Appendix. Confidence Banking and Strategic Default. Guillermo Ordoñez. University of Pennsylvania and NBER

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1 Appenix Confience Banking an Strategic Default Guillermo Oroñez University of Pennsylvania an NBER 1 Proofs 1.1 Proof of Proposition 1 Since s ( ) is the signal that makes a goo firm with a given reputation inifferent between covering a security in trouble or not, the conition at s ( ) is clearly E s [V (, b (s ))] = R( s ), where b (s i )=1 Pr(E j ( ) <E i ( ) s i ), which is the probability that investors expect a funamental uner the one the firm expects conitional on the signal s i that the firm observes. Since at the cutoff s firms are inifferent between covering securities in trouble or not, b (s ) is the probability firms assign to investors believing is such that the firm covers securities in trouble, an hence the belief investors use to upate reputation at the cutoff s. The upate belief of the firm about the funamental, after observing a signal s i is E i ( s i )= µ + s s i + s. The upate istribution of the funamental after the firm observes the signal s i is s i N(E i ( s i ), 1 + s ), an the istribution of investors signals s j, conitional on the firm s signal s i is s j s i N(E i ( s i ), ). (1) + s s 1

2 Hence, Pr(E j ( ) <E i ( ) s i ) = Pr s j <E i ( )+ = ( p (s i µ)), (E i ( ) µ) s i s where = s ( + s)( + s) As s!1,! 0, then b (s i )= 1 for all s i. Hence, in the limit the unique cutoff s is uniquely etermine by E s V (, b (s )= 1) = R( s ). Investors upate reputation base on their beliefs, which epen on their signals. When investors observe a signal s j, they infer that the probability the firm observes a signal s i below the cutoff s ( ), an ecies not to cover securities in trouble, is b (s j )=1 Pr(s i <s s j )=1 "s s( + s ) + s (s µ + s s j + s ) where is just the stanar normal istribution from equation (1). As s! 1, b (s j )! 0 if s j <s ( ) an b (s j )! 1 if s j >s ( ). This implies that in the limit, whenever investors observe a signal above s ( ), they believe firms cover securities in trouble an upate reputation. Similarly, whenever investors observe a signal below s, they believe firms o not cover securities in trouble an o not upate reputation. Q.E.D. #, 1. Proof of Proposition The proof applies for a given, hence for simplicity I enote s ( ) just as s. Differentiating the conition E s apple V, b (s )= 1 = R( s ) () that pins own s with respect to µ, E s [V (, b (s ))] µ + E s [V (, b (s ))] s s µ = R( s ) s s µ + R( s ), µ E s [V (, b (s ))] R( s ) s s s µ = R( s ) µ E s [V (, b (s ))]. µ

3 Recall that, since, N (s ) < 0, then R( s ) < 0. Also E s [V (, b (s ))] > 0. From µ µ µ assumptions 1 an the term in parenthesis is positive. Combining these results using the envelope conition shows that s < 0. µ Intuitively, a ecline in µ increases R( s ) for a given s (by an increase in the cumulative istribution up to s ). This requires a larger s to raise E s [V (, b (s ))] an fulfill equation (). This irect effect increases s. Furthermore, this increase in s implies a further increase in R( s ), which reinforces the irect effect generate by a lower µ. There is also a secon effect that comes from reucing beliefs b (s i ) an p reputation upating at each s i, (since b (s i )=1 (si µ), weakly reucing E si [V (, b (s i ))], for every signal s i. Hence, a further increase in s is necessary to compensate for this reuction an still fulfill equation (). Q.E.D. 1.3 Proof of Proposition 3 Value functions from issuing ebt an securities, as s!1(almost perfect information), are UG D (, µ) =p(y + z)+ G E µ V ( 0. ) R D ( ) (3) an respectively. U S G(, µ) = p(y + z)+n (s (, µ))p E µ, <s V (, ) R S ( s (, µ)) (4) +(1 N(s (, µ))) G E µ, >s V ( 0, ) R S ( s (, µ)) Since b G = N (s (, µ))p +(1 N(s (, µ))) G an N (s (, µ))e µ, <s V ( 0, )+(1 N (s (, µ)))e µ, >s V ( 0, )=E µ V ( 0. ) we can rewrite the ifference between these two values as UG( S, µ) UG D (, µ) =[ G R D ( ) b G R S ( s (, µ))] {z } B(,µ) where an G R D ( )= G 1+[1 ( G +(1 ) B )]C G +(1 ) B, b G R S ( s (, µ)) = b G b G +(1 ) B, N (s (, µ)) EV (, µ s (, µ)) C(,µ) (5) EV (, µ s (, µ)) G E µ, >s V ( 0, ) pe µ, >s V (, ) > 0. The net benefits of securitization, B(, µ), come from firms paying lower rates for funs. The net cost of securitization, C(, µ), come from efaulting more frequently an from losing the reputation upate in those cases. 3

4 First, I evaluate the function (UG S UG D ) in the extremes, for very large an very small µ. When µ is high enough such that N (s )! 0, then i) C(, µ)! 0 an ii) as b G! G, (1 B(, µ)! G (1 ) B )C G G +(1 ) B > 0. This implies that there is always a µ( ) large enough such that a firm with reputation prefers to issue securities, not ebt. At the other extreme, when µ is low enough such that N (s )! 1, then i) as b G! p, 0! an C(, µ)! ( G p)e µ V (, ) > 0 an ii) as b G R S ( s (, µ))! 1, then B(, µ)! G R D ( ) 1 > 0. This implies that there may be a µ L ( ) low enough such that a firm with reputation prefers to issue securities, not ebt, for all µ<µ L ( ) if an only if G R D ( ) 1 > ( G p)e µ V (, ). This is naturally the case when µ is so low that E µ V (, ) =0, as this is isomorphic to a static situation in which the future oes not matter. In such case securities are preferre because the firm pays $1 in expectation for the loan of $1, but involves a lower probability of firm continuation. Secon, to assess what happens for intermeiate levels of µ, we evaluate the change of the expression (UG S UG D) as a function of µ, this is (U G S U G D). Taking erivatives of µ each component. B(, µ) µ = b GR S ( s ) b G b G N (s ) = (1 ) B >0 = (1 p) b G +(1 ) B 6 4 N (s ) µ + N (s ) s >0 s µ {z} < 0 (6) C(, µ) µ = 6 4 N (s ) µ + N (s ) s >0 s µ {z} EV + N (s ) 6 4 EV µ? + EV s? s µ {z} (7) We can always characterize these erivatives for relatively high an small values of µ. When µ is high enough such that N (s )! 0, then N (s )! 0 an s! 0. This µ µ implies that i) C(, µ)! 0 an ii) B(, µ)! 0 an the net positive incentives to issue securities over ebt o not change when µ is high enough. Intuitively, the expecte funamentals are so goo that the assesse probability of strategic efault is so low that the probability of continuation, an hence the upate of reputation, is high. At the other extreme, when µ is low enough such that N (s )! 1, still it is the case that N (s ) µ! 0 an s µ! 0. This implies that i) C(, µ)! EV µ = ( G p) E µv (, ) µ > 0 an ii) B(, µ)! 0, then the potential net positive incentives to issue securities over ebt when µ is low ecreases as we increase µ. Intuitively, the higher probability of efault from securities becomes more costly in terms of continuation as funamentals improve in expectation. 4

5 For intermeiate levels of µ, the characterization of these erivatives epen on the shape of the value function with respect to. In principle there may be many threshols for which UG S UG D =0an then many regions of µ<µ H ( ) for which firms issue securities. As long as the value V (, ) is smooth enough in, however, at most two threshols exist an then firms of reputation issue ebt for µ L ( ) <µ<µ H ( ). The conition epens on value function not isplaying jumps or large changes as function of µ. Q.E.D. 1.4 Proof of Proposition 4 As iscusse, µ H ( ) is etermine by equation (5) equal to zero, when N (s ) < 1. Also, if µ L ( ) exists, it is for N (s )! 0. I will analyze each of these threshols as function of reputation in steps. Step 1:Taking erivatives of firms expecte profits with respect to, U D G (, µ) apple E µ V ( 0, ) 0 = G 0 R D ( ), (8) which is positive by construction of value functions increasing with an because R D ( ) = (1 + C)( G B ) ( G +(1 ) B ) < 0. U S G (, µ) = N (s (, µ)) p E µ, <s V (, ) +(1 N(s E µ, >s V ( 0, ) (, µ))) G 0 +N (s (, µ)) p E µ, <s V (, ) s +(1 N(s E µ, >s V ( 0, )s 0 (, µ))) s G s 0 + N (s (, µ)) s s p E µ, <s V (, ) R S ( s (, µ) (9) N (s (, µ)) s s G E µ, >s V ( 0, ) R S ( s (, µ) [N (s (, µ)) p +(1 N(s (, µ))) G ] R S( s (, µ)) N (s (, µ)) N (s (, µ)) s s Differentiating the conition that pins own s with respect to, E s [V (, b (s ))] = R S( s ). 5

6 Since R S = R( s ) + R( s ) s s = N (s ) s (b G (s ) B ) ( b G (s )+(1 ) B ) + p(1 p) s ( b G (s )+(1 ) B ), apple E s [V (, b (s ))] R( s ) s s s = R S( s ) E s [V (, b (s ))]. The term in brackets on the left is positive (by assumptions 1 an ) an the term on the right is negative. By the envelope conition, s < 0 an R S < 0. This implies the steep part of the value function UG S (, µ) moves to the left when grows. Since both UG S(, µ) an U G D (, µ) increase with for each µ, the threshol µ H ( ) eclines with if US G (,µ H ( )) UG D(,µ H ( )). Since the threshol µ H ( ) is given by the value µ at which equation (5) is equal to zero, by evaluating equations (8) an (9) at µ H it is clear that this conition is fulfille. Then µ H < 0. Step : µ L ( ) is etermine by equation Taking the erivative with respect to, G R D ( ) 1 ( G p)e µ L ( )V (, ) G R D ( ) apple E µ L ( G p) ( ) V (, ) + E µ L ( ) V (, ) µ L µ L Since we have shown R D( ) 0 an E µ ( )V (, ) L µ L > 0. Then µ L < 0 an by assumption of value functions E µ L ( ) V (, ) > < 0. Q.E.D. 1.5 Formal iscussion of Section.5 Proposition 1 Assume a transfer policy such that V b (, ) =V (, )T ( ) an µ is such that G R D (0) < ( G p)e µ V (0, ). From Proposition 3 there is a unique reputation level (µ) that makes goo firms inifferent between ebt an securities in the absence of cross subsiization. It exists a subsiy scheme increasing in reputation, T( ) > 0 such that T ( b )=1, where b > (µ) an (µ) is also the reputation level that make goo firms inifferent in the presence of cross subsiization. The expecte profits of firms with reputation < (µ) remain unchange an of firms with reputation > (µ) increase, as their ex-ante probability of strategic efault (N ( (, µ))) ecline. 6

7 Proof First I prove the impact of subsiies on the incentives to cover securities in istress, summarize by. Imposing V ( 0, b ( ))T ( 0 ) in the conition that pins own, an ifferentiating with respect to T ( 0 ), V ( 0, b ( ))T ( 0 ) R( ) T ( 0 ) = V( 0, b ( )). (10) The right han sie is negative an the term in brackets is positive, which implies that T ( 0 ) < 0. In wors, the ex-ante probability of strategic efault for all reputations for which the upate 0 is subsiize with T ( 0 ) > 1. In contrast, the ex-ante probability of strategic efault increases for all reputations for which the upate 0 is taxe with T ( 0 ) < 1. This result is important to prove the first part of the proposition. Assume T ( )=1 such that T ( 0 ) > 1. This implies that, in the presence of cross-subsiization, goo firms with reputation strictly prefer to issue securities. This is clear from comparing equations (3) an (4). Equation (3) remains constant while equation (4) increases for two reasons. First, fixing, the value of reputation upating is larger because E µ, > V ( 0, )T( 0 ) >E µ, > V ( 0, ). Secon, as shown above, eclines, which reuces R S an further increases the gains from securitization in equation (4). Combining this result with proposition 4, when T ( )=1, then >, where is the reputation level that makes goo firms inifferent between using ebt or securitization in the presence of cross subsiization. By imposing T ( ) < 1, equation (3) eclines while equation (4) oes not increase so much as in the previous case. This implies there is always a (µ) < ˆ < 0 (µ) such that T ( ˆ) =1an (µ) = (µ). If the government imposes such a scheme, the firms that issue ebt an securities o not change. The firms with reputation < issue ebt an since they are subject to contractual provisions, they keep paying loans with successful ongoing projects. In contrast, the goo banks with reputation > issue securities, but because subsiies ecrease ( ), they use successful ongoing projects to cover securities in istress an securitization is less fragile. Whether cross-subsiization can be self-finance or not epens on the istribution of reputation across firms an on the value functions for ifferent reputation levels. In particular, cross-subsiization is self finance at each expecte future conition if transfers are such that Z 1 0 V (, )T ( ) = Z 1 0 V (, ). where is the istribution of reputation, conitional on a realize funamental. Q.E.D. 7

8 Institutional Details of Special Purpose Vehicles (SPV) Securitization involves the following steps: (i) a sponsor or originator of receivables sets up a remote special purpose vehicle (SPV), pools the receivables, an transfers them to the SPV as a true sale; (ii) the cash flows are tranche into asset-backe securities, the most senior of which are rate an issue in the market; the procees are use to purchase the receivables from the sponsor; (iii) the pool revolves in that over a perio of time the principal receive on the unerlying receivables is use to purchase new receivables; (iv) there is a final amortization perio, uring which all payments receive from the receivables are use to pay own the tranche principal amounts. A critical step in securitization then involves sponsoring SPVs. By financing the firm using off-balance sheet instruments, the issuer maintains control over the business ecisions while the financing is one in the SPVs. The two key characteristics of SPVs are the following: Bankruptcy remoteness an privilege information. First, SPVs are not subject to bankruptcy costs because, as a matter of esign, they cannot in practice go bankrupt. Secon, investors holing SPVs have privilege access to information about the proceeings of the assets composing the SPVs. First, with respect to bankruptcy remoteness, in the U.S. it is not possible to waive the right to use a bankruptcy proceure, but it is possible to structure an SPV so that there cannot be an event of efault that woul throw the SPV into bankruptcy. How? Accoring to (Klee an Butler 00) an (Gorton an Souleles 006), an SPV is a legal entity which has been set up for a specific, limite purpose by another entity (the sponsoring firm), an can take the form of a corporation, trust, partnership, or a limite liability company. The SPV may be a subsiiary of the sponsoring firm, or it may be an orphan SPV, one that is not consoliate with the sponsoring firm for tax, accounting, or legal purposes (or may be consoliate for some purposes but not others). An SPV is off-balance sheet of the sponsor firm if meeting the requirements set forth in Financial Accounting Stanar 140. To fulfill these requirements the SPV must be a separate an istinct legal entity from the sponsor (the sponsor oes not consoliate the SPV for accounting reasons). It must be an automaton in the sense that there are no substantive ecisions for it to ever make, just simply rules that must be followe. SPVs are essentially robot firms that have no employees, make no substantive economic ecisions, have no physical location, an cannot go bankrupt. That the SPV itself must (as a practical matter) never be able to become bankrupt is its most essential feature. As it is legally unenforceable for an firm to waive its right to file a voluntary bankruptcy petition, it can completely eliminate the risk of either voluntary or involuntary bankruptcy by creating the SPV in a legal form that is ineligible to be a ebtor uner the U.S. Bankruptcy Coe. The SPV can be structure to achieve this result. As (Klee an Butler 00) highlight, the use of SPVs is simply a isguise form of bankruptcy waiver. 8

9 Even though uner accounting an regulatory rules sponsors are not suppose to provie support, still this support is recognize by U.S. bank regulators who usually refer to it as implicit recourse or moral recourse: the provision of creit support, beyon contractual obligations. (Gorton an Pennacchi 1995)) iscusse the issue of implicit recourse in financial markets in the context of the bank loan sales market an provie empirical evience for its existence. Secon, investors have access to proprietary information about the proceeings of the pool. As escribe by (Plantin 009), a number of securities, such as securitize pools of loans, are not trae publicly but are sol to institutional investors who, from then on, receive from the issuer information that is not publicly available. Thus, investors in such privately place securities buy a bunle comprise of not only a claim to future cash flows but also a flow of future privilege information about these cash flows. References Gorton, Gary, an George Pennacchi Bank an Loan Sales: Marketing Non- Marketable Assets. Journal of Monetary Economics 35 (3): Gorton, Gary, an Nicholas Souleles Special Purpose Vehicles an Securitization. In Risks of Financial Institutions, eite by Rene Stulz an Mark Carey, University of Chicago Press. Klee, Kenneth, an Brent Butler. 00. Asset-Backe Securitization: Special Purpose Vehicles an Other Securitization Issues. Uniform Commercial Coe Law Journal, no. 35:3 67. Plantin, Guillaume Learning by Holing an Liquiity. Review of Economic Stuies 76 (1):