The Liquidation Decision

In this section I analyze the originator’s liquidation strategy at date 2 for both resale structures. Like in the benchmark case, the originator obtains control and has to decide whether to liquidate the loan whenever the borrower fails to meet its interest payments at date 2. I want to answer the following questions in this section: Are there any di¤erences in the liquidation decision between the two structures? And, will there be any ine¢ cient behavior as compared to the benchmark case? To answer these questions I …rst derive the originator’s date 2 expected pro…ts and then compare the liquidation decisions under syndication (Proportionate Sale) and securitization (First Loss Provision).

With a Proportionate Sale (PS), date 2 expected pro…ts are given by

E t=2_{P S;L} = (1 ) D; (1.4)

E t=2_{P S;C} = (1 ) [p+ (1 p) ]D: (1.5)

Note that the originator’s date 2 expected pro…ts with PS are proportionate to the expected pro…ts in the benchmark case. This is due to the fact that the originator holds a proportionate fraction (1 ) of the total loan.

With a First Loss Provision (FLP), date 2 expected pro…ts are given by

E t=2_{F LP;L} = max_f0; ( )D_g; (1.6)

As the originator’s share (1 ) in the loan is subordinate to the external investor’s share , liquidation only entitles him to the surplus of the liquidation value after the external investor has been paid o¤. If the liquidation value is too low, the originator receives nothing. Continuing the loan, on the other hand, gives the originator the chance (with probability p) of a full repayment; with the probability of (1 p) he obtains nothing, since < .

In this section I introduce a further hypothetical resale structure, which I call a Last Loss Provision (LLP). The LLP structure di¤ers from the FLP structure only in that the originator keeps the senior part of the debt and sells the junior equity tranche.26 As will become clear further down, considering LLP leads to a better understanding of the incentive e¤ects associated with a senior/subordinate structure.27

With a Last Loss Provision, the originator’s pro…ts would be given by

E t=2_LLP;L = min_f ; _gD; (1.8)

E t=2_LLP;C = [p + (1 p) ]D: (1.9)

Liquidating the debt yields the originator a safe payment of at least min_f ; _gD: If the liquidation value is relatively high, his fraction in the debt is completely safe. On the other hand, if the originator decides to continue the loan, he runs the risk (with probability of (1 p)) of obtaining the lower payment of D < D.

Under all resale structures the originator chooses the action (to liquidate or to continue) that maximizes his date 2 expected pro…ts. Hence, he liquidates a non- performing loan at date 2 whenever ei; with i = P S; F LP; LLP (derivation see Appendix). ei is given by

e_{P S} = e_{N S} =p+ (1 p) ; (1.10)

e_{F LP} = p+ (1 p) ; (1.11)

e_LLP = p+ (1 p) : (1.12)

By comparing these threshold levels I derive the following Proposition (for a graphical

26_{In order to keep the modeling as simple as possible, I assume that the sizes of the tranches are the}

same under LLP and FLP. Of course, in this case, the regulatory capital relief under LLP would not be the same as under FLP. However, as the main insights derived here carry forward to a modeling with more accurate fractions, it su¢ ces to consider identical fractions.

27_{Interestingly, there is no real world instrument of credit risk transfer which resembles this LLP}

structure in its pure form. However, in the context of synthetic CDOs there are arrangements which incorporate elements of this structure. These are discussed in more detail at the end of chapter 1.6.2.

illustration see Appendix):

Proposition 1.2 The originating bank’s liquidation strategy is always e¢ cient under a Proportionate Sale (PS). Under a First Loss Provision (FLP) the originator ine¢ - ciently continues the loan for eN S < eF LP. Under a Last Loss Provision (LLP)

he ine¢ ciently liquidates the loan for eLLP <eN S.

Proof:See Appendix.

For very low and very high liquidation values all resale structures lead to e¢ cient continuation (for < e_LLP) or liquidation (for e_{F LP}) as in the benchmark case. In these cases the liquidation pro…ts are so low (high) that it is optimal to continue (liquidate) the loan –irrespectively of the resale structure employed.

However, Proposition 1.2 shows that for intermediate levels of the originator’s liquidation incentives are distorted for senior/subordinate resale structures. Consider FLP …rst: The originator ine¢ ciently continues the loan under FLP whenever e_{N S}

< e_{F LP}. For this intermediate level of the liquidation value he has an incentive to "gamble for resurrection". What is the underlying reason? Consider for example the originator’s liquidation decision at e_{N S} = p+ (1 p) . At e_{N S} expected total repayments are equal under liquidation and continuation and hence both strategies are equally e¢ cient. Under FLP, the originator holds the junior tranche and only receives the surplusmax_f0; [p+ (1 p) ]D_gin case of liquidation. With < and hence p+ (1 p) < p+ (1 p) ;this is unambiguously lower than his expected pro…ts under continuation of p(1 )D. Thus, if the liquidation value is not too large, liquidating the debt would give the originator only negligible pro…ts (if any at all). For these liquidation values he prefers to play for the (small) chance of a full repayment under continuation instead of settling for the negligible certain liquidation pro…t.

Under LLP, the originator ine¢ ciently liquidates the loan for eLLP < eN S. In this case he is the …rst to be repaid and prefers to enjoy his certain intermediate repayment rather than running the risk of the very low repayment of D. Thus, as opposed to FLP, the originator would intervene and liquidate the debt too often.

Both for FLP and LLP the distortions in the liquidation decision arise due to the senior/subordinate structure of the debt. As the senior debtholder is paid o¤ …rst, holding a subordinate fraction in the loan renders the bank too soft on the borrower, whereas holding a senior fraction makes him too tough.

Interestingly, under PS, the e¢ cient liquidation strategy is attained irrespective of the liquidation value. This is due to the fact that under PS the originator has a proportionate share in the underlying debt and hence prefers the structure generating higher overall returns.