Stability of Funding Models: An Analytical Framework

Transcription

1 Thoa Eienbach, Todd Keiter, Jae McAndrew, and Tanju Yorulazer Stability of Funding Model: An Analytical Fraework During the recent financial crii, any intitution and oe arket-baed interediation arrangeent experienced train owing to declining aet value and a drying-up of funding ource. Although thee tre event led everal intitution to fail and other to require extraordinary public upport, a full undertanding of their caue till prove eluive. Thi tudy clarifie that undertanding by providing a rigorou, yet eaily applicable, fraework for analyzing the ource of the tre event and the effect of variou funding tructure characteritic on financial tability. The fraework can potentially help policyaker for view on regulatory refor and evaluate the way that policy option ay affect financial tability.. Introduction The recent financial crii highlighted the fragility of any financial interediarie. A large nuber of coercial bank, invetent bank, and oney arket utual fund (MMF) experienced train created by declining aet value and a lo of funding ource, a did oe arket-baed interediation arrangeent uch a aet-backed coercial paper (ABCP). Thee train were evere enough to caue everal intitution to fail and other to require extraordinary public upport. In reviewing thee event, one notice that oe arrangeent appear to have been ore table that i, better able to withtand hock to their aet value and/or funding ource than other. The precie deterinant of thi tability are not well undertood. Gaining a better undertanding of thee deterinant i a critical tak for both arket participant and policyaker a they try to deign ore reilient arrangeent and iprove financial regulation. In thi article, we ue a iple analytical fraework to illutrate how the characteritic of an arrangeent for financial interediation (a funding odel) affect it ability to urvive tre event. There i a large and growing literature on thi iue; ee Yorulazer (204b) for a detailed review. Our See Yorulazer (204a) for a detailed dicuion of the experience of everal ditinct type of interediation arrangeent during the crii. Thoa Eienbach i an econoit at the Federal Reerve Bank of New York; Todd Keiter i a profeor of econoic at Rutger Univerity; Jae McAndrew i an executive vice preident and the director of reearch at the Federal Reerve Bank of New York; Tanju Yorulazer i a reearch officer at the Bank. The view expreed are thoe of the author and do not necearily reflect the poition of the Federal Reerve Bank of New York or the Federal Reerve Syte. All error are the author. Correpondence: [email protected] FRBNY Econoic Policy Review / February

2 ai here i to preent an approach that i ufficiently general to encopa a wide range of interediation arrangeent, but ufficiently iple to illutrate the econoic force at work in a tranparent and intuitive way. Our hope i that thi analyi will provide policyaker with a ueful tarting point for ore detailed evaluation of alternative arrangeent and for the analyi of regulatory propoal. Our fraework begin with the iplified balance heet of a repreentative financial interediary. The interediary hold two type of aet: afe and riky. Safe aet are alway liquid, but riky aet ay be illiquid in the hort run. On the liability ide of it balance heet, the interediary ha hortter debt, long-ter debt, and equity. Thi interediary face two type of rik: The value of it aet ay decline and/or it hort-ter creditor ay decide not to roll over their debt. We eaure the tability of the interediary by looking at what tre event it can urvive, that i, what cobination of hock to the value of it aet and to it funding it can experience while reaining olvent. An iportant iue in any uch analyi lie in deterining the condition under which hort-ter creditor will and will not chooe to roll over their debt. We do not try to explain creditor behavior in our fraework; intead, we treat thi behavior a exogenou. Thi approach greatly iplifie the odel and allow u to preent an intuitive analyi of the deterinant of tability. Again, a way to think of our analyi i that it ubject bank to different type of tre event. In ot of our application, we hold fixed the balance heet of the bank, and ak whether the bank i table for different ize of hort-ter creditor run and decline in the value of it aet. The creditor behavior in our fraework i ued a a paraeter that generate a certain ize of run on the bank. The inight fro our analyi are likely to carry over to ore coplex odel where creditor behavior i endogenou; developing uch odel i a proiing area for future reearch. 2 We tudy how the tability of thi interediary depend on variou balance-heet characteritic, uch a it leverage, the aturity tructure of it debt, and the liquidity and rikine of it aet portfolio. Soe of the reult we derive are traightforward, uch a the effect of higher leverage and a higher liquidation value of the riky aet. Higher leverage increae the debt burden of the financial interediary, ake it ore uceptible to creditor run, and decreae the buffer 2 Within the growing literature on thi topic, our paper i ot cloely related to that of Morri and Shin (2009), who alo tudy the tability of an interediary. They define the illiquidity coponent of credit rik to be the probability that the interediary will fail becaue it i unable to roll over it hort-ter debt, even though it would have been olvent had the debt been rolled over. Morri and Shin (2009) ue technique fro the theory of global gae to deterine creditor behavior a part of the equilibriu of their odel. provided by equity capital. A a reult, higher leverage alway ake the interediary ore vulnerable to hock. A the liquidation value of the riky aet increae, the interediary need to liquidate a aller portion of the riky aet in it portfolio to ake the payent to the hort-ter creditor that chooe not to roll over. A a reult, a higher liquidation value of the riky aet alway ake the interediary ore reilient to creditor run. Other reult, however, deontrate that the deterinant of tability can be ubtle. For exaple, lengthening the aturity tructure of the interediary debt tend to ake it ore reilient to funding hock by decreaing reliance on hort-ter debt that can be withdrawn. However, ince long-ter debt can be a ore cotly way of finance copared with hort-ter debt, lengthening the aturity tructure can increae the debt burden and ake the interediary ore vulnerable to hock to the value of it aet. Siilarly, holding a afer aet portfolio can ake the interediary either ore or le vulnerable to hock, depending on the other characteritic of it balance heet. Soe of thee effect are dependent on the characteritic of both the aet and liability ide of the bank balance heet, and one advantage of our fraework i that it allow u to conider the influence of both ide of the balance heet iultaneouly. We then how how our fraework can be applied to tudy variou policy iue. While capital requireent have traditionally been a tool for regulator, recently there have been attept at introducing liquidity requireent. Firt, we analyze how liquidity holding and equity capital interact in achieving bank tability. Again, the reult can be quite ubtle. A one would expect, liquidity and capital can be ubtitute but they can alo be copleent. If the riky aet pay ore than cah in expectation, higher liquidity holding can decreae the return on the bank portfolio and therefore would reult in the bank requiring ore equity capital to achieve the ae level of tability. In the wake of the crii, a nuber of policie related to financial interediation are being reconidered and new regulation are being deigned. We how how our fraework can help illutrate the effect of the Bael III Liquidity Coverage Ratio. We how that liquidity requireent can have copeting effect on tability, aking a bank ore reilient to funding hock but le reilient to hock to the value of it riky aet. We alo how how the fraework can be ued to tudy dicount window (DW) policy, where the bank can borrow fro the window rather than liquidating the riky aet at a cot. We how that a lenient DW policy that ha a lower haircut and a lower interet rate can allow the bank to withtand higher hock ex pot. However, we hould ention that any 30 Stability of Funding Model

3 uch ex pot benefit hould be weighed againt the effect on bank behavior ex ante. Since the crii, the difference between collateralized and uncollateralized funding and aet encubrance ha received attention. We ue our fraework to tudy the effect of aet encubrance on bank tability. We how that aet encubrance can increae inolvency rik when the fraction of encubered aet i ufficiently high. Money arket utual fund were at the heart of any iportant debate ince the Reerve Priary Fund broke the buck after the failure of Lehan Brother. We ue our fraework to analyze different approache to reforing oney arket utual fund. In particular, we analyze the effect of the iniu-balance-at-rik propoal, where creditor can only redee up to a fraction of their clai early while the reaining fraction becoe a long-ter junior debt clai. Thi increae the reilience of the fund to funding hock and itigate the fragility created by the requireent to utain a net aet value of. In the next two ection, we preent our baeline odel and exaine the deterinant of tability within thi fraework. In ection 4, we adapt the odel in order to apply it to a collection of current policy iue, including the effect of liquidity regulation, dicount window policie, and approache to reforing oney arket utual fund. We offer oe concluding reark in ection A Siple Model There are three date, labeled t = 0,, 2, and a ingle, repreentative financial intitution. We refer to thi intitution a a bank for iplicity but, a we dicu below, it can be thought of a repreenting a variety of different arrangeent for financial interediation. We begin by pecifying the eleent of thi bank balance heet. 2. The Balance Sheet At t = 0, the bank hold unit of a afe, liquid aet, which we call cah, and y unit of a riky, long-ter aet. Cah earn a gro return r between period 0 and and a gro return r between period and 2. The riky aet yield a rando gro return if held until t = 2, but a aller return τ if liquidated at t =. The realized value of i oberved by all agent at the beginning of t =. The bank ha iued unit of hort-ter debt that ature at t = and l unit of long-ter debt that ature at t = 2. To iplify the analyi, we aue that the proied return on the bank hort-ter debt i the ae a the return it earn on the liquid aet, that i, r between period 0 and and r between period and 2. 3 The long-ter debt l proie a gro interet rate r l > r between period 0 and 2. In addition, the bank ha an aount e of equity. We noralize r = throughout the analyi. 4 The bank balance heet thu ha the following for: Aet y Liabilitie l Short-ter debtholder decide whether to roll over their clai at t = after oberving the realized value of. If the bank i able to eet it obligation to all debtholder, any reaining fund at t = 2 are paid to equityholder. If the bank i unable to eet it obligation, it enter bankruptcy and a fraction ϕ of it aet i lot to bankruptcy cot. The reaining aet are then ditributed to debtholder on a pro-rata bai. We ake the following auption on paraeter value: Auption : r < r l < _ τ. Thi auption enure that neither for of financing long-ter or hort-ter debt trictly doinate the other. A will becoe clear below, τ i the cot of repaying hort-ter debtholder that withdraw early and force aet liquidation, while r i the cot of repaying hort-ter debtholder that roll over. Since r l i the cot of repaying a long-ter debtholder, Auption tate that hort-ter debt i cheaper than long-ter debt ex pot if and only if it i rolled over or doe not force early liquidation. Auption 2: τ. Thi econd auption iplie that paying an early withdrawal with cah i alway cheaper than liquidating the riky aet. 3 The fraework can be eaily generalized by allowing thee return to differ. 4 Alternatively, we can interpret, l, and a the t = value of each variable, including all interet accrued between t = 0 and t =. e. FRBNY Econoic Policy Review / February 204 3

4 2.2 Solvency The bank i olvent if it i able to eet all of it contractual obligation in both period. The olvency of the bank will depend on the realized return on it aet a well a the rollover deciion of the hort-ter debtholder. Let denote the fraction of hort-ter debtholder who decide not to roll over that i, to withdraw funding fro the bank at t =. If, the bank can pay all of thee clai fro it cah holding. If >, however, the bank doe not have enough cah to ake the required payent and ut liquidate oe of the long-ter aet. The atured value of the bank reaining aet at t = 2 when hold i given by y + r ( - ). In thi cae, paying out an additional dollar at t = would reduce the bank cah holding by one unit, lowering the t = 2 value of aet by r. When, however, paying out an additional dollar at t = require liquidating (τ) unit of the long-ter aet, which lower the t = 2 value of the bank aet by τ. In thi cae, the atured value of the bank reaining aet at t = 2 can be written a (y - τ We can cobine thee two expreion by defining χ() to be the arginal cot at t = 2 of fund ued to ake t = payent, that i, { ) χ() r for τ for >. The atured value of the bank reaining aet at t = 2 can then be written for any value of a 2) y + χ()( - ). Note that if expreion 2 i negative, the bank i actually inolvent at t =, a it i unable to eet it iediate obligation even after liquidating all of it aet. In thi cae, hort-ter debtholder that withdraw funding at t = in expectation receive a pro-rata hare of the liquidation value of the bank aet while all other debtholder receive zero. 5 When ). expreion 2 i poitive, hort-ter debtholder that withdraw funding at t = receive full payent and the bank i olvent at t = 2 if and only if the atured value of it reaining aet i larger than it reaining debt, that i, 3) y + χ()( - ) ( - )r + lr l. Note that olvency of the bank at t = 2 iplie that it i alo olvent at t =. We can rewrite condition 3 a r + lr l + [χ() - r ] - χ() 4) y (). The variable () identifie the iniu return on the riky aet that i needed for the bank to be olvent, conditional on a fraction of hort-ter debtholder withdrawing funding and the reaining ( - ) rolling over their clai. For, thi cutoff value iplifie to 5) () = r + lr - r l y _ for all. When none of the long-ter aet i liquidated at t =, olvency of the bank depend only on the t = 2 value of it aet and debt. Within thi range, the value of doe not atter becaue additional withdrawal at t = reduce the value of the bank aet and liabilitie by exactly the ae aount. For >, the cutoff becoe 6) () = r + lr l + [ τ - r ] - ( τ) y *() for all >. In thi cae, Auption iplie that *() i increaing in. Additional withdrawal at t = now force liquidation of the long-ter aet and thu reduce the value of the bank aet ore than they reduce the value of it liabilitie. A a reult, a higher return on the long-ter aet i required to aintain olvency. If all hort-ter creditor withdraw funding, we have 7) () = + τlr l - τy _. If the realized return i greater than _, the bank will be olvent at t = 2 regardle of the action hort-ter debtholder take at t =. 5 We aue that the bank cannot upend convertibility, o that the bank pay in full the proied aount to hort-ter debtholder that withdraw at t = until it run out of fund. We aue that the poition of the hort-ter debtholder that decide to withdraw at t = in the line i randoly aigned fro a unifor ditribution. Thu, hort-ter debtholder that withdraw at t = in expectation receive a pro-rata hare of the liquidation value of the bank aet while all other debtholder receive zero. 32 Stability of Funding Model

5 2.3 Stability We eaure the tability of the bank by aking for what cobination of and it reain olvent. In other word, what tre event, in ter of both aet value and funding condition, will the bank urvive? Exhibit illutrate the anwer by dividing the pace of pair (, ) into four region. When i below _, the return on the riky aet i o low that the bank will be inolvent regardle of how any hort-ter debtholder roll over their clai. In thi cae, we ay the bank i fundaentally inolvent. When i between _ and _, the bank will urvive if ufficiently any hort-ter debtholder roll over their clai, but will fail if too few do. In the forer cae, we ay the bank i conditionally olvent, eaning that the fact that it reain olvent depend on the realized rollover deciion of the hort-ter debtholder. In the latter cae, when (, ) fall in the triangular region below the blue line in the exhibit, we ay the bank i conditionally inolvent. Finally, when i larger than _, the bank will be olvent regardle of the action of hort-ter debtholder. In thi cae, we ay the bank i fundaentally olvent. In the ection that follow, we ak how the characteritic of the bank balance heet deterine the ize of the four region in the diagra in Exhibit. We then ue thi diagra to tudy how variou change and policy refor would affect the bank ability to urvive thee tre event. 2.4 Dicuion Our goal i to preent an analyi of bank tability that can be largely undertood graphically, uing diagra like that in Exhibit. Thi approach require keeping the odel iple, o that the relevant inforation can be conveyed clearly. One of our key iplifying auption i that the behavior of hort-ter debtholder i exogenou to the odel. In particular, we aue that the joint probability ditribution over the rando variable (, ) i independent of the bank balance heet. It i worth noting, however, that hort-ter debtholder incentive are perfectly aligned with the region in thi diagra. Specifically, we how in the appendix that individual hort-ter debtholder would prefer to roll over their clai at t = if and only if the realization of (, ) place the bank in one of the two olvency region in Exhibit. In thi ene, our analyi i at leat broadly conitent with optiizing behavior by debtholder. There i a large literature that ue equilibriu analyi to tudy the deterinant of creditor behavior in etting iilar to the one we tudy here. The einal paper by Diaond and Dybvig (983), for exaple, how how ultiple equilibria Exhibit Solvency Region Conditionally olvent Fundaentally olvent can arie in the gae played by a bank depoitor one in which they leave their fund depoited and the bank urvive, and another in which they withdraw their fund and the bank fail. The ubequent literature ha debated the extent to which hitorical banking panic were driven by thi type of elf-fulfilling belief or by real hock that ade bank fundaentally inolvent. 6 Other paper have aied to uniquely deterine creditor behavior within the odel in order to pin down the et of tate in which inolvency occur. 7 We do not attept to contribute to either of thee debate here. Intead, we take an intentionally agnotic view of creditor behavior: The fraction of hort-ter creditor that withdraw funding i rando and i deterined by factor outide of our iple odel. Doing o allow u to focu on our quetion of interet the deterinant of a bank ability to urvive tre event with inial technical coplication. 3. Deterinant of Bank Stability In thi ection, we invetigate how the tability of the bank depend on the paraeter of the odel. We begin by exaining how the olvency region in Exhibit depend on two characteritic of the bank liabilitie: it leverage and the aturity tructure of it debt. We then evaluate 6 See, for exaple, Gorton (988), Saunder and Wilon (996), Allen and Gale (998), and Enni (2003). * Conditionally inolvent Fundaentally inolvent 7 Contribution on thi front include Potlewaite and Vive (987), Chari and Jagannathan (988), and Goldtein and Pauzner (2005). FRBNY Econoic Policy Review / February

6 the effect of changing two aet-ide characteritic: the liquidation value of the riky aet and the copoition of the bank aet portfolio. Exhibit 2 Effect of Leverage 3. Leverage Let d + l denote the bank total aount of debt and let 8) σ + l denote the fraction of thi debt that i hort ter. We noralize the total ize of the bank balance heet to, o that the aount of equity i given by e = - d. We can then write the quantitie of hort-ter and long-ter debt, repectively, a Lower leverage = σ( - e) and l = ( - σ)( - e). To exaine the effect of leverage, we hold the aturity tructure σ of the bank debt fixed and vary the aount of equity e. Uing thi odified notation, the cutoff value _ below which the bank i fundaentally inolvent, a defined in equation 5, can be written a. [σr 9) _ = + ( - σ)r l ]( - e) - r y. Thi cutoff i trictly decreaing in e: More equity (that i, lower leverage) reduce the ize of the fundaental inolvency region becaue there i le total debt that ut be repaid. In the region where > and the bank ut liquidate aet at t =, the critical value eparating conditional olvency and inolvency defined in equation 6 can be written a 0) *() = [σ( τ + ( - )r ) + ( -σ)r ]( - e) - l τ y. Thi cutoff i alo trictly decreaing in e, for exactly the ae reaon. The change in thee two olvency boundarie are depicted in Exhibit 2, where an increae in equity (that i, a decreae in leverage) correpond to a ove fro the blue curve to the black one. The exhibit deontrate that lower leverage trictly reduce the bank inolvency rik by aking it better able to withtand hock to both it aet value and it funding. In other word, lower leverage i aociated with unabiguouly greater tability. The enitivity of the olvency threhold *() to additional withdrawal i given by the derivative d*() ) d = σ( _ τ - r )( - e) y. Thi derivative correpond to the lope of the line eparating the conditionally olvent and conditionally inolvent region in the exhibit. The lope i poitive becaue additional withdrawal reduce the value of the bank reaining aet by ore than they reduce the value of it reaining liabilitie, effectively increaing the debt burden at t = 2. Notice, however, that the lope i decreaing in e. Holding ore equity (and le debt) reduce the enitivity of the debt burden to withdrawal and thu alo reduce the enitivity of the conditional olvency threhold to withdrawal. In other word, lower leverage ake the lope of the olvency boundary flatter, a depicted in Exhibit Maturity Structure of Debt Next, we tudy the effect of changing the aturity tructure of the bank debt. Recall fro equation 8 that σ eaure the fraction of the bank debt that i hort ter. Our interet i in how changing σ, while holding equity e and total debt d fixed, affect the bank ability to urvive tre event. The cutoff value _ below which the bank i fundaentally inolvent wa given in equation 9. Auption tate that r l > r and hence thi cutoff i trictly decreaing in σ. In other word, lengthening the average aturity of the bank debt (by hifting oe fro hort ter to long ter) ake the bank ore likely to becoe fundaentally inolvent. Intuitively, long-ter debt i ore cotly than hort-ter debt and therefore lengthening the average aturity increae the bank total debt burden at t = 2. The higher debt burden, 34 Stability of Funding Model

7 Exhibit 3 Effect of Maturity Structure of Debt ' ' Le ST debt in turn, iplie that a higher return on the riky aet i required to avoid inolvency. Thi change i illutrated in Exhibit 3, which how the effect of lowering the quantity of hort-ter debt fro to while increaing the quantity of long-ter debt by the ae aount. For return in the interval ( _, _ ), the bank will now be fundaentally inolvent, wherea it would have potentially been olvent with the higher level of hort-ter debt. Exhibit 3 alo highlight two countervailing effect of decreaing hort-ter debt. Firt, the cutoff point increae, eaning that the bank can withtand a larger funding hock () without having to liquidate any of it longter aet. In addition, the lope of the olvency boundary in the region where > becoe flatter. Thi lope wa given in equation and becaue τ > r i eaily een to be increaing in σ. Taken together, thee two change iply that decreaing the bank hort-ter debt hrink the conditional inolvency region in the diagra. For any given funding hock, a bank with le hort-ter debt will have le need to liquidate aet at t = and i thu le likely to becoe inolvent due to the lo of funding. Our fraework thu deontrate how changing the aturity tructure of a bank debt ha two copeting effect on it ability to urvive tre event. Having le hort-ter debt ake the bank le vulnerable to funding hock by decreaing it dependence on the action of hort-ter debtholder. At the ae tie, however, it alo increae the bank total debt burden at t = 2 and therefore increae the likelihood that the return on the bank aet will be inufficient to cover thee debt. Put differently, a bank financed largely by long-ter debt and equity i protected fro the conditional inolvency caued by a lo of funding fro hort-ter debtholder. However, it i alo clear that long-ter debt i not equivalent to equity and increaing the long-ter debt burden can raie the likelihood of fundaental inolvency. A key takeaway fro our analyi therefore i that having bank lengthen the aturity tructure of their liabilitie doe not ake the unabiguouly ore table or le likely to becoe inolvent. Intead, the benefit of having lower rollover rik ut be balanced againt the cot aociated with a higher debt burden. 3.3 Liquidation Value We now turn to the characteritic of the bank aet holding and ak how the olvency and inolvency region in Exhibit depend on the liquidation value τ. Equation 5 deontrate that the bound for fundaental inolvency, _, i independent of τ. Thi lower bound repreent a cenario in which the bank ha enough cah to pay hort-ter debtholder that do not roll over at t =, o that no liquidation i needed and the value of τ ha no effect on the bound. Looking next at the threhold for conditional olvency in equation 6, we have d*() dτ = - < 0. τ 2 y We know thi expreion i negative becaue *() applie only in the region where >. Thi reult deontrate that for all uch value of, the threhold value * i trictly decreaing in τ. Exhibit 4 illutrate thi reult. The blue curve correpond to the baeline value of τ ued in the previou exhibit. If the liquidation value i lower, uch a at τ low, the curve hift to that depicted in black. For value of aller than, there i no change in the threhold value * becaue no liquidation take place; inolvency in thi cae i deterined olely by the period-2 value of aet and liabilitie. For higher value of, however, the threhold value * becoe larger (hift up in the exhibit) becaue payent ade to hort-ter creditor are now ore expenive in ter of period-2 reource. A the exhibit how, hifting to τ low, hrink the region of conditional olvency and expand the region of conditional inolvency. If the liquidation value rie, however, the threhold value of * fall (hift down in the exhibit) and the olvency region becoe larger. The extree cae i where τ = r, which ean that liquidating the long-ter aet i not ore cotly than uing cah to pay invetor at t =. In thi cae, the FRBNY Econoic Policy Review / February

8 (τ) threhold value * i equal to _ for all value of. The curve eparating the olvency and inolvency region in thi cae correpond to the dahed black line in Exhibit 4 the bank i olvent for value of above _ and inolvent for value below _, regardle of the value of. 3.4 Liquidity Holding We now tudy the effect of changing the copoition of the bank aet holding. We again noralize the ize of the bank balance heet to, o that we have + y =. Both the critical value _ for fundaental inolvency and the critical value *() for conditional inolvency depend on the copoition of the bank aet. Subtituting y = into equation 5 and 6, thee two critical value becoe r 2) _ = + lr l - r - and Exhibit 4 Effect of Aet Liquidation Value τ 3) *() = ( τ + ( - )r ) + lr - l τ. - Looking firt at the critical value for fundaental inolvency, the effect of increaing cah and decreaing riky aet holding by the ae aount i given by d _ d = _ - r -. *( τ ) low *( τ) *( τ ) ax Thi expreion i negative, and hence the rik of fundaental inolvency i reduced by a ore liquid aet portfolio, if and only if _ < r. Intuitively, if _ i le than r, then at the inolvency boundary, the return on the riky aet i lower than the return on cah, which ean that having ore cah raie the bank total return on aet. In thi cae, inolvency rik i decreaing in liquidity holding. However, if _ > r, then the riky aet pay off ore than cah at the inolvency boundary and holding ore cah lower the bank total return on aet. In thi cae, inolvency rik i increaing in liquidity holding. To ee when thi latter cae of harful liquidity applie, we can ue the expreion for _ in equation 2 to how that _ > r if and only if r + lr > r. l Thi condition i ore likely to be atified, firt, when total debt + l i large and econd, when l i large relative to for given total debt. Since we have fixed the ize of the balance heet to + l + e =, thi ean ituation with high leverage and/or long debt aturity, repectively. The intuition for thi reult i a follow: Cah ha return r, which i le than the interet rate on long-ter debt r l. The only way to repay long-ter debt i with aet that pay a higher return than cah. A bank with little equity and a large aount of long-ter debt therefore increae it rik of fundaental inolvency if it hift to a ore liquid aet portfolio. Thee two poibilitie are illutrated in Exhibit 5 for a bank with ore long-ter debt and higher leverage (thin black line) and a bank with le long-ter debt and lower leverage (thick black line). Both bank hare the ae initial inolvency boundary (blue) but repond differently to an increae in their cah holding fro to. We now turn to the effect of aet copoition on the rik of conditional inolvency. Uing equation 3, we have 4) d*() d = *() - τ -. Siilar to above, the effect of liquidity on conditional inolvency rik depend on the relative return of riky aet and cah at the inolvency boundary. However, now the effective return to holding an extra unit of cah i τ > r becaue it ave on the liquidation of long-ter aet at t =. Uing the expreion for *() in equation 3, we can how that the derivative in equation 4 i alway negative. Firt, equation 3 iplie that *() < hold if and only if τ 5) ( τ + ( - )r ) + lr l < τ. 36 Stability of Funding Model

9 Exhibit 5 Effect of Liquidity Holding High LT debt, high leverage Low LT debt, low leverage ' Note that the left-hand ide of condition 5 i increaing in, eaning that the condition i harder to atify with higher value of. Setting = and uing the fact that + l + e =, the condition iplifie to ( τ r l)l + e > 0, τ More Liquidity which hold becaue Auption tate that r l < τ. Since condition 5 i atified for =, it i alo atified for any <. We can therefore conclude that d *() d < 0, that i, extra liquidity unabiguouly reduce the rik of conditional inolvency. Looking at how liquidity holding affect the lope of the conditional olvency threhold, we have d*() d = σ( τ r ) ( - e). - Recall that the lope d *() d repreent the enitivity of the olvency threhold *() to additional withdrawal. Becaue we are in the region where oe long-ter aet ut be liquidated at t =, additional withdrawal reduce the value of the bank reaining aet by ore than they reduce the value of it reaining liabilitie, increaing it debt burden at t = 2. Meeting thi higher debt burden require a higher total return on aet (( ) + ). Holding a τ ore liquid aet portfolio reduce the enitivity of thi total payoff to the aet payoff, eaning that for a given increae in, a larger increae in i required to aintain conditional olvency: The lope get teeper. Thee different effect of liquidity on bank tability are all preent in Exhibit 5. Where inolvency i conditional that i, the boundary ha a poitive lope the curve hift down and becoe teeper for both bank (thin black and thick black line): More liquidity reduce inolvency rik but increae the enitivity to withdrawal. Where inolvency i fundaental and the boundary i horizontal the line can hift up or down: More liquidity can reduce the rik of fundaental inolvency (thick black line), but it can alo increae it if leverage i high and/or debt aturity i long (thin black line). 3.5 Dicuion The reult in thi ection have hown how the deterinant of a bank ability to urvive tre event are often intuitive, but can oetie be rather ubtle. Decreaing leverage, for exaple, clearly iprove tability, ince it decreae both the probability of fundaental inolvency and the probability of conditional inolvency. Having a higher liquidation value for aet alo unabiguouly iprove tability. While thi change ha no effect on the likelihood of a bank becoing fundaentally inolvent, it alway reduce the likelihood of conditional inolvency. For other change in balance-heet characteritic, however, a trade-off can arie in which iproving tability in one dienion tend to underine it in the other. Lengthening the average aturity of a bank debt lower the probability of conditional inolvency, for exaple, but raie the probability of fundaental inolvency. In other word, thi change tend to ake the bank better able to withtand hock to it hortter funding ource, but le able to withtand hock to the value of it aet. Shifting the copoition of the bank aet toward afe, liquid aet alo tend to lower the probability of conditional inolvency, but can either raie or lower the probability of fundaental inolvency. In cae like thi where the reult are abiguou, our fraework help illutrate the ource of thi abiguity and when a trade-off i ot likely to arie. Increaing the bank liquid aet holding i ot likely to raie the probability of fundaental inolvency when the bank i highly leveraged or ha a large aount of long-ter debt. In the next ection, we build on the reult preented o far to tudy a range of current policy iue. In each cae, we tudy how a particular change or policy propoal would affect the balance-heet characteritic of the relevant financial interediarie. We then derive the correponding change in the olvency region of our diagra and interpret the reult. FRBNY Econoic Policy Review / February

10 4. Application Exhibit 6 Different Region in -e Space In thi ection, we utilize our fraework to analyze a erie of current policy iue. Firt, we analyze the effect of liquidity and capital on tability and the trade-off between the two. We then tudy the effect of policy tool uch a the Liquidity Coverage Ratio and dicount window lending. Another iue we analyze i the effect of encubered aet on bank tability. A a pecific interediation tructure, we tudy aet-backed coercial paper tructure, which illutrate an intereting cae with their aet tructure and heavy reliance on hortter debt. Finally, we analyze oney arket utual fund and variou policy propoal to ake the ore table. e Conditionally olvent or inolvent Fundaentally olvent or inolvent 4. Liquidity veru Capital σ Traditionally, capital requireent have been the ain tool of bank regulator. Since the financial crii, liquidity requireent have received increaed attention. Further below we analyze a pecific liquidity requireent, the Liquidity Coverage Ratio. But firt, we tudy ore generally how liquidity holding (on the aet ide) and equity capital (on the liability ide) interact in our fraework and whether they are ubtitute or copleent. A in ection 3. and 3.4, we noralize the ize of the bank balance heet to o that y + = on the aet ide and + l + e = on the liability ide, and then denote the fraction of hort-ter debt by σ ( + l). We now take and a given and tudy bank olvency for different cobination of and e. Note the difference fro the analyi before, where we took and e a given and tudied bank olvency for different cobination of and. A before, one of two olvency condition will be relevant, depending on whether the bank i facing fundaental inolvency or conditional inolvency. The ditinction i whether the bank ha to liquidate aet to atify withdrawal or not, that i, σ( e). Thi condition divide the -e pace into two region with the dividing line given by: e = - σ. Exhibit 6 illutrate the two region. For cobination (, e) above and to the right of the line, the bank ha enough cah to pay all withdrawing creditor o it i either fundaentally olvent or fundaentally inolvent. For cobination (, e) below and to the left of the line, the bank i forced to liquidate aet o it i either conditionally olvent or conditionally inolvent. We tart with the region of conditional olvency/inolvency where the olvency contraint i given by: ( ) + τ [σ( τ + ( )r ) + ( - σ)r l ]( - e). To depict thi olvency threhold in the -e pace, we olve for e: e = ( ) + τ σ( _ τ. + ( - )r ) + ( - σ)r l For a given level of withdrawal and a given aet payoff, thi line i the olvency threhold in ter of liquidity and capital e. Therefore, it repreent the trade-off between different cobination of liquidity and capital that keep the bank on the olvency threhold. To illutrate thi trade-off, we note that the lope of the line i: de d = τ σ( τ + ( -)r ) + ( - σ)r < 0. l The lope i negative ince τ < by Auption 2. Thi iplie that liquidity and capital are ubtitute: An increae in liquidity holding can copenate for a decreae in capital while aintaining the ae level of bank tability. The blue line in Exhibit 7 repreent thi threhold between conditional olvency and conditional inolvency. We now turn to the region of fundaental olvency or inolvency. Here the olvency contraint i given by: ( ) + r [σr + ( σ)r l ]( e). 38 Stability of Funding Model

11 e Exhibit 7 Trade-Off Liquidity veru Capital Conditionally olvent Conditionally inolvent Fundaentally inolvent σ Fundaentally olvent High aet payoff > r Low aet payoff < r Liquidity Coverage Ratio require bank to hold ufficient high-quality liquid aet to cover their total net cah outflow over thirty day under a tre cenario. In thi ection, we analyze the potential effect of the Liquidity Coverage Ratio on bank tability. In particular, we focu on a liquidity requireent where bank are required to hold high-quality liquid aet equal to at leat a fraction γ of their hort-ter liabilitie, that i, γ. Since holding liquid aet entail opportunity cot in ter of forgone invetent opportunitie in the riky aet, we aue that thi requireent will be binding, that i, bank will hold = γ on their balance heet. We analyze the effect of aking the liquidity requireent ore trict, that i, increaing γ. Thi would qualitatively have a iilar effect a increaing liquidity holding, a analyzed in ection 3.4. In particular, we obtain for the fundaental inolvency threhold: r _ = ( γ) + lr l, γ Again, we olve for e to depict the olvency threhold in the -e pace: e = ( ) + r. σr + ( σ)r l To illutrate the trade-off between liquidity and capital, we derive the lope of the olvency threhold: de d = r. σr + ( σ)r l The ign of thi lope depend on the relative ize of and r. For low aet payoff < r, the lope i negative o that liquidity and capital are ubtitute a in the region of conditional olvency/inolvency. The thin black line in Exhibit 7 illutrate thi trade-off. For any aet payoff > r, however, the lope i poitive a illutrated by the thick black line in Exhibit 7. Thi iplie that liquidity and capital are copleent, o an increae in liquidity holding require an increae in capital for the bank to aintain the ae level of tability. The intuition for thi cae i iilar to the ituation of harful liquidity in ection 3.4. If the aet pay off ore than cah, higher liquidity holding reduce the bank total payoff and therefore weaken it olvency poition. To copenate, the bank ha to hold ore capital. 4.2 Liquidity Coverage Ratio The new regulatory fraework propoed by Bael III introduce new liquidity requireent for bank. In particular, the which iplie d _ dγ = ( _ r ) γ. Analogou to ection 3.4, if the critical value i le than the return on cah r, then the rik of fundaental inolvency i decreaing in the liquidity requireent; at the inolvency boundary, the aet pay off le than cah, o having ore cah i better than having ore aet. However, if intead r, then fundaental inolvency rik i increaing in the liquidity requireent; the aet pay off ore than cah at the inolvency boundary, o having ore cah i wore than having ore aet. A dicued in ection 3.4, thi poibility of liquidity regulation being harful i ore likely for intitution with high leverage and/or long debt aturity. In the cae of inufficient cah to pay for withdrawal and therefore liquidation ( ), the critical value for conditional olvency i ( τ *() = + ( )r ) + lr l τ γ. γ The overall effect of γ on *() i again ot clearly illutrated by the following: d*() dγ = (*() τ ). γ A in ection 3.4, we can how that *() < τ, and therefore the rik of conditional inolvency i unabiguouly reduced by tricter liquidity requireent. Finally, looking at the lope of *(), FRBNY Econoic Policy Review / February

12 Exhibit 8 Dicount Window Contraint d ( h d )y. Subtituting in for d, thi i a contraint on and : 6) ( h d )y. Market olvency contraint DW olvency contraint DW borrowing contraint A long a the hortfall i not too large, the bank can ue the DW loan to pay all withdrawal in period. In period 2, the bank receive back the aet it pledged but ha to pay off the DW loan in addition to the long-ter creditor and the reaining hort-ter creditor. The olvency condition in period 2 i therefore: y ( ) r + lr l + dr d. Subtituting in for d, thi condition becoe: 7) y r + lr l - r d + (r d r ). d*() d = ( τ r ) γ, we ee that aking the liquidity requireent ore trict (increaing γ) trictly increae the enitivity of the critical value to withdrawal. The effect are analogou to the effect of increaing, which are illutrated in Exhibit Dicount Window Traditionally, central bank have attepted to addre bank liquidity proble with dicount window lending, where the principle of lending to bank that are olvent but illiquid i et out by Bagehot (873). In our odel, thi correpond to bank in the conditional inolvency region that would be olvent if fewer of their creditor deanded liquidity. An intereting quetion i whether dicount window lending can eliinate the entire conditional inolvency region. We aue that in period a bank can borrow fro the central bank dicount window at an interet rate r d r, but ha to pledge aet a collateral ubject to a haircut h d. Since the DW doe not addre iue of fundaental inolvency, the threhold reain unchanged fro the benchark etting: r _ = + lr l - r y. When facing conditional inolvency, that i, once the bank run out of cah ( > ), it can acce the DW to borrow the hortfall d =. However, due to the haircut h d, DW borrowing i contrained: Hence, the DW entail two contraint on the rate of withdrawal and the aet return. Contraint 6 i a period- contraint ince it liit the DW borrowing capacity in period when the bank ha to eet withdrawal. If i too high or i too low o that contraint 6 i violated, the bank cannot urvive period even if it pledge all it aet to the DW. Thi borrowing contraint i repreented by the blue line in Exhibit 8. Only for cobination (, ) above and to the left of the blue line can the bank eet all withdrawal in period with cah and DW borrowing. Contraint 7 i a period-2 contraint ince it give the olvency condition in period 2 which i iilar to the tandard cae. The key difference i that with DW acce the bank regain the aet it pledged a collateral but ha to pay off an additional loan. Thi olvency contraint i repreented by the dahed line in Exhibit 8. The DW olvency contraint i very iilar to the arket olvency contraint in the benchark cae. The difference i that uing the DW, the bank doe not have to ell aet but incur an additional liability. The olvency contraint ipoed by the DW i flatter than the one ipoed by the arket iplying a larger olvency region a long a r d < τ, that i, a long a the DW interet rate i all relative to the liquidation dicount. The cobination of both DW contraint eparate the olvency fro the inolvency region with the tricter contraint foring the boundary at every point. To the left of the interection of the two contraint the olvency contraint i binding while to the right of the interection the borrowing contraint i binding. Exhibit 9 copare two different DW policie (h d, r d ) and (h d, r d ); the firt policy i tricter while the econd policy i 40 Stability of Funding Model

13 Exhibit 9 Coparion of Dicount Window Policie For a given haircut h, the fraction x of aet that i encubered i deterined by the following condition: 8) E[]( h)x = cr c, Strict DW Lenient DW o that the expected value of the collateral in period 0 net of the haircut ha to be ufficient to cover the ecured creditor clai. A the key feature of encubered aet, we aue that they are held by the collateralized creditor and can therefore not be ued by the bank to atify payout to uncollateralized creditor. Denoting the fraction of uncollateralized lender that withdraw at t = by, the bank olvency contraint in t = 2 becoe: ( x) u τ ( - )ur u. ore lenient: h d > h d and r d > r d. The lower haircut and lower interet rate of the ore lenient policy iply flatter lope for both the borrowing contraint and the olvency contraint. The olvency region i therefore trictly larger for the ore lenient policy. Thi condition tate that the payoff of the unencubered aet net of t = liquidation ha to be ufficient to repay the reaining uncollateralized creditor at t = 2. Subtituting in for x uing equation 8, we can olve for the critical value: *() = u τ + ( - )ur u cr - c E[]( - h). 4.4 Aet Encubrance Since the financial crii, the difference between collateralized and uncollateralized funding ha received increaed attention. 8 We can ue our fraework to tudy the effect of aet encubrance on bank tability. For iplicity, we aue that the bank ha only hort-ter debt, oe of which i collateralized debt c, the reainder i uncollateralized debt u. Both have the ae interet rate r = between t = 0 and t = and potentially different interet rate r c and r u, repectively, between t = and t = 2. On the aet ide, we aue that the bank only hold long-ter aet, y =, a fraction x [0, ] of which i encubered a collateral for the debt c. The bank balance heet therefore ha the following for: Aet Liabilitie x c x u e 8 See Perotti (200) for a dicuion of the rik originating in collateralized funding. For theorie on the ue of collateral ee, for exaple, Beter (985), Geanakoplo (2003), or Hart and Moore (994). We ee that the critical value *() i increaing in the haircut h: With a higher haircut, ore of the bank aet are encubered. Effectively, there i le iplicit collateral for the unecured creditor, which increae the rik of bank failure. Keeping in ind that u = e c, we can differentiate the critical value *() with repect to the aount of collateralized debt to get: -( τ d*() + ( - )r ) u ( - (c + u)r c dc = E[]( - h) ) ( - cr c. E[]( - h) ) 2 Subtituting in E[]( h) = cr c x fro equation 8, we can iplify the expreion and arrive at: d*() dc = ( τ + ( - )r ) u ( x) (x u_ 2 c ( x)) > 0 x x > c u. Thi iplie that replacing uncollateralized funding with collateralized funding increae the critical value and therefore inolvency rik if and only if the ratio of encubered to unencubered aet i greater than the ratio of collateralized to uncollateralized funding. The reaon i that FRBNY Econoic Policy Review / February 204 4

14 Exhibit 0 Effect of Aet Encubrance Higher haircut, ore ecured debt Furtherore, the ABCP conduit would have a credit and/or liquidity enhanceent fro a ponoring intitution. Firt, we focu on the ABCP conduit olely, leaving aide the effect of the credit and liquidity enhanceent. Note that the ABCP conduit doe not hold any cah, o that all early clai hould be paid by liquidating the riky aet. Uing our fraework, we can how that the ABCP conduit i olvent at t = 2 if and only if ( τ ) ( )r, which give u ( - )r + τ *(). the explicit overcollateralization of ecured funding due to haircut reduce the iplicit collateral for unecured funding. Exhibit 0 illutrate the effect of ecured funding for bank tability; for higher haircut and/or greater reliance on ecured funding, the olvency region hrink (the curve hift up). 4.5 Aet-Backed Coercial Paper Structure Aet-backed coercial paper i a for of ecured, hortter borrowing. Prior to the crii, ABCP wa widely iued by off-balance-heet conduit of large financial intitution. Thee conduit increaingly held long-ter aet, thu becoing ignificant vehicle of aturity tranforation. In order to enhance their attractivene, they relied on both credit and liquidity guarantee, typically provided by the ponoring intitution. The ABCP arket experienced ignificant ditre tarting in Augut 2007 a a reult of increaing uncertainty about the quality of aet backing coercial paper iuance. Thi enhanced uncertainty, coupled with the pronounced aturity iatch of conduit balance heet, triggered a run on their liabilitie (Covitz, Liang, and Suarez 203). Here we ue our fraework to illutrate the inolvency rik aociated with ABCP tructure. The tructure typically have long-ter (riky) aet backing their hort-ter funding. Hence, the balance heet of an ABCP conduit would look like: Aet Liabilitie y = = l = 0 e = 0 If all creditor roll over their debt at t =, that i, when = 0, the ABCP conduit i olvent when r _. If no creditor roll over it debt at t =, that i, when =, we obtain *() = τ. _ Note that the ABCP tructure doe not hold any cah ( = 0). Hence, we do not oberve a flat region, a in the cae of an interediary that hold oe cah, where = _ for [0, ]. Thi i all illutrated in Exhibit. A argued, ABCP conduit would typically have credit and/or liquidity enhanceent fro ponoring intitution, which would ake the liquidation of the aet le cotly. For exaple, in a cae where the ponor guarantee i trong, the cot aociated with liquidation can be copletely eliinated, that i, τ = r, o that there i only the rik of fundaental inolvency. Hence, the trength of the guarantee affect τ, which ha already been analyzed in ection Money Market Mutual Fund Money arket utual fund typically attract highly rikavere invetor. Their liabilitie are otly hort ter that can be claied at hort notice, o that =. On the aet ide, they have otly afe aet, that i, the aet ide of the balance heet would have a high value for and a relatively all value for y. An iportant feature of an MMF i that when it tate a hare price lower than $.00, the fund break the buck. Hence, our analyi focue on when an MMF break the buck, which would be analogou to a bank being inolvent in the benchark cae. 9 Uing our benchark fraework, we can find the threhold value for a follow. Suppoe that a fraction of creditor redee at t =, wherea the reaining - wait until t = 2. The fund can pay all creditor one unit and it doe not break the buck when y + χ()( - ) -. 9 In a recent paper, Parlatore Siritto (202) develop a general equilibriu odel of MMF and analyze the effect of recently propoed regulation on liquidity provided by thee fund and their fragility. 42 Stability of Funding Model

15 Exhibit Stability of Aet-Backed Coercial Paper Structure Exhibit 2 Money Market Mutual Fund Region for Breaking the Buck Doe not break the buck * Stronger upport (higher τ) y Break the buck Note the difference between thi cae and an interediary olvency contraint, where the MMF doe not break the buck when it can pay all creditor a iniu gro return of, wherea the interediary ha to pay the proied interet to the creditor to be olvent. Thi give u - χ()( - ) y *(). If, the fund can pay all early clai fro it cah holding o that χ() = r. For >, the fund doe not have enough cah for all early clai and need to liquidate oe of the riky aet o that χ() = τ. Hence, we obtain { - - r ( - ) y for [0,] 9) *(), - - ( τ)( - ) y for (,] which i illutrated in Exhibit 2. 0 Note that if all creditor redee at t =, that i, for = we have *() = τ. If the realized return fro the riky aet i high enough, that i, for, the fund never break the buck at t = 2 regardle of the action creditor take at t =. Refor Propoal. While MMF have perfored well hitorically and are appreciated by invetor for their tability, during the recent crii the Reerve Priary Fund broke 0 Exhibit 2 illutrate the cae where r >. the buck after the failure of Lehan Brother. Thi, in turn, affected financial arket ignificantly. Since then, there ha been oe debate about and refor propoal to increae the tability of MMF. McCabe et al. (202) develop a refor propoal for MMF called iniu balance at rik. The propoal iplie that a creditor can only redee up to a fraction μ of the clai early and the reaining fraction μ becoe a junior debt clai at t = 2 (or an equity clai, a we analyze in thi ection). In that cae, the balance heet of the fund effectively look a follow: Aet y Liabilitie = μ l = μ e = 0 At t =, the realization of withdrawal i ( - μ). At t = 2, the creditor that redeeed at t = are owed l J = μ, where l J repreent junior debt. The creditor that did not redee at t = are owed l S = -, where l S repreent enior debt. The balance heet of the fund look a follow after the withdrawal deciion at t = : Aet Liabilitie = ( μ) y l S = l J = μ e = 0. FRBNY Econoic Policy Review / February

16 The fund doe not break the buck at t = 2 if and only if it can pay a return of to all creditor, that i, when y + χ()( - ( - μ)) μ +, which give u Exhibit 3 Money Market Mutual Fund Refor Propoal with Junior Debt and Equity μ χ()( ( - μ)) * R () = y. If ( - μ), the fund can pay all of the early clai fro it cah holding o that χ() = r. When ( μ) >, the fund need to liquidate oe of it riky aet o that χ() = τ. Hence, we obtain { μ r ( ( - μ)) y for [0, - μ ] 20) * R (), μ ( τ)( ( - μ)) y µ With junior debt With equity for (, ] - μ which i illutrated by the black boundary in Exhibit 3, along with the blue original boundary for the MMF characterized in equation 9. Next, we analyze the effect of the refor propoal on the tability of MMF. Note that the region over which the fund can ue it cah holding for the early withdrawal i larger in thi cae ince <. We can alo how that - μ * R () = *() - μ(χ() - ) y < *(). In the region where (, ], the lope of *, which - μ i τ, i larger than the lope of * R, which i r. Hence, with the refor propoal the region in which the MMF break the buck hrink, a illutrated in Exhibit 3. The reaon for thi i that the refor propoal liit the aount that can be redeeed early and hence itigate the advere effect of early withdrawal by lowering the aount of the riky aet the fund ha to liquidate. Thi, in turn, ake it le likely that the fund break the buck. Equity veru Junior Debt. A variant of the propoal i that the creditor that redee at t = becoe equityholder, rather than junior debtholder, at t = 2. In that cae, the balance heet look a follow after the withdrawal deciion: Aet Liabilitie = ( μ) y l = e = μ. Hence, the withdrawal at t = help create an equity buffer, which ake it harder for the fund to break the buck. The fund doe not break the buck at t = 2 if and only if - - χ()( - ( - μ)) y * (). E Note that if ( - μ), the fund can pay all of it early clai fro it cah holding o that χ() = r. When ( - μ) >, the fund need to liquidate oe of it riky aet o that χ() = τ. Hence, we obtain { - - r( - ( - μ)) y for [0, - μ ] 2) * E (), - - ( τ)( - ( - μ)) y for (, ] - μ which i illutrated by the dahed boundary in Exhibit 3. The iportant difference between thi propoal and the firt propoal, where the creditor that redee at t = becoe junior debtholder at t = 2, i that in thi cae early withdrawal generate an equity cuhion o that the region over which the fund doe not break the buck widen. In particular, we have μ * E () = * R () y. Hence, the region over which the fund break the buck hrink further under the econd propoal. 44 Stability of Funding Model

17 5. Concluion During the recent financial crii, we oberved diruption and the near diappearance of iportant arket, recordhigh borrowing rate, haircut alot reaching 00 percent, ignificant hortening of aturitie, and intitution alot unable to borrow even againt high-quality collateral. We are yet to fully undertand the exact deterinant of thee diruption. In thi article, we preent a iple analytical fraework to tackle thi iportant quetion. The fraework provide an analytical and rigorou, yet eaily applicable, tool to analyze the ource of fragility and the effect of variou characteritic of funding tructure on financial tability. Hence, it can be ued to illutrate the trade-off that ay ait policyaker in foring their view about appropriate way to approach regulatory refor and to evaluate variou policy option in ter of their conequence for financial tability. FRBNY Econoic Policy Review / February

18 Appendix We exaine the rollover deciion of an individual hort-ter debtholder. At t =, each agent oberve the realized value of and anticipate oe behavior of other hort-ter creditor, a uarized by the value of. The agent then decide whether or not to roll over it debt; the payoff aociated with each deciion are: Roll Over Not Roll Over Solvent r y + χ()( - ) Inolvent at t = 2 ( - ϕ) [ ( - )r + lr ]r l Inolvent at t = 0 + τy If the bank i olvent, the agent would clearly prefer to roll over it clai and earn the return r >. If the bank i inolvent at t =, the agent would receive nothing if it rolled over it debt, o the agent would clearly prefer to redee it clai at t = and receive in expectation a pro-rata hare of the bank liquidated aet. Thing are lightly ore ubtle in the interediate cae, where the bank urvive at t = but i inolvent at t = 2. In thi cae, the agent would receive the face value of it clai at t = if the agent doe not roll over. If the agent doe roll over, it receive a pro-rata hare of the bank atured aet at t = 2, after the bankruptcy cot have been paid. If we aue that ϕ > - r, then thi return i alway aller than, which give u the following reult: Propoition : For ϕ > - r, a hort-ter debtholder will chooe to roll over it clai if and only if (, ) i uch that the bank i olvent in all period. To keep thing iple, we aue that an agent anticipate a particular value of rather than having a belief repreented by a probability ditribution over different value of. 46 Stability of Funding Model

19 Reference Allen, F., and D. Gale Optial Financial Crie. Journal of Finance 53: Bagehot, W Lobard Street: A Decription of the Money Market. London: H. S. King. Beter, H Screening v. Rationing in Credit Market with Iperfect Inforation. Aerican Econoic Review 75, no. 4: Chari, V. V. and R. Jagannathan Banking Panic, Inforation, and Rational Expectation Equilibriu. Journal of Finance 43: Covitz, D., N. Liang, and G. Suarez The Evolution of a Financial Crii: Collape of the Aet-Backed Coercial Paper Market. Journal of Finance 68, no. 3: Diaond, D., and P. Dybvig Bank Run, Depoit Inurance, and Liquidity. Journal of Political Econoy 9: Enni, H. M Econoic Fundaental and Bank Run. Federal Reerve Bank of Richond Econoic Quarterly 89, no. 2: Geanakoplo, J Liquidity, Default, and Crahe: Endogenou Contract in General Equilibriu. Advance in Econoic and Econoetric: Theory and Application. Eighth World Congre, Volue 2. Cabridge Univerity Pre. Goldtein, I., and A. Pauzner Deand Depoit Contract and the Probability of Bank Run. Journal of Finance 60, no. 3: Hart, O. D., and J. Moore A Theory of Debt Baed on the Inalienability of Huan Capital. Quarterly Journal of Econoic 09, no. 4: McCabe, P. E., M. Cipriani, M. Holcher, and A. Martin. 202 The Miniu Balance at Rik: A Propoal to Mitigate the Syteic Rik Poed by Money Market Fund. Federal Reerve Bank of New York Staff Report, no. 564, July. Morri, S., and H. S. Shin Illiquidity Coponent of Credit Rik. Princeton Univerity working paper. Parlatore Siritto, C The Regulation of Money Market Fund: Adding Dicipline to the Policy Debate. New York Univerity working paper. Perotti, E Syteic Liquidity Rik and Bankruptcy Exception. Duienberg School of Finance Policy Paper, no. 8. Potlewaite, A., and X. Vive Bank Run a an Equilibriu Phenoenon. Journal of Political Econoy 95, no. 3: Saunder, A., and B. Wilon Contagiou Bank Run: Evidence fro the Period. Journal of Financial Interediation 5, no. 4: Yorulazer, T. 204a. Cae Studie on Diruption during the Crii. Federal Reerve Bank of New York Econoic Policy Review 20, no. (February): b. Literature Review on the Stability of Funding Model. Federal Reerve Bank of New York Econoic Policy Review 20, no. (February): 3-6. Gorton, G Bank Panic and Buine Cycle. Oxford Econoic Paper 40: The view expreed are thoe of the author and do not necearily reflect the poition of the Federal Reerve Bank of New York or the Federal Reerve Syte. The Federal Reerve Bank of New York provide no warranty, expre or iplied, a to the accuracy, tieline, copletene, erchantability, or fitne for any particular purpoe of any inforation contained in docuent produced and provided by the Federal Reerve Bank of New York in any for or anner whatoever. FRBNY Econoic Policy Review / February