LEVERAGED BUYBACKS OF SOVEREIGN DEBT: A MODEL AND AN APPLICATION TO GREECE ANGELO BAGLIONI∗

The model presented in this article shows that the outcome of a leveraged buyback of sovereign debt depends on the priority structure of the deal. If the institution lending the funds needed for the buyback is senior, the debtor country benefits from the deal: the government debt is reduced, implying a lower probability of default; at the same time, the deal makes the price of outstanding bonds go down, since their recovery rate declines. The opposite holds if the lending institution is junior. If the loan is underpriced, the implied subsidy is shared between the borrowing country and its bondholders, who can benefit from a price increase of their bonds. This is actually what happened with the buyback of Greek sovereign bonds in 2012, as it is shown in the empirical section. Those results do not depend on the share of country’s endowment devoted to debt repayment, which instead plays a crucial role in shaping the outcome of unlevered buybacks. (JEL F34, H63) I.

This article provides a simple model, analyzing the effects of a “leveraged buyback”: this is the label I use to identify the case where a government borrows the money, needed to purchase some of its own debt, from an international organization (named “Fund”). I will show that the priority structure, defining the rights of the lenders in the default state, is crucial to determine which party benefits from the deal: either the borrowing country or the bondholders. If the Fund is senior, the deal benefits the country at the expense of bondholders: on one hand, the overall amount of government debt is reduced, implying a lower probability of default; on the other hand, the deal makes the price of outstanding bonds go down, since their recovery rate in the default state declines. The opposite happens if the Fund is junior. If the Fund and the private lenders have the same creditor status, the deal has no impact on payoffs and on the bond price. Those results are derived under the assumption that the loan made by the Fund is fairly

INTRODUCTION

When the outstanding debt of a sovereign borrower quotes significantly below its face value, the government of that country may try to improve the financial position of the public sector by purchasing some of its own debt through a buyback transaction. The interest for this kind of deal was originated in the 1980s by the debt overhang problem affecting several developing countries.1 The current crisis of sovereign debt, hitting particularly some countries in the euro area, has revived the interest in this matter at the policy level.2 A buyback operation was actually one of the tools employed in 2012 to try to fix the Greek issue. ∗ I wish to thank three anonymous referees for their extremely useful comments, which enabled me to improve this article over a previous version. Baglioni: Universit`a Cattolica, Largo Gemelli, n.1, Milano 20123, Italy. Phone 3902/72344024, Fax 3902/7234 2781, E-mail [email protected]

1. Krugman (1988b) defines a debt overhang as follows: “A country has a debt overhang problem when the expected present value of potential future resource transfers is less than its debt” (p. 5). Panizza, Sturzenegger, and Zettelmeyer (2009) provide an excellent survey of the economic theories and legal issues related to sovereign debt and defaults. The empirical research in this area is reviewed by Tomz and Wright (2012). For institutional details on debt buybacks, see Medeiros, Polan, and Ramlogan (2007). 2. See for example: Claessens and Dell’Ariccia (2011), Baglioni (2011), Hufbauer and Kirkegaard (2011).

ABBREVIATIONS EFSF: European Financial Stability Facility IFIs: International Financial Institutions IMF: International Monetary Fund OMT: Outright Monetary Transactions OSI: Official Sector Involvement PSI: Private Sector Involvement

1 Contemporary Economic Policy (ISSN 1465-7287)

doi:10.1111/coep.12053 © 2014 Western Economic Association International

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priced, so it fully incorporates the credit risk incurred by the Fund. The model is then extended to analyze the case where the loan is underpriced, for some political reasons. This underpricing is equivalent to a subsidy, which benefits not only the borrowing country but also its private lenders. The buyback has a positive impact on the price of outstanding bonds, even if the Fund retains the same creditor status as private lenders. The buyback transaction made by the Greek government in December 2012 allows me to complement the model with a case study. The deal was funded by the European Financial Stability Facility (EFSF), so it was a leveraged buyback. Moreover, the loan made by the EFSF to the Greek government was significantly underpriced. The EFSF retains officially the same creditor status as private lenders, although it can be expected to be actually junior. The model prediction, that this kind of transaction should have a positive impact on the price of outstanding bonds, is confirmed by the econometric analysis. The traditional literature, initiated by the seminal contributions of Krugman (1988a) and Bulow and Rogoff (1988), has considered the case where a country employs its own resources to fund a buyback: I label this deal as “unlevered buyback.” In this literature, the crucial parameter, determining the payoffs of the parties involved in the deal, is the share of country’s endowment available for debt repayment: if the bondholders (as a group) can seize only a tiny share of the country’s endowment in the default state, the buyback turns out to be a good deal for them and a bad one for the government. While this result is true for an unlevered buyback, it does not hold anymore for a leverage transaction: in the latter case, I will show that the share of country’s endowment that creditors can seize in the default state is totally irrelevant. Following Krugman and Bulow-Rogoff, other models of sovereign buybacks have been proposed, showing that debt repurchases can have some positive effects, overlooked by those initial contributions. In particular, Rotemberg (1991) shows that debt repurchases by highly indebted sovereign nations are advantageous for all the parties concerned. The reason is that when sovereign debts are large, bargaining costs between the government and its creditors (e.g., resources spent in negotiations and sanctions when there is no agreement) are large; therefore buybacks, which reduce the face value of the

outstanding debt, can be beneficial. Detragiache (1991) models a debt buyback within the context of intertemporal consumption smoothing, showing that it can be viewed as the purchase of an asset, enabling the country to carry consumption into the future; under this perspective, a buyback must be seen as an option to be compared with other types of investments, like foreign exchange reserves and physical capital. Acharya and Diwan (1993) show that a country can signal through a debt buyback its willingness to invest, since the buyback reduces current consumption; as a consequence, creditors are more willing to grant some debt relief; in addition, this signaling effect should lead to a higher market price for government debt. Prokop and Wang (1997) take into account the costs associated with a default, such as trade sanctions and exclusion from financial markets, and they show that a debt buyback can make a debtor country better off by reducing the probability of default. Thomas (2004) takes a similar view, showing that the Bulow-Rogoff framework treats default as an event with no dead-weight loss, so it underestimates the potential gains from a debt buyback. My results are in line with some of those studies, namely: (1) the ability of buybacks to reduce the face value of debt and consequently the default probability of a country; (2) the impact of the transaction on the market price of government debt; (3) the positive role played by subsidies, which are often part of the deal. The specific contribution of my model is to analyze the role of an official creditor lending the funds needed for the buyback, and to show how the outcome of the transaction crucially depends on terms of the loan and on the priority structure of the government obligations. A limitation of my model must be acknowledged. The focus of my analysis is on the financial implications of a buyback. As we shall see, the purpose of the government is to reduce its own expected liability with all lenders. I will abstract from any real effect, namely any efficiency gain possibly arising from some positive incentive effects of the buyback.3 Therefore, the debt overhang issue is in the background of my analysis, but it will not be explicitly addressed. Despite this limitation, I believe that the model is able to give a useful contribution, by identifying the conditions under which a buyback can 3. These effects are considered—among others—by Bulow and Rogoff (1991): they show that a buyback may stimulate investment by relieving to some extent the debt overhang.

BAGLIONI: BUYBACKS OF SOVEREIGN DEBT

reduce the debt burden inherited from the past, thus relieving a debt overhang problem faced by a country. The rest of this article is organized as follows. Section II starts with a simple two-state model of leveraged buybacks, under the assumption that the loan made by the Fund is fairly priced; then it extends the model to allow for the underpricing of the loan. In Section III, the model is extended to the more general framework where the country’s endowment is a continuous random variable. Section IV provides an empirical analysis of the Greek buyback. Finally, in Appendix A the model is used to review the theory of unlevered buybacks. All the proofs of the propositions are given in Appendix B. II.

LEVERAGED BUYBACKS: A SIMPLE TWO-STATE MODEL

Consider a country, whose endowment is assumed to be a random variable W , which can take up two values: WH > WL , with probabilities (1 − πd ), πd , respectively. The share of endowment that creditors can seize in case of default is θ ∈ (0, 1]. The amount of debt (including interest payments) is D, with θWL < D < θWH . Then πd is the probability of default. Assuming risk neutrality and setting the riskless interest rate to zero for simplicity, the present value of the total outstanding debt is (1)

V (D) = (1 − πd )D + πd θWL

so the market price of each unit (say each euro) of debt is (2) P0 = V (D)/D = (1 − πd ) + πd (θWL /D) < 1 which we label the “pre-buyback” price of debt. The first term on the right-hand side shows that, for each euro of government debt held, a bondholder recovers one euro with probability (1 − πd ), while with probability πd the recovery rate is lower than one: the amount θWL must be shared among all lenders. Now, the government of the country borrows an amount C from an international organization, which we label “Fund,” in order to buy back part of its outstanding debt. We denote by X the amount of debt (at face value) that can be purchased by spending C. Hereafter the holders of the outstanding bonds will be called “private lenders.” We denote by F the face value (including interest payments) of the Fund’s claim. In

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addition, we label k the recovery rate of the Fund in the default state. By assigning specific values to parameter k, we can define the seniority structure of the country’s obligations. In particular, we shall distinguish between three cases.4 (1) The Fund is senior to private lenders: k = 1. (2) The Fund is junior to private lenders: k = 0. (3) The Fund and the private lenders enjoy the same status (pari passu): k = θWL /(D − X + F ) (the amount of resources available for debt repayment are shared between the Fund and private lenders in proportion to their nominal claim). Therefore, the expected value of the Fund’s claim is (3)

V (F ) = (1 − πd )F + πd kF.

As a consequence of the buyback, the face value of the outstanding government bonds is D − X, and their market value is (4)

V (D − X) = (1 − πd )(D − X) + πd (θWL − kF )

where the claim of the Fund must be subtracted from the country’s resources available to pay out the bondholders in the default state. The objective function of the government is to reduce the debt burden inherited from the past, more precisely its own expected liability with all lenders. Before the buyback, such liability is V (D). Thanks to the buyback, the country’s expected liability becomes V (D − X) + V (F ), which turns out to be: (5) V (D − X) + V (F ) = (1 − πd )(D − X + F ) + πd θWL and it is easy to see that V (D) − [V (D − X) + V (F )] = (1 − πd )(X − F ). So we can define the country’s expected benefit from the buyback deal as: (6)

Y = (1 − πd )(X − F ).

We can easily get the intuition behind this result by asking: What is the outcome of the buyback deal for the debtor country? As far as the default state is concerned, nothing changes, since the transaction implies just a redistribution 4. In what follows, we are implicitly assuming that F < θWL < D − X. This allows to say that in the default state the Fund is repaid in full if its claim is senior; to the contrary, it gets nothing if its claim is junior. This is a simplifying assumption, which will be dropped in Section III, where the country’s endowment W is supposed to be a continuous random variable.

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of resources (equal to kF ) from the private lenders to the Fund, without altering the endowment devoted to repaying its obligations to all lenders (equal to θWL ). The debtor country can benefit from the buyback only in the nondefault state, and this happens if the total face value of its obligations after the buyback (D − X + F ) is lower than before (D), or equivalently if F < X: in this case some of the outstanding debt with private lenders is replaced by a lower debt with the Fund. Of course, the transaction hurts the country in the opposite case (F > X), and it has no relevant effect if F = X. It is worth stressing that the opportunity of buying a share of its own outstanding debt at a price lower than face value does not necessarily imply a gain for the debtor country. A. Fairly Priced Fund’s Loan We begin our analysis by assuming that the Fund loan is priced at market conditions (this assumption will be dropped in the next subsection, to account for a subsidized loan). Thus, the face value (F ) of the Fund’s claim is determined in such a way that its expected claim equals the amount lent: (7)

V (F ) = C.

When the announcement of the buyback is made, the market price of bonds adjusts to a new value P1 : the “post-buyback” price. The equilibrium value of X can be computed as follows. By definition, it is P1 = V (D − X)/ (D − X). Since in equilibrium the private lenders must be indifferent between selling and holding their bonds, the government buys at price P1 , so C = P1 X. Therefore,the following condition must be met: (8)

C/X = V (D − X)/(D − X)

which determines the equilibrium value of X. This in turn defines the equilibrium level of P1 . Thanks to the condition in Equation (7), the transaction between the government and the Fund has a zero expected value. Therefore, Y is a transfer of wealth between the private lenders and the debtor country; in other words, the buyback is a zero-sum game between them. The sign of Y crucially depends on the seniority structure of the transaction, that is, on the parameter k. The following proposition identifies the relationship between the priority structure of the country’s obligations and the outcome of a leveraged buyback for the debtor country, together with

the impact of the deal on the market price of bonds. Depending on the priority structure, we can distinguish among the following three cases. (1) If the Fund is given a senior claim over private lenders, the outcome of the buyback is a transfer of wealth from the existing bondholders to the debtor country. Accordingly, the market price of bonds goes down, due to the decline of their recovery rate in the default state. The reason is that the whole amount spent for the buyback (C) is subtracted from the resources available to pay out the private lenders in the default state, since it is used to repay the country’s obligation with the Fund. Then a share (X) of the outstanding debt is replaced by the riskless debt held by the Fund, and its face value can be lowered to C. (2) The opposite holds if the Fund is given a junior claim. In such a case, the resources available to repay the private lenders are unaffected, and they go to repay a lower amount of debt (D − X): so the recovery rate of the outstanding bonds in the default state goes up, and so does their market price. But this implies that a share (X) of the existing bonds are replaced with a debt, held by the Fund, with a higher face value (C/(1 − πd )), because the Fund does not recover anything in the default state. (3) We have an intermediate case where the resources available for debt repayment are shared among all lenders, both private ones and the Fund, in proportion to their nominal claim. In other words, the Fund is given the same recovery rate as bondholders. Therefore, through the buyback the country replaces some bonds with a Fund’s claim with the same face value (X), and the deal has no real effect. PROPOSITION 1. (i) If k = 1, F = C, Y > 0 and P1 < P0 . (ii) If k = 0, F = C/(1 − πd ), Y < 0 and P1 > P0 . (iii) If k = θWL /(D − X + F ), F = X, Y = 0 and P1 = P0 . Note that the outcomes obtained in cases (i) and (ii) parallel those obtained for unlevered buybacks by Krugman (1988a) and BulowRogoff (1988), respectively (see Appendix A for a formal review of their arguments). They analyze the case where a country employs an amount of its own resources to buy some of its outstanding debt. Krugman considers the case where the share of endowment that can

BAGLIONI: BUYBACKS OF SOVEREIGN DEBT

5

be seized by creditors in the default state is equal to one (θ = 1 in my notation); hence the sum spent for the buyback (C) goes entirely to reduce the resources available for debt repayment in the default state, so the debtor country bears the cost of the buyback only in the nondefault state. Since in that state the country gets a debt reduction equal to X > C, the net effect of the buyback is a transfer of wealth (equal to (1 − πd )(X − C)) from the lenders as a group to the debtor country, and the market price of debt declines when the buyback is announced: these are the same outcomes obtained in case (i). To the contrary, Bulow and Rogoff consider the case where the resources that creditor can seize in the default state are not affected by the buyback. In such a case, the country bears the full cost C of the buyback, so the country’s payoff from the deal is (1 − πd )X − C < 0: the buyback transfers some wealth from the debtor country to its lenders, who gain from an increase of the market price of their bonds; I get a similar result in case (ii) of Proposition 1. Despite those similarities, there is an important difference between my results and those obtained in the previous literature. The outcome of an unlevered buyback crucially depends on the share of country’s endowment that creditors can seize in case of default (θ): if θ is high the country is able to shift a large share of the cost of the buyback to bondholders, since θC must be subtracted from the resources available for debt repayment in the default state. To the contrary, the results stated in Proposition 1 do not depend on the value of θ. The outcome of a leveraged buyback is independent of the amount of country’s resources seized by all creditors in the default state; what is crucial is how such resources are allocated among them.

To keep things simple, we shall assume here that the Fund lends to the government the money, needed for the buyback, at the riskless rate of interest (assumed to be zero); so F = C. Of course, this pricing does not imply any subsidy if the Fund is senior (k = 1) and its claim is actually risk free; so Proposition 1-(i ) still applies. Let us focus on the other two cases, where either the Fund is junior or it has the same status as private lenders (pari passu). In such cases, the underpricing of the loan implies an expected loss for the Fund. The other side of the coin is a subsidy, which goes to the benefit not only of the debtor country, but also of its private lenders. The latter gain can be easily explained if the Fund is junior: in such a case, the buyback leaves unchanged the amount of resources available to repay the private lenders but it lowers the face value of the outstanding debt, leading to a higher recovery rate in the default state. Under the pari passu assumption, this result is less straightforward, since the transaction reduces the resources available to repay the private lenders; however, the underpricing makes this reduction smaller than it was with fair pricing, leading to a higher recovery rate. For the same reasons, we should expect that the market price of bonds goes up, due to the buyback. The following proposition tells us that this happens in both cases indeed: when the Fund is junior and when it retains the same status as private lenders; however, in the latter case the price increase is smaller. For notational purposes, in this proposition I denote by P1 the post-buyback price of bonds in the case where the Fund is supposed to be junior, and by P1∗ the post-buyback price under the pari passu assumption.

B. Subsidized Fund’s Loan

PROPOSITION 2. Let F = C.

So far, we have assumed that the loan made by the Fund is fairly priced, so the Fund is compensated for the risk incurred in the deal. As a consequence, the buyback was a zerosum game between a sovereign borrower and its bondholders. In this subsection, we turn to the case where the loan is underpriced, so it incorporates a subsidy: this often happens for political reasons, and it is true for the Greek buyback that we are going to analyze below. Since the transaction is now supposed to be funded at concessionary terms by the Fund, it is no more a zero-sum game between the country and its private lenders.

(i) For both k = 0 and k = θWL /(D − X + F ), the Fund incurs an expected loss, and this subsidy is shared between the debtor country and its private lenders. (ii) P1 > P1∗ > P0 . As an extreme case of subsidized financial assistance, we can suppose the Fund to be a “donor.” This case can be easily incorporated into the above framework by setting F = 0: the Fund provides an amount of money C to the government, and it does not have any claim. It is immediate to see that Proposition 2 still holds. The subsidy C is shared between the

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debtor country and its private lenders. The country gains Y = (1 − πd )X. The market price of government bonds raises from P0 to P1 : of course, the bondholders get the same benefit as in the case where the Fund’s claim is junior.

III.

TABLE 1 Payoffs with Senior Fund (D − X + F )/θ W ≤W ≤ F /θ ≤ W ≤ F /θ (D − X + F )/θ ≤W ≤W Fund Private lenders

θW 0

F θW − F

F D−X

A MORE GENERAL MODEL

The above analysis relies on the simplifying assumption that the country’s endowment W can take up only two values: either WH or WL . In this section, I will show that the results obtained so far can be extended to a more general setting, where W is a continuous random variable, with a density function g(W ) (and G(W ) the cumulative density function) defined   over the interval W , W . The amount of debt (including interest payments) D is such that θW < D < θW , where θ continues to denote the share of endowment that creditors can seize in the default state. Under this framework, the probability of default is  D/θ G(D/θ) = (9) g(W )dW W

and the present value of the outstanding debt is (10)   V (D) = 1− G(D/θ) D +



D/θ

θWg(W )dW.

W

The “pre-buyback” price of debt can still be defined by P0 = V (D)/D. Now suppose, as we did in the previous section, that the government engages in a leveraged buyback: the country borrows an amount C from the Fund, which is used to purchase an amount of debt with face value X. Under the more general framework used here, the payoffs of the Fund and of private lenders are more complex than it was in the simplified framework of Section II. They cannot be simply determined by the parameter k; rather, they have to be examined in detail, depending on the priority structure of the country’s obligations. This is done in the following three tables, which allow us to write the expected payoffs of the Fund and of private lenders. First, if the Fund is senior the payoffs are those shown in Table 1, where F still denotes the face value (interest included) of the Fund’s claim from which the expected payoffs of the

Fund and of private lenders can be computed as follows: (11)   V (F ) = 1 − G(F /θ) F +



F /θ

θWg(W )dW

W

(12)   V (D− X) = 1− G((D− X + F )/θ) (D − X)  (D−X+F )/θ (θW − F )g(W )dW. + F /θ

Second, if the Fund is junior the payoffs are as shown in Table 2, and their expected values are the following: (13)   V (F ) = 1 − G((D − X + F )/θ) F  (D−X+F )/θ [θW − (D − X)] g(W )dW + (D−X)/θ

(14)   V (D − X) = 1 − G((D − X)/θ) (D − X)  (D−X)/θ θWg(W )dW. + W

Third, if the Fund and private lenders enjoy the same creditor status, the payoffs are those as shown in Table 3, and their expected values are TABLE 2 Payoffs with Junior Fund W ≤W ≤ (D − X)/θ Fund Private lenders

0 θW

(D − X)/θ (D − X + F )/θ ≤W ≤ (D − X + F )/θ ≤W ≤W θW −(D − X) D−X

F D−X

BAGLIONI: BUYBACKS OF SOVEREIGN DEBT

TABLE 3 Payoffs with Pari Passu Rule W ≤W ≤ (D − X + F )/θ Fund (F /(D − X + F ))θW Private ((D − X)/(D − X + F ))θW lenders

(D − X + F )/θ ≤ W ≤ W F D−X

the following: (15)   V (F ) = 1 − G((D − X + F )/θ) F  (D−X+F )/θ θWg(W )dW + F /(D − X + F ) W

(16)   V (D − X) = 1 − G((D − X + F )/θ) (D − X) + ((D − X)/(D − X + F ))  (D−X+F )/θ θWg(W )dW. × W

As we already know, the purpose of the buyback deal is to reduce the expected liability of the country. Before the buyback, the expected liability is V (D), which is given by Equation (10). Following the buyback, the expected liability is V (D − X) + V (F ),which (independently of the seniority structure) turns out to be: (17)   V (D − X) + V (F ) = 1 − G((D − X + F )/θ)  (D−X+F )/θ × (D − X + F ) + θWg(W )dW. W

The government is able to reduce its expected liability if it can lower the total face value of its obligations: D − X + F , which of course will happen if F < X: in this case some of the outstanding debt with private lenders is replaced by a lower debt with the Fund. This intuitive concept is formally stated in the following proposition. PROPOSITION 3. If F  X, then V (D − X) + V (F )  V (D). Note that, if F < X, the probability of default is reduced as a consequence of the buyback: G((D − X + F )/θ) < G(D/θ). The simple model of the previous section was not

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able to capture this effect, due to the assumption that the default probability (πd ) was exogenous. The extension to the continuous case allows to say that, by lowering the overall face value of its obligations, the government pursues a twofold target: reducing its expected liability as well as the probability of default. The latter objective may be quite relevant in an environment where a sovereign default might coincide—although not necessarily—with the exit from a monetary union; of course, this issue applies to the high debt countries belonging to the euro area, first of all Greece, which will be the focus of the empirical analysis below. Let me briefly expand on this issue here. Countries belonging to a monetary union have two ways of defaulting on their sovereign debt, which are not mutually exclusive. First, they can apply a haircut on the value of their debt, possibly together with a rescheduling of the maturities of the outstanding securities. This is the more direct way of declaring a default. In the euro area, this actually happened when the Greek government applied a severe haircut (more than 50%) to its own outstanding bonds: this was the so-called “Private Sector Involvement” (PSI) taking place in March 2012, which has been imposed on private creditors as a precondition for the financial assistance provided by the official creditors (other European governments, EU Commission, and International Monetary Fund [IMF]). The second way of defaulting is to leave the monetary union and introduce a new currency (better: come back to the old one, say the Dracma), which would immediately depreciate right after its adoption. As a consequence, the foreign securityholders would suffer heavy losses, due to the re-denomination of their securities into the new currency. Both ways of defaulting may imply complex bargaining and litigations with security-holders, together with high legal costs. In the policy debate, the inability of a European country to repay its own debt has been very often tied to its exit from the euro area. On technical grounds this is a wrong idea, since a country can apply a haircut on its debt even without leaving the common currency (this is what happened to Greece). However, the threat of being forced to leave the monetary union can play an important role at the policy level, and it can be the reason why a government may want to reduce the likelihood of a default on its debt. The “post-buyback” market price of government bonds is still defined by P1 =

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V (D − X)/(D − X), and in equilibrium this must be equal to the price paid by the government in the buyback deal, which by definition is P1 = C/X. So the equilibrium condition in Equation (8) still holds. A. Fairly Priced Fund’s Loan Let us first examine the case where the loan made by the Fund is fairly priced, so the Fund’s expected claim equals the amount lent. In such a case, the face value F of the Fund’s credit is determined by the condition (7): V (F ) = C. Since the transaction has a zero net expected value for the Fund, the buyback is a zerosum game between the country and its private lenders. It can be shown that the main results of the previous section still hold here. In particular, if the Fund is given a senior claim over private lenders, a share X of the outstanding debt is replaced by another obligation (F ) with a lower face value, so the buyback enables the government to reduce its total expected liability together with the probability of default; the outcome of the transaction is a wealth transfer from the bondholders to the debtor country. The opposite happens if the Fund is given a junior claim: in this case, the private lenders benefit from the deal through an increase of the equilibrium price of government bonds; the country faces an increase of its expected liability and of the likelihood of default. Finally, the buyback has no impact if the Fund is given the same priority as private lenders (pari passu). These results are formally stated in the following proposition (which parallels Proposition 1). PROPOSITION 4. (i) If the Fund is senior, F < X. (ii) If the Fund is junior, F > X and P1 > P0 . (iii) If the Fund has the same priority as private lenders, F = X and P1 = P0 . Note that the results stated in this proposition—like those stated in Proposition 1—do not depend on the value of θ. So the outcome of a leveraged buyback is independent of the share of the country’s resources seized by all creditors in the default state; what is crucial is how such resources are allocated among them. B. Subsidized Fund’s Loan We come here to the case where the loan made by the Fund incorporates a subsidy. In

particular, the Fund is supposed to charge the riskless rate of interest (set to zero for simplicity) independently of the priority structure of the buyback deal and of the risk incurred. Formally: F = C. I will focus on those cases where the Fund is given either a junior or the same status as private lenders, since these are the two relevant priority structures in the empirical application of the model that we are going to make in next section. I keep denoting by P1 the post-buyback price of bonds in the case where the Fund is supposed to be junior, and by P1∗ the post-buyback price under the pari passu assumption. In the previous section we obtained that P1 > P1∗ > P0 : the buyback leads to an increase of the market price of government bonds even if private lenders enjoy the same creditor status as the Fund, although such increase is lower than in the case where the Fund is junior. The reason is that in both cases the Fund provides a subsidy, which partly goes to the benefit of bondholders. This result carries over to the present framework, as it is shown in the next proposition. The extension to the continuous case enables us to add a further insight: the market value of bonds benefit from a reduction of the probability of default, since the face value of the government obligations is lowered. This price behavior of the outstanding government bonds will be the focus of the empirical test performed below. PROPOSITION 5. Let F = C. Then P1 > P1∗ > P0 . Finally, the extreme case where the Fund is a donor can be considered again here by setting F = 0. The payoff of private lenders (V (D − X)) is the same as in the case where the Fund was supposed to hold a positive claim (F > 0) and to be junior (see Equation (14)), and P1 is determined accordingly. Therefore, the same computation made in the proof of Proposition 4 (ii) allows us to say that P1 > P0 still holds.

IV.

A CASE STUDY: THE GREEK BUYBACK

A. Descriptive Evidence On December 3, 2012, the Greek Ministry of Finance announced a buyback invitation. The bondholders of the Hellenic Republic were given the opportunity to sell their bonds at

BAGLIONI: BUYBACKS OF SOVEREIGN DEBT

specific prices and within a 1-week deadline.5 The eligible securities were those issued by the Hellenic Republic with the swap operation taking place at the beginning of March 2012 (PSI): 20 bonds with maturities ranging from 10 to 30 years. The deal was funded by the EFSF, with a 30-year loan to the Greek government. Actually the bondholders participating in the deal have been directly paid by the EFSF (with zerocoupon 6-month notes). On December 12, the outcome of the transaction was announced: the aggregate principal amount of bonds purchased by the Greek government was 31.9 euro billions, at the weighted average price of 33.8%, and the size of the loan made by the EFSF was set at 11.29 billions (equal to the aggregate amount of EFSF notes issued to pay for the delivered securities, including the accrued interests). This deal fits well into the above framework: it is a leveraged buyback. Some specific features must be considered. First, the interest rate paid by the Greek government on the EFSF loan (3.5%) is well below market rates, implying a substantial subsidy: at the time of the buyback, the market quotes for the 30-year yield of the Hellenic Republic debt was above 12% (and even much higher in the preceding weeks). Second, the creditor status of the EFSF: this is officially on the same level of private lenders (pari passu). However, there are good reasons to believe that, should the Greek government be unable to fulfill its obligations, the EFSF and the European governments giving bilateral loans to Greece will have to bear the burden: following the PSI in 2012, there is a growing consensus that the next Greek default (if any) will result in an “Official Sector Involvement” (OSI), before any further losses will be possibly imposed on private bondholders.6 Thus, the information available at the time of the buyback leaves open the way to the interpretation that the EFSF is actually a junior creditor. Finally, the bidding price must be taken into account. In order to enhance the chances of a large participation in the deal, the Greek Ministry of Finance announced a price significantly above the market price of eligible bonds at the announcement date: the overpricing was about five basis points on all maturities. 5. I will not enter into all the details of the auction rules. The interested reader can find them on the web site of the Greek Public Debt Management Agency (www.pdma.gr). 6. This view has received an official endorsement, albeit with the ambiguity typical of official statements, by the Eurogroup statement of November 27, 2012.

9

Thanks to those features, the Greek buyback can be analyzed within the framework of Propositions 2 and 5. In particular, we can expect that the impact of the transaction on the bond price is positive, for both reasons: (1) the subsidized interest rate applied by the EFSF, and (2) the creditor status of the EFSF: either pari passu with private lenders or even junior. I want to test empirically whether this conjecture is correct. To this aim, I collected the daily market prices of six bonds purchased with the buyback transaction: those with maturities ranging from 2023 through 2028 (available in the Thompson Reuters-Datastream dataset from the date of their quotation, following the PSI). Those prices are plotted in Figure 1 for the whole sample: from March 9, 2012 through January 9, 2013. The first vertical line in the graph marks the well-known announcement made by President Draghi on July 26, 2012: in a speech in London, he declared that the ECB was ready to do “whatever it takes” to save the single currency, and that was “within the mandate” of the ECB itself. This speech was followed by two decisions taken by the Governing Council of the ECB (August 2 and September 6, 2012), leading to the introduction of the Outright Monetary Transactions (OMT) into the monetary policy framework of the ECB. This new instrument implies a commitment of the ECB to curb cross-country sovereign spreads within boundaries justified by fundamentals, in order to implement a correct transmission of the single monetary policy. This commitment, although conditional on the request by a government and on the financial assistance granted by the ESM, has been a turnaround in the policy followed by the ECB in dealing with the sovereign debt crisis: starting from that date, the ECB is ready to buy government bonds for potentially unlimited amounts, thus becoming de facto the lender of last resort of governments in the euro area. Before that date, the ECB had always denied that such a role was within its duties. This turnaround had a remarkable impact on the expectations of financial market participants, leading to a sharp reduction of the likelihood of a euro area break up. As a consequence, starting with August 2012 the price of Greek bonds (together with those of other high debt European countries) shows an upward trend. The second vertical line in Figure 1 marks the announcement of the buyback invitation made by the Greek Ministry of Finance. From the graph there is a suggestive evidence that the

10

CONTEMPORARY ECONOMIC POLICY

FIGURE 1 Greek Sovereign Bond Prices, Whole Sample (Several Maturities) 60 2024

2023

2028

2027

2026

2025

50

40

30

20

10

0 3/9/2012

4/9/2012

5/9/2012

6/9/2012

7/9/2012

8/9/2012

announcement had a positive impact on the price of the securities purchased through the transaction, as expected. A more accurate picture emerges from Figure 2, which reports the same prices reported in Figure 1 but it is focused on a shorter time span, so to expand the evidence around the date of the buyback. Here the first line refers to the announcement date again, while the second line marks the closing date of the deal: after this date the bond prices stop increasing for about 1 week, for the reason explained below (related to the aggressive pricing of the buyback invitation). B. Econometric Evidence While the descriptive evidence shown in Figures 1 and 2 is suggestive and consistent with the theory developed in the previous section, it needs to be confirmed by an econometric analysis, so to test whether the effects of the buyback, detected by the simple plot of the bond price time series, are actually statistically significant. Moreover, the analysis below will allow us to

9/9/2012 10/9/2012 11/9/2012 12/9/2012 1/9/2013

check whether the empirical findings presented here are robust when we take into account other developments related to the European sovereign debt crisis. To test my hypothesis about the price impact of the buyback, the following model has been run for each of the six time series available: (Model 1) dPt = α + β1 D_ECBt + β2 D_NEWSt + β3 D_ENDt + εt where the dependent variable dPt is the day-today differenced bond price, for each maturity: first differences (dPt = Pt − Pt−1 ) are used to deal with the trend and to avoid any problem related to the nonstationarity of the bond price time series (Pt ). D_ECBt is a dummy variable taking value 1 on those days starting with July 27, 2012 and zero before then: this variable should capture the impact of the change of strategy of the ECB, announced on that date by President Draghi; the expected sign of β1 is positive. D_NEWSt takes value 1 since

BAGLIONI: BUYBACKS OF SOVEREIGN DEBT

11

FIGURE 2 Greek Sovereign Bond Prices, Focus Around Buyback (Several Maturities)

2024

2023

2028

2027

2026

2025

44 42 40 38 36 34 32 30 28

December 3, 2012 and zero before then: this was the announcement date of the buyback transaction; for all the reasons outlined above, the expected sign of β2 is positive. D_ENDt takes value 1 since December 12, 2012 and zero before then: this was the date when the transaction was closed and its outcome was announced. Given that December 11 was the last day when the bondholders could sell their bonds at the aggressive bidding price announced by the Greek Ministry of Finance, the expected sign of β3 is negative: as suggested in Figure 2, the day-to-day price change turns from positive to null right after the closing date. However, we should expect the sum (β2 + β3 ) to be still positive, since the overall price impact of the transaction is supposed to be positive, for the same arguments leading to Propositions 2 and 5. Finally, εt is the error term. Table 4 reports the outcomes of the regressions. The estimated coefficients have the expected sign and their significance level is generally quite satisfactory. In particular, the new stance of the ECB policy had a clear positive impact on the pattern of Greek bond prices. The

announcement of the buyback invitation had an even larger impact: following such announcement, the daily price change shows an increase between 0.6 and 0.8 basis points. After the closing day of the transaction, the daily price change was lower by 0.5/0.6 b.p. than before. So, as expected, the overall price impact of the leveraged buyback was positive (the daily price change increased by more than 0.1 b.p.), reflecting both the subsidized interest rate applied on the EFSF loan and the creditor status of the EFSF. The outcome of the Greek buyback for the parties involved in the transaction is consistent with the statement of Proposition 2, namely that the subsidy provided by the Fund is shared between the debtor country and its private lenders. On one hand, the interest rate applied on the official loan to Greece does not reflect the risk incurred by the EFSF and by the euro area governments: an OSI is rather likely, or at least it was considered so at the time when the loan was made; therefore, the deal implies an expected loss for the official lenders. On the other hand, the buyback enabled the Greek

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CONTEMPORARY ECONOMIC POLICY

TABLE 4 Greece: Model 1 Estimation (OLS) (Dependent Variable: dPt [Several Bond Maturities]) α β1 β2 β3 β2 + β3 Adjusted R 2

2023

2024

2025

2026

2027

−0.064 0.271∗∗ 0.808∗ −0.645 0.163 0.061

−0.083 0.287∗∗∗ 0.729∗∗∗ −0.585∗∗ 0.144 0.058

−0.090 0.299∗∗∗ 0.668∗∗ −0.555∗ 0.113 0.076

−0.093 0.306∗∗∗ 0.632∗∗ −0.484∗ 0.148 0.101

−0.084 0.300∗∗∗ 0.638∗∗∗ −0.530∗∗ 0.108 0.096

2028 −0.087 0.285∗∗∗ 0.634∗ −0.513 0.121 0.089

Notes: Range: 2012/03/12 to 2013/01/09. No. of observations: 218 (daily data). ∗∗∗ Significant at 1% level; ∗∗ significant at 5% level; ∗ significant at 10% level based on HAC standard errors.

government to reduce the face value of its obligations, thus reducing the payments to be made to its creditors and contributing to the stabilization program agreed between Greece and its European partners, which should lead to a gradual decline of the debt-to-GDP ratio over the medium term. That program, which includes heavy austerity measures, is aimed at allowing Greece to regain access to financial markets, also by minimizing any chance of exit by Greece from the euro area. As far as private creditors are concerned, they are better off since the probability of a second default (after the PSI of March 2012) has been reduced, and this has been reflected in the higher price of the securities they hold. The empirical results obtained here are consistent with the few available previous studies on debt buybacks. In particular, Sachs (1988) finds that the buyback of the Bolivian government debt in 1986 made the market price of debt increase from 5% to 11% of its face value. According to Sachs, the deal was beneficial not only to creditors, but also to the debtor country, since the debt relief allowed the Bolivian government to put in place a successful stabilization program. A crucial element behind that success was the subsidy provided by some foreign governments, which donated the money used in the buyback. As we have seen, the subsidy provided by other European governments (through the EFSF) was one of the key elements also in the Greek buyback deal, although in this case it was in the weaker form of a concessionary interest rate applied to the official loan. Acharya and Diwan (1993), using a sample of 17 highly indebted countries over the period 1985 to 1987, find that for those countries engaging in buyback deals the secondary market price of government debt was significantly higher (by 16.5%) than for the other countries. They interpret their findings

in two ways: (1) buybacks signal the willingness of a government to invest and to increase debt repayment, (2) debt repurchases reduce the default risk of the remaining debt, thus raising its price. The latter interpretation is consistent with my model, particularly with the continuous version of Section III, and with the evidence I provide for the Greek deal. C. Robustness Checks In this subsection, I present some robustness checks of the empirical analysis presented above. In doing so, I will take as a benchmark another highly indebted country of the euro area: Italy. This country, with a debt-to-GDP ratio above 120% in 2012, has been heavily hit by the European sovereign debt crisis from mid2011 onwards; since then, the Italian government bond prices have reflected all the global developments of such a crisis, in addition to the specific Italian events. Therefore, they are a good benchmark to be compared with the patterns of the Greek government bond prices. As a first check, the same regression run above for Greek bonds (Model 1) has been run for the Italian 10-year government bonds. My expectation here is that Italy has been affected by the announcement of the change of strategy made by the ECB in July 2012, since this announcement leads to sharp decrease of the fears of a break-up of the monetary union, to the benefit of those holding bonds issued by the so-called “peripheral” countries (also called “PIIGS”: Portugal, Italy, Ireland, Greece, Spain). To the contrary, I do not expect that the buyback deal had a significant impact on the Italian government bonds, since that has been a specific event, with an impact presumably limited to the creditors of Greece. Table 5 shows the regression results, which confirm those

BAGLIONI: BUYBACKS OF SOVEREIGN DEBT

TABLE 5 Italy: Model 1 Estimation (OLS) (Dependent Variable: dPt [10-year Maturity]) α β1 β2 β3 β2 + β3 Adjusted R 2

−0.080 0.206∗∗ −0.420 0.469 0.049 0.012

Notes: Sample range: 2012/03/12 to 2013/01/09. No. of observations: 218 (daily data). ∗∗ Significant at 5% level based on HAC standard errors.

expectations. On one hand, the price of the Italian government bonds has been positively affected by the announcement made by President Draghi: the impact is statistically significant, and its size is similar (although a bit lower) to that obtained for the Greek government debt, thus confirming the relevance of the turnaround in the ECB strategy. On the other hand, both the announcement of the Greek buyback deal and its closing date had no significant impact on the Italian government bonds, thus confirming the specificity of this event, related to the management of the Greek sovereign debt. The second robustness check has to do with all the factors, related to the developments of the European sovereign debt crisis other than the Greek buyback, that possibly affected the price of the Greek securities during the period under study. In order to control for those factors, the following regression (Model 2) has been run, where the dependent variable is again the day-to-day differenced price of the Greek government bonds (with maturities ranging from 2023 through 2028), and St is the yield spread between the Italian and German 10-year government bonds: the day-to-day

13

differenced yield spread between Italy and Germany (dSt = St − St−1 ) has been added into this model to check whether, after controlling for other developments of the crisis, the outcomes obtained above still hold. (Model 2) dPt = α + β1 D_ECBt + β2 D_NEWSt + β3 D_ENDt + β4 dSt + εt By looking at Table 6, we get a definite positive answer: the size and statistical significance of all the coefficients are quite similar to those shown in Table 4, confirming the robustness of the previous estimates. Moreover, the estimated coefficient of the Italian spread over Germany is significant and it has the expected negative sign: an increase of this spread signals higher tensions in the market for the PIIGS government bonds, possibly due to some bad news, which not surprisingly have a negative impact on the price of the Greek government bonds as well. V.

CONCLUDING REMARKS

In this article, we have seen that the outcome of a leveraged buyback crucially depends on the priority structure defining the rights of the different lenders to a country. If part of the existing debt is replaced by senior debt held by an official creditor (the Fund in this paper), the country is able to benefit from the deal at the expense of private lenders: the government debt is reduced, implying a lower probability of default; the recovery rate of private lenders declines, leading to a lower market price of outstanding bonds. The opposite holds if part of the existing debt is replaced by junior debt. In the intermediate case, where the Fund retains the same creditor status as private

TABLE 6 Greece: Model 2 Estimation (OLS) Dependent Variable: dPt [Several Bond Maturities] α β1 β2 β3 β4 β2 + β3 Adjusted R 2

2023

2024

2025

2026

2027

−0.044 0.232∗∗ 0.879∗∗ −0.735∗ −1.102∗∗∗ 0.144 0.085

−0.065 0.252∗∗ 0.793∗∗∗ −0.665∗∗ −0.974∗∗ 0.128 0.077

−0.077 0.274∗∗∗ 0.714∗∗ −0.613∗∗ −0.702∗∗ 0.101 0.088

−0.073 0.267∗∗∗ 0.703∗∗ −0.574∗∗ −1.094∗∗∗ 0.129 0.144

−0.072 0.275∗∗∗ 0.687∗∗∗ −0.584∗∗ −0.694∗∗ 0.103 0.111

2028 −0.071 0.255∗∗∗ 0.689∗∗ −0.583∗ −0.850∗∗ 0.106 0.113

Sample range: 2012/03/12 to 2013/01/09. No. of observations: 218 (daily data). ∗∗∗ Significant at 1% level; ∗∗ significant at 5% level, and ∗ significant at 10% level based on HAC standard errors.

14

CONTEMPORARY ECONOMIC POLICY

lenders, the deal does not imply any wealth redistribution between the debtor country and its bond-holders. Moreover, if the loan made by the Fund is underpriced, the implied subsidy is shared between the borrowing country and its private lenders, who can benefit from a price increase of their bonds. This is actually what happened with the buyback of Greek sovereign bonds in 2012: the empirical analysis confirms the predictions of the model, and it is robust to the control for other factors affecting the euro area government debt crisis. It is worth stressing that all the results, obtained here for leveraged buybacks, do not depend on the share of country’s endowment that creditors can seize in case of default, which instead plays a crucial role in shaping the outcome of unlevered buybacks. The issue of priority in sovereign debt markets has been debated for a long time. In particular, the seniority of international financial institutions (IFIs)—like the IMF and the Word Bank—is a controversial issue. The IFIs do not retain a legal seniority: they are formally on the same grounds of private lenders. However, they are informally considered senior: governments prefer to use the available resources to repay the IFIs before private lenders, in order to maintain the availability of their financial assistance. Under this regard, IFIs play the same role as a lender of last resort: they typically lend to governments when private financial markets do not, and they do so at concessionary terms. So a government will always try to avoid losing this source of funding. However, it also true that the IFIs are often willing to reschedule their claims, leaving the debtor country the time to repay when its economy recovers enough that it can sustain the burden of repayments: this behavior, which is quite different from that of private lenders, weakens substantially the preferred creditor status of the IFIs. Bulow, Rogoff, and Bevilaqua (1992) found that official creditors—IFIs and governments—received de facto equal priority with private creditors in the debt crisis episodes of the 1980s. Roubini and Setser (2004, chapter 7) provide arguments supporting the seniority of the IFIs, but they acknowledge that the preferred status of the IFIs has been often disputed by private creditors (in particular, they have a detailed report on Argentina). In Europe, a dispute over the de facto seniority of the ECB has taken place, when the Greek government has inflicted heavy losses to private bondholders through the PSI (March 2012): the

bonds held by the ECB were not hit by the swap operation; however, the ECB has committed to give back any profit made on those bonds to national governments, which in turn should use them as a source for financial aid to Greece. The bottom line is that the seniority of official lenders to sovereigns is controversial and it remains an open issue. APPENDIX A: UNLEVERED BUYBACKS The literature on buybacks traditionally considers the case where the government of a country decides to use an amount of own resources (reserves, tax revenues, or else) to purchase part of its own debt.7 My model can be applied to review this case, and this is done in this appendix by using the simple two-state version of Section II. We keep denoting by C the money spent by the government to buy an amount (face value) of own debt equal to X. Following this deal, the country is left with an endowment equal to W − C. Hence the post-buyback present value of its debt is V (D − X) = (1 − πd )(D − X) + πd θ(WL − C), and the post-buyback price of debt is determined accordingly: P1 = (1 − πd ) + πd (θ(WL − C)/(D − X)).8 Does the country gain or lose from the buyback? To answer this question, we have to compute its net benefit (Y ), which of course is the difference between the expected gain and cost of the deal. The gain comes from the reduction of the expected liability of the country: (A1)

(1 − πd )X + πd θC

which is the sum of two terms: the reduction of the face value of outstanding debt (times the probability of the nondefault state), and the reduction of the resources left for debt repayment in the default state (times its probability). The cost of the deal is C. Hence the net benefit for the country is given by: (A2)

Y = (1 − πd )X − C[1 − θπd ].

The deal is a zero-sum game: the net benefit for the country is matched by a net loss of the same size for the bondholders. We can check that this is the case by computing the difference between the post-buyback and the pre-buyback expected claim of the bondholders as a group (including both those holding and those selling their bonds): V (D − X) + C − V (D), which turns out to be equal to −Y . Equation (A2) shows that Y depends, among other things, on θ. This parameter is crucial to determine whether the buyback goes to the benefit either of the debtor country or of its lenders. Intuitively, if θ is high the country is able to shift a large share of the cost of the buyback to bondholders, by reducing the resources available for debt repayment in the default state; then the country benefits from the buyback at the expense of bondholders (Y > 0). The opposite holds if θ is low enough. This argument is formally stated in the following proposition. 7. Actually, the literature has also considered the case where the buyback is financed by a donor, as in the example of Bolivia. I have already incorporated this case into my model as an extreme type of subsidized loan (see Sections II.B and III.B). 8. We are implicitly assuming that θ(WL − C) < D − X < θ(WH − C), so that πd is still the probability of default.

BAGLIONI: BUYBACKS OF SOVEREIGN DEBT PROPOSITION 6. ∃θ ∈ (0, 1) such that Y ≥ 0 iff θ ≥ θ. A limit case is that where θ = 1. From Equation (A2) we get: Y = (1 − πd )(X − C) > 0 (since C/X = P1 < 1). When the sum C spent for the buyback goes entirely to reduce the resources available for debt repayment in the default state, the debtor country bears the cost of the buyback only in the nondefault state. Since in this state the country also gets a debt reduction equal to X > C, the net effect of the buyback is a transfer of wealth (equal to Y ) from the lenders as a group to the debtor country. This is the case analyzed in Krugman (1988a), where the whole sum spent for the buyback is subtracted from the reserves of the country. If the lenders lose from the deal, we should expect that the market price of debt declines when the buyback is announced. The following proposition says that this is the case: the post-buyback price of debt must be lower than the pre-buyback price. PROPOSITION 7. If θ = 1, it is P1 < P0 . At the opposite extreme, there is the special case analyzed by Bulow and Rogoff (1988), where the resources available for debt repayment are not affected at all by the buyback.9 In such a case, the deal reduces the country’s expected liability only by (1 − πd )X (the second term in (A1) vanishes), and the country bears the full cost C of the buyback. Then the net benefit for the country is Y = (1 − πd )X − C < 0 (since C/X = P1 > (1 − πd )). In other words, the buyback transfers some wealth from the debtor country to its lenders. The latter gain from an increase of the market price of their bonds, due to the higher recovery rate in the default state: the same amount of resources is devoted to repay a lower face value of debt. Formally: P0 = (1 − πd ) + πd (θWL /D) and P1 = (1 − πd ) + πd (θWL / (D − X)), implying that P1 > P0 .

APPENDIX B: PROOFS Proof of Proposition 1 (i) Condition in Equation (7) with k = 1 implies F = C. Hence Y = (1 − πd )(X − C) > 0 (since C/X = P1 < 1). The post-buyback price of debt is the following: (A3)

P1 = (1 − πd ) + πd (θWL − C)/(D − X)

15

(iii) Conditions in Equations (7) with k = θWL /(D − X + F ) and (8) together imply the following equation, which determines the equilibrium value of F : (1 − πd )F + πd (θWL /(D − X + F ))F = (V (D − X)/(D − X))X and the solution is F = X. Hence Y = 0 and P1 = (1 − πd ) + πd (θWL /D) = P0 . Proof of Proposition 2 (i) Let k = 0. The Fund’s expected payoff is: −C + (1 − πd )C = −πd C. From Equation (6), the country’s expected payoff is Y = (1 − πd )(X − C) > 0. The private lenders’ expected payoff can be computed by taking the difference between their post-buyback expected claim as a group (including those lenders holding as well as those selling their bonds) and their pre-buyback expected claim: V (D − X) + C − V (D) = C − (1 − πd )X > 0. The expected gains obtained by the country and by its private lenders add up to πd C. Let k = θWL /(D − X + F ). The Fund’s expected payoff is −C + (1 − πd )C + πd (θWL /(D − X + C))C, which can be written as: −πd C (1 − (θWL /(D − X + C))) .

(A4)

Again, the country’s expected payoff is Y = (1 − πd )(X − C). The private lenders’ expected payoff, V (D − X) + C − V (D), is: C − (1 − πd )X − πd (θWL /(D − X + C))C > 0 where the inequality can be checked by substituting P1∗ X to C and writing the above expression as: X(1 − P1∗ )(πd θWL /(D − X(1 − P1∗ ))). Simple algebra shows that the expected gains obtained by the country and by its private lenders add up to minus as in Equation (A4). (ii) k = 0 implies P1 = (1 − πd ) + πd (θWL /(D − X)). k = θWL /(D − X + F ) and F = C imply P1∗ = (1 − πd ) + πd (θWL /(D − X + C)). Hence P1 > P1∗ . Since C < X and P0 = (1 − πd ) + πd (θWL /D), it is P1∗ > P0 . Proof of Proposition 3 Let F < X. The difference V (D) − [V (D − X) + V (F )] can be expanded by using Equations (10) and (17):  D/θ   1 − G(D/θ) D + θWg(W )dW W

where, in the second term on the right-hand side, the recovery rate has been derived by subtracting the Fund’s claim (C) from the resources available to repay private lenders (θWL ): this residual amount must be shared among all those creditors holding the outstanding debt, whose face value is D − X. Let P1 ≥ P0 . By substituting Equations (2) and (A3) into this inequality, we get P1 ≤ θWL /D. But since P0 > θWL /D, P1 ≥ P0 implies P1 > θWL /D. This is a contradiction. Therefore it cannot be P1 ≥ P0 . (ii) Condition in Equation (7) with k = 0 implies F = C/(1 − πd ). Hence Y = (1 − πd )X − C < 0 (since C/X = P1 > (1 − πd )). P0 = (1 − πd ) + πd (θWL /D) and P1 = (1 − πd ) + πd (θWL /(D − X)) imply that P1 > P0 . 9. This does not mean that θ is set to zero.

  − 1 − G((D − X + F )/θ) (D − X + F )  (D−X+F )/θ − θWg(W )dW W

which in turn can be written as follows:  (D−X+F )/θ   1 − G(D/θ) D + θWg(W )dW  +

W D/θ (D−X+F )/θ

−(D − X + F )

θWg(W )dW + 

D/θ

g(W )dW (D−X+F )/θ

  − 1 − G(D/θ) (D − X + F ) −



(D−X+F )/θ

θWg(W )dW

W

16

CONTEMPORARY ECONOMIC POLICY

which simplifies into:

which, through computations similar to those made in point (i), can be simplified into:

  1 − G(D/θ) (X − F )  D/θ [θW − (D − X + F )] g(W )dW > 0. +

 1/(D − X) 

W

  > 1 − G(D/θ) + 1/D

F /θ

 +

(1 − θW/D)g(W )dW > 0.

(iii) By using Equations (15) and (16), it is immediate to see that V (F )/F = V (D − X)/(D − X), which—for the same reason as in point (i)—implies F = X. Therefore   V (D − X)/(D − X) = 1 − G(D/θ)  D/θ + 1/D θWg(W )dW

W (D−X+F )/θ

W

(θW − F )g(W )dW > 0.

implying P1 = P0 . Proof of Proposition 5 The inequality P1 > P1∗ can be written as follows (by inserting Equations (14) and (16), respectively into V (D − X)/(D − X)):  (D−X)/θ   1 − G((D − X)/θ) + 1/(D − X) θWg(W )dW

F /θ

Since G((D − X + F )/θ) can be written as  G(F /θ) +

(D−X+F )/θ

g(W )dW F /θ

inequality in Equation (A5) can be simplified into:

W

  > 1 − G((D − X + C)/θ)  (D−X+C)/θ +1/(D − X + C) θWg(W )dW

F /θ 1/F θWg(W )dW W (D−X+F )/θ

D/θ

(D−X)/θ

G((D − X + F )/θ) − G(F /θ)  F /θ + 1/F θWg(W )dW − 1/(D − X)



θWg(W )dW

W

or equivalently:

+

D/θ

and simplified into:  (D−X)/θ   θW/(D − X) − θW/D g(W )dW

θWg(W )dW

F /θ

×



W

  > 1 − G((D − X + F )/θ) + 1/(D − X)  (D−X+F )/θ × (θW − F )g(W )dW



 1 − (θW − (D − X))/F g(W )dW > 0

where (θW − (D − X))/F < 1 in the relevant integration interval. The inequality P1 > P0 is equivalent to V (D − X)/(D − X) > V (D)/D, which can be written as follows:  (D−X)/θ   1 − G((D − X)/θ) + 1/(D − X) θWg(W )dW

W

(A5)



(D−X)/θ

Proof of Proposition 4 (i) F < X is equivalent to C/F > C/X, which in turn can be written as V (F )/F > V (D − X)/(D − X) (thanks to the assumption that V (F ) = C and to the price equilibrium condition in Equation (8)). Therefore (by using Equations (11) and (12)) F < X is true if the following inequality holds:  1 − G(F /θ) + 1/F

(D−X+F )/θ

+

Similar computations show that V (D) − [V (D − X) + V (F )] < 0 if F > X. If F = X, V (D − X) + V (F ) is trivially equal to V (D).



θWg(W )dW

W

(D−X+F )/θ



(D−X)/θ



W

 1 − (θW − F )/(D − X) g(W )dW > 0

which can be simplified into:  (D−X)/θ   θW/(D− X)− θW/(D− X + C) g(W )

F /θ

which is true since (θW − F )/(D − X) < 1 in the relevant integration interval. (ii) For the same reason as in point (i), F > X is true if the following condition holds (where Equations (13) and (14) have been used):



 1 − G((D − X + F )/θ) + 1/F

W



(D−X+C)/θ

×dW +

  1 − θW/(D − X + C) g(W )dW > 0.

(D−X)/θ



(D−X+F )/θ

[θW − (D − X)] g(W )dW

(D−X)/θ

  < 1 − G((D − X)/θ) + 1/(D − X)



(D−X)/θ

W

θWg(W )dW

BAGLIONI: BUYBACKS OF SOVEREIGN DEBT The inequality P1∗ > P0 can be written as:   1 − G((D − X + C)/θ)  (D−X+C)/θ +1/(D − X + C) θWg(W )dW W



 > 1 − G(D/θ) + 1/D



D/θ

θWg(W )dW

W

which can be simplified into:  (D−X+C)/θ   θW/(D − X + C) − θW/D g(W )dW W

 +

D/θ

(1 − θW/D)g(W )dW > 0

(D−X+C)/θ

where the first integral is positive since C < X. Proof of Proposition 6 Define θ =

1−

(1−πd ) P1 πd

. P1 > (1 − πd ) ⇒ θ > 0. P1 < 1

⇒ θ < 1. By solving the inequality Y ≥ 0 (where Y is given by Equation (A2)) for θ, we get θ ≥ θ. Proof of Proposition 7 The same argument which was used to prove that P1 < P0 in Proposition 1-(i) applies here (with θ = 1). REFERENCES Acharya, S., and I. Diwan. “Debt Buybacks Signal Sovereign Countries’ Creditworthiness: Theory and Tests.” International Economic Review, 34(4), 1993, 795–817. Baglioni, A. “Leveraged Buyback: A Proposal for the Greek Debt Overhang.” VOX, May 21, 2011. Bulow, J., and K. Rogoff. “The Buyback Boondoggle.” Brookings Papers on Economic Activity, 1988(2), 1988, 675–704. . “Debt Repurchases: No Cure for Overhang.” Quarterly Journal of Economics, 106(4), 1991, 1219–35.

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Bulow, J., K. Rogoff, and A. Bevilaqua. “Official Creditor Seniority and Burden-Sharing in the Former Soviet Bloc.” Brookings Papers on Economic Activity, 1992(1), 1992, 195–222. Claessens, S., and G. Dell’Ariccia. “Are Buybacks an Efficient Way to Reduce Sovereign Debt?” VOX, March 5, 2011. Detragiache, E. “Sensible Debt Buybacks for Highly Indebted Countries.” The World Bank, Working Paper 621, 1991. Hufbauer, G., and J. Kirkegaard. “National Buybacks: The Solution for Greek Debt.” VOX, July 14, 2011. Krugman, P. “Market-Based Debt-Reduction Schemes.” NBER Working Paper no.2587, 1988a. . “Financing vs. Forgiving a Debt Overhang.” Journal of Development Economics, 29, 1988b, 253–68. Medeiros, C., M. Polan, and P. Ramlogan. “A Primer on Sovereign Debt Buybacks and Swaps.” IMF Working Paper 07/58, 2007. Panizza, U., F. Sturzenegger, and J. Zettelmeyer. “The Economics and Law of Sovereign Debt and Default.” Journal of Economic Literature, 47(3), 2009, 651–98. Prokop, J., and R. Wang. “Strategic Buybacks of Sovereign Debt.” Queen’s University Economics Department, Working Paper no. 957, 1997. Rotemberg, J. “Sovereign Debt Buybacks Can Lower Bargaining Costs.” Journal of International Money and Finance, 10(3), 1991, 330–48. Roubini, N., and B. Setser. “Bailouts or Bail-Ins? Responding to Financial Crises in Emerging Economies”. Washington, DC: Peterson Institute for International Economics, 2004. Sachs, J. “Comprehensive Debt Retirement: The Bolivian Example.” Brookings Papers on Economic Activity, 1988(2), 1988, 705–13. Thomas, J. “Default Costs, Willingness to Pay, and Sovereign Debt Buybacks.” Journal of Restructuring Finance, 1(1), 2004, 35–47. Tomz, M., and M. Wright. “Empirical Research on Sovereign Debt and Default.” Federal Reserve Bank of Chicago, Working Paper 2012-06, 2012.