Chapter

Optimal Collective Action Clause Thresholds*

Author(s):
International Monetary Fund
Published Date:
September 2005
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Introduction

Over the past year, tangible progress has been made towards improving the resolution of sovereign financial crises. In February 2003, Mexico made a policy decision to include collective action clauses (CACs) in its sovereign bonds issued under New York law, contrary to market convention.1 With the first-mover problem solved, most other emerging markets issuing in New York have followed suit. A new market standard for emerging market sovereign bonds appears to have been set, with CACs as its centrepiece.

The potential advantages of CACs have of course long been recognised. They have been standard in English law bonds since the 19th century (Buchheit and Gulati (2002). But under New York law, unanimity clauses have until recently remained the market convention. This is generally felt to be suboptimal. Unanimity bonds mean that debt restructurings are potentially held hostage to the actions of recalcitrant or rogue creditors. More specifically, they may engender rent-seeking among some creditors, with attendant welfare externalities for the system (see Kletzer 2003 and Haldane, Penalver, Saporta and Shin 2003).

In response to these concerns, a push to introduce CACs in New York law bonds was first made by the official sector after the Mexican crisis, with the publication of the Rey Report (1996) by the Group of Ten countries (see also Eichengreen and Portes 1995). Little action followed. A second push was made by the official sector in 2002, following crises in Turkey, Brazil and most prominently Argentina. Again under the auspices of Group of Ten, a working group was set up to draft model CACs. These draft clauses were published in March 2003.

The aims of the Group of Ten working group were twofold. First, to examine a range of potential contractual clauses that could be included in sovereign bonds and recommend which ones to include. For example, they specified a threshold voting majority of 75% for changes in a bond’s financial terms. Second, to set a new market standard. Contractual clauses set the rules of a debt restructuring and if the rules vary too much, restructurings become more uncertain. The precise details of the clauses would depend on the jurisdiction of issuance but the intention was to make the substance as similar as possible.

The bonds issued by Mexico in February 2003 followed closely the G10 model clauses, including a 75% threshold. But some subsequent issues by other countries—Brazil, Belize, Guatemala and Venezuela—opted for higher 85% thresholds. These are closer to the levels proposed by private sector trade associations (EMCA 2002).

Some within the official sector have taken a dim view of these developments. First, because these higher thresholds take us closer to a 100% unanimity bond, thereby increasing the risk of holdouts. And second, because different voting thresholds risk a splintering of the market standard (see Portes 2003). A combination of standard and non-standard thresholds could create unnecessary uncertainty during a debt restructuring (see Gray 2004). One contribution of this paper is to critically evaluate these propositions using a theoretical model of financial crisis. In particular, we ask: what factors might determine the choice of optimal CAC threshold for a debtor? Is a lower threshold always better? And are there valid reasons why different issuers may want to set different, but country-specific, thresholds? To our knowledge, the literature has not yet addressed these questions within an analytical framework.

Our findings suggest that there are costs to a policy of the ‘lower the better’. A lowering of CAC thresholds provides assurance to the debtor that in the event of debt restructuring holdout creditors can be held in check with a lower offer. But this insurance benefit of CACs has to be weighed against the prospect of a lower offer increasing the likelihood of creditors running for the door and, consequently, higher exante interest rates.2 The choice of threshold that strikes the optimal balance between these costs and benefits depends on debtor risk preferences and creditworthiness. Riskneutral debtors prefer high thresholds because the ex-post costs of getting away with a lower offer are more than outweighed by the ex-ante benefits of lower interest rates and a lower probability for a liquidity run. Risk-averse debtors may however prefer lower CACs. Moreover, for a given level of risk aversion, the lower the debtor’s creditworthiness the more likely they will want to issue bonds with higher CAC thresholds. In other words, different choices of threshold between countries emerge as an optimal debtor response to different risk preferences and creditworthiness.3

A second contribution of this paper is to develop a model which nests both liquidity runs and debt restructuring following a solvency crisis. Typically, the two are treated separately.4 In practice, however, it is rarely straightforward to partition crises in this way. Liquidity crises affect prospects for solvency; and expected recovery rates for creditors following a debt restructuring will in turn affect short-term decisions on liquidity. These interactions mean that most crises lie in the ‘grey zone’ between pure liquidity and pure insolvency.

The model presented here is one such ‘grey-zone’ model, which allows behavioural interactions between short-term liquidity and debt restructuring following a solvency crisis. The framework allows us to explore the interaction between liquidity and solvency crisis tools. For clarity of analysis, insolvency is determined by inability to pay and therefore would be also applicable to corporate financial crises. But this does sidestep the additional sovereign constraint of willingness to pay (Eaton and Gersovitz 1981). But this additional layer of uncertainty only reinforces the complexity of ‘grey-zone crises’. Taking account of these interactions is important when assessing the design and potential benefits of CACs as a crisis resolution measure.

The paper is planned as follows. Section 2 presents the stylised grey-zone model. Section 3 discusses the determination of interest rates in the model and Section 4 the debtor’s choice of optimal CAC threshold. Section 5 concludes with some policy implications.

The Model

A debtor who wishes to finance a risky project issues a bond with collective action clauses. These clauses stipulate that if a proportion κ or more of creditors vote to change the financial terms of the contract they bind the rest. The debtor chooses a collective action clause threshold κ from a set of thresholds [κ1, κu] where κ1, for example, could be 65% and κu 85%.

A continuum of small risk-neutral creditors buys the bond. Each creditor has a legal cost li>0, which is the cost that this creditor would face if creditors collectively chose to reject a restructuring offer from the debtor. It captures the disutility arising from the costs of taking the debtor to court and prolonging the bargaining process.5 The probability distribution function of legal costs across the creditors is common knowledge. The bond is short term. Creditors face the choice of whether to roll over their funding at an interim stage and can decide not to roll over their funding to the last period of the game.

The project’s return depends on the realisation of a fundamental, θ. We assume that the ex-ante distribution of θ is uniform on [0,b]. Before creditors make their decision to foreclose or roll over they receive a private signal about the fundamentals Xi = θ+si where si, is i.i.d. with a uniform distribution over the interval [-ε, ε]. The noise term s¡ is independent of i’s legal costs. Creditors who foreclose receive a fixed pay-off of 1. Creditors who roll over get a gross return (1+r) if the project succeeds. If the project fails, they participate in a bond restructuring.6

The bond restructuring proceeds as follows. The debtor makes an offer to write down the debt according to the contractual conditions of the bond. The creditors vote to accept or reject the offer. If κ or more creditors vote to accept the offer, it goes ahead. Otherwise, creditors get a pro-rata share of the residual project return less their private legal costs.7

More precisely, the extensive form of the game is as follows:

  • 1. The debtor chooses a CAC threshold κ from [κ1, κu] to insert into the bond contract used to finance a risky project.

  • 2. The bond contract is offered to multiple risk-neutral creditors who buy an equal share of the total debt stock (normalised to one here) at a market-determined interest rate r.

  • 3. Creditor i observes signal xi= θ+si, as described above.

  • 4. Creditors decide whether to flee or roll over their bond contracts. We denote by f the proportion of creditors who flee.

  • 5. Fundamental θ is realised. This in turn determines the return on the project which is given by

where f is the deadweight damage to the project from early liquidation.8

The project succeeds if there is enough project return to pay the creditors who stay after the fleeing creditors have been paid out. That is, if

then the debtor repays the creditors who roll over in full and keeps the residual project return for itself. The game ends. Otherwise, the project fails, the debtor defaults and we enter the restructuring phase of the game described below.

  • 6. The debtor makes an offer to write down (1-f)(1+r).

  • 7. Creditors vote to accept or reject.

  • 8. If the offer is accepted all creditors receive a payment equal to the offer. In the event that the offer is rejected, each creditor i gets a pro-rata share of the return to the project less their private legal costs li.9

  • 9. Final pay-offs are determined.

We proceed to solve the game.

Restructuring Subgame

Stages 6-8 of the game are a voting subgame. The debtor makes a request to its creditors to write down the repayment on its bond. Creditors decide whether to accept or reject the offer. Since the bond has collective action clauses, the debtor’s offer will bind any dissenting creditors as long as the incidence of accepting creditors is κ or higher. If fewer than κ creditors accept the offer, claims are pursued through the courts and the debtor remains in default. In this event, each creditor will eventually receive a pro-rata share of gross project return, θ, net of payouts to fleeing creditors, f, and net of the damage done by early liquidation, f, and less the legal costs spent pursuing their claim.10 The debtor receives whatever is left from the project after it has paid its creditors.

So the debtor’s pay-offs are:

where U(.) is the utility function of the debtor. The pay-off to the creditor in the (1-κ)-th quantile of the distribution of legal costs from a given offer is:

So from the point of view of the creditor and assuming full information, it is a weakly dominant action to vote to accept the offer provided that the debtor’s offer is greater or equal to θ-2f-l1-κ. From the point of view of the debtor, again under full information, and since legal costs are positive it is optimal to make an offer which is just large enough to persuade the (1-κ)-th creditor to accept, that is to offer:

This offer would be exactly equal to the net project return (after payouts to fleeing creditors have been met) less the legal costs of the (1-κ)-th most stringent creditor from the pool of (1-f) creditors who participate in the restructuring.11

From (2), this offer is just large enough for the marginal (1-κ)-th creditor who votes on a restructuring to accept the offer and for the deal to go through. In this set-up, CACs ensure that restructuring is not delayed and resources are not expended on litigation; they neuter rent-seeking among bondholders.12

In the event of a restructuring, therefore, the pay-off to the debtor is

whereas the pay-off to each creditor who rolled over is equal to the offer made by the debtor, given by (3). Comparing (3) and (4) we can see that after default has occurred, a lowering of the CAC threshold would shift the allocation of residual project return from the creditors to the debtor and vice versa. Hence looking at solvency crises in isolation, debtors would always prefer a lower voting threshold. We will see below, however, that this result is modified when crises are neither pure insolvency nor pure liquidity, i.e., when we have ‘grey-zone’ crises.

Rollover Subgame

Working backwards, we now determine the proportion of creditors who flee. This involves solving stages 3-6 of the extensive form of the game, which form a rollover global game in the manner of Morris and Shin (1998).

The aggregate strategy of creditors is a rule of action which depends on whether the signal creditors receive is above a critical threshold x*. A creditor will flee if his private signal is lower than x* and will roll over otherwise. More formally, the strategy υ(x*) is an indicator function which takes the value one if x<x* and takes the value of zero, otherwise. This implies that the proportion of investors who flee given the aggregate strategy and the uniform distribution of private signals is

The equilibrium in switching strategies, in turn, implies that there is a critical state of fundamentals, θ*, above which the project succeeds and below which the project fails. At the equilibrium switching point, two conditions need to be met.

First, the proportion of creditors who flee must be such that the solvency constraint just binds. We refer to this condition as the ‘solvency condition’. The solvency condition is given by θ*–2f(ν(x*))=(1 – f(ν(x*)))(1 + r), which simplifies to

From (5) and (6), we obtain

In the limit as ɛ →0, we have θ*x*.

The second condition is that, at the switching point, the marginal creditor must be indifferent between fleeing and staying. We refer to this as the ‘indifference condition’. This says that the expected pay-off from rolling over if the debtor defaults plus the expected pay-off from rolling over if the debtor repays must equal the deterministic pay-off from fleeing. That is:

where we have used the fact that the pay-off from rolling over if the debtor defaults is equal to (3) and where p(θ|x) is the density of θ conditional on x. Since the prior over θ is uniform and the noise is also uniform with support [-ε, ε], the conditional density p(θ|x) is uniform with support [x*-ε, x*+ε]. So, (8) can be written as:

Using (7) to eliminate x* and (5) to eliminate f we can express (9) as a quadratic equation in θ*. In Appendix 1, we show that (9) can be written as

where the coefficients Fj are simple functions of ε and the interest rate r. Appendix 1 also shows that, in the economically meaningful case where (10) has a positive root for θ*, there is precisely one such positive root. Hence, the switching equilibrium is unique. This root gives the trigger point of fundamentals at which a liquidity crisis will commence. This trigger point lies between two points: a ‘fundamental insolvency’ point and a ‘fundamental solvency’ point, denoted θ1 and θu respectively. Fundamental insolvency occurs when the project return is insufficient to pay out creditors even if they all roll over (f=0), that is when θ <θ1 =(1+r). Fundamental solvency occurs when the project return is so high that there is enough to pay out all creditors even if they all foreclose (f=1), that is θ≥θu =2. In the region in between ((1+r)≤θ*< 2), we have liquidity crises—that is defaults which would not have occurred were it not for the decision of a sufficient proportion of creditors to flee.

Interest Rate Determination

Having solved for the rollover stage of the game, we now solve for the marketdetermined, actuarially fair interest rate. In equilibrium, the expected return to the risky project must equal creditors’ outside option if they invest elsewhere, which for convenience we normalise to one.

That is

where p(θ) is the unconditional density of θ which is equal to 1b. Appendix 2 shows that in the limit as the signals about fundamentals received by all creditors become very precise, i.e., as ε → 0 (11) can be rewritten as:

where

is the positive root of (10) and where the coefficients Fj have been evaluated in the limit as ε → 0. Expression (12) is an equation in three variables: r, 11-κ and b. So, for a given value of the CAC threshold, κ, or equivalently, for a given legal cost of the (1-κ)-th creditor, 11-κ, and a value for the upper support of the unconditional distribution of the project, b, we can determine the market interest rate r. Because the market interest rate is actuarially fair it is equal to creditors’ expected loss in the event of crisis. This expected loss, in turn, is equal to the product of the loss in the event of crisis and the ex-ante probability of a liquidity crisis. From (3), we know that creditors’ loss in the event of crisis (recovery rate) is decreasing (increasing) in the voting threshold κ. We would therefore expect the interest rate to decrease as the CAC threshold, κ, increases.

Chart 1 illustrates for a simple parameterisation that this is indeed the case.13 The ex-ante probability of a liquidity crisis, on the other hand, depends on both fundamentals and on the voting threshold. First, we would expect the probability of crisis to increase as the debtor’s fundamentals, b, deteriorate.14Chart 1 confirms this. Second, the ex-ante probability of crisis depends on the voting threshold chosen by the debtor. Intuitively, other factors being equal, lower voting thresholds make creditors more trigger-happy during the rollover game because in the event of crisis they would allow the debtor to get away with a lower offer and still keep holdout creditors in check.15

Chart 1:Variation of interest rates with CAC threshold

It is also interesting to note that although interest rates increase linearly as the CAC threshold decreases, they increase at an increasing rate as fundamentals deteriorate. Therefore, given a certain CAC threshold, κ, one would expect to observe a greater premium above risk-free rates for bonds issued by poor credit quality borrowers than for bonds issued by better quality borrowers. Chart 2 illustrates this more clearly by plotting interest rates against fundamentals for two different values of the CAC threshold. Lower voting thresholds raise the probability of a liquidity run, the more so the less creditworthy the borrower because the higher interest rate itself affects the solvency constraint. So lower-rated sovereigns need to offer creditors greater compensation ex ante, for a given threshold. This finding is consistent with the empirical findings of Eichengreen and Mody (2003) who find that lower-rated borrowers are charged a premium to issue bonds with collective action clauses, whereas higher-rated borrowers can issue at a discount.16 The reason suggested by Eichengreen and Mody, and modelled in Eichengreen, Kletzer and Mody (2003), is borrowers’ greater propensity to default strategically when they lack creditworthiness. In our setup, a premium could arise even without an additional incentive to default. Rather, investors require extra compensation as a result of the increased fragility of short-term creditors when creditworthiness is low.

Chart 2:Variation of interest rates with fundamentals

Debtor’s Choice of CAC Threshold

Arbitrage among creditors establishes a relationship between interest rates, the collective action voting threshold and the range of fundamentals (equation 12).

The debtor can use this relationship when it chooses the voting threshold in bonds it issues. We now turn to the first stage of the extensive form of the game, to determine the debtor’s choice of optimal collective action threshold.

Intuitively, the debtor cares about three things: the probability of crisis (which depends on fundamentals b and on the expected rollover behaviour of creditors); its pay-off in the event of non-crisis (which depends on the market interest rate); and its pay-off in the event of a crisis. As we have seen from (4), the CAC threshold directly affects the debtor’s pay-off in the event of crisis. The lower the CAC threshold, the higher the legal costs of the marginal creditor and the higher the debtor’s pay-off in the event of crisis. But Chart 2 shows that a lower collective action clause threshold results in a higher interest rate. What the debtor gains from a higher pay-off in the bad state, it loses in the good state. So a crucial question for the debtor in determining the optimal voting threshold is its impact on the probability of crisis.

This can be determined by differentiating θ* with respect to l1-κ. The analytical expression—a function of r and l1-κ—is complicated so results are better illustrated pictorially. In Chart 3 we plot θ*dl1κ for all valid combinations of r and l1-κ.

Chart 3:Variation of crisis threshold with legal costs of marginal creditor

Given that the surface always lies in the positive region, θ*dl1κ>0 or, equivalently, θ*κ<0. Therefore, the debtor can lower the probability of crisis by raising the CAC threshold, κ. A higher voting threshold provides short-term creditors with additional assurance, and so lowers their incentive to run and hence the probability of crisis.

This is the essence of the ‘grey-zone’ dimension to the model. Decisions regarding outcomes in the event of solvency crisis affect the probability of liquidity crisis, and hence shape ex-ante choices about optimal debt contracts. Previous papers have looked at the effects of solvency crisis measures on contract design (e.g., Haldane et al. 2003 and Kletzer 2003) or the effects of liquidity crisis measures on contract design (e.g., Dooley 2000 and Gai and Shin 2003) but none, to our knowledge, have considered the interaction among these measures.

More formally, the debtor would choose the CAC threshold, κ to maximise its expected return on the project. In doing so the debtor takes into account the pay-off they expect to receive in the event of a crisis, U(l1-κ), and the pay-off they expect to receive if no crisis occurs, U[θ-(1+r)].17 So the debtor solves the following maximisation problem:

where θ* is the trigger point at which short-run creditors flee, (13), and p(θ), as before, is 1b.

In what follows, we assume that the debtor has utility U(x)=xρ1ρ1, where 2-ρ is the coefficient of relative risk aversion. As a result,

Taking into account the endogeneity of the crisis threshold and interest rates, this can be rewritten as

The maximisation problem in equation (16) does not have a closed-form solution, but simulated results provide interesting insights.

  • First, for all values of creditworthiness b, a risk-neutral debtor (ρ=2) will prefer a higher collective action threshold to a lower one. This is illustrated in Chart 4. Intuitively, a risk-neutral debtor does not care about the distribution of possible pay-offs, only their expected value. And the expected repayment by the debtor to its creditors is equal to 1 from equation (11). What the debtor gains by increasing its ex-post payout in a crisis by lowering the collective action threshold is offset exactly by higher ex-ante interest charges when there is no crisis. Since the debtor makes a surplus when the project succeeds, a risk-neutral debtor gains by simply minimising the probability of crisis, which is achieved by issuing bonds with high collective action thresholds.

  • Second, this conclusion is modified if the debtor is risk-averse (ρ <2). This is illustrated in Chart 5. The more risk-averse the debtor, the more it weighs the pay-offs it receives in a crisis period over those in a noncrisis period. With strong risk-aversion, the debtor may prefer to issue bonds with a low voting threshold, so that it reduces what it has to pay out ex post in a debt restructuring, even though this increases the ex-ante risk of crisis and raises the ex-ante interest rate.

  • Third, the lower the creditworthiness, the more likely it is that a moderately risk-averse debtor will want to issue bonds with a high collective action threshold (Chart 6). This occurs because creditors considering their rollover decision require increasingly more compensation for the risk of default as creditworthiness declines (Chart 2): when fundamentals are weak, short-term creditors are more triggerhappy. This will tend to lead lower-rated debtors to choose a higher threshold to minimise this risk.

Chart 4:Variation of debtor utility with CAC threshold – risk-neutral debtor

Chart 5:Variation of debtor utility with CAC threshold – effect of risk aversion

Chart 6:Variation of debtor utility with CAC threshold – effect of fundamentals

Policy Implications

The model of grey-zone crisis developed here suggests the following policy implications:

In choosing the optimal CAC threshold, there are costs to a policy of ‘the lower the better’. A lowering of CAC thresholds may provide some assurance to the debtor in the event of a default, because it allows holdout creditors to be held in check with a lower offer. But there is a down side to this CAC benefit. The prospect of a lower offer increases the likelihood of creditors running for the door in the first place. So a lower CAC threshold risks increasing the chances of liquidity crisis, thereby raising initial borrowing costs for the debtor. For example, in the simple model presented here, if a debtor is risk-neutral they would prefer a higher collective action threshold to a lower one because the ex-post benefit of having CACs is more than outweighed by its ex-ante cost.

  • In more general settings, higher thresholds may no longer be optimal. For example, a risk-averse debtor—one which places greater weight on the adverse consequences of default—is more likely to choose a lower CAC threshold.18 This suggests there may be a role for the international official community in promoting lower thresholds. It is tantamount to asking the sovereign to behave in a more risk-averse way. Put differently, if CACs are insurance, then asking sovereigns to self-insure by choosing a lower threshold lowers the burden on the official sector as a centralised provider of sovereign insurance.

  • Even when there is a demand (voluntary or induced) for CAC insurance, the optimal degree of insurance will vary across borrowers. The more creditworthy the debtor, the lower the tolerable CAC threshold, for a given level of risk aversion. Therefore, although there may be benefits in having a market standard for CAC thresholds to reduce uncertainty in debt restructurings, such a standard may be suboptimal for some debtors.

  • The most general policy lesson which emerges from the model is that solvency crisis tools and liquidity crisis tools cannot and should not be viewed in isolation. The interaction and spillovers between them need to be weighed carefully when crafting both sets of policy. This has been demonstrated here in the context of CAC design and its important implications for liquidity crisis. But it equally applies in reverse when considering the efficacy of liquidity crisis measures. The model presented here provides a framework for assessing these welfare questions in an integrated fashion. It also provides a vehicle for exploring complementarities between different (liquidity and solvency) tools.

Appendix 1

Recall from the main text that there are two equations, (7) and (9), in two unknowns, θ*, the trigger value of fundamentals for a crisis and x*, the signal of the marginal creditor who flees. The relationship between θ* and x* also determines the proportion of people who flee, f(ν(x*)), and final project return at the trigger value of crisis θ*f(ν(x*)).

The first step in the solution is to rewrite (7) for x*. For convenience, this can be written in two forms:

where A1=2ε(θ*(1+r)1r) and

where B1=1r+2ε1r and B2=3+r1r. The indifference condition (9) can be written as

where C1=ε+12ε and C2=ε12εC3=ε+32+l1κ+1+r. Expressions (A-1) and (A-2) are two equations in two unknowns x* and θ*. Substituting (A-1) and (A-2) into (A-3) we obtain:

which is equal to

where D1=11r and D2=21r. This can then be rewritten in the form

where F1=(ε1)(3+r)2(εr)+2+1rεr[(ε+32)+1+r],F2=1rεr

F3=(ε1)(3+r)r(1r)2(ε1)+21rεr[(ε+32)+1+r] and F4=21rεr.

For ε0F1=r2+4r1r,F2=1rεrF3=r3+5r2r and F4=21rr. Provided that F3 + F4l1-κ, (A-4) will have one negative root and one positive root. The positive root will be the economically meaningful solution for θ*. Therefore,

Appendix 2

Since θ is distributed uniformly on [0,b], Pr(θθ*)=θ*0b and p(θ)=1b. Substituting p(θ) into (11) we obtain:

In the limit, as ε → 0, signals become fully informative and all creditors would flee if θ ≤ θ*, i.e., f=1 for ε → 0. Therefore as ε→0, (B-1) becomes

where θ* is given by (13).

References

This paper represents the views and analysis of the authors and should not be thought to represent those of the Bank of England or Monetary Policy Committee members. We would like to thank Ken Kletzer, Charles Goodhart, Chris Salmon, Misa Tanaka, David Wall, seminar participants at the Bank of England, attendees at the IMF/Banco de España conference ‘Dollars, Debts and Deficits: Sixty Years After Bretton Woods,” and an anonymous referee for helpful comments. Correspondence should be directed to Adrian Penalver at the Bank of England, Threadneedle St, London, EC2R 8AH. Telephone: +44 20 7601 3303. Fax +44 20 7601 5080. Email: adrian.penalver@bankofengland.co.uk

It was not nearly as strict a convention as generally thought. Richards and Gugiatti (2003) document that Bulgaria, Egypt, Kazakhstan, Lebanon and Qatar had issued bonds with CACs in New York prior to 2003.

The analysis by Eichengreen et al. includes the potential for the insurance element of CACs to induce moral hazard on the part of debtor.

The paper does not assess whether a country should maintain a uniform threshold in all issues if creditworthiness and rating circumstances change.

See, for example, Chang and Velasco (1999) for a model of liquidity crises and Bolton and Jeanne (2002) for a model of sovereign solvency crises.

There are many reasons why such costs may differ across creditors. For example, some creditors (e.g., bond mutual funds) may have investors with shorter investment horizons than others (e.g., pension funds and life insurance companies). There may also be differences in balance sheet structures, in agency problems related to compensation structure, and in accounting and regulatory rules. Equivalently, 1i can be thought of as measuring the elative degree of risk aversion of different sets of creditors, in deciding between choosing a certain option (accepting the offer) and an uncertain one (holding out).

We have allowed for secondary market trading because there are no pure strategy equilibria to such a subgame (full proof available from the authors). Vulture funds have weak incentives to bid for bond issues when: (i) ownership of the issue is widely dispersed; (ii) each creditor owns a small proportion of the total issue; and (iii) contractual provisions ensure that during the subsequent restructuring stage holdouts are kept in check, so that all creditors that hold on to their bonds get the same return. In essence, the argument is identical to the one made by Grossman and Hart (1980) but in the context of corporate raids. Creditors (shareholder) have very little incentive to tender their bonds (shares) to a vulture fund (raider) whose participation in the restructuring stage (in management of the company) is expected to increase the value of the debtor’s offer (the value of the stock) for all, when each creditor (shareholder) is small enough not to affect the outcome of the vulture’s (raider’s) bid.

For the purpose of our analysis, this assumption can be interpreted to mean that foreign creditors are able to attaché assets with value equal to the residual project return in the jurisdiction where the bonds were issued. In practice, there are few tangible assets that creditors can attach in foreign jurisdictions. The important aspect of this assumption is that the higher the available project return, the greater the payout to creditors who decide to pursue their claim in courts. Other aspects of the analysis can be generalised as long as this assumption is maintained. See also Haldane et al. (2003).

Implicitly, we have assumed that the marginal damage to the project of one fleeing creditor is equal to 1. The model can be easily generalised by assuming that the damage is equal to kf with k ≠ 1. All the results that follow are still valid as long as we allow for the possibility of a liquidity crisis, i.e., as long as k>r.

The model does not nest the case of unanimity provisions according to which all creditors are required to agree before an offer can go through. The reason is because it is assumed that creditors lie on a continuum. For a welfare analysis of CACs versus unanimity provisions from an ex-post perspective, see Kletzer (2003) and Haldane et al. (2003).

This restructuring subgame is very similar to the one set out in Haldane et al. (2003). The main difference is that here we do not assume that the debtor exerts adjustment effort after learning the outcome of the vote. For our purposes, including adjustment effort would complicate the notation without changing the analysis.

Say the threshold κ is 75%, then for the offer to go through the debtor needs only to persuade the creditor with the highest legal cost in the first quartile of the distribution of legal costs.

Haldane et al. (2003) show that this outcome in no longer guaranteed when there is two-sided information asymmetry between the debtor and its creditors about how much they stand to gain or lose if the restructuring does not take place.

For the purposes of generating this figure and all the ones that follow we assume that the distribution of legal costs is uniform on [0,1]. Under this assumption collective action clauses of 0.65, 0.75 and 0.85 imply marginal creditor legal costs, 11-k, of 0.35,0.25 and 0.15 respectively.

As θ is uniform on [0,b], the ex-ante expected value of the fundamental is b/2.

In the next section we show this more formally.

Richards and Gugiatti (2003), on the other hand, find no discernible difference from the inclusion of CACs, whatever the credit rating of the issuer.

Recall that we are conducting our analysis as ε> 0. A consequence of this is that the proportion of creditors who flee becomes polar 0,1.

There may be other (than risk aversion) reasons why a lower CAC threshold may have a benefit—for example, in situations where there is two-sided information asymmetry between debtors and creditors (Haldane et al. 2003). On the other hand, others argue that mitigating the costs of crisis of the debtor by lowering the CAC threshold may weaken the disincentives to default (Dooley 2000).

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