale price were below the defaulted value of the asset, firms that take on risky positions would not be inclined to take on secured debt, leaving only unsecured debt holders and eliminating the fire sale altogether. To simplify the analysis, I assumed there were no default costs in the final period. This dramatically reduces the number of cases to analyze in each regime since solvent firms refinancing problem becomes trivial: in case of a fire sale, purchase as much of the asset as possible. No default costs in the final period can be motivated by assuming that it is less costly to resolve the bankruptcy of a firm with assets “closer to maturity” or alternatively that the capital requirement bound is so strict that in the final period only safe debt can be raised (i.e., ηCL < CLL).21 Knowing firms’ portfolio values and default costs under both regulatory regimes, their initial debt contracts are detailed in the following subsections. 3.4.1 Stay Regime In period 1 if a firm defaults, its claimants receive their payoff in the final period making the worstpossible asset value CLL. Therefore, in period 0 if a risky firm decides to purchase Q risky assets, leave AI −A in 0 0 0 cash,raiseϕ CLLQ insecuredfunding, andraiseIu inunsecuredfunds; period0unsecuredlenderschoose 0 0 0 Fu from 0 Iu =αFu+(1−α) DS(ϕ )Q +λ(AI −A )−ϕ CLLQ , (3) 0 0 0 0 0 0 0 0 (cid:0) (cid:1) where the default value per unit of risky asset is DS(ϕ )=ϕ CL+λ(1−ϕ )CL. 0 0 0 Since there is no market for defaulted collateral, the asset price is set to reflect fundamental value, which eliminates incentives for solvent firms to trade. 19Similartoleasesinthecontext ofEisfeldtandRampini(2009). 20An additional cost for secured assets locked inbankruptcy inthe stay regimecan be incorporated. This does not change anyqualitativefeaturesoffirmsoptimalstrategies,northeresultingequilibrium;itonlyintroducesanadditionalparameterin thecostbenefitanalysismakingthecomparisonbetween regimesmorecumbersome. SeeSection7formoredetails. 21Bothoftheseinterpretationscanbeseenastwoextremecasesthatwillimpacttheseverityofthefiresale: easyresolution ofmatureassetsincreasesdebtcapacitymitigatingthecash-in-the-marketdiscount;orstrictcapitalrequirementslimitfunding, reducingdemand,andamplifyinganymispricing. 10

3.4.2 Stay Exemption Regime In period 1 if a firm defaults, secured creditors receive the asset and sell it immediately, implying that the worst possible asset value is SL. Therefore, in period 0 if a risky firm decides to purchase Q risky assets, 0 leaveAI−A incash,raiseϕ SLQ insecuredfunding, andraiseIu inunsecuredfunds; period0unsecured 0 0 0 0 0 lenders choose Fu from 0 Iu =αFu+(1−α) DSE(ϕ ,SL)Q +λ(AI −A )−ϕ SLQ , (4) 0 0 0 0 0 0 0 0 (cid:0) (cid:1) where the default value per unit of risky asset is DSE(ϕ ,SL)=ϕ SL+λ(1−ϕ )CL. 0 0 0 UpondefaultϕSLQ gotosecuredcreditors,leavingtheremainingassetstobearthe directcostsofdefault, 0 which are resolved in the following period. 4 Firm’s Optimal Strategies In each period solvent firms must decide how much debt to raise to refinance their existing risky asset positionandpotentially finance a new assetpurchase. This sectioncharacterizesthe problemfirms face and under what conditions they choose positions that may lead them to default (labeled risky firms), or avoid it altogether (labeled safe firms). It is important to note that there’s no difference between secured and unsecured debt if a firm’s leverage doesn’t put it at risk of default. Since there is neither a concern about a safe firm’s bankruptcy cost nor a change in the supply of defaulted collateral, unsecured and secured debt will turn out to be equivalent. All proofs are relegated to the appendix. In addition, the refinancing problem in case of a high outcome in period 1 is straightforward. Firms do notdefault, andthere is noopenmarketfordefaultedcollateral,nordo privatebenefit firmshaveincentives to purchase the asset from nondefaulting firms since they only enjoy b in the initial period.22 All firms are able to refinance their portfolio making the problem trivial. Thus, all discussions and characterizations of firms’ optimal strategies in period 1 were assumed to be after a low outcome in the initial period. For generality, the analysis was done from the perspective of a firm that enjoys private benefits. Strategies and payoffs for firms that do not enjoy private benefits were given by the general set up with b=0. 22Inthiscasethepriceequalsthefinalcashflow,SH =CH,thusthereisnoincentivetotrade. 11

4.1 Stay Regime Theanalysisofthestayregimeisrelativelysimple. Inperiod1thereisnoopenmarkettopurchasedefaulted collateral,thussurvivingfirmsonlyneedtodecidehowmuchdebttoraisetopaypreviouscreditors,i.e.,roll over their debt. Conditional on the firm’s current balance sheet (Q ,AI −A ,F ), where Q is the initial 0 0 0 0 period’s risky asset position, AI −A the remaining dry powder, and F the total amount of debt to be 0 0 paid in period 1, the firm must decide how much to raise to pay off F . The firm is restricted to raise new 0 debt up to its capital requirement, and may also use its remaining dry powder to pay off its previous debt. Since there are no default costs in the final period, the firm is willing to maximize its debt capacity, which is done by taking on debt and exhausting any remaining dry powder. Therefore, the firms will be able to avoid default in period t=1 if F ≤ηCLQ +AI −A . (5) 0 0 0 Having the default condition in the refinancing period one can postulate the firm’s initial financing decision. Firms have the choice to take on small levels of debt that will allow them to refinance their positionin t=1 (safe firms), or they canmaximize their debt capacityrisking defaultin t=1(risky firms). In case a firm decides to become risky, lenders charge a higher interest rate on the loan. Therefore, using lenders’debtpricingequation(3)togettheappropriateexpressionforF ,firms’payoffunderbothstrategies 0 can be characterized. Given the size of firms’ risky asset position, the amount of secured and unsecured debt, and the amount of dry powder committed purchase the risky asset, firms have the following possible payoffs:23 πS(Q ,A ,Iu,ϕ ;AI,b) = CQ +AI −A −ϕ CLLQ −Iu+bQ , 0 0 0 0 0 0 0 0 0 0 πR(Q ,A ,Iu,ϕ ;AI,b) = [αCH +(1−α)(ϕ CL+(1−ϕ )λCL)]Q + 0 0 0 0 0 0 0 :=CD(ϕ0) ( | α+(1−α)λ)(AI{ − z A )−ϕ CLLQ − } Iu+bQ . 0 0 0 0 0 Using equation (5) I define the no default set for this regime: NS ={(Q ,A ,Iu,ϕ ):Iu+ϕ CLLQ ≤ 0 0 0 0 0 0 0 ηCLQ +AI−A } thatcharacterizesthe portfoliosthatcanrollovertheir debt. Thus,firmsmustsolvethe 0 0 following optimization problem,24 {Q0,A m 0 a ,I x 0 u,ϕ0} πS(Q 0 ,I 0 u,ϕ 0 ,A 0 )1 {(Q0,A0,I0 u,ϕ0)∈NS} +πR(Q 0 ,I 0 u,ϕ 0 ,A 0 )1 {(Q0,A0,I0 u,ϕ0)∈(NS)c} 23Detailsareintheappendix 24Intheinterestofbrevity,Ishallomittheutilityfunction’sdependence onprimitiveparametersAI andb. 12

subject to, A ≤AI Dry Powder 0 SQ ≤ϕ CLLQ +Iu+A Budget 0 0 0 0 0 Iu+ϕ CLLQ ≤η(SQ +(AI −A )) Capital Requirement 0 0 0 0 0 Iu,A ,Q ≥0, ϕ ∈[0,ϕ]. 0 0 0 0 Conditionalonbeingsafeorrisky,thefirmistheresidualclaimholderoftheportfolioplusanyadditional privatebenefitsitmayperceive.25 Thefirstrestrictionlimitstheamountofcashthefirmcanusetopurchase the asset. The second restriction is the firm’s budget constraint, i.e., the amount it raises from lenders plus the amount of dry powder used must be enough to purchase the risky asset portfolio. The third restriction is the firm’s capital requirement. In this regime a firm’s decision to become risky or safe depends on the size of its private benefits. Firms that have large private benefits would be willing to pay for their expected default costs to maximize their asset holdings and enjoy more of said rewards. To ensure that firms which adopt risky strategies actually default after a low asset outcome, firms’ initial capital requirements can’t be too restrictive. In effect, for low values of η firms wouldbe unable to increasetheir debt capacityto violate inequality (5), thus I assume Assumption A1. The capital requirement restriction η is larger than the defaulted value of the firm: η ≥ ϕ +λ(1−ϕ ). 0 0 Assumption A1 states that the maximum amount the firm can raise is larger than the default value of the asset. The solution to the firm’s initial financing problem in this regime is Proposition 1. In the stay regime if S > CL and A1 holds, there exists a function b∗(S) such that if b<b∗(S) the solution to the firm’s initial financing problem is 0 if S >C+b  Q∗ 0 = Qu 0 ndet if S =C+b AI if S <C+b,  S−ηCL where Qundet may take any value between 0, AI . If b ≥ b∗(S) the solution to the firms initial 0 C+b−ηCL h (cid:17) financing problem is AI Q∗ = . 0 S(1−η) 25Conditional on being safe or risky the firms’ optimization problem is very similar to the variable investment model of HolmstromandTirole(1997). 13

These strategies lead to the following payoffs: AI if S ≥C+b and b<b∗(S)  π 0 (S;b)= (C S + − b− ηC S L )AI +AI if S <C+b and b<b∗(S) (CD(ϕ)+b−S)AI +AI if b≥b∗(S).  S(1−η) The solution to the firm’s investment and financing problem can be split in two. Conditional on the decision to become safe or risky, the firm’s problem is linear. For relatively large private benefits firms will prefer to maximize their risky asset position, assuming the cost of potential default. For relatively low private benefits, firms take a safe strategy where they either retain their dry powder, raise debt up to their refinancingcondition,orareindifferentbetweenthesestrategies. Thepriceatwhichsafefirmsareindifferent is called the breakeven price, which in this case is equal to C+b. The function b∗(S) characterizesfor what prices firms decide to take on safe or risky strategies, which ultimately pins down the amount of default in the economy.26 4.2 Stay Exemption Regime Inthis regime,firms mustinternalizethe possibility ofanopenmarketafter a lowoutcome. Survivingfirms notonlyhavetorefinancetheirexistingportfoliosbutmustalsoraiseadditionalfundstopurchasedefaulted collateral. As noted earlier, the price for the defaulted asset may be lower than the expected value of its future cash flows due to limited demand. The potential price discount has two effects: first it generates a profit for nondefaulting firms, creating incentives to underinvest in the initial period. Second, because of mark-to-market pricing, firms’ capital requirements limit their ability to raise debt, which aggravates the price discount. The focus of the model will be in a context where SL ≤CL, and a fire sale is said to occur when the inequality is strict. Sincetherearenodefaultcostsinthefinalperiod,inperiod1iftheassetpriceisbelowitsexpectedfuture cashflow,firmswillwantto maximizetheirdebtcapacityandmakeasmanynew purchasesaspossible,i.e., maximize Q . This will be restricted by their period 1 capital requirements. Therefore, for SL <CL firms 1 will solve, SLQ = ϕ CLL(Q +Q )+Iu+AI −A −F , 1 1 0 1 1 0 0 Iu+ϕ CLL(Q +Q ) = ηSL(Q +Q ), 1 1 0 1 0 1 where the first equality is the firm’s budget constraint and the second is its capital requirement restriction. 26Seeappendixfordetails. 14

Firmsraisesecuredfunding earmarkingtheirexistingandnewassetholdings,andalsoraiseunsecureddebt. As in the stay regime, it is optimal for the firm to exhaust its remaining dry powder to maximize the asset purchase. Therefore, in case of a fire sale a firm’s asset purchase in t=1 is ηSLQ +AI −A −F Q∗ = 0 0 0 . (6) 1 SL(1−η) Note that Q∗ <0 implies the firm is unable to pay off existing creditors and therefore must default. In case 1 SL = CL, firms will have no incentive to purchase the asset, and their t = 1 demand is undetermined. A firm with (Q ,AI −A ,F ) that can roll over its debt gets the following expected payoff when refinancing: 0 0 0 CLQ +AI −A −F if SL =CL π (Q ,AI −A ,F ;b)= 0 0 0 1 0 0 0  CLQ +AI −A −F +(CL−SL)Q∗ if SL <CL. 0 0 0 1  Having the firm’s optimal asset choice, and refinancing condition in t = 1, one can postulate the firm’s initial financing decision. Similar to the stay regime, firms have the choice between taking on small levels of debt that allow them to refinance their position in t = 1 (safe firms), or they can maximize their debt capacity,riskingdefault(risky firms). Thoughinthis regime safe firmsinternalize thatif they use too much of their debt capacity in the initial period, they will reduce their ability to purchase defaulted collateral in the future. Specifically, if they expect a large price discount in the refinancing period it may be optimal to withhold their initial dry powder rather than participate in the initial market. Using the firm’s payoffin the refinancing period, and lenders debt pricing equation(4) to get the appropriate expression for F , firms’ payoff under both strategies can be characterized. In effect, given the firm’s 0 asset position, its initial debt structure, and the amount of dry powder committed to the initial purchase, the firm’s expected payoffs are expressed as:27 πS(Q ,,A ,Iu,ϕ ;AI,b,SL) = CQ +AI −A + 0 0 0 0 0 0 ηSLQ +AI −A −ϕ SLQ −Iu (1−α)(CL−SL) 0 0 0 0 0 − (cid:18) SL(1−η) (cid:19) ϕ SLQ −Iu+bQ , 0 0 0 0 πR(Q ,A ,Iu,ϕ ;AI,b,SL) = [αCH +(1−α)(ϕ SL+(1−ϕ )λCL)]Q + 0 0 0 0 0 0 0 :=CD(ϕ0,SL) | (α+(1−α)λ)(AI{ − z A )−ϕ SLQ − } Iu+bQ . 0 0 0 0 0 From equation (6), the firm’s default condition can be deduced (whenever Q∗ < 0), and I can define 1 27Detailsareintheappendix. 15

the no-default set for this regime: NSE = {(Q ,A ,Iu,ϕ ) : Iu + ϕ SLQ ≤ ηSLQ + AI − A } that 0 0 0 0 0 0 0 0 0 characterizes the portfolios that can roll over their debt in t = 1, which depends on SL. This gives the following optimization problem for t=0, 28 {Q0,ϕ m 0 a ,I x 0 u,A0} πS(Q 0 ,I 0 u,ϕ 0 ,A 0 )1 {(Q0,A0,I0 u,ϕ0)∈NSE} +πR(Q 0 ,I 0 u,ϕ 0 ,A 0 )1 {(Q0,A0,I0 u,ϕ0)∈(NSE)c} subject to, A ≤AI Dry Powder 0 SQ ≤ϕ SLQ +Iu+A Budget 0 0 0 0 0 Iu+ϕ SLQ ≤η(SQ +(AI −A )) Capital Requirement 0 0 0 0 0 Q ,Iu,A ≥0, ϕ ∈[0,ϕ]. 0 0 0 0 Conditional on being safe or risky, the firm is the residual claim from the initial portfolio, their private benefits, and the payoff from purchasing more of the asset in the refinancing period. The firm’s restrictions arethesameasinthestayregime: adrypowderbound,it’sbudgetconstraint,andit’scapitalrequirements. Note that given firms’ default costs, secured funding will be preferred over unsecured funding only if SL ≥ λCL. Otherwise the costof raising securedfunding wouldbe too high and firms would only raise unsecured debt. Using the same parameter assumption as in the stay regime to ensure that firms that take on full leverage actually default, the solution to the firms initial financing problem in this regime is given by, Proposition 2. In the stay exemption regime if S > SL, SL ∈ (λCL,CL] and A1 holds, there exists a function b∗∗(S,SL) such that if b<b∗∗(S,SL) the solution to the firm’s initial financing problem is 0 if S >SBE(SL,b)  Q∗ 0 = Qu 0 ndet if S =SBE(SL,b) AI if S <SBE(SL,b),  S−ηSL where Qundet may take any value between 0, AI and 0 SBE(SL,b)−ηSL h i C+b+(1−α) CL−SL ηSL SBE(SL,b)= (cid:16) SL(1−η) (cid:17) . (7) 1+(1−α) CL−SL SL(1−η) (cid:16) (cid:17) 28Intheinterestofbrevity,Ishallomittheutilityfunction’sdependenceonprimitiveparametersAI,b,andthefinalperiod’s priceSL. 16

If b≥b∗∗(S,SL) the solution to the firm’s initial financing problem is, AI Q∗ = . 0 S(1−η) These strategies lead to the following payoffs, (1−α) CL−SL AI +AI if S ≥SBE(SL,b) and b<b∗∗(S,SL)  (cid:16) SL(1−η) (cid:17) π 0 (S,SL;b)= (C S + − b− ηS S L )AI +AI if S <SBE(SL,b) and b<b∗∗(S,SL) (CD(ϕ,SL)+b−S)AI +AI if b≥b∗∗(S,SL).  S(1−η) Thesolutionto the firms’probleminthis regimeissimilarto the solutioninthe previousone. Firmsare either risky or safe, and if safe, their investment strategy depends on the breakevenprice that induces them to participate. The important difference is that in this regime the safe firms’ breakeven price (denoted by SBE(SL,b)) not only depends on firms’ private benefits but also on the next period’s market price, i.e., the fire sale. It can be easily verified that SBE(SL,b) is increasing in SL, which implies that a larger fire sale in the refinancing period increases firms’ incentives not to participate in the initial market and hold on to their dry powder. The intuition for this behavior is straight forward. If a safe firm invests in t = 0, it risks reducing its ability to purchase defaulted collateral at the fire sale price. Thus, it must be compensated to induce it to participate in the market initially, which translates into a lower breakeven price. It is important to note that if SL = CL, then SBE(SL,b) is equal to C+b. That is, absent the fire sale, safe firms’ strategies and payoffs are exactly the same as in the stay regime. With this in mind, whenever b = 0, SBE(SL,0) can be rearranged to give a more intuitive expression. After some algebraic manipulation SBE(SL,0) solves the following equality: (1−α)(CL−SL) C (1−α)(CL−SL)ηSL 1+ = + , (8) SL(1−η) S SL(1−η) S for S. The left-hand side is the gross return of holding on to dry powder to purchase defaulted collateral at a fire sale price, and the right-hand side is the return from investing in the initial period. Dry powder receives a gross interest rate of 1 plus the expected net profit of CL −SL of purchasing 1/(SL(1−η)) of the defaulted collateral. The right-hand side gives a gross return of C/S plus the expected net profit of CL−SL of purchasing 1/(SL(1−η)) of the defaulted collateral. This lastpurchase is realizedusing ηSLQ 0 of the original asset as collateral, which has an initial costs SQ .29 Thus, for a non private benefit firm to 0 29ThesizeofthedefaultedassetpurchasecanbeappreciatedintheexpressionofQ∗ inequation(6). 1 17

be indifferent between investing in t=0 or t=1, condition (8) must hold. As in the stay regime, for high enough private benefits firms would be willing to assume the ex ante default costs. The equilibrium of interest will be one with parameter values such that private benefit firms will prefer to take on risky strategies, which will be the source of the asset supply in case of default. In the following section, conditions will be set so that in equilibrium private benefit firms choose a risky strategy over a safe one. 5 Equilibrium This section analyzes the equilibrium outcome in both regimes. The main setting under consideration will have private benefit firms taking on risky positions in the first period and at least a fraction of non private benefit firms holding on to spare capacity for the second. These two conditions are necessary to have interesting equilibrium in the stay exemption regime: in t = 1 default is needed to generate a supply, and surviving firms need spare capacity to generate demand. The initialriskyassetsupply K is fixedandset exogenously. Firms’demand,the riskyassetsupply, and the fraction of private benefit firms θ pins down market clearing and the nature of the equilibrium. The relative size of the firm’s initial endowment compared to the asset supply will be paramount to determine prices, especially to induce a fire sale in the stay exemption regime. The focus will be in a setting in which the stay regime’s initial asset price is equal to its expected future cash flows. This is an economically reasonable starting point: With no forced sale in the refinancing period to cause a fire sale, demand and supply aresuchthat pricesreflectfundamentalvalues. Inthe stayexemptionregime,the samesetting leads to a very different equilibrium outcome since the potential fire sale in the low state alters firms investment and financing decisions. The equilibrium concept employed in the model is a standard Walrasian equilibrium. Specifically, given an initial endowment AI, asset supply K, and a fraction θ of private benefit firms, an equilibrium is given by pricessuchthatfirms adoptoptimalstrategiesandmarketsclear. The differencebetweenregimesis that in the stay regime, firms’ optimal strategies are characterized by Proposition 1 and market clearing is only imposed in t = 0. In the stay exemption, regime firms’ initial strategies are given by Proposition 2 and market clearing is imposed in t∈{0,1}. 18

5.1 Stay Regime The equilibrium of interest for this regime has S = C. If private benefit firms adopt a risky strategy, from Proposition 1 firms’ individual demands are given by AI AI QPB = , QNPB ∈ 0, , 0 C(1−η) 0 (cid:20) C−ηCL(cid:19) where QPB and QNPB denote private benefit and non private benefit firms’ individual demand in t = 0. 0 0 Given non private benefit firms indifference when S = C their individual demand cannot be precisely specified. But integratingoverallagentsandimposing marketclearing,the resultingaggregatedemandcan be deduced. Thus, the initial fixed supply of the asset K that results in an equilibrium with S =C is AIθ AIθ AI(1−θ) K ∈ , + :=[K ,KS ), (cid:20)C(1−η) C(1−η) C−ηCL (cid:19) min max which corresponds to private benefit firms taking on risky strategies and Q NPB ∈ 0,AI(1−θ) . In effect, 0 C−ηCL h (cid:17) for K < K private benefit firms would still choose the maximum leverage allowed, increasing the asset min price above C. For K > KS , non private benefit firms would take on the maximum amount of leverage max (though still avoiding default), reducing the asset price below C. To make sure private benefit firms adopt a risky strategy, the size of their position and magnitude of their benefits must compensate the cost of default. Specifically, from Proposition 1, private benefits must be set so that b>b∗(C). This leads to the following theorem: Theorem 1. If parameter assumption A1 holds and K ∈[K ,KS ), then there exists a b∗ >0 such that min max for all b>b∗ private benefit firms take on risky positions and non private benefit firms adopt safe strategies. In this setting, there exists a stay regime equilibrium with S =C. Theorem 1 presents the benchmark setting from which to compare the outcomes of both regimes. The initialcapitalcommittedtothemarketAI,themarketcompositionθ,andthesupplyoftheassetK aresuch that prices reflect fundamental values. Figure 3 shows non private benefit firms’ individual demand and the resulting equilibrium in the stay regime. The following section will show that in the stay exemption regime prices deviate from fundamental values because capital must also be allocated to the refinancing period to purchase defaulted collateral. 19

IndividualDemandofNon-PB QN 0 P B AggregateDemand&Supply Q K N 0 P B +Q P 0 B C C 0 QN 0 PB S S Kmin Q Km S ax Figure 3: Stay Regime optimal strategies and equilibrium outcome — left hand side plot show the individual demand of a non private benefit firm in the stay regime when S = C. Right hand side shows firms aggregate demand, and the relevant range where the asset supply implies prices equal to fundamental value. AI =1,CH =110,CL =70,α=.9,λ=.5,η=.75,ϕ=.5. 5.2 Stay Exemption Regime In this regime, market clearing is imposed in both the initial and refinancing period. In the refinancing period, the supply of defaulted assets comes from secured lenders who received collateral from bankrupt firms and demand stems from solvent firms raising additional funds to purchase those assets. The special feature of this regime is the possibility of a fire sale, which creates a premium for having spare capacity in period t=1. When firms decide not to exhaust their debt capacity in t=0 they have the potential to purchase the asset at a discounted price in period t=1, increasing their expected profits. This premium for liquidity creates a reduction in the breakeven price for non private benefit firms to participate in the market initially: firms must be compensated in the initial period to give up the additional upside of holding on to dry powder. Dependingontheseverityofthesubsequentfiresale,thepricediscountinperiodt=0couldalsoinduce a group of non private benefit firms to take on risky positions initially. That is, the initial price discount could be large enough to compensate non private benefit firms to bear the cost of a potential default. This would give rise to an equilibrium where a fraction of non private benefit firms adopt a safe strategy and the remaindertake a riskyone. Consideringthe payofffunctions characterizedinProposition2,the indifference condition πS(S,SL;0)=πR(S,SL;0) is equivalent to30 0 0 CL−SL CD(ϕ,SL)−S 1+(1−α) =1+ . (9) SL(1−η) S(1−η) The left-hand side of condition (9) is the gross expected return of holding on to dry powder to purchase the defaulted asset at a fire price. The right-hand side is the expected return from taking on a levered 30IntermsofProposition2thisoccurswhenever b∗∗(S,SL)=0. 20

position that results in default if the asset has a bad outcome. The additional leverage stemming from a depressed price is enough to compensate the loss from default and the missed opportunity of earning a fire sale profit. The asset price that satisfies this condition will be denoted SM: if S > SM non private benefit firms will only undertake safe strategies; if S = SM(SL) there will be mixing where a fraction ξ of these firms will take a risky strategy. Under the assumption that private benefits are high enough for those firms to adopt a risky strategy in the initial period, Proposition 2 characterizes their individual demand in t=0. Integrating over all private benefit firms, their aggregate demand in the first and second period is PB AIθ PB ϕAIθ Q = , Q =− , (10) 0 S(1−η) 1 S(1−η) PB where the negative sign in Q indicates these firms are supplying the asset in the second period. Note 1 that only ϕ of private benefit firms’ risky asset position is supplied in t = 1, i.e., the fraction earmarked to secured lenders. ConditionalonS,nonprivate benefitfirmshavethreepotentialstrategiesthey couldundertakeint=0. They could take a relatively small position leaving some debt capacity for the refinancing period, adopt a fullyleveredpositionriskingdefaultinthedownstate,orrefrainfrominvestingaltogethertotakeadvantage of the fire sale. These strategies,characterizedby Proposition2, lead to four potential aggregatestrategies: 1. Dry Powder Strategy (DP): Non private benefit firms hold on to dry powder for the next period, NPB NPB AI(1−θ) Q =0, Q = , (11) 0 1 SL(1−η) which occurs whenever S >SBE(SL;0) and S >SM(SL). 2. Breakeven Strategy (BE): Non private benefit firms participate in the initial asset purchase but maintain spare capacity to purchase the defaulted asset in t=1, Q NPB =Q undet ∈ 0, AI(1−θ) , Q NPB = AI(1−θ)−(S−ηSL)Q N 0 PB , (12) 0 0 (cid:20) S−ηSL (cid:19) 1 SL(1−η) which occurs whenever S =SBE(SL;0) and S >SM(SL). 3. Dry Powder Mixing Strategy (DPmix): A fraction ξ of non private benefit firms take on risky positions and the remaining hold on to dry powder for the following period, NPB AI(1−θ)ξ NPB AI(1−θ)(1−ξ) ϕAI(1−θ)ξ Q = , Q = − , (13) 0 S(1−η) 1 SL(1−η) S(1−η) 21

which occurs whenever S >SBE(SL;0) and S =SM(SL). 4. Breakeven MixingStrategy(BEmix): Afractionξofnonprivatebenefitfirmstakeonriskypositions and the remaining participate in the initial asset purchase but maintain spare capacity to purchase the defaulted asset in t=1, NPB undet AI(1−θ)ξ undet AI(1−θ)(1−ξ) Q = Q + with Q ∈ 0, , (14) 0 0 S(1−η) 0 (cid:20) S−ηSL (cid:19) Q NPB = AI(1−θ)(1−ξ)−(S−ηSL)Q u 0 ndet − ϕAI(1−θ)ξ , (15) 1 SL(1−η) S(1−η) which occurs whenever S =SBE(SL;0) and S =SM(SL). 5.2.1 Dry Powder - Dry Powder Mixing Strategy Thissubsectionfocusesonaparameterizationthatgivesrisetoasimple andtractableequilibriumoutcome: Non private benefit firms either adopt a Dry Powder or a Dry Powder Mixing strategy. This approach simplifies the analysis since in both cases it isn’t necessary to characterize non private benefit firms’ safe demand in t = 0. The main conclusions of the model will be illustrated for these specific equilibrium outcomes, but the results will not depend on the parameter assumptions adopted herein. To compare the equilibrium of this regime to the benchmark case characterized in Theorem 1 where asset prices reflect fundamental values, I assume K ∈ [K ,KS ). The main difference between regimes min max characterized in this paper stems from an environment where the potential shortage of capital in t = 1 induces afiresaleinthe downstate. Tothateffect, the fractionofprivatebenefitfirms issetsothatsolvent firms’ demand isn’t sufficient for prices to reflect fundamental values. Therefore, θ is set so that the split between private benefit and non private benefit firms implies S = C and SL = CL when K = K . In min other words, for the minimum asset supply, all non private benefit firms adopt a dry powder strategy, and their demand is high enough for prices to reflect fundamental values in the down state. Arguably, this is a rather extreme case, since any increase in asset supply will entail a shortage of capital in the refinancing period,yetitisusefultoillustratethemodel’smainresult. Accordingly,parameterassumptionsarespecified as follows: Assumption A2. The fraction of private benefit firms θ is such that non private benefit firms take a DP strategy for K =K , and market clearing prices are S =C and SL =CL: θ = C . min C+ϕCL Toensurethatnonprivatebenefitfirmsdon’tchoosetoparticipatesafelyint=0(whichisonlyassumed for tractability), parameters must be set so that S >SBE(SL,0), 22

Assumption A3. Non private benefit firms do not take a BE strategy: S >SBE(SL,0): C > (1−α)η. CL η−α Conditionsmustalsobe providedso thatprivatebenefit firmsdo infactchooseariskystrategyint=0. This is guaranteed if b > b∗∗(S,SL) of Proposition 2 for all (S,SL) in equilibrium. In addition, to use Proposition2 directly the fire sale price mustbe largerthan the default value of the asset: SL >λCL. This conditionincentivizes riskyfirmsto exhausttheir securedfunding first, whichshouldholdfor the lowestfire sale price, Assumption A4. The fire sale price is larger than the default value of the asset SL > λCL for all K ∈ [K ,KS ]: C >η+ λ(1−η)ϕ. min max CL 1−λ Finally,the interestofthissubsectionistoconsiderasettinginwhichthe initialdiscountislargeenough to induce a fraction of non private benefit firms to take on risky positions: S =SM. That is, the mismatch between private benefit firm demand and asset supply is large enough to motivate more risk taking, AssumptionA5. TheinitialassetpriceS isequaltoSM forsomeKM ∈[K ,KS ]: (1−ϕ)(1−λ) < min max αC−(1−α)[ϕ+(1−ϕ)(1−λ)]CL ϕ(1−η). C−ηCL All of the aforementioned assumptions put together lead to the following result, Theorem2. Ifparameter assumptions A1–A5holdthenthereexistsb∗∗ >0,KM, andKSE ≤KS such max max that for all b > b∗∗ private benefit firms take on risky strategies. For K ∈ [K ,KM] non private benefit min firms adopt a DP strategy, and for K ∈ (KM,KSE ) non private benefit firms adopt a DPmix strategy. In max this setting, for K ∈[K ,KM], there exists a stay exemption regime equilibrium with min AIθ S = , K(1−η) 1−θ SL = S. ϕθ For K ∈(KM,KSE ), there exists a stay exemption regime equilibrium with max AI(θ+ξ(1−θ)) S = , K(1−η) (1−θ)(1−ξ) SL = S, ϕ(θ+ξ(1−θ)) CL CD(ϕ,SL) (1−α) −1 = −1, (cid:18)SL (cid:19) S where ξ >0 is the fraction of private benefit firms that take on risky strategies. 23

The equilibrium characterized in Theorem 2 has non private benefit firms take a dry powder strategy whenever K is low and a dry powder mixing strategy when K is high. This equilibrium outcome highlights one of the main results of the paper: The stay exemption can induce more firms to adopt risky strategies. 5.2.2 Breakeven – Breakeven Mixing Strategy: Numerical Exercise It can be shown that similar conclusions result from alternative setups with different equilibrium outcomes. Many of the previously parameter assumptions can be dismissed, which were only adopted for tractability; but others are important for fire sales to manifest themselves and for additional risk-taking to arise. In particular, it is necessary to have a shortage of capital in the refinancing period, which was adopted by AssumptionA2. Maintainingthisassumption,andensuringthatprivatebenefitfirmspreferleveredstrategies in t=0 (i.e., a high enoughb), Figure 4 shows the resulting first-periodprice, fire sale price, and fractionof non private benefit firms that adopt a risky strategy. For relatively low levels of asset supply, non private benefit firms invest some of their capital initially, holdingsparecapacityforthefiresale. ForhigherlevelsofK,nonprivatebenefitfirmsreducetheirpurchase in t = 0, which is picked up by firms that take on risky strategies. Finally, for relatively large values of K, non private benefit firms either wait for the fire sale or take on a risky position initially. 5.3 Comparative Statics This subsection explores how the equilibrium of both regimes react differently to changes in underlying parameters. The main variables of interest are firms capital requirement η, which effectively caps surviving firms demand in the stay exemption regime resulting in a fire sale; the firms value upon default λ, which measures the economic loss of a firm’s default; and changes in the probability of of a good outcome α. Changes in the stay regime equilibrium are relatively straight forward. Private benefit firms’ portfolios remain largely unchanged: They take out the maximum amount of leverage allowed. Non private benefit firm aggregate demand increases or decreases, adjusting to different supply levels to maintain prices at fundamental values. Therefore, the equilibrium price remains the same for changes in λ and η, and changes in α are straight forward. The more interesting exercise is to study how parameter changes can alter the stay exemption regime equilibrium. The analytical characterizationof Theorem 2 and Lemma 1 in the appendix, shows that when 24

C CL Kmin K Km S ax S LS ξ InitialPriceS BE BEMix DPMix FireSalePriceSL FractionofRiskyNon-PBFirmsξ 0 Figure 4: Breakeven, Breakeven Mixing, and Dry Powder Mixing Strategy equilibrium outcomes — plot shows the initial price, the fire sale price, and the fraction of firms that adopt risky strategies in period t=0. For low levels of asset supply non private benefit firms take a breakeven strategy. Higher levels ofsupply depress the initial price untilsome nonprivate benefit firms mix betweenriskyandsafe strategies. For relativelyhigh levels ofassetsupply, nonprivate benefit firms cease to participate safely in the initial market. Parameter values are: AI = 1,CH = 110,CL = 70,α = .9,λ = .5,η = .75, and ϕ=.5 25

non private benefit firms take a dry powder strategy the equilibrium changes as follows: ∂S >0 ∂S =0 ∂S =0. ∂η ∂λ ∂α Ascapitalrequirementsincrease,firms’abilitytotakeonleverageisgreater. Thisgenerateshigherlevels of demand in the initial financing period, increasing the S. The effect on SL is only transmitted through changes in S. Though higher leverage in the initial period increases the supply of defaulted collateral in t=1,solventfirms havelargerpurchasingpowerinthe downstate,canceling the effect. Thus,the only real effect is in the initial price increase. In this equilibrium, changes in λ and α don’t have an impact on prices since firms’ decisions remain the same: Private benefit firms still insist on taking a risky position initially, and non private benefit firms still opt to hold their dry powder for the second. The analysis when the equilibrium outcome involves non private benefit mixing into risky strategies is slightly more involved. Using the characterization of Theorem 2, and adopting the additional parameter assumption of θ >(1−α), Lemma 1 in the appendix gives the following result:31 ∂S >0 ∂S >0 ∂S >0, ∂η ∂λ ∂α ∂ξ <0 ∂ξ >0 ∂ξ >0. ∂η ∂λ ∂α Changesinη causethe initialassetprice to increase,since private benefit firms areable to increasetheir position, pushing up the price. The impact on ξ stems from the increase in S, which reduces non private benefit firms profits for taking risky strategies. The increase in λ is straight forward: a higher value for defaulted assets reduces financing costs for firms who take risky strategies. This increases the fraction of nonprivatebenefitfirmswhoparticipateintheinitialassetpurchaseandthereforeincreasestheinitialasset price. An increase in α implies an increase in profits for a risky strategy and a decrease in profits in a dry powder strategy, and the fraction of non private benefit firms who adopt risky strategies increases, raising the market clearing price. The effects on the fire sale price can be deduced from the interaction between S and ξ. Lemma 1 states ∂SL >0 ∂SL <0 ∂SL <0. ∂η ∂λ ∂α As λ andα increase,the payofffor undertaking risky strategiesalso increase,therefore more nonprivate benefitcapitalmigratestothefirstperiod,increasingthefiresale(i.e., reducingSL). Increasesinη resultin anincreaseintheinitialassetpriceandareductioninthenonprivatebenefitfirmswhotakeriskystrategies, which increases SL. 31Notethatintheappendixp=θ+ξ(1−θ),and ∂ξ = ∂p 1 . ∂x ∂x(1−θ) 26

6 Model Discussion In this section I discuss the main trade-offs in the stay vs. stay exemption debate for repos and highlight in whichmarketthepotentialofafiresaleislikelytobeafirst-ordereffectrelativetootheraspects. Specifically, I argue that a fire sale of repo collateral is more relevant for illiquid markets that may suffer from cash-inthe-marketpricing andfor assetsthat do nothaveany additional benefits beyondtheir payoff. Inaddition, I will provide anecdotal evidence of the model’s main mechanism, namely firms’ incentive to hold on to dry powder to exploit future fire sales. 6.1 Stay vs. Stay Exemption Discussion In the context of repo, the potential benefits of automatic stay exemption can be summarized as follows: a reduction in creditors’ incentives to run and the liberation of collateral that can be used more efficiently elsewhere.32 With regard to the first point, Skeel and Jackson (2012) provide anecdotal evidence that the stay exemption had little or no effect on lenders’ incentives to renew their loans with debtors that were perceived to be in financial trouble. Even though creditors were certain to receive the underlying collateral in case of a firm bankruptcy, they preferredto avoida default event altogether. This preference casts doubt on the effectiveness of repo’s exemption from stay to mitigate runs on a firm. The liberation of assets tied up in a bankruptcy proceeding may be a compelling argument if the assets in question have additional benefits above and beyond their payoff. In effect, U.S. Treasury securities do provide added value given their flexibility to use as collateral to raise funding and their relatively low risk, whichhelpsfirmsfulfillregulatorycapitalrequirements. Theseadditionalbenefitshavebeendocumentedfor on-the-runTreasuries,measuredby the difference betweenthe generalcollateralrepo rate andthe repo rate on a specific instrument, which is referred to as an asset’s specialness (see Duffie (1996)). For these types of assets the effective “lock-up” of collateral could limit the additional benefits they may bring. But this issue may not be as relevant for assets in a relatively thin and illiquid market. In fact, during the financial crisis it was precisely the use of MBS as collateral that created difficulties for firms to raise funding (see Krishnamurthy et al. (2012) for evidence of the contraction of repo’s using MBS). Thus, the efficient use of collateral is not likely to be an important factor for the types of markets this paper has in mind. Key potential costs in the stay vs. stay exemption debate relevant for repos are: counterparties limited incentive to monitor, firm’s inefficient substitution from traditional financing, and the potential to trigger a fire sale.33 The first point, stressed by Roe (2011), may have limited importance in the context of money 32A detailed analysis of the key arguments surrounding the stay vs. stay exemption debate, along with their intuition, is givenbyDuffieandSkeel (2012). 33Anotherpotentialcostisfirms’reducedincentivestofileforbankruptcy,giventhatexemptionsfromstaylimitbankruptcy 27

market funds financing large broker–dealers whose operational complexities would be hard to gauge from an outsider’s perspective. With regard to a firm’s preferred financing vehicle, though it is true that repo’s exemption from stay makes it less costly, an additional friction must be taken into account to argue a reduction in the firms total financing cost. Moreover, why would an increase in repo funding relative to other alternatives be “inefficient”? The default costs in this paper do give firms incentives to increase their repo funding, which is beneficial since only non-earmarked assets suffer a default cost. But these features of the model are assumed. To address this issue a more extensive analysis is necessary taking into account firms’ total debt capacity, incorporating a specific friction to explain firms’ preference for repo funding, and specifying the inefficiency stemming from the excessive use of repo. Although this may be an interesting analysis, it is outside the scope of this paper. Given the above, a fire sale stemming from the mass sale of collateral posted by defaulted firms is arguably an important aspect in the debate for relatively illiquid markets.34 The model in this paper not onlyaddressestheconsequencesduringthefiresale,butalsostudiestheeffectsonmarketsbeforethedefault event. Thepartialevidenceprovidedinsubsection6.2suggeststhatthemechanismofhoardingliquidityand its impact on prices could have playedan important role in the MBS marketduring the 2007–2009financial crisis. 6.2 Supporting Evidence The model presentedin this paper points to a liquidity hoardingmechanismthat ultimately results inanex ante price reduction that alters firms’ decisions. In essence, the main difference between regimes is that the stay exemption regime increasesfirms’investment opportunity set, attracting capital to exploit a future fire sale and causing the initial price to deviate from fundamentals. Inarelatedpaper,Acharyaetal.(2011)provideanecdotalevidenceofinstanceswhenfirmsstrategically hoarded liquidity to take advantage of future price dislocations. They present the case of National City Bank, which later became Citibank, that foresaw the banking panic of 1893 and 1907 and strategically accumulated liquidity to take advantage of the future crisis. In both cases, before the crisis National City Bank accumulated significantly larger reserve ratios than other competing banks. This allowed the firm to increase deposits andexpand their lending while other competitors were forcedto contract. The motivation behind the bank’s strategic decision was made evident by a quote from the bank’s president prior to the 1907 crisis, “If by able and judicious managementwe have money to help our dealers when trust companies protection. Butinthecontext ofrepofinancing thisisrelatedtothepotential withdrawalof fundsfromcreditors –that is,a run. 34Firesaleswereaprimeconcernforregulatorsinthe2007–09 financialcrisis. SeeSkeel andJackson(2012) fordetails. 28

have suspended, we will have all the business we want for many years.”35 Acharyaet al. (2011)also provide anecdotalevidence of communications with bankers during the recent financial crisis, who claimed that the “...reasons for drying up of inter-bank lending markets has been the hoardingofliquiditybybanksforacquisitionsoftroubledinstitutionsatfire-saleprices,theothertworeasons being precautionary motive from the risk of being distressed oneself and adverse selection about borrowing institutions.” This suggests that during the crisis firms may have had the capacity to purchase assets, but refrained from doing so to await the collapse of another firm that would trigger a fire sale. One interpretation of the model in the context of the financial crisis of 2007–09 is to consider private benefit firms as dealer banks and hedge funds holding large positions of MBS. Krishnamurthy et al. (2012) show that before the demise of Bear Stearns, 50% of repo transactions of four important dealer banks used non-agency MBS as underlying collateral (see Figure 8 of that paper). Table 7 in He et al. (2010) provides evidence thatthese samefirms hadsubstantialpositionsincreditandmortgage-relatedsecuritiesbefore the crisis. Nonprivatebenefit firmscanbe thoughtofascommercialbankswhoalsohadsignificantpositions in MBS,butdidn’trelyasheavilyonrepotofinancethem(seeGortonandMetrick(2012)pp. 443). Arguably, the total leverage of dealer banks and hedge funds was larger than that of the commercial banking sector, whichatthattime hadconsiderablymoreregulatoryrestrictions. Evidencefromthe financialcrisissuggests thatthebankingsectorasawholedidhaveliquidity,yetoptednottouseit. Heetal.(2010)provideevidence of a mass sale of securitized products by hedge funds and dealer banks (approximately $800 billion), much ofwhichwaspickedupbycommercialbanks(approximately$550billion). Butonaggregatethecommercial banking sectoractually increasedits liquidity holdings,with supportfromthe government,which highlights the sector’s limited participation in MBS. Although the above analysis is subject to different interpretations, these stylized facts fit well with the arguments presented in this paper. The fact that commercial banks, which possessed the expertise to participate in the MBS market, held back some of their cash points to the mechanismof the model. As was previously mentioned, this could have been for precautionary reasons or a potential lemons problem in the market, but this behavior is also consistent with liquidity hoarding. The lack of demand for these assets in expectation of other firms defaulting, triggering a fire sale, could well have affected pricing throughout the crisis. 35Formoredetailsofthecase,seeClevelandetal.(1985). 29

7 Equilibrium Analysis and Extensions This section presents a cost–benefit analysis of the equilibrium under both regimes, some potential policy implications, and alternative settings of the model. Specifically, the policy subsection will consider alternativesinthestayexemptionregimethatwouldmitigateanydistortionsstemmingfromafiresale. Themodel extension considers a setting where neither firms nor lenders internalize the potential fire sale, aggravating the price discount in a default event. 7.1 Cost–Benefit Analysis The main distortionsin the model arefirms’private benefits for holding largeriskyassetpositions36 vs. the deadweight cost brought on by default. These are the distortions that induce firms to take on leverage or refrainfromdoing so. Thoughitmay be misleadingto talk of“welfare”insucha stylizedsetting,37 onecan at least weigh the positive and negative aspects within the model. Private benefits are proportional to the size of the risky asset position held by private benefit firms in t = 0, and the deadweight costs are the losses incurred by all defaulting firms. Therefore, the expected benefits and costs are θAI PB gain = b , (16) S(1−η) (θ+(1−θ)ξ)AI Total Cost = (1−ϕ)(1−λ)(1−α)CL , (17) S(1−η) where a fraction ξ ≥ 0 of non private benefit firms take risky strategies. Note that the costs (1−λ of the expected portfolio value in the downstate) are assumed by all firms that take risky strategies,which affects the non-earmarkedfraction(1−ϕ) of their portfolio. Fromthese expressionsit is clear that whenever ξ >0 costs are proportionally larger than benefits, since private benefits are only perceived by a fixed fraction of firms, whereas costs are borne by all firms who choose a risky strategy. Inthestayregime,fromTheorem1,theeconomy’scostsandbenefitsdonotdependonK ∈[K ,KS ). min max In effect, PB gain=bK , Total Cost=(1−ϕ)(1−λ)(1−α)CLK . min min Since the fraction of firms that undertake risky strategies remains the same and prices are fixed for all K ∈ [K ,KS ), firms’ portfolios remain unchanged, making costs and benefits constant. In effect, in min max 36It isimportantnot tomisinterpretthelabelingof themodel’s “benefits”. These benefits areonlyperceivedby firmsthat takeonlargeamountsofdebt,andinfactarejustamodelingdevicetoaltertheseagents’incentives. Theyshouldbethought ofasfirms’incentive distortion,ratherthanbenefits fortheeconomy. 37For example, itwouldbe necessary toincorporate the impact onagents supplyingthe asset initially,which isoutside the scopeofthispaper. 30

this regime the same amount of the asset supply is held by private benefit firms, which are the only firms that risk default.38 This is not the the case in the stay exemption regime. In a setting where Theorem 2 holds for K ∈ [KS ,KM] (when ξ =0), replacing the initial market clearing price in equation (16) and (17) gives min PB gain=bK, Total Cost=(1−ϕ)(1−λ)(1−α)CLK. Asinthestayregime,theexantecostsandbenefitsarebornebyprivatebenefitfirms. Butsincetheyarethe onlytypeoffirmparticipatinginthemarketinitially,theirriskyassetpositionbecomeslargerforhigherlevels of asset supply. Thus, they enjoy more benefits but also pay for more costly default. When the equilibrium outcome has a fraction ξ of non private benefit firms mixing, from Theorem 2 when K ∈ (KM,KSE ), the max private benefits and costs are θ PB gain= bK, Total Cost=(1−ϕ)(1−λ)(1−α)CLK. θ+ξ(1−θ) Thecost–benefitanalysisforthisequilibriumoutcomeissimilartothepreviousone: Theinitialassetsupply is purchasedby firms who adopt risky strategies — either private benefit or non private benefit firms. Note that in this case the total cost has the same expression as when K ∈[KS ,KM], but the benefits are only min reaped by a fraction of those firms that risk default. Therefore, this outcome has proportionally more costs than benefits because of mixing. In case the equilibrium outcome consisted of non private benefit firms participating safely in the initial assetpurchase (i.e., a breakevenor breakevenmixing strategy), the results would be qualitatively the same. In this scenario, for higher levels of K there would be a price depreciation, increasing private benefit firms’ asset position and giving rise to higher private benefits and higher default costs. No matter what the equilibrium outcome in the stay exemption regime, the costs and benefits increase as cash-in-the-market pricing deviates prices from fundamentals. Whereas in the stay regime, since prices reflect fundamental values, private benefit firms’ participation is constant, thus the costs and benefits are held at a minimum. 38Note that if there were an additional cost for locking up secured asset in the stay regime, the total costs would take on the followingform: [ϕ(1−λˆ)+(1−ϕ)(1−λ)](1−α)CLKmin where λˆ (withλˆ<λto ensureapreference forsecuredloans) would be the distress cost of resolvingsecured collateral in bankruptcy. Then the comparison between regimes would involve comparing this expression with the cost under stay exemption, which implies a condition between exogenous parameters. To keeptheanalysissimple,Ihaveassumedsecuredlendingisalwaysresolvedseamlessly. 31

7.2 Policy Recommendations Themotivationofthispaperistoaskwhichregimeisbestwhenfirmsfaceapotentialfiresaleinthe future. The analysis in subsection 7.1 shows that in the stay regime costs and benefits (i.e., incentive distortions) are held at a minimum, whereas in the stay exemption regime these trade offs will vary with the ratio of assetsupplytoinitialcapitalcommittedtothemarket. Therefore,areasonablepolicyimplicationmaybeto maintainthesedistortionsandcoststoaminimum,whichisequivalenttoeliminatinganycash-in-the-market effectsthatcausepricestodeviatefromfundamentals. Attheveryleast,thiswoulddeternonprivatebenefit firms from undertakingrisky strategies,unduly increasingthe amountof default in the economy. Fromthat perspective, the policy recommendation would be to have repo subject to automatic stays; at least for the type of collateral this paper has in mind. But there may be other reasons to want repo exempt from automatic stay that are not captured in this model, prompting other solutions to the cash-in-the-market distortion. I consider two possibilities: an intervention by the government and a contract modification to eliminate incentives to sell after default. 7.2.1 Government Asset Purchase If a largeoutside investorwithoutcapital constraintswereto committo purchasedefaulted assets incase of a bad outcome, the fire sale would completely disappear along with any distortions it causes. The natural agent to undertake this task would be the government. In this context, agents would internalize that in the refinancing period the market clearing condition would take on the following form: PB NPB Q +Q +G=0, 1 1 where G would be the government’s demand for defaulted collateral. The role of the government would be to purchase the asset until SL = CL, eliminating any ex ante fire sale premium. Thus, non private benefit NPB firm capital can be totally committed in the initial financing period (i.e, Q = 0), essentially reducing 1 the setup to the stay regime. Thoughthisisarelativelysimpleexerciseinthecontextofthemodel,thismaynotbeasstraightforward in practice. Besides a commitment by the government to purchase assets in case of a cash-in-the-market discount,thegovernmentmustbeabletorecognizewhetherapricereductionisinfactduetolimitedliquidity oradeteriorationinfundamentals. Thisevaluationwouldbe difficulttodoatamoment’snotice. Moreover, the government’s strategy does involve some degree of risk since CL > CLL, which may be undesirable. In spite of that, efforts made by the government during the 2007–09 financial crisis can be interpreted as exactly that: an attempt to purchase assets trading at prices below their economic value. 32

7.2.2 Lender Participation and Contracting Change An important ingredient of the model is lenders’ incentives to sell the asset upon default, irrespective of its tradingprice. Thisismotivatedbytwoaspectsthatcanbeobservedincurrentmarketpractice. First,many of the lenders participating in repos have restrictions on holding risky long-dated assets. In addition, given the specific contracting arrangement of repos, conditional on wanting to sell the lender has limited interest in the final price. This is because any upside on the collateral after the loan is repaid is property of the original borrower. In the model, this is taken to an extreme since the initial face value on the loan is set to the fire sale price, eliminating all incentives to hold the asset. In a world in which the lender does in fact receive the asset’s upside after default, risk-neutral lenders that have the ability to hold the asset would have no incentive to sell it in the presence of a fire sale. In essence, the return that was previously captured by solvent firms that purchased the defaulted collateral would now disappear. These changes would imply that trade only occurs whenever SL = CL, irrespective of the amountofcapitalheld by firms. By eliminating the fire sale, there is no initial price discountand the resulting equilibrium is identical to the stay regime. In the context of the model, this modification must be considered carefully. An important ingredient of the paper is market segmentation and limited capital committed to the market. Specifically, the standing assumption throughoutthe model is that lenders cannot participate in the risky asset marketdirectly. This is motivated by some expertise necessary to actively trade in the market that firms are initially endowed with. Allowinglendersto holdontotheircollateralincaseofdefault, effectivelyparticipatinginthemarket in the down state, leads to the question, why didn’t they participate initially? It could be argued that the initialassetpurchasestillinvolvessomedegreeofexpertisebecauseofanunmodeledlemonsproblempresent in the risky asset market, with which lenders need not concern themselves once they receive collateral from a defaulted firm. From this perspective the “bad” assets were already filtered out by expert firms in the initial stage. An important aspect of this policy prescription is that it does not rely on an active government. In this setting, firms and lenders would eliminate the potential fire sale themselves. Undoubtedly, this recommendation would have important effects on other aspects of the repo market, particularly in the determination of haircuts. But for the analysis of this paper, the outcome is straightforward. 7.3 Myopic Agents An interesting exercise is to consider a case in which agents in the economy do not internalize the potential fire sale that can arise in the stay exemption regime. Specifically, firms and lenders do not realize that, 33

because of limited capital in the down state, the market clearing price may be below the asset’s expected future payoff, perhaps because the total initial capital committed to the market is believed to be sufficient to satisfy any supply shock. This outcome results in non private benefit firms committing their capital in the first period, disregarding the potential payoff from a future fire sale. In the very least, this implies less capital in the refinancing state and a more severe fire sale. More formally, in the stay exemption regime, non private benefit firms would adopt the strategy characterized by Proposition 2 where SL = CL. In this case, the breakeven price is equal to the fundamental value of the asset: SBE(CL,0) = C. Therefore, for K ∈ [K ,KS ) non private benefit firms would min max increaseaggregatedemanduntilthe first-periodpriceequalsthe asset’sfundamentalvalue. Giventhe linear structure of the problem whenever the trading price equals the breakeven price, non private benefit firms’ individual demand is undetermined. Thus, for a given asset supply K, it is unclear how many non private benefitfirmswouldhaveraiseddebtto causethemto default. Thisimplies thatinthe downstateaggregate demand and supply is undetermined since it cannot be established how many firms will default nor how much spare capacity surviving firms will have. What is clear is that surviving firms’ aggregate demand in t=1 will be lower compared to a setting where agents account for the fire sale, making the price distortion even larger. This larger price distortion is because there is less dry powder to raise funds in the refinancing period and because the fire sale will reduce firm debt capacity substantially. This setting arises naturally in instances where there is uncertainty as to the severity of any cash-inthe-market pricing. During March 2008, because of Bear Stearn’s financial troubles, regulators “...worried that a mass sale of repo collateral could drive down the values of mortgage-related securities and further destabilize the markets.”39 In the myopic model, because of repos’ exemption from stay and the degree of uncertainty around the amount of capital available to withstand a supply shock, the magnitude of the fire sale would be impossible to determine. Moreover, the severity of the fire sale could cause woes for other firms, exacerbating the illiquidity problem further by triggering more defaults. This is precisely the type of externalitypolicymakersarecurrentlyconcernedwithwhenconsideringfiresalesinrepomarkets(seeStein (2013)). 8 Concluding Remarks This paper explores the consequences of repo’s exemption from automatic stay in the presence of potential firesalesthatresultfromlimitedcapitalcommittedtoamarket. Themainfindingofthepaperisthatfuture fire sales alter firms investment opportunity set, giving them incentives to hold their initial capital to take 39SeeSkeel andJackson(2012). 34

advantageofapossiblepricediscountinthefuture. Thisimpliesthatmoreoftheriskyassetisheldbyfirms thathaveincentivesto takeonhighlevelsofleverage,increasingthe amountassetsheldby defaultingfirms, which is assumed to be costly. The mechanism disappears when repo is subject to stay, since in the model secured lenders receive their payments when market turmoil has subsided and prices reflect fundamental values. A mix of ingredients is necessary for fire sales to arise endogenously in the model. The firms that participate in the risky assetmarket must have limited resources. Though they receive funding from an unconstrainedlendingsector,theyhaveaceilingontheamountoffundingtheycanraisebecauseofregulatory or skin-in-the-game constraints. These funding constraints limit the size of their risky asset position, which inducescash-in-the-marketpricing. Importantlyafractionoffirmshaveincentivestoincreasetheirportfolio size,motivating them to maximize their debtcapacityandrisk default. Inessence,this is amodeling device to introduce leverage heterogeneity so that a fraction of firms default and the rest remain solvent. The setting described in the model is most relevant for scenarios where the asset market is relatively thin, leaving the possibility for cash-in-the-market pricing. I draw on anecdotal evidence from the 2007–09 financial crisis to motivate the model’s setup and main mechanism. Firms in the model can be thought of as large broker–dealers, hedge funds, or commercial banks with the expertise to participate in a relatively specialized market, like, for example, the market for MBS. The lenders can be thought of as money market fundsandregularbondinvestorscateringtothesefirmsfinancingneeds. Arguably,moneymarketfundsand regular bond investors would not have the same expertise as broker–dealers or specialized hedge funds to purchase these types of assets. Moreover, it is natural to think that the initial capital committed to a thin market is relatively small compared with the amount of capital held by regular cash investors, thus making firm capital relevant. In this setting, future fire sales create incentives for firms to hold on to their liquidity to take advantage of them. The main mechanism of the model consists of a group of firms reducing their participation in a risky asset market in anticipation of a future price discount. In one of the model’s extensions, when agents do not anticipate the full extent of the cash-in-the-market pricing, firms’ initial participation is increased and the severity of the fire sale is uncertain. This involves a larger price discount and potentially more defaults. Anecdotalevidencefrommarketparticipantsandregulatorssuggeststhatinthe2008crisiselementsofboth modelswerepresent: afractionofagentshoardingcapitalinanticipationoffuturediscountsanduncertainty totheextentofthepricedeclineupondefault. Comparedtotheoriginalmodel,amixtureofthetwosetups would prescribe a smaller initial discount, a larger fire sale, and potentially more defaults, arguably making the stay exemption regime less desirable. This paper shows how exemption from automatic stay can distort incentives in some specific settings. 35

When highly levered firms participate in a relatively illiquid market, prices can deviate from fundamentals, altering firms’ decisions and the total costs of default. Though this paper cannot completely resolve the issue whether stayor stay exemption is anoptimal bankruptcy regime,it does give insights as to how firms’ behavior would change under different regulatory settings when fire sales are a prime concern. References Acharya,V., Shin, H.andYorulmazer,T.(2011),‘Crisis resolutionandbank liquidity’, Review of Financial Studies 24(6), 2166–2205. Acharya, V. and Skeie, D. (2011), ‘A model of liquidity hoarding and term premia in inter-bank markets’, Journal of Monetary Economics 58(5), 436–447. Adrian,T.,Colla,P.andShin,H.S.(2012),Whichfinancialfrictions? parsingtheevidencefromthefinancial crisis of 2007-9, in ‘NBER Macroeconomics Annual 2012, Volume 27’, University of Chicago Press. Allen, F. and Gale, D. (1994), ‘Limited market participation and volatility of asset prices’, The American Economic Review pp. 933–955. Allen, F. and Gale, D. (1998), ‘Optimal financial crises’, The Journal of Finance 53(4), 1245–1284. Allen,F.andGale,D.(2005),‘Fromcash-in-the-marketpricingtofinancialfragility’,JournaloftheEuropean Economic Association 3(2-3), 535–546. Antinolfi, G., Carapella, F., Kahn, C., Martin, A., Mills, D. and Nosal, E. (2012), Repos, fire sales, and bankruptcy policy, Technical report, Working Paper, Federal Reserve Bank of Chicago. Bolton, P. and Oehmke, M. (2011), Should derivatives be privileged in bankruptcy?, Technical report, National Bureau of Economic Research. Brunnermeier, M. and Pedersen, L. (2009), ‘Market liquidity and funding liquidity’, Review of Financial studies 22(6), 2201–2238. Cleveland, H., Huertas, T. and Strauber, R. (1985), Citibank, 1812-1970, Harvard University Press Cambridge, MA. Copeland, A., Martin, A. and Walker, M. (2011), ‘Repo runs: Evidence from the tri-party repo market’, New York Federal Reserve Bank Staff Report 506. 36

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Krishnamurthy, A., Nagel, S. and Orlov, D. (2012), Sizing up repo, Technical report, National Bureau of Economic Research. Martin, A., Skeie, D., Thadden, V. et al. (2012), ‘Repo runs’, New York Federal Reserve Bank Staff Report (444). Oehmke, M. (2013), ‘Liquidating illiquid collateral’, Journal of Economic Theory . Roe, M. J. (2011),‘The derivatives market’s payment priorities as financial crisis accelerator’, Stanford Law Review 63(3), 539. Shleifer, A. and Vishny, R. (1992), ‘Liquidation values and debt capacity: A market equilibrium approach’, The Journal of Finance 47(4), 1343–1366. Shleifer, A. and Vishny, R. (1997), ‘The Limits of Arbitrage’, Journal of Finance 52(1), 35–55. Shleifer, A. and Vishny, R. (2011), ‘Fire sales in finance and macroeconomics’, Journal of Economic Perspectives 25(1), 29–48. Skeel, D. (2001), Debt’s dominion: A history of bankruptcy law in America, Princeton University Press. Skeel, D. and Jackson, T. (2012), ‘Transaction Consistency and the New Finance in Bankruptcy’, Colum. L. Rev. 112. Stein, J. (2012), ‘Monetary policy as financial stability regulation’, The Quarterly Journal of Economics 127(1), 57–95. Stein, J. (2013), ‘The fire-sales problem and securities financing transactions’. URL: http://www.federalreserve.gov/newsevents/speech/stein20131004a.htm Appendix Proof of Proposition 1: Theanalysisoffirmsoptimalbehaviorcanbesimplyseenbysplittingtheproblemintwo. First,considerparameterssuch that firmsoptimallychoose to take onasafestrategy. Thisinvolves solvingtheirinvestment and financing problemimposing one additional restriction: I 0 u+ϕ0CLQ0 ≤ηCLQ0+AI−A0, i.e. (Q0,A0,I 0 u,ϕ0)∈NS. This condition ismore restrictive thanthefirmscapitalrequirementssinceS>CL. Therefore,thesafefirmsoptimizationlagrangiantakes thefollowingform, L = (C+b)Q0+AI−A0−I 0 u−ϕ0CLLQ0+µB(ϕ0CLLQ0+I 0 u+A0−SQ0)+ µD(ηCLQ0+AI−A0−I 0 u−ϕ0CLLQ0)+µA(AI−A0)+µϕ(ϕ−ϕ0), 38

notethatA0+I 0 uappeartogetherinallexpressionexceptfortherestrictiononthefirm’sdrypowder. Ignoringthedrypowder restriction,callingH=A0+I 0 u,andtakingFOCgives, ∂L = C+b−ϕ0CLL+µB(ϕ0CLL−S)+µD(ηCL−ϕ0CLL)≤0, ∂Q0 ∂L = −1+µB−µD ≤0, ∂H ∂L ∂ϕ0 = −CLLQ0+µBCLLQ0−µDCLLQ0−µϕ0 ≤0. Case H∗ >0 & Q∗ 0 >0: Implies µB =µD+1>0, thus the budget constraint isactive. Replacing µB inthe firstequation gives, C+b−S µD = S−ηCL , thus if S < C+b (since S > ηCL by assumption) the firm takes on the maximum amount of leverage: Iu∗+ϕ∗CLLQ∗ = 0 0 0 ηCLQ∗+AI−A∗. TogetherwiththebudgetconstraintsolvesforQ∗. IfS=C+b,thentheamountofdebtandassetpurchase 0 0 0 areundetermined. Notethatinbothofthesesubcases ϕ∗ isnotpinneddown. 0 Case H∗>0 & Q∗ 0 =0: ImpliesµB =µD+1,thusthebudgetconstraintisactiveandH∗=0leadingtoacontradiction. Case H∗=0: ImpliesµB <µD+1whichfromthefinalequationimpliesϕ∗ 0 =0. ThebudgetconstraintimpliesQ∗ 0 =0and the refinancing condition is slack. Usingthe firstFOC, and noting that µB <1, gives µBS >C+b, thus S >C+b pinning downthefirm’sstrategies. Turningtotheriskyfirm,usingequation(3), thepriceofriskydebtaltersthevalueofthefirmsriskyassetpositionto CD(ϕ0)=(αCH+(1−α)(ϕ0CL+(1−ϕ0)λCL)). Theoptimization’slagrangiantakes thefollowingform, L = (CD(ϕ0)+b)Q0+(α+(1−α)λ)(AI −A0)−ϕ0CLLQ0−I 0 u+µA(AI−A0)+ µB(ϕ0CLLQ0+I 0 u+A0−SQ0)+µD(η(SQ0+AI−A0)−I 0 u−ϕ0CLLQ0)+µϕ(ϕ−ϕ0). TakingFOCgives, ∂L = CD(ϕ0)+b−ϕ0CLL+µB(ϕ0CLL−S)+µD(ηS−ϕ0CLL)≤0, ∂Q0 ∂L ∂Iu = −1+µB−µD ≤0, 0 ∂L ∂ϕ0 = (1−α)(1−λ)CLQ0−CLLQ0+µBCLLQ0−µDCLLQ0−µϕ0 ≤0, ∂L = −(α+(1−α)λ)−µA+µB−ηµD ≤0. ∂A0 Sincethispartoftheproofcharacterizes theoptimalstrategyofaleveredfirmconsiderthecasewhenµD >0. Case µD >0 & Iu>0: ImpliesµB =µD+1whichfromthefinaltwoequationsimpliesµϕ0 ,µA>0. Giventhatthebudget constraintisactiveandA∗ 0 =AI,necessarilyQ∗ 0 >0. ReplacingµB inthefirstequationgives, CD(ϕ)+b−S µD = , S(1−η) thus ifCD+b>S, the firm takes on maximal leverage I 0 ∗u+ϕCLLQ0 =ηSQ0. Together withthe budget constraint solves forQ∗. 0 Case µD > 0 & Iu = 0: The capital requirement restriction implies ϕ0CLLQ0 = η(SQ0+AI −A0), therefore in the very 39

leastϕCLL≥ηS. ButfromassumptionA1andS>CL itcanbededuced thatηS>ϕCLL,leadingtoacontradiction. Itmust beverified that the firmwouldinfact default inthe downstate, that is the firmcannot rollover it’sdebt. From equation(5)themaximumfirmcanraiseafterabadoutcomeisηCLQ0+(AI−A0). Fromequation(3)andthefirmsdefault costs,riskyunsecureddebtis αF 0 u=I 0 u−(1−α) (ϕ0CL+λ(1−ϕ0)CL)Q0+λ(AI 0 −A0)−ϕ0CLLQ0 , (cid:16) (cid:17) thenforfirmstodefaultF 0 u+ϕ0CLLQ0>ηCLQ0+(AI−A0)whichisequivalent to, I 0 u+ϕ0CLLQ0>(αη+(1−α)[ϕ0+λ(1−ϕ0)])CLQ0+(α+λ(1−α))(AI−A0). UnderassumptionA1,consideringtheoptimalstrategyA∗=AI,andS>CL thisinequalityholds. Pinning down both types of firms optimal strategies and payoffs, the threshold function b∗(S) must be characterized to determinewhenfirmstakeariskyorsafestrategy. Ineffect,forriskyfirmstohaveapositivepayoffitisnecessarytoconsider S≤CD(ϕ)+b,withb>0,givingthefirsttworestrictionsforb∗(S). Inthatpricerange,theoptimalstrategyforsafefirmsis toincreasetheirdebtcapacitytilltheycanrollovertheirdebt. Thus,ariskystrategywillbepreferredif, CD(ϕ)+b−S C+b−S ≥ ⇐⇒ S(1−η) S−ηCL (C−S)S(1−η)−(CD(ϕ)−S)(S−ηCL) ′ b ≥ :=b(S), η(S−CL) definingb∗(S)=max{0,S−CD(ϕ),b′(S)},forb≥b∗(S)firmswillchooseriskystrategies,completingtheproof. (cid:4) Proof of Proposition 2: The analysis of firms’ optimal behavior is similar to the stay regime, which can be simply seen by splitting the problem in two. First consider parameters such that firms optimally choose to take on a safe strategy. This involves solving their investment and financing problem on additional restriction: I 0 u+ϕ0SLQ0 ≤ηSLQ0+AI−A0, i.e. (Q0,A0,I 0 u,ϕ0)∈NSE. Thisconditionismorerestrictivethanthefirmscapital requirementssinceSL>CL. Therefore,thesafefirmsoptimizationlagrangiantakes thefollowingform, L = (C+b)Q0+(AI−A0)+(1−α)(CL−SL) ηSLQ0+(AI S − L( A 1 0 − )− η) I 0 u−ϕ0SLQ0 ! − ϕ0SLQ0−I 0 u+µB(ϕ0SLQ0+I 0 u+A0−SQ0)+µA(AI−A0)+µϕ(ϕ−ϕ)+ µD(ηSLQ0+AI−A0−I 0 u−ϕ0SLQ0), note that A0+I 0 u appear together in all expressions except for the restriction on the firm’s dry powder. Ignoring the dry powderrestriction,callingH=A0+I 0 u,andtakingFOCgives, ∂L CL−SL ∂Q0 = C+b−ϕ0SL+(1−α) (cid:18) SL(1−η) (cid:19) (η−ϕ0)SL+µB(ϕ0SL−S)+µD(η−ϕ0)SL≤0, ∂L CL−SL ∂H = −1−(1−α) SL(1−η) +µB−µD ≤0, (cid:18) (cid:19) ∂L CL−SL ∂ϕ0 = −SLQ0−(1−α) (cid:18) SL(1−η) (cid:19) SLQ0+µBSLQ0−µDSLQ0−µϕ≤0. Case H∗>0 & Q∗ 0 >0: ImpliesµB =1+(1−α) S C L L ( − 1− S η L ) +µD >0,thusthebudgetconstraintisactivesinceSL≤CL. (cid:16) (cid:17) 40

ReplacingµB inthefirstequation gives, C+b−S+(1−α) S C L L ( − 1− S η L ) (ηSL−S) µD = S−(cid:16)ηSL (cid:17) , thusif CL−SL CL−SL S 1+(1−α) <C+b+(1−α) ηSL, SL(1−η) SL(1−η) (cid:18) (cid:18) (cid:19)(cid:19) (cid:18) (cid:19) since S > SL by assumption the firm takes on the maximum amount of leverage: Iu∗ +ϕ∗SLQ∗ +A∗ = ηSLQ∗ +AI. 0 0 0 0 0 Together withthe budget constraint solves forQ∗ 0 . If S issuchthat µD =0, then the amount ofdebt and assetpurchase are undetermined, and theabove inequality iswithequality andcharacterizes S(SL,b). Note that inboth cases ϕ∗ is notpinned 0 down. Case H∗>0 & Q∗ 0 =0: ImpliesµB =1+(1−α) S C L L ( − 1− S η L ) +µD. SinceCL≥SL itfollowsthat thebudget constraint is activeandH∗=0,leadingtoacontradiction. (cid:16) (cid:17) Case H∗ = 0: Implies µB < 1+(1−α) S C L L − − η S S L L +µD which from the final equation implies that ϕ∗ 0 = 0. The budget constraint implies Q∗ 0 =0 and that the refi (cid:16) nancing c (cid:17) ondition isslack: µD =0. Noting that µB <1+(1−α) S C L L ( − 1− S η L ) the (cid:16) (cid:17) firstFOCgives, CL−SL µBS>C+b+(1−α) SL(1−η) ηSL, (cid:18) (cid:19) thereforeS>SBE(SL,b). Turningtotheriskyfirm,usingequation(4)thepriceofriskydebtaltersthevalueofthefirmsriskyassetpositionto, CD(ϕ0,SL)=(αCH+(1−α)(ϕ0SL+(1−ϕ0)λCL)). NotethatthelowerboundonSL>λCL istoensurethatthefirmsdecidestofirstexhaustit’ssecuredfundingbeforeitraises unsecuredfunding. Theoptimization’slagrangiantakes thefollowingform, L = (CD(ϕ0,SL)+b)Q0+(α+(1−α)λ)(AI−A0)−ϕ0SLQ0−I 0 u+µA(AI−A0)+ µB(ϕ0SLQ0+I 0 u+A0−SQ0)+µD(η(SQ0+(AI−A0))−I 0 u−ϕ0SLQ0)+µϕ(ϕ−ϕ0). TakingFOCwehave, ∂L = CD(ϕ0,SL)+b−ϕ0SL+µB(ϕ0SL−S)+µD(ηS−ϕ0SL)≤0, ∂Q0 ∂L ∂Iu = −1+µB−µD ≤0, 0 ∂L ∂ϕ0 = (1−α)(SL−λCL)Q0−SLQ0+µBSLQ0−µDSLQ0−µϕ0 ≤0, ∂L = −(α+(1−α)λ)−µA+µB−ηµD ≤0, ∂A0 sinceSL>λCL theargumentsareidenticalasintheproofofproposition2. Thustheoptimalstrategiesandfinalpayoffstake thesameformbyreplacingCD(ϕ)byCD(ϕ,SL),CLL bySL andCL bySL inpartoftheFOCforϕ0. Itmust beverified that the firmwouldinfact default inthe downstate, that is the firmcannot rollover it’sdebt. From equation(6)themaximumafirmcanraiseafterabadoutcomeisηSLQ0+(AI−A0). Fromequation(4)andthefirmsdefault costs,riskyunsecureddebtis αF 0 u=I 0 u−(1−α) λ(1−ϕ0)CLQ0+λ(AI 0 −A0) , (cid:16) (cid:17) 41

thereforethedefaultconditionisF 0 u+ϕ0SLQ0>ηSLQ0+(AI−A0)whichisequivalentto, I 0 u+ϕ0SLQ0> αηSL+(1−α)[ϕ0SL+λ(1−ϕ0)CL] Q0+(α+λ(1−α))(AI −A0). (cid:16) (cid:17) AssumingA1,consideringtheoptimalstrategyA0=AI,andS>SL>λCL thisinequalityholds. Pinning down both types of firms optimal strategies and payoff, the threshold function b∗∗(S,SL) must be characterized todeterminewhenfirmsinfacttakeariskyorsafestrategy. Todoso,itmustbethatfirmswithaprivatebenefitbpreferthe riskystrategy above both safealternatives; whereone of the safestrategies gives them apotential firesaleprofit. Incase the optimalsafestrategyistomaintaindrypowderthefollowinginequalitymusthold, (CD(ϕ,SL)+b−S)AI CL−SL +AI ≥ (1−α) AI+AI ⇐⇒ S(1−η) SL(1−η) (cid:18) (cid:19) b ≥ S (1−α) CL−SL − CD(ϕ,SL)−S :=b ′′ (S,SL) SL S (cid:20) (cid:18) (cid:19) (cid:18) (cid:19)(cid:21) Incasetheoptimalsafestrategyistoincreasedebtcapacitytillthefirmcanrolloverit’sdebt,firmswillchooseariskystrategy if (CD(ϕ,SL)+b−S)AI (C+b−S)AI +AI ≥ +AI ⇐⇒ S(1−η) S−ηSL b ≥ (C−S)S(1−η)−(CD(ϕ,SL)−S)(S−ηSL) :=b ′′′ (S,SL), η(S−SL) definingb∗∗(S,SL)=max{0,b ′′ (S,SL),b ′′′ (S,SL)},forb≥b∗∗(S,SL)firmswillchooseriskystrategies,completingtheproof. (cid:4) Proof of Theorem 1: With the conjectured equilibrium has S = C, it is clear that non private benefit firms will adopt a safe strategy since otherwisetheirpayoff wouldbelowerthan theirinitialendowment. Forthese firms,proposition1states that theirdemand is undeterminedQundet∈[0,AI/(C−ηCL)),andfinalpayoffistheirinitialendowment. Private benefit firms have to be motivated to take on the risky strategy. From the proof of proposition 1, the condition b>b∗(C)ensuresthesefirmstakeriskystrategies. Thisamounts tohaving, b>(C−CD(ϕ)) C−ηCL :=b ∗ , η(C−CL) sincethisismorerestrictivethanC−CD(ϕ)andb∗>0. Thusifb>b∗ privatebenefitfirmswilladoptariskystrategy. Integratingoverfirmsdemandandimposingmarketclearinggives, AIθ NPB +Q =K, C(1−η) whichholdsforallQ NPB ∈ 0,AI(1−θ) ,pinningdownthesupplyintervalinwhichtheequilibriumholds. C−ηCL h (cid:17) (cid:4) Proof of Theorem 2: I conjecture that the equilibrium for relatively low levels of asset supply has firms adopt DP strategies. The fire sale premium for these firms must be relatively large. In the conjectured equilibrium, the relation between the first and second 42

periodpricestemsfrommarketclearingintherefinancingperiod(imposingtheparameterizationofθ fromA2),i.e. AIθ AI(1−θ) 1−θ CL ϕ = =⇒SL= S= S:=φS, S(1−η) SL(1−η) ϕθ C thatis,inthissetting, theinitialgrossreturnoftheassetisequal tothegrossfiresalereturn. IfS>SBE(SL,0)nonprivate benefitfirmswillrefrainfrominvestingintheinitialperiod. Thisisequivalentto, (1−α)(CL−SL) C (1−α)(CL−SL)ηSL 1+ > + , SL(1−η) S SL(1−η) S imposingtherelationshipbetweengrossreturnsgives, (1−α)(1−ηφ)>(1−η), (18) which,byreplacingφ,isconditionA3. Thus,nonprivatebenefitfirmsopttoonlyinvestintherefinancingperiodforrelatively lowlevelsofassetsupply. Toconcludethatprivatebenefitfirmstakeonriskystrategies,itisnecessarytodeterminethevalue of b∗∗ such that b∗∗ ≥b∗∗(S,SL) for all S and SL inthe conjectured equilibrium. From the proof of Proposition 2there are twopossibleexpressionsforb∗∗. Thefirstissothatprivatebenefitfirmspreferriskystrategies overinvestinginadrypowder strategy, and the other is so that private benefit firms prefer riskystrategies over investing with low levels of debt. Imposing theconjecturedequilibriumgives, b ′′ (S) = (1−α) CL +αS−CD(ϕ,φS), φ ′′′ C(1−η)−CD(ϕ,φS)(1−φη) b (S) = +S. η(1−φ) Therefore,choosingprivatebenefitssuchthatb∗∗>max{b ′′ (S),b ′′′ (S)}forallSintheconjecturedequilibrium,privatebenefit firmswilladoptariskystrategy.40 Havingpinneddownprivateandnonprivatebenefitfirmsstrategies,marketclearinginthefirstperiodisexpressedas, AIθ =K. S(1−η) ItmustbeverifiedSL>λCL forproposition2tohold. FrommarketclearingandSL=φS,thisequates to AIθ λK< . C(1−η) Toensurethatthefiresaleisn’ttoolowitissufficienttoprovethatKS satisfiesthisbound,i.e. max 1 (1−λ) −η >λ(1−η)ϕ. φ (cid:18) (cid:19) ThisinequalityispreciselyassumptionA4. Finally,toensuretheexistenceofKM inwhichfirmsenteraDP-mixingequilibrium, is must be shown that there exists a price low enough for non private benefit firms to mix between safe and riskystrategies. Themixingcondition(equation (9))gives, Aθ Aθ α +(1−α)C=CD ϕ,φ , K(1−η) K(1−η) (cid:18) (cid:19) 40Foralargesetofprimitiveparametersofthemodel,theaboveexpressionsforb ′′ (S)andb ′′′ (S)areincreasinginS. Thus, imposing private benefits to be equal to these functions when S = C (which coincides with the stay regime private benefits) willensurethecorrectbehavior. 43

whichdefines Aθ (1−ϕ)(1−λ)CL Aθ KM = + . C(1−η) αC−(1−α)[ϕ+(1−ϕ)(1−λ)]CLC(1−η) Thus,KM mustbesmallerthanKS ,whichisassumptionA5. max The above proof ensures that for K ∈[KS ,KM] non private benefit firms adopt a DP strategies. For levels of supply min greaterthanKM,nonprivatebenefitfirmsmixbetweenriskyandsafestrategies. Thereforemarketclearingint=1takes on thefollowingform, AI(θ+ξ(1−θ)) AI(1−ξ)(1−θ) (1−θ)(1−ξ) ϕ = ⇐⇒SL= S:=φˆ(ξ)S, S(1−η) SL(1−η) ϕ(θ+ξ(1−θ)) whereξ isthe fractionofnonprivatebenefit firmsthat take onriskystrategies. Note thatξ=0forK =KM,φˆ(0)=φ,and φˆ(ξ)isdecreasinginξ. Giventheconjectured strategies,marketclearingintheinitialperiodisgivenby, A(θ+ξ(1−θ)) =K, S(1−η) andnonprivatebenefitfirmsmixingcondition(equation(9)) isequivalentto, CL CD(ϕ,SL) (1−α) −1 = −1 ⇐⇒ SL S (cid:18) (cid:19) (1−θ)(1−ξ) (θ+ξ(1−θ)) S α−(1−α) = αCH+(1−α)(1−ϕ)λCL−(1−α)ϕ CL. (θ+ξ(1−θ)) (1−θ)(1−ξ) (cid:18) (cid:19) Toverifythatthis infactwillconstitute anequilibrium,itmustbechecked thatprivatebenefit andnonprivatebenefit firms adopt the corresponding DP-mixingstrategies. This analysis is equivalent to the DP strategy analysis, replacing φ with φˆ(ξ) forconditionsstemmingfromequation(18),SL>λCL,b ′′ ,andb ′′′ . Notethatconditionsinequation(18)andb ′′′ arerelaxed as ξ increases, which hold for ξ =0. Conditions stemming from SL >λCL and b ′′ become tighter as ξ increases, thus there exists a ξ∗ such that for all ξ <ξ∗ both these inequalities continue to hold. Defining KSE as the minimum between KS max max andthe assetsupplysuchthat thefractionof mixingfirmsisequal toξ∗,ensures that forallK ∈(KM,KSE )firmsenter a max DP-mixingequilibrium,completingtheproof. (cid:4) Lemma 1. Under the assumptions of Theorem 2, comparative statics of the Dry Powder equilibrium for K ∈ [KS ,KM] min depend on the equilibrium equation AIθ S= , K(1−η) with SL= 1−θS. ϕθ Comparative staticsof the DryPowder Mixing equilibrium for K∈(KM,KSE ] depend on the equilibrium equations, max AIp T1 = −S=0, K(1−η) p 1−p T2 = Γ(CH,CL,α,ϕ,λ)−(1−α)ϕ CL−S α−(1−α) =0, 1−p p (cid:18) (cid:19) where Γ(CH,CL,α,ϕ,λ) = αCH +(1−α)(1−ϕ)λCL and p = θ+ξ(1−θ) > θ with SL = 1−pS. If θ > 1−α, for all ϕp parameters x∈{AI,K,η,λ,α,CH,CL}either ∂T1 =0 and sgn ∂ ∂ x p =sgn ∂ ∂ T x 2 , ∂x  ∂S   ∂T2  ∂x ∂x     44

with sgn ∂SL =sgn −∂T2 , or ∂x ∂x (cid:16) (cid:17) (cid:16) (cid:17) ∂T2 =0 and sgn ∂ ∂ x p =sgn −∂ ∂ T x 1 , ∂x  ∂S   ∂T1  ∂x ∂x     with sgn ∂SL =sgn ∂T1 ∂x ∂x (cid:16) (cid:17) (cid:16) (cid:17) Proof of Lemma 1 The first part of the Lemma is direct from the DP equilibrium characterization of Theorem 2 as well as the equilibrium equations T1,T2 for the DP Mixing equilibrium. Holding θ fixed, by inspection it can be appreciated that for any change in x ∈ {AI,K,η,λ,α,CH,CL} results in either ∂T1 = 0 or ∂T2 = 0. Using the implicit theorem I can study how equilibrium ∂x ∂x variablesS andpchangewithunderlyingparameters. ∂T1 A = >0, ∂p K(1−η) ∂T1 = −1<0, ∂S ∂T2 = −(1−α) ϕCL + S <0, ∂p (1−p)2 p2 (cid:18) (cid:19) ∂T2 = (1−α) 1−p −α<0, ∂S p wherethe signof thelastpartial derivativestems fromthe factthat θ>1−α, forξ=0(1−α)1−p <α, and 1−p decreases p p withp. Denoting ∂T1 ∂T1 A −1 M = ∂p ∂S = K(1−η) .  ∂ ∂ T p 2 ∂ ∂ T S 2   −(1−α) (1 ϕ − C p L )2 + p S 2 (1−α)1− p p −α      (cid:16) (cid:17)   Notethatdet(M)<0. Thusapplyingtheimplicitfunctiontheorem, ∂ ∂ x p =−M −1 ∂ ∂ T x 1 = −1 (1−α)1− p p −α 1 ∂ ∂ T x 1 .  ∂ ∂ S x   ∂ ∂ T x 2  det(M) (1−α) (1 ϕ − C p L )2 + p S 2 K(1 A −η)  ∂ ∂ T x 2        (cid:16) (cid:17)    Thus,x∈{AI,K,η}gives ∂T2 =0and ∂x ∂ ∂ x p = −1 (1−α)1− p p −α ∂ ∂ T x 1 .  ∂ ∂ S x  det(M) (1 (cid:16) −α) (1 ϕ − C p L )2 + p (cid:17)S 2 ∂ ∂ T x 1      (cid:16) (cid:17)   Andx∈{λ,α,CH,CL}gives ∂T1 =0and ∂x ∂p −1 ∂T2 ∂x = ∂x .  ∂S  det(M) A ∂T2  ∂x K(1−η) ∂x     Finally,notethatinbothcases oftheDPmixingequilibrium ∂SL ∂S 1−p ∂p S = − , ∂x ∂x p ∂xp2 (cid:18) (cid:18) (cid:19) (cid:19) therefore,incase ∂T2 =0thisimplies, ∂x ∂SL = −1 (1−α) ϕCL +α S ∂T1, ∂x det(M)ϕ p(1−p) p2 ∂x (cid:18) (cid:19) 45

andincase ∂T1 =0thisimplies, ∂x ∂SL 1 S∂T2 = . ∂x det(M)ϕ p ∂x (cid:4) 46