Writing-down debt with heterogeneous creditors: lock laws and late swaps 1. Sayantan Ghosal and Marcus Miller. October, 2015

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1 Writing-down debt with heterogeneous creditors: lock laws and late swaps 1 Sayantan Ghosal and Marcus Miller University of Glasgow University of Warwick & CEPR October, 2015 Abstract The presence of holdouts in recent sovereign debt swaps poses a challenge to bargaining models with homogeneous creditors. We modify the Rubinstein alternating offers framework so as to accommodate exogenous creditor heterogeneity - specifically holdouts more patient than other bondholders. The second best equilibrium outcome derived is an initial offer and an associated lock-law sufficient to tempt impatient creditors into a prompt bond exchange. This is followed by a delayed, but more generous, swap with the patient creditors, timed to take place when the lock-law expires. In practice, however, the presence of patient holdouts is endogenous, late-comers who buy distressed bonds with a view to litigating for the full face value plus their costs of waiting. Provisions for protecting the debtor and other bond holders from the negative externality caused by such tactics are discussed. JEL Classification: F34, C78. Keywords: sovereign, debt, holdouts, lock law, signalling, externalities, aggregation, restructuring. 1 The paper has benefitted from discussion with Stephany Griffith-Jones, Jay Newman, Sebastian Soler, Leonardo Stanley and Dania Thomas and comments received at seminars at Warwick University and Columbia University. The usual disclaimer applies. 1

2 1. Introduction In the current paradigm, sovereign debt restructuring by debt swaps or otherwise - is treated as an integral part of the risk-sharing involved in sovereign lending, Obstfeld and Rogoff (1996, Chapter 6) 2. For domestic junk bonds, the risk-spread over Treasuries is expected to cover the potential effects of restructuring or liquidation under a bankruptcy code administered by a judge. So, by analogy, the sovereign debt write-downs involved in a crisis should, in principle, be balanced by risk-premia paid in non-crisis states of the world. The writing-down of sovereign debt obligations is much more problematic, however, as they have to be restructured by negotiation between the sovereign and its creditors. In their classic paper on debt-recontracting, Bulow and Rogoff (1989) proposed an elegant solution: that the Rubinstein alternating-offers model be used to characterise these negotiations and to predict their outcome. In this framework, the settlement essentially depends on the relative impatience of debtor and creditor (i.e. how their subjective rates of discount compare); and, with complete information, it is achieved without delay. The presence of holdouts in recent debt swaps, i.e. creditors who do not accept a swap which has been taken up by other exchange bond holders, implies, however, that creditors are heterogeneous. Can the alternating-offers bargaining approach still be used? We show that it can be adapted appropriately where such heterogeneity is exogenous - when, for example, the population of creditors, independently of the crisis, happens to be divided between some who are patient and others who are impatient. Specifically, we show that, given the type of individual creditors is not known to the debtor, there is a role for more than one debt swap, each tailored to attract a different type of creditor, with lock laws put in place to ensure that the swaps get taken up by the creditors for whom they are intended. These lock laws correspond to the Rights Upon Future Offers ("RUFO") clauses used in practice, which (as the name implies) ensure that creditors who have agreed to an 2 The insurance that is extended to the debtor in this way will, however, be limited for familiar reasons - moral hazard and adverse selection. 2

3 earlier swap can, for a determined period, participate in later swaps if they so desire 3. In the two-creditor case of Section 2, the outcome derived is an initial offer which, together with the RUFO clause, is sufficient to tempt impatient creditors (the exchange bondholders) into a prompt bond swap. This is followed by a delayed - but more generous - swap with the patient creditors (the holdouts), timed to take place when the lock law expires. The waiting-time involved before the second swap represents a loss in bargaining efficiency; but it functions as a costly signal to identify the more patient creditors. The theoretical question we address is whether such clauses can lead to second-best or constrained efficient outcomes in the presence of creditor heterogeneity 4. We find that there are, in fact, multiple equilibria; but a second-best benchmark can be derived. A simple calibration of such a benchmark settlement is provided to illustrate how the shares of creditors and debtor and the duration of the RUFO clause change as the degree of creditor heterogeneity increases specifically as the holdouts become more patient. The presence of a holdout whose discount rates are lower than the discount rates of the debtor and the exchange bondholder not only reduces both their shares in the bargaining surplus: it also delays substantially the earliest point in time (corresponding to the second-best delay benchmark) at which the debtor is able to access its share of the surplus. In our model, patience is power. (The welfare losses if the debtor and the holdout are unable to coordinate on the second-best benchmark also increase with the patience of the holdout.) An important caveat is considered in Section 3, namely that the presence of holdouts may be induced by the crisis: they may be late-comers who buy distressed bonds with a view to holding out for better terms than first on offer. In fact some of the late-comers the so-called vulture funds - aim to recover all their waiting costs, including those of delay and of litigation; and their activities (which typically involve insistent attempts 3 In the initial debt swap of 2005, where only about 70% of the bonds were exchanged, the Argentina sovereign added a RUFO clause (ratified in Parliament) to assure those in the bond exchange that they would have access any improved offers made over the following decade. Further details on the Argentine case are to be found in Annex 2 4 The first best would require contrary to what we assume that the debtor knows the type of each creditor. 3

4 to seize debtor assets) can seriously disrupt the process of debt restructuring. We do not model the aggressive litigating strategies of vulture funds. But we do make use of the results obtained earlier to model the endogenous entry of latecomer creditors; and show how their presence in the debt restructuring process imposes a negative externality on the debtor and other creditor(s) involved in debt restructuring. We go on to discuss provisions for protecting other bond-holders from the negative externality caused by the activities of aggressive vulture funds. These include adding aggregation clauses to the Collective Action Clauses now included in sovereign debt contracts; the regulation of secondary debt markets; finding substitutes for US-law bonds; creating some form of SDRM; and promoting soft law. In conclusion, however, we suggest that the second-best bargaining scenario we outline may be useful in finding a basis for a compromise with holdouts ex post. The recovery rate and the waiting time so derived will, of course, fall far short of the punishing claims typically pursued by vulture funds. But they should, we believe, describe fair compensation for pre-existing creditors who holdout simply because they are more patient than those keen to settle without delay. This may be useful for an adjudicator charged with finding a just accord. 2. Patience as power: negotiating a write-down with heterogeneous creditors 2.1 Exogenous creditor heterogeneity To characterise debt renegotiation, Bulow and Rogoff (1989) adopt the alternating offers approach of Ariel Rubinstein, where two parties bargaining over fractions of a pie in principle take it in turns to propose how it be shared; and it is the relative impatience of debtor and creditor to achieve a settlement that determines the outcome. (Broadly speaking, the pie could be thought of as the face value of the debt to be restructured, with the fraction retained by the sovereign debtor indicating the writedown involved in restructuring.) 5 In the light of significant numbers of holdouts who - in the case of Argentina for example - decline to enter the initial swap, some modification of this bilateral approach 5 This bilateral approach was indeed applied by the current authors to analyse the Argentine debt swap of 2005 (in Dhillon et al. 2006). 4

5 is called for. Here we show how the alternating offers approach may be extended to accommodate creditor heterogeneity. Alternating Offers with delayed swap for more patient creditors For simplicity, consider the case of a sovereign debtor negotiating with two creditors. The debtor, denoted by D has a discount rate δδ DD > 0 and associated discount factor ee δδ DD tt, where tt (which can be assumed to be negligibly small) is the minimal time interval between two successive rounds of bargaining 6. The creditors, denoted by XX for the Exchange bond holder, and by HH for the Holdout, are distinguished by their discount rates 0 < δδ HH < δδ XX (with associated discount factors ee δδhh tt > ee δδxx tt ). We assume that each creditor knows its own discount rate; but the sovereign does not know who is which. At each t, the debtor and the two creditors must decide whether or not to settle. If both the debtor and one of the two creditors 7 agree to settle, then bargaining proceeds according to Rubinstein alternating offers bargaining game where the debtor makes the first offer; once an agreement has been reached, the creditor exits the process with a payment equal to the settlement offer. A lock law (the RUFO clause) effectively bans any improved offer to the other creditor for TT periods (to be derived as part of the equilibrium calculations). At TT, the remaining creditor and the debtor must choose whether or not to settle. Once they do so, bargaining proceeds according to Rubinstein alternating offers bargaining game; once an agreement has been reached, the creditor exits the process with a payment equal to the settlement offer. We focus on Perfect Bayesian Equilibria 8 where strategies and beliefs are configured so that (i) the debtor and the exchange bond holder choose to settle immediately and agree to a split; (ii) after the specified period of waiting time TT implied by the RUFO 6 All our results are stated for the case when tt is negligibly small at the continuous time limit as tt 0. 7 If both creditors agree to settle, one of the two is chosen, with equal probability, to bargain with the debtor. 8 In Appendix 1, we show all the Perfect Bayesian Equilibria of the bargaining game where tt is strictly positive but close to zero involve delay. It follows that, at the continuous time limit as tt 0., the minimum delay compatible with a pure strategy Perfect Bayesian equilibrium is the second-best benchmark derived below. 5

6 clause elapses, the debtor and the Holdout creditor choose to settle immediately and agree to a split (iii) the beliefs are such that debtor believes with probability one that (a) the creditor who chooses to settle at tt = 0 is the exchange bond holder and (b) the creditor who chooses to settle at tt = TT is holdout. (Note that the equilibrium concept requires consistency between beliefs and actions so that we need to check that appropriate incentive constraints are satisfied for both creditor types.) For convenience the bargaining surplus (the potential gains to debtor from reaccessing capital markets) is taken to be constant and normalised to one. A useful simplification is that it is possible to solve for the shares of the two creditor types separately from the deriving the waiting time implied by the incentive constraints. To derive the shares, note that after the period TT > 0 waiting time, there is only one creditor present so, given the initial offer ss XX which has been accepted by the Exchange bondholder, the bargaining surplus remaining is 1 ss XX. Consider, next, the complete information bargaining game between the debtor and the Holdout at time TT: a straightforward calculation shows that as tt 0, there will be immediate agreement where (at the limit) the share of the Holdout is ss HH = δδ DD δδ DD +δδ HH (1 ss XX ). Likewise, at tt = 0, in anticipation that ss HH will be committed to the Holdout creditor, the offer (at the limit as tt 0) made by the debtor to the Exchange bondholder (and immediately agreed to) is ss XX = δδ DD δδ DD +δδ XX (1 ss HH ). So, at the limit as tt 0, the shares may be derived as depending simply on the discount rates: ss XX = δδ DD δδ HH δδ DD (δδ XX +δδ HH )+δδ XX δδ HH, ss HH = δδ DD δδ XX δδ DD (δδ XX +δδ HH )+δδ XX δδ HH. In order to calculate the waiting time, at the limit as tt 0, we need to consider the relevant incentive compatibility conditions, namely: ss HH ee δδ XXTT ss XX ; ss HH ee δδ HHTT ss XX 6

7 where ss XX and ss HH are defined as above and δδ XX is the discount rate of the Exchange bondholder, δδ HH is the (lower) discount rate of the Holdout. The first inequality implies that the offer to the Holdout, discounted back at the discount rate of Exchange holder, leaves the latter content with early settlement, with no incentive to join the Holdout. The second inequality implies that the Holdout creditor has no incentive to deviate and join the Exchange bondholder to settle early. The key feature of the two-stage procedure is that the Holdout has to wait, being induced to do so by an offer which will be better than that accepted by the impatient Exchange bondholder who settles early, i.e. ss HH > ss XX. Why should the Exchange bond holder accept an initial offer from the debtor, when the latter is free to settle later with the Holdout? Why not delay acceptance to get a higher offer? How long will the Holdout have to wait? This is where the mechanism of the RUFO clause 9 plays a key role. Such a clause, a lock-law which prevents the debtor from giving a more attractive offer exclusively to the holdouts for a fixed period, reassures the creditor who settles early; and effectively allows the more patient creditor to give a costly signal of his/her type. Ideally, the expiry of the clause defines the shortest period of waiting acceptable to the more patient creditor, but not the impatient type. It is implicitly assumed that the swap will remain open for those who have not settled either (in line with RUFO) to accept the terms first agreed: or to negotiate better terms when the RUFO expires. Let TT > 0 be the solution to ss HH ee δδhhtt = ss XX ; and let TT be the solution to the equation ss HH ee δδ XXTT = ss XX. Then, at the limit as tt 0, in equilibrium, waiting time T TT, TT where (i) TT is the earliest point in time at which a second-offer will be made to the holdout (the second-best benchmark), and (ii) TT is the maximum time the holdout is willing to wait for an offer by the debtor. Therefore, an agreement is reached at some 9 The RUFO clause is a form of most favoured creditor clause indicating that, over a specified horizon, any improved offer made to the holdouts must be made available to the exchange bondholders as well. 7

8 T > TT, T TT, is the result of a form of coordination failure between the debtor and the holdout over agreeing when to settle 10. We may depict all the equilibria at the limit as tt 0 in Figure 1 where the ratio ss HH ss XX is measured on the y- axis and time on the x-axis; and the discount factors of the two creditors show how much more patient is the holdout. Figure 1 Creditor shares and the waiting time Note first that the incentive conditions immediately imply the relative shares shown by the horizontal line where higher its share. ss HH ss XX = δδ XX δδ HH, i.e. the lower the discount rate of the holdout the Note second that TT, the constrained-efficient RUFO clause, is the point at which the Exchange bond-holder s incentive constraint is satisfied as an equality; while TT is the point at which the Holdout creditor s incentive constraint is satisfied as an equality. So, in equilibrium, delay can be for any length of time TT [TT, TT ]; and we discuss later 10 There are other Perfect Bayesian Equilibria which involve coordination failure between the debtor and both the exchange bondholder and the holdout creditor. These are described in Appendix 1. 8

9 circumstances under which the debtor might want to commit to protracted negotiations. Observe that as δδ HH becomes smaller (so that the Holdout creditor is more patient), the curve depicting ee δδ HHTT swivels anti-clockwise from 1 on the y-axis; and the line showing the relative shares moves down. Therefore, TT is increasing in δδ HH : i.e. the more patient is the Holdout creditor, the longer is the delay associated with any equilibrium of the debt restructuring game. Note that creditor heterogeneity is crucial for obtaining equilibrium delay in our model: if both creditors are identical, then there will be no delay in the continuous time limit. This can be seen in the above diagram where if δδ HH = δδ XX, ss HH ss XX = 1 and the two exponential curves coincide and intersect the line depicting ss HH ss XX delay. at 1, so there is no Although the model is stated for the case with two creditors, this analysis can be extended (see Appendix 1.2) to cover the case where there are many creditors but only two types (distinguished by different discount factors and/or waiting costs). However, the debtor, who does not know which creditor is of which type, is assumed to know the overall distribution of creditors over the two types 11. The simple model studied here, then, corresponds to the case where the proportion of creditors of each type is one half each and the debtor bargains with a representative creditor from each type Calibration: Next, we provide a simple calibration to quantify some of the comparative statics already described above. Given that the real interest rate of much developing country debt is 5% p.a., we set the discount rate of the debtor and the exchange bondholder at 0.05 i.e. δδ DD = 0.05 = δδ XX. 11 For the purpose of discussion, we leave on one side the role of third parties, like the IMF. In Appendix 1, we present the solutions for the case with NN creditors where a proportion αα are exchange bondholders and a proportion (1 αα) are holdouts, 0 αα The assumed proportion of creditors of each type need not be a half. In Appendix 1, we show that reducing the proportion of holdouts will reduce their shares; but equilibrium delay depends on the relative patience the holdout with respect to the exchange bondholder. 9

10 As a benchmark, consider, first the case when δδ HH = 0.05 = δδ XX. In this case, at any Perfect Bayesian equilibrium, agreement occurs at tt = 0 and ss XX = ss HH = ss DD = 1, where 3 ss DD denotes the Debtor s share 13. We vary the discount rate of the Holdout creditor 14 and in the table below report the second-best equilibrium delay TT, the maximum equilibrium delay TT compatible with coordination failure between the Debtor and the Holdout over when to settle, the share of the Holdout ss HH, the share of the Exchange bondholder ss XX and that of the Debtor ss DD. TT TT ss HH ss XX ss DD δδ HH = δδ HH = years 2.5 years δδ HH = years 5.5 years δδ HH = years 10 years δδ HH = years 17 years δδ HH = years 28 years δδ HH = years 80 years δδ HH = years 460 years Table 1: Calibration of the benchmark waiting time and creditor shares These results are illustrated in Figure 2 with the debtor s share measured on the vertical axis, Exchange bondholder s to the right and that of the Holdout to the left. 13 In general ss DD = 1 ss XX ss HH = δδ XX δδ HH δδ DD (δδ XX +δδ HH )+δδ XX δδ HH. 14 In Appendix 1 we report the algebra underpinning the comparative statics with respect to δδ HH.. 10

11 S D S H 1 1 S X Figure 2 Settlement shares for an increasingly patient Holdout creditor The points all lie on a simplex whose corners indicate outcomes most favourable to each of the participants in turn. The outcome with no creditor heterogeneity, where all participants get a third, is shown with the label 0 to indicate zero delay. The effect of increased patience on the part of the Holdout is shown by the arrow heading towards the lower left corner, with the second-best delay times in years indicated by the numbers 0, 10,,. Evidently the Holdout gains at the expense of both the Exchange bondholder and Debtor as heterogeneity is increased; and, in the limit, the Holdout takes all. Numerically, we see from the table that as δδ HH drops below 0.05 to 0.045, for example, the shares of the Exchange bondholder and debtor both fall to 0.32; the Holdout gets 36% of the bargaining surplus and agreement with the Debtor occurs after a delay of 2 years in the second-best setting. The maximum equilibrium delay resulting from coordination failure between the debtor and the Holdout creditor over agreeing when to settle in this case, as shown in the table, is 2.5 years; as the gap between the two isn t too large, the failure to coordinate on the second best will result in small welfare losses. 11

12 But as the Holdout creditor becomes more patient relative to the Exchange bondholder and the debtor, their shares drop monotonically and agreement between the debtor and the Holdout creditor occurs after a longer period of second-best delay. As the gap between the latter and the maximum delay also increases, moreover, failure to coordinate on second-best could lead to larger welfare losses. To generate a second-best delay of 10 years (corresponding to the lock law passed by the Argentine parliament in 2005, when the first batch of bond-holders settled), one would need to assume δδ HH = As δδ HH drops towards zero, the second-best delay increases exponentially (as does the gap between it and maximum equilibrium delay) and the share of the Exchange bondholder and the Debtor falls towards zero with share of the Holdout increasing towards one. Two key insights emerge from the calibration exercise. First, the Holdout gains at the expense of both other parties. This is consistent with Judge Griesa seeing the value of holdouts for the maintenance of creditor rights in general, as discussed in Miller and Thomas (2007); but it offers small comfort to the Exchange bondholder, who loses out. Second, the more patient the Holdout, the greater are the signalling costs of handling creditor heterogeneity, i.e. the delay that falls upon the debtor. (The gap between the second best and the maximum delay driven by coordination failure between the debtor and the holout creditor over the decision to settle also increases, indicating greater welfare losses associated with such failure to coordinate the settlement decision.) 3. An important caveat: endogenous entry (a) Patient latecomers So far, the heterogeneous composition of the creditor group has been taken as exogenous: there just happen to be differences in discount rates between Holdouts and the rest. Taking these differences as predetermined, we have looked for a constrained efficient equilibrium outcome. But what if the participation of the holdouts is endogenous? What if they are patient latecomers joining the creditor pool by buying 15 As a 10 year delay also corresponds to the maximum equilibrium delay resulting from coordination failure between the debtor and the holdout creditor when δδ HH = 0.035, this evidently represents a welfare-dominated scenario. 12

13 distressed bonds when restructuring is expected? This is what we analyse here in the context of the simple model outlined above, Before new entry, suppose that there are two Exchange bondholders with the same discount rate; and debt restructuring is anticipated. A straightforward implication of the formulae shows that there will be immediate settlement and both Exchange bondholders will obtain ss XX = δδ DD 2δδ DD +δδ XX, as in the top line of the Table above. Now, suppose a late-comer with a lower discount rate approaches one of the Exchange bondholders (the debtor does not know which one) and offers ss XX + εε (where εε > 0 can be negligibly small) before bargaining begins. Suppose the Exchange bondholder sells its claim to the distressed bond to the late-comer who now takes its place in the bargaining game as a Holdout creditor and obtains ss HH with a delay of TT periods. It follows that as long as ss HH ee δδ HHTT > ss XX the Holdout creditor will buy out the Exchange bondholder and enter the bargaining game with the exchange bondholder and the Debtor. Let TT denote the maximum delay that the patient creditor can tolerate given the price paid for entry, i.e. it is the solution to the equation ss HH ee δδhhtt = ss XX.Then, as long as TT > TT, the a second-best equilibrium of the debt restructuring game, it follows that entry will occur, if the endogenous patient creditor anticipates such an outcome,. As both ss HH and TT are increasing in δδ HH, it isn t evident that TT > TT. To illustrate that this is a robust possibility, we may use the calibration results already reported above, fixing δδ DD = δδ XX = If δδ HH = 0.04, then, TT = 3.5 < TT = 4.5: in this case, the no entry occurs. But if δδ HH = (so that the holdout is twice as patient as the exchange bondholder and the debtor) then, TT = 16 > TT = 14. Thus, if the late-coming creditor is sufficiently patient relative to both the debtor and the Exchange bondholder, there will be entry given anticipation of second-best equilibrium. In such a case, the Holdout creditor will be able to recover a greater portion of the debt at the expense of the other parties, and in the process generate costly delay in the bargaining game, imposing a negative externality on both the debtor and the remaining Exchange bondholder. 13

14 Interestingly, it turns out that the patient creditor s decision to enter depends on the equilibrium anticipated in the debt restructuring game. For as ss XX > ss XX, it follows that TT < TT, i.e. because the latecomer has to buy out one of the existing creditors, the maximum delay the latecomer can tolerate is less than the upper limit on time-to-settle for bargaining without entry. If the equilibrium anticipated is one entailing such protracted negotiations between the debtor and the Holdout, then no entry will occur as TT < TT. So if the debtor could commit to a strategy where such coordination failure is built in (i.e. the debtor announces it will delay settlement till the maximum equilibrium delay is reached), entry will not occur! (In this respect the implementation of a decadelong RUFO clause by the Argentine government in conjunction with the debt swap of 2005, may have created a useful precedent: it was made to look like daunting delay.) We can moreover extend the analysis to the more realistic case where it is only a small fraction of the existing pool of creditors who holdout. From the results reported in Appendix 1.2 for the N creditor case, we know that TT only depends on discount rates of the Exchange bondholder and the Holdout creditor; so we can continue to use the calibration calculations reported above. Let NN = 50, for example, and suppose, to begin with, all the creditors in the pool are Exchange bondholders. Assume a Holdout creditor buys out just one of the 50 Exchange bondholders; and as in the calibration exercise, fix δδ DD = δδ XX = In this case, before the entry of the holdout creditor, each Exchange bondholder expected to obtain a share of 1 NN+1. If δδ HH = (so that, as before, the Holdout creditor is twice as patient as the both the Debtor and the representative Exchange bondholder) then ss HH = and TT = 26 > TT = 14. So a holdout creditor who obtains a small fraction of the overall bargaining surplus and is sufficiently patient relative to the remaining exchange bondholders and the debtor can continue to impose a significant negative externality on all other participants in the debt restructuring process. (b) Litigenous latecomers so-called vulture funds Can the endogenous entrants who buy distressed debt in anticipation of debt restructuring as analysed above be interpreted as what are called vulture funds? Consider, for example, what Martin Kanenguiser (2014), in a recent contribution 14

15 mainly critical of the Argentine government, says of the methods and objectives of such funds: The vulture funds, like many other investor funds, bought Argentine bonds a little before and a little after the default at a very low price. But, unlike the other investors who buy these bonds cheap to make some profit when the country does better, the mission of the vultures is to litigate so as to recover 100% of the value of the debt. For this reason they focus on maintaining a team of expert lawyers rather than economists and prefer to wait and collect rather than on negotiating a write-down. (italics added) 16 If the motivation of these funds is as described that they buy bonds in order to collect full repayment at whatever the consequences may be in terms of delaying the restructuring and y pursue their objective with relentless harassment then there is evidently more than just extra patience involved. It should be noted that, for vulture funds who enter the pool of creditors by purchasing sovereign bonds at distressed prices, their objective of 100% recovery with costs is only feasible for a minority of creditors; and is achieved part by diverting resources from other creditors and from the debtor, using legal strategies that may involve prolonged delay 17. In our model, patience is power and is the sole driver of inefficient delay in the debt restructuring process. We do not explicitly model aggressive behaviour and the impact such tactics have on other participants in the debt restructuring process. In courts of law, such funds may claim to be patient creditors simply seeking to assert their contractual rights. A just accord is what Robert Shapiro, a spokesperson for the holdouts, says that they seek (see Appendix 2 A) 18.But this is belied in practice by the relentless pursuit of inventive tactics for seizing assets of the debtor, tactics for which vulture funds have become world-famous, Burgueno (2013). 16 How appropriate this description may be can be checked by examining past activities of these funds. The account given in Chapter 7 of Kanenguiser s book does imply a business model of buy and collect by determined litigation is plausible for at least for two of the principal funds involved. 17 Note that an efficient punishment strategy for a rogue debtor would also involve tranfsers from the debtor but without long delay and not from other creditors. 18 In Appendix 2, we also sketch a brief history of the Argentine debt restructuring where we note that key elements of that, as yet, incomplete debt restructuring process differ from the assumptions made in our formal model of bargaining with creditor heterogeneity. 15

16 Hence a different approach will be appropriate, taking deliberate steps to dissuade them from buying distressed bonds in the first place. The obvious strategy for limiting the negative externalities imposed on the debtor and other creditors is to empower a super-majority to cram down on all creditors a settlement they find acceptable. That is typical of domestic bankruptcy law that governs the restructuring of commercial debt. As noted by Buchheit and Gulati (2002), Collective Action Clauses were inserted into English-law corporate bonds in the nineteenth century to outwit socially inefficient holdout behaviour. In the next section we discuss analogous steps currently being made to check those who would disrupt sovereign debt restructuring for their own private benefit. (c) Changing the rules to block vulture funds The principal response by the institutions directly involved has been to enhance the operation of the Collective Action Clauses (CACs) now commonly included in sovereign debt contracts. To block the strategy of vulture funds who - to avoid being crammed down by others acquire super-majority holdings of individual series of bond issues, aggregation clauses have been proposed which would be to allow a super-majority of all bond holders to over-rule intransigent holdouts in accepting a restructuring. A boiler-plate for CACs modified in this respect has been prepared by ICMA, endorsed by the International Monetary Fund, see IMF(2014), and has already been included in new bond issues by significant sovereign borrowers such as Mexico. One possible development is the use of substitutes for US-law bonds, now subject to the precedent of Judge Griesa s ruling (that the claims for full settlement by holdouts be treated pari passu with those of exchange bondholders in possession of restructured bonds). These substitutes could be dollar bonds issued in other familiar jurisdictions, such as London or Paris. Should the UK or France be reluctant to challenge the US ruling in this way, however, new entrants like Shanghai may be ready to do so, as J. Stiglitz has suggested. It might also involve the issue of dollar bonds under local law, as proposed by Sebastien Soler Could such prospects have helped motivate the amicus curiae brief supplied by the US Treasury opposing the pari passu doctrine endorsed by Judge Griesa? 16

17 Other initiatives have been proposed, though they still remain on the drawing board. One of these is for institutional change at a regional level e.g. European Treaty changes which could protect the claims of creditors engaged in good faith negotiations, an initiative discussed in Miller and Thomas (2013). Another, much more ambitious, is to revive the idea of a Sovereign Debt Restructuring Mechanism at a global level, as in the development of an international bankruptcy court, an initiative currently being considered by the UN. Finally, there is the evolution of soft law where anti-social practices are branded as such, with attendant reputational costs - and possible reverse discrimination. 4. Conclusion In the Rubinstein model of bargaining, only relative patience matters in dividing up the bargaining surplus between the debtor and its creditors: yet settlement is reached without delay. With heterogeneous creditors and asymmetric information, however, we show that delay is necessary for the more patient creditors to signal their claim to a greater share. The bargaining approach we use does not incorporate the aggressive legal tactics used by so-called vulture funds, opportunistic late-comers who seek the full face value plus their costs of waiting; but it may nevertheless be useful for an adjudicator charged with finding a just accord 20. It implies there should indeed be a patience premium in a second swap, but there is no case for awarding the legal costs of debtor harassment. On the contrary, there are good reasons to dissuade late entry by those seeking profits from what is essentially a zero sum game. As for corporate Insolvency, the other creditors need the power to block holdouts who generate negative externalities. 20 This, according to Robert Shapiro, is what the vultures seek: For more than a decade we have been seeking what any other creditor seeks after sovereign default: the chance to negotiate a just accord. Kanenguiser (2015, p.150) 17

18 In future research, we plan to extend the model to take explicit account of aggressive legal tactics, and their consequences for debt restructuring; to allow for the bargaining surplus to evolve over time; and to study a more general distribution of creditor types. References Buchheit, L. and Gulati, G. M. (2002). Sovereign bonds and the collective will, Working Paper No. 34. Georgetown University Law Center, Washington D.C. Bulow, J. and K. Rogoff (1989) A constant recontracting model of sovereign debt, Journal of Political Economy, vol. 97, no.1, Burgueno, C. (2013) Los buitres. Buenos Aires: Edhasa Dhillon, A., J Garcia-Fronti, S. Ghosal and M.Miller (2006) "Debt Restructuring and Economic Recovery: Analysing the Argentine Swap," The World Economy, vol 29(4) IMF (2014) Strengthening the contractual framework to address collective action problems in Sovereign Debt Restructuring,IMF Staff Papers, Washington DC Kanenguiser, M, (2014) El default mas tonto de la historia Argentina. Buenos Aires: Planeta Miller, M. and D. Thomas (2007) The Judge, the vultures and creditor rights World Economy, 30(10), pp Miller M. and D. Thomas (2013) Sovereign debt restructuring: keeping the vultures at bay Oxford Review of Economic Policy, 29(4), pp Obstfeld, M. and K. Rogoff(1996) Foundations of International Macroeconomics. Cambridge MA: MIT Osborne M.J, and A. Rubinstein (1994), A Course in Game Theory. MIT Press Prat-Gay, A (2013) Amicus curiae brief to Second Circuit court. US Court of Appeals Appendix 1 Alternating offers: technical detail for the 2 creditor case; and generalisation of the bargaining model with N creditors Appendix 1.1: Further characterization of the 2 creditor case In this part of Appendix 1, as well as showing that any Perfect Bayesian equilibrium of the debt restructuring game involves delay, we point out the existence of other Perfect Bayesian equilibria, we provide additional technical detail to some of the comparative 18

19 statics reported in the main text, with Osborne and Rubinstein(1994) as recommended background reference. With creditor heterogeneity, any Perfect Bayesian Equilibrium must involve delay and the minimum delay compatible with a pure strategy Bayesian equilibrium is the one studied in the main text. We show that any Perfect Bayesian equilibrium must involve delay. Consider the debt restructuring game studied in the main text when the gap between two rounds in the bargaining is tt where 0 < tt < εε for some εε > 0. At any equilibrium with immediate agreement, the two creditors must obtain the same payoff; let SS HH denote this common δδ payoff. As tt 0, it follows that SS ss = DD δδ HH δδ = DD. Therefore, for every δδ DD (δδ HH +δδ HH )+δδ HH δδ HH 2δδ DD +δδ HH εε > 0, there exists εε 1 > 0 such that when the gap between any two rounds of bargaining is tt, 0 < tt < εε 1, SS ss εε. Both the exchange bond holder and the holdout creditor choose to settle at tt = 0 with probability one although only one of the two is selected to bargain with the debtor. Therefore, at a Perfect Bayesian Equilibrium with immediate agreement, the debtor must attach a probability 1 that the creditor who 2 is chosen to bargain with him is the exchange bondholder. Let SS XX denote the minimum offer that the exchange bondholder is willing to accept at a Perfect Bayesian equilibrium. At the continuous time limit as tt 0, by construction, ss XX is the minimum offer that the exchange bondholder is willing to accept. Therefore, SS XX ss XX as tt 0 and for every εε > 0, there exists εε 2 > 0 such that when 0 < tt < εε 2, SS XX ss XX + εε. Now, by construction, ss > ss XX so that there exists εε 3 > 0, εε > 0, εε > 0 such that when 0 < tt < εε 3, SS ss εε > ss XX + εε SS XX. But then there is a value of εε > 0 such that the debtor can make an offer which is εε less than SS: the offer made at tt = 0, is accepted by the exchange bondholder and not the holdout (who would prefer to wait tt and bargain with the debtor to obtain SS). In this way, the debtor obtains a higher share of the bargaining surplus. Therefore, for εε 3 > 0 such that when 0 < tt < εε 3, there is no Perfect Bayesian equilibrium with immediate agreement: any Perfect Bayesian equilibrium must separate the two types of creditors. It follows that, at the continuous time limit as tt 0, the minimum delay compatible with a pure strategy Perfect Bayesian equilibrium is the second-best benchmark derived in the main body of the paper above. Other Perfect Bayesian equilibria with longer delay due to lack of coordination between the debtor and creditor At the second-best equilibrium, TT = TT (the constrained efficient RUFO clause) but there will be other equilibria with TT < TT TT where delay is longer than is required in order to satisfy second-best incentive compatibility constraints: these equilibria result from a coordination failure between the debtor and the holdout creditor over the decision to settle. There are PBE as well (e.g. neither the debtor nor the exchange bondholder chooses to settle before for TT >0 quantum of time has elapsed; at TT 19

20 periods, the debtor settles with the exchange bondholder and after TT TT, TT periods, settles with the holdout creditor: by construction such equilibria involve longer delay than the second-best RUFO clause and result from a coordination failure between the debtor and both the creditors over agreeing when to settle. Comparative statics in δδ HH As T, e δht 0 and e δ HT is decreasing and continuous in T, there exists T > 0 such that whenever T T, s H e δ HT s X with equality when T = T. Further, as 0 < δ H < δ X, it follows that s H e δ XT < s X. Let T be the solution to the equation ss HH ee δδ XXTT = ss XX. Clearly, TT < TT. Therefore, at an equilibrium, the waiting time TT TT, TT. Moreover, for each TT TT, TT, given the strategies of the two creditors, the debtor cannot gain by deviating: any deviation on part of the debtor can only involve further delay which, given δδ DD > 0, the debtor dislikes. As ss XX is decreasing in δδ ss HH, it follows that HH TT is increasing in δδ HH. As both ss XX and ee δδ HHTT are decreasing in δδ ss HH, TT is increasing in HH δδ HH. Therefore, as δδ HH 0, both TT, TT are both increasing. Note that ss XX = δδ DD δδ HH δδ DD (δδ XX +δδ HH )+δδ XX δδ HH = δδ XX δδ HH δδ DD (δδ XX +δδ HH )+δδ XX δδ HH = δδ DD δδ DD δδ XX δδ HH +1 +δδ XX so that ss XX is decreasing in δδ HH. Finally, ss DD = δδ XX δδ DD δδ XX δδ HH +1 +δδ XX so that that ss DD is decreasing in δδ HH. Appendix 1.2: The NN creditor case In this part of Appendix 1, we study the bargaining model with NN creditors where a fraction αα are assumed to be exchange bondholders and a fraction (1 αα) are assumed to be holdouts, 0 αα 1. For convenience, we will assume that both αααα and (1 αα)nn are integers. As before, the bargaining surplus (the potential gains to debtor from re-accessing capital markets) is taken to be constant and normalised to one. With creditor heterogeneity, any Perfect Bayesian Equilibrium must involve delay We show that any Perfect Bayesian equilibrium must involve delay. Consider the debt restructuring game studied in the main text when the gap between two rounds in the bargaining is tt where 0 < tt < εε for some εε > 0. At any equilibrium with immediate agreement, the all creditors must obtain the same payoff; let SS denote this common δδ payoff. As tt 0, it follows that SS ss = DD. Therefore, for every εε > 0, there NNNN DD +δδ HH exists εε 1 > 0 such that when 0 < tt < εε 1, SS ss εε. All exchange bond holders and holdout creditors will choose to settle at tt = 0 with probability one although only one is selected to bargain with the debtor. Therefore, at a Perfect Bayesian Equilibrium with immediate agreement, the debtor must attach a probability αα that the creditor who is chosen to bargain with him is an exchange bondholder. Let SS XX denote the minimum offer that the exchange bondholder is willing to accept at a Perfect Bayesian equilibrium. At the continuous time limit as tt 0, by construction, ss XX (derived below) 20

21 is the minimum offer that the exchange bondholder is willing to accept. Therefore, SS XX ss XX as tt 0 and for every εε > 0, there exists εε 2 > 0 such that when 0 < tt < εε 2, SS XX ss XX + εε. It is easily checked that ss > ss XX so that there exists εε 3 > 0, εε > 0, εε > 0 such that when 0 < tt < εε 3, SS ss εε > ss XX + εε SS XX. But then there is a value of εε > 0 such that the debtor can make an offer which is εε less than SS : the offer made at tt = 0, is accepted by the exchange bondholder and not the holdout (who would prefer to wait at most (NN 1) tt, 0 < tt < εε 3, and bargain with the debtor to obtainss ). In this way, the debtor obtains a higher share of the bargaining surplus. Therefore, for εε 3 > 0 such that when 0 < tt < εε 3, there is no Perfect Bayesian equilibrium with immediate agreement: any Perfect Bayesian equilibrium must separate the two types of creditors. It follows that, at the continuous time limit as tt 0, the minimum delay compatible with a pure strategy Perfect Bayesian equilibrium is the second-best benchmark derived below. Second-best Perfect Bayesian Equilibria We focus on Perfect Bayesian Equilibria where strategies and beliefs are configured so that (i) the debtor and each exchange bond holder choose to settle immediately and whenever an exchange bondholder is matched to the debtor, a split of the bargaining surplus is immediately agreed to; (ii) after the specified period of waiting time TT implied by the RUFO clause elapses, the debtor and each holdout creditor choose to settle immediately and whenever a holdout is matched to the debtor, a split of the bargaining surplus is immediately agreed to; (iii) the beliefs are such that debtor believes with probability one that (a) the creditor who chooses to settle at tt = 0, tt,., αααα tt, is a exchange bond holder and (b) each creditor who chooses to settle at or after tt = αααα tt + TT is a holdout. Checking for consistency between beliefs and actions so that we need to check that appropriate incentive constraints are satisfied for both creditor types. In the continuous time limit as tt 0, each exchange bondholder reaches an immediate agreement with the debtor and after TT periods, each holdout reaches an immediate agreement with the debtor. As before, a welcome simplification is that it is possible to solve for the shares of the two creditor types separately from the deriving the waiting time implied by the incentive constraints. To derive the shares, note that after the period TT > 0 waiting time, there are only holdouts present so, given that ss XX has been accepted by each exchange bondholder and ss HH by each of the other holdouts, the bargaining surplus remaining for an individual holdout is 1 αααααα XX (1 αα)nn 1 ss HH. In the complete information bargaining game between the debtor and the holdout, at the continuous time limit, there will be immediate agreement where the share of the holdout is ss HH = δδ DD δδ DD +δδ HH 1 αααααα XX (1 αα)nn 1 ss HH. 21

22 Likewise, in anticipation that ss HH will be committed to each holdout creditor and ss XX will be committed to each other exchange bodholder, the offer made by the debtor to an individual exchange bondholder (and immediately agreed to) as tt 0 is ss XX = δδ DD δδ DD +δδ XX (1 (αααα 1)ss XX (1 αα)ss HH ). So the shares may be derived as depending on the discount rates, the number of creditors as well as the proportion of holdouts/exchange bondholders is: ss XX = δδ DD δδ HH δδ DD NN (1 αα)δδ XX +ααδδ HH +δδ XX δδ HH, ss HH = 22 δδ DD δδ XX δδ DD NN (1 αα)δδ XX +ααδδ HH +δδ XX δδ HH. Notice that ss XX = δδ HH as before. In the continuous time limit, the relevant incentive ss HH δδ XX compatibility conditions for each individual exchange bondholder and holout creditor is, as before: ss HH ee δδ XXTT ss XX ee δδ XXTT δδ HH δδ XX ; ss HH ee δδ HHTT ss XX ee δδ HHTT δδ HH δδ XX. where ss XX and ss HH are defined as above and δδ XX is the discount rate of the exchange bondholder, δδ HH is the (lower) discount rate of the holdout. Let TT > 0 be the solution to ss HH ee δδhhtt = ss XX ; and let TT be the solution to the equation ss HH ee δδ XXTT = ss XX. Then, at the limit as tt 0, in equilibrium, waiting time T TT, TT where (i) TT is the earliest point in time at which a second-offer will be made to the holdout (the second-best benchmark), and (ii) TT is the maximum time the holdout is willing to wait for an offer by the debtor. Therefore, an agreement is reached at some T > TT, T TT, is the result of a form of coordination failure between the debtor and the holdout over the decision to settle. Note that TT = TT = δδ XX 1 llll δδ HH δδ XX so that second-best delay is a function of only the discount rates of the exchange bondholder and the holdout; even the presence of one holdout creditor in a pool of exchange of bondholders can cause delay and the length of the delay does not depend how small a fraction of all creditors the holdout creditors are. A similar point holds for TT = TT. As before, other Perfect Bayesian equilibria where the debtor fails to coordinate the decision to settle with both exchange bondholders as well as holdouts exist. Comparative statics in δδ HH As T, e δ HT 0 and e δ HT is decreasing and continuous in T, there exists T > 0 such that whenever T T, s H e δ HT s X with equality when T = T. Further, as

23 0 < δ H < δ X, it follows that s H e δ XT < s X. Let T be the solution to the equation ss HH ee δδ XXTT = ss XX. Clearly, TT < TT. Therefore, at an equilibrium, the waiting time TT TT, TT. Moreover, for each TT TT, TT, given the strategies of the two creditors, the debtor cannot gain by deviating: any deviation on part of the debtor can only involve further delay which, given δδ DD > 0, the debtor dislikes. As ss XX is decreasing in δδ ss HH, it HH follows that TT is increasing in δδ HH. As both ss XX and ee δδ HHTT are decreasing in δδ ss HH, TT is HH increasing in δδ HH. Therefore, as δδ HH 0, both TT, TT are both increasing. Note that ss XX = δδ DD δδ HH δδ DD NN (1 αα)δδ XX +ααδδ HH +δδ XX δδ HH = δδ XX δδ HH δδ DD NN (1 αα)δδ XX +ααδδ HH +δδ XX δδ HH = δδ DD NNNN DD (1 αα) δδ XX δδ HH +αα +δδ XX so that ss XX is decreasing in δδ HH. Finally, ss DD = δδ XX NNNN DD (1 αα) δδ XX δδ HH +αα +δδ XX so that that ss DD is decreasing in δδ HH. Appendix 2 Good cases make bad law: the Argentine debt swaps As is well-known, Argentina did implement a RUFO clause - one that expired at the end of But there were two subsequent developments at variance with the simple bargaining model we propose: (a) a delayed and relatively successful swap was effected in 2010, well before the expiry of the RUFO clause; and (b) despite the lapse of the clause - meaningful negotiations with the remaining holdouts have never really started; and there is no resolution yet in sight 21 How to account for these developments? (a) Bargaining surplus evolves over time For convenience the surplus was taken to be constant, but in practice the bargaining surplus could, and does evolve, as bargaining unfolds over time. In Argentina s case, this had an important impact as its economy recovered from recession, and increased greatly the value of the GDP warrants included in the initial settlement in 2005 agreed to by the first round of exchange bondholders. As these warrants turned out to be unexpectedly generous (see Amicus brief by Prat-Gay, 2013) so, consistent with the RUFO clause, a second settlement could be reached with the majority of holdouts in the second swap of 2010, i.e. well before the date of expiry. (b) Confrontation with holdouts There were three key developments which have up-ended the incentives to reach a negotiated outcome. 21 While there have been no formal face to face meetings involving the sovereign and key holdouts, informal negotiations, subject to Presidential veto, have taken place from time to time. 23