18 . Debt restructuring schemes - SWEETsweet.ua.pt/afreitas/aulas/notas apoio/debtcrisis.pdf ·...

Politicas macroeconomicas, handout, Miguel Lebre de Freitas ([email protected])

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15/08/2018, http://sweet.ua.pt/afreitas/aulas/notas%20apoio/notasmacro.htm

18 . Debt restructuring schemes

Index:

18 . Debt restructuring schemes..............................................................................1

18.1 Introduction........................................................................................2

18.2 When the sovereign is insolvent ........................................................2

18.2.1 Why liquidity problems?..........................................................................2 18.2.2 Main assumptions ....................................................................................2 18.2.3 The deterministic case..............................................................................3 18.2.4 Maximum expected repayment under uncertainty...................................4 18.2.5 Expected to be solvent .............................................................................4 18.2.6 Expected to be insolvent ..........................................................................6 18.2.7 Defensive lending ....................................................................................7 18.2.8 Incentive problems...................................................................................8

18.3 Debt reduction schemes .....................................................................8

18.3.1 Debt forgiveness ......................................................................................9 18.3.2 Third party buy backs ..............................................................................9 18.3.3 Self-financed Debt buy-back .................................................................10 18.3.4 Debt swap...............................................................................................11

18.4 The debt-relief Laffer curve.............................................................12

18.4.1 Endogenous probability .........................................................................12 18.4.2 Debt forgiveness under endogenous probability....................................13 18.4.3 Limits on debt forgiveness.....................................................................14 18.4.4 Debt Laffer Curve ..................................................................................15

18.5 Debt restructuring: practical difficulties ..........................................16

18.6 Main ideas........................................................................................17

Further reading.............................................................................................18

Review questions and exercises...................................................................................19

Review questions .........................................................................................19

Problems ......................................................................................................19


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18.1 Introduction

This note addresses the case of a sovereign that is expected to fail its debt obligations.

When creditors believe that the sovereign will not be able to service its debt, the market value

of that debt will fall short its contractual (face) value. This situation is labelled “debt

overhang”.

In this note, we address the problem of debt overhang and the avenues that can be

explored to get rid of it. The analysis is restricted to debt that is denominated in foreign

currency, that is, debt that the sovereign cannot get rid off by printing money. This note is

organized as follows: In Section 16.2, we distinguish the case in which the sovereign is

expected to be insolvent from the case in which the sovereign is expected to be solvent, even

if some probability exists of not being so. In Sections 16.3 and 16.4 we review alternative

mechanisms through which a country debt can be sized down, accounting for an eventual

impact on the probability of repayment. Finally, in Section 16.5 we discuss the coordination

failure underlying debt restructuring deals, and the role of collective action clauses in

mitigating that failure.

18.2 When the sovereign is insolvent

18.2.1 Why liquidity problems?

Liquidity concerns the ability of a country to attract new borrowing. A liquidity

problem arises when, in face of some new information, a country’ solvency comes into

question. The following examples illustrate this.

18.2.2 Main assumptions

Consider a two period economy. In this economy, there is a sovereign that inherits

some positive debt, 0D , which matures at the beginning of period 1. To service its debt, the

government relies on primary surpluses (deficit if negative), 1s , and 2s . Depending on the

framework, the primary surplus in period 2 may be deterministic or stochastic.


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In case 01 Ds , a new loan 1L , will be needed in period 1. Since there are only two

periods, there will be no new loan at the end of period 2.

It is further assumed that the opportunity cost of funds for creditors is equal to i . For

simplicity, it is assumed that all government debt takes the form of discount bonds – that is,

the yield is implied by the difference between the price at which debt is purchased in the

primary market and the redemption value.

18.2.3 The deterministic case

In a context with certainty, the conditions for solvency is 01

210

i

ssD . Thus, as

long as

MaxLi

ssD 1

210 1

, (1)

the sovereign will be solvent. In this case, it will be easy to hire a new loan, equal to

101 sDL . Since the sovereign is solvent, the interest rate in the new loan will be the risk

free one. The face value of the new debt will be iLD 111 (remember that the debt is sold

at discount).

The market value of the new debt will be equal to the present value of the promised

repayment:

11

1 1L

i

DV

. (2)

Hence, the secondary market price of each individual bond will be equal to:

iD

Vq

1

1

1

1 . (3)

This discount delivers exactly a yield equal to the opportunity cost of capital.

The case in which the sovereign is insolvent arises when:

MaxLi

ssD 1

210 1

(4)

In this case, the country will not be able to roll over the remaining debt. Holders of

the previous debt have to accept an immediate “write off”. The new lending shall be, at most


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i

sL

12

1 , because this is the maximum loan the government can serve. Hence, holders of the

initial debt will face an “hair cut” amounting to i

ssD

12

10 .

Once the debt reduction is achieved, the sovereign becomes exactly solvent. Thus, the

interest rate in the new loan will be the risk free rate. The face value of the new debt will be

211 1 siLD . As before, the secondary market price of this debt will be (3), delivering a

yield equal to the opportunity cost of capital.

18.2.4 Maximum expected repayment under uncertainty

The more interesting case arises in a context of uncertainty. Expected insolvency

arises when debt is so large relative to future revenue prospects that lenders no longer expect

to be fully repaid.

To examine this case, assume that the government’ future surplus can be high or low,

depending on the materialization of two alternative states of nature.

Let Gs2 be the primary surplus in the good state, Bs2 the primary surplus in the bad

state, and p the probability of bad state. In this case, the present value of the maximum

amount of resources the country is expected to generate in the future is

i

spps

i

sEL

GBMax

1

1

1222

1 . (5)

Even in this stochastic context, there are two trivial cases: the country will not be

solvent for sure if:

i

ssD

G

12

10 (6)

The country will be solvent for sure if:

i

ssD

B

12

10 . (7)

Otherwise, we don’t know.

18.2.5 Expected to be solvent


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Assume that the government is insolvent in the bad state, but is expected to be solvent

on average. That is, condition (7) does not hold, but

i

sEsD

12

10 . (8)

In this case, risk neutral lenders will be willing to roll over the existing debt, even

knowing that the country will be unable to meet its obligations in case the bad state

materializes. The only issue is to set out a high enough interest rate in the new loan, Gi , to

compensate lenders for the risk of default. The face value of the new debt GiLD 111 will

be such that the current value of expected repayments is equal to the amount lent today:

1

11 1

1L

i

psDpV

Bs

.

Implying

p

Lpsii

Bs

g

1

11 1 (9)

Thus, the required yield will depend on the probability of the bad state and also on the

dimension of the “hair cut” in the principal, in case the bad state materializes.

Reflecting the higher promised yield, the secondary market price of each individual

bond will be equal to:

GiD

Vq

1

1

1

1 . (10)

As for a numerical example, consider the following:

10010 sD , i=1%, Gs2 120, 752 Bs , p=1/3.

In this case,

10096.103

01.01

8025

12

1

i

sELMax

Hence, the sovereign is expected to be solvent, even if it will not be in case the bad

scenario materializes.

The interest rate in the new loan, Gi has to be such that the promised repayment (the

face value of the new debt, GiLD 11 ), obeys to the arbitrage condition


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100

1

751 11

Li

pDpV . This gives 1141 D . That is, the government hires a loan

amounting to 100 today, promising to repay 114 in one year time. The expected repayment of

these bonds is 101, which present value (market value of the new debt) is exactly 1001 V .

The new debt will be sold at discount:

114

100

1

1 D

Vq

Implying the promised yield of 14%. Note however this yield will hold with the

probability of 2/3, only. With probability 1/3 the yield will be -25%. On average, the

expected yield exactly matches the opportunity cost of capital, 1%.

18.2.6 Expected to be insolvent

Consider now the case in which condition (6) does not hold, but

i

sEsD

12

10 , (11)

In this case, full repayment is possible but not likely. In other words, the country is

expected to be insolvent, even if there is some probability that the debt is fully repaid.

The maximum possible interest rate in the new loan is such that GG siLD 211 1 .

That is1:

1

21L

si

G

G (12)

In this case, creditors get all the reward in the good state.

1 Note that the interest rate in the new loan may be lower than the risk free rate.


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Because the market price of the new debt is less than the amount lent, the new lending

will come along with an expected loss. The write off does not occur immediately, however,

because it is the interest of creditors to lend again and be entitled with full repayment in case

the good scenario materializes.

Example:

10010 sD , i=1%, Gs2 120, 302 Bs , p=1/3. In this case,

10

21 109.89

01.01

8010

1sD

i

sELMax

The maximum achievable interest rate in the new loan, Gi is 20% (that is,

1201 D ).

The market value of the new debt will be MaxL

ppV 11 01.01

301201

. Hence, the

new loan L will involve a market value loss equal to 10.9 to creditors.

The secondary market price of the new bond will be:

7425.0120

109.89

1

1 D

Vq

The implied yield is 34.6%, but this will happen with probability 2/3. With probability

1/3 the buyer of this bond will get 30 out of an investment of 89.109, which delivers a yield

of -66.3%. On average, the expected yield is only 1%.

Note that the maximum possible interest rate in the new loan can be lower than the

risk free rate. If, for instance, Gs2 100, the maximum interest rate in the new loan will be

zero, while the risk free rate is 1%.

18.2.7 Defensive lending

We just saw that lending to a country that is expected to be insolvent involves a loss.

Hence, no lender will voluntarily engage in new lending, unless it has a stake in the old debt.

Old creditors, however, will have an incentive to roll over the existing debt, so as to

avoid an immediate default. If no lending takes place, the country will find impossible to

meet all its obligations with the current resources, 1s , and will default immediately. A


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disordered default is not of the interest of existing creditors. Those with a stake in the old

debt have incentive to keep lending in order to protect their claims. By rolling over the

existing debt, current debt holders preserve the possibility of getting paid, in case the

favourable outcome materializes. This is called “defensive lending”: by lending enough to

avoid an immediate default and accepting a loss, creditors actually raise the value of the

claims they already have.

Note however that each creditor will be willing to engage in a new loan provided the

others do the same. Any individual lender would benefit if she could drop out (free riding).

Defensive lending involves a coordination failure. A collective action is therefore needed in

order to avoid the immediate default.

18.2.8 Incentive problems

Setting the interest rate at the maximum possible level GG siLD 21 1 raises a

problem of incentives: if the good state materializes, all the reward accrues to creditors.

Hence, if effort (unpopular measures) is needed for the good state to materialize, the debtor

will have no incentive to do so.

In general, as long as the debtor has the capability to influence the probability of the

good state, it is a good idea to let him share the benefits. Creditors may wish to forgive part

of a country’s debt to increase the likelihood of the good scenario. This can be done setting

an interest rate such that GG siLD 21 1 . To keep the incentives right, it may also be a

good idea to make the payment obligation contingent on events that are out of the country’

control.

18.3 Debt reduction schemes

When the sovereign debt is denominated in foreign currency, it is not possible to

reduce it using inflation or financial repression. Hence, when the time comes that it becomes

the interest of creditors and debtors to reduce a country’ debt, alternative mechanisms have to

be found.


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A debt restructuring is a process through which the stressed debtor reduces its debt

obligations or renegotiates the obligations in the contract, so as to have financial conditions to

proceed. In general, one can distinguish two types of debt-restructuring:

Market based debt-reduction schemes: debt buy-backs, securitization, debt-

equity swaps.

Concerted actions: debt forgiveness, concessional rates, debt rescheduling.

The difference is that the former can be implemented through voluntary actions by

individual lenders, without the need for collective arrangements.

We will see that, the conditions in which market based debt reduction schemes are

beneficial are the same as for concerted debt relief.

18.3.1 Debt forgiveness

Consider the following example:

1201 D , 302 Bs , p=2/3, i=0%.

In this case the expected repayment of the debt will be 60303

2120

3

11 V . The

debt will be sold in secondary markets at discount: 5.0120

60

1

1 D

Vq .

Suppose now that lenders agree to forgive 15. Then: 105'1 D .

The secondary market price of the remaining debt will be:

52.0105

55

105

303

2105

3

1'

'1

1

D

Vq

Thus, bonds appreciate in the secondary markets.

Was this a good deal for creditors? The expected repayment declined by 5, so

creditors are definitely worse off. The reason is that debt forgiveness deprives creditors from

an option value, of sharing the benefits in the case of good fortune.

18.3.2 Third party buy backs


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Consider, in alternative a debt buy-back financed by cash donated by a third party

(say, the World Bank).

Let’s start with

1201 D , 302 Bs , p=2/3. In this case 5.0120

60q .

Suppose the World Bank buys B=15 and then destroys the paper.

After the buy back,

105'1 D , 52.0105

55

105

3032

10531

q

- The debt appreciates in the secondary markets

- The WB spends 0.52*15=7.8

- Total expected payments to private bond-holders are now 7.8+55=62.8>60 (the

private sector gets better by 2.8)

- Expected repayment declined to 55<60 (the sovereign borrower is better).

All in all, the operation comes along with a net loss, because 7.8 of cash reduced

expected repayments by 5 only. The difference is appropriated by the private sector.

Since the benefit of this debt reduction scheme accrues to private creditors, there is no

point for the World Bank to participate, unless there are risks of this crisis to spill over to

other countries (externality).

18.3.3 Self-financed Debt buy-back


1201 D , 302 Bs , p=2/3, i=0.

In plus, the government has 30 of cash that could be used in case the bad state

materialized (for instance, gold reserves at the central bank).


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In this case, the expected repayment of the debt in the base-line scenario will be

80603

2120

3

11 V . Hence, bonds will be priced in secondary markets at

3/2120

80q .

Suppose the government used the cash to buy back its debt in the secondary markets.

The problem is to find out how much of the debt the government can purchase with 30 of

cash. This will be '/30 qB where q’ is the secondary market price of the these bonds after

the buy-back.

After the buy back, the remaining debt will be '/30120'1 qD , worthing

'

106030

3

2

'

30120

3

1'1 qq

V

. Hence,

'30120

'' 1

q

Vq

, which solves for 6143.0'q .

Substituting back, the amount of debt purchased will be B=48.831, 169.71'1 D ,

723.43'1 V .

Note that the secondary market price declined with the buy-back. The reason is that

payments to creditors in the bad state reduced by 30. With the buy-back, the total expected

repayment to creditors declines to 73.723<80. Hence, creditors got worse.

Did the borrower situation improve? The country spends 30 to have the expected

repayment reduced by 36.277 (pocketing 18.831 in the good state). So the country is

definitely better off.

Debtors are normally prohibited to repurchase their debt at discount. One reason is

that this gives sovereigns the incentive to signal low commitment, so as to achieve low

secondary market prices just before the buy back.

18.3.4 Debt swap

Debt buy backs are only possible when governments have cash (foreign exchange)

enough. An alternative possibility is to issue new debt and use the proceeds to buy old debt in

the secondary markets, or even to directly swap the two bonds. As long as the new debt is

senior relative to the old debt, its market price will be higher and the swap will involve a net

debt reduction.



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1201 D , 302 Bs , p=2/3. In this case, the expected repayment of the debt is

60303

2120

3

11 V , so the debt will be priced in secondary markets at discount

5.0120

60q .

Suppose the government issues a new bond (A), senior relative to the old bond, to be

exchanged for old bonds. The amount to be issued is 30.

How much will worth the new bonds? Since the government can repay the new bonds

whatever the scenario is (note that 302 Bs ), the price of the senior bond will be 1.

How much will worth the old bonds? Since the old bonds are only repaid in the good

scenario, their price is q=1/3. This means that:

- The bond-holders will lose (1/3<1/2).

- The swap will consist in exchanging 30 new bonds by 90 old bonds

- After the swap, there will be 30 old bonds priced at 10 and 30 new bonds priced at

30.

- The total expected repayment will be 40, which is less than the initially 60.

In conclusion, a debt buy back financed with the issuance of senior debt benefits the

debtor at the expense of creditors. With no surprise, many lending contracts protect creditors

against the issuance of bonds with higher seniority.

As will see next this conclusion may change if the probability of the good scenario

increases with the debt swap.

18.4 The debt-relief Laffer curve

18.4.1 Endogenous probability

The assumption that the probability of the good state is exogenous is not entirely

reasonable: governments have the potential to influence budgetary outcomes, engaging in

higher or lower adjustment efforts. So when the government is committed, the probability of

default is expected to be lower. In the debt relief debate, it is frequent to assume that the


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government effort declines when the debt level gets too high. The reason is that the effort is

perceived to be useless.

On the other hand, a higher level of debt may impact negatively on private

investment: the reason is that, when the debt level is very high, a significant fraction of the

output gain achieved with the investment will be deviated to debt repayment, through high

taxes. Hence, from an investor’s point of view, a high level of debt acts like a tax on

investment, reducing the after tax return on capital. High indebtedness can then lead to low

investment, low output and ultimately a lower probability of repayment.

In general, when the debt level is very high, the implied fiscal effort will come along

with a depressed economy, and eventually with social and political instability, further

reducing the country growth prospects.

Another reason why the probability of repayment may increase when the debt level

declines is that, when international help is called for, a deal is typically made, whereby the

country commits to some adjustment in exchange for some form of debt relief (haircuts,

restructuring, concessional interest rates, or other). This is equivalent to assume that the

probability of repayment increases when the debt gets smaller.

To account for all these effects, in the following, we discuss the case in which

1Ddp , with d’>0. That is, the higher the debt, the higher the probability of default.

18.4.2 Debt forgiveness under endogenous probability

We now return to the previous numerical example, but assuming instead that the

probability of the bad scenario rises proportionally to the level of debt. That is:

1201 D , 302 Bs , i=0, but replace the probability of default by the following linear

rule: 1801Dp .

In the initial state, the expected repayment of the debt is 60303

2120

3

11 V , so

the secondary markets is 5.0120

60

1

1 D

Vq .


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Now, suppose that a write-off of 15 comes along with a higher effort, so that the

probability of full repayment increases to 12518010511 p . In this case, after the

write off, the market value of the remaining debt will be:

6025.6112

730

12

51051 V

583.0105

25.61q

Note that in this case there is a free lunch:

- The expected repayment increased by 1.25: creditors are better off.

- The government is only committed to pay 105 in case the god state materializes (it

saves 15). This provides the proper incentive for the government to engage in

higher effort.

Hence, it is the interest of both the sovereign borrower and its creditors to negotiate a

certain amount of debt forgiveness, under conditionality.

Note however that no isolated creditor will gain with a unilateral write off. On the

contrary, it will pay to free ride on the others’ efforts. In general, debt forgiveness requires a

concerted action.

18.4.3 Limits on debt forgiveness

In the example above, we saw that a debt level of 105 delivers a higher expected

repayment than a debt level of 120. Hence, it pays for creditors to write off 15.

The question is whether it would be the interest of creditors to engage in a second

write off amounting15, so that the amount of debt outstanding reduced to 90. In that case, the

probability of default would reduce to p=90/180=0.5. Hence, the market value of the

remaining debt would be

25.61602

130

2

1901 V

This example shows that it doesn’t pay to forgive any amount of government debt,

even when the probability of repayment depends negatively on the stock of debt. At some


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point, the benefit to investors of inducing a higher effort is more than offset by the fact that

investors lose the option of receiving the full amount in case the good state materializes.

18.4.4 Debt Laffer Curve

In general, the expected repayment with endogenous probability is given by:

DDpsDpV B 121

This equation implies an inverted U-shape relationship between the level of debt and

expected repayment. This relationship is described in Figure 1, and is known as the debt

Laffer curve. Point B in Figure 1 corresponds to the level of debt that maximizes its market

value, 1V (not its price, q). Analytically, it may be found solving 01 DV .

The debt Laffer curve results as the balance between two opposing effects:

- Debt forgiveness deprives creditors from the option value of sharing the good

fortune.

- Debt forgiveness may increase the probability of the good scenario, by improving

the incentives to the government and private investors.

When D is low (on the left hand side of point B) the first effect dominates the second:

a decline in D will come along wit a fall in the value of expected repayment.

When D is high (on the right hand side of B), the second effect dominates the former:

additional amounts of debt actually lower expected repayments, because the country is so

indebted that the likelihood of the good scenario is very small In that case, a country is said to

be lying on the wrong side of the Laffer curve. In such conditions, a reduction in the size of

government debt, by easing the government budget constraint and also the tax rates on

entrepreneurs, will impact positively on the market value of the remaining debt.

Note that, along the debt Laffer curve, the bonds market price, q, also depends on the

level of debt: pD

sp

D

Vq

B

121 .

Figure 1: The debt Laffer Curve


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18.5 Debt restructuring: practical difficulties

We saw that in some circumstances it may be the interest of both creditors and

sovereigns to restructure a given debt. This happens when the debt reduction initiative comes

along with an increase in the probability of repayment, so that the expected value of

repayment actually increases with the debt relief. In other words, the sovereign must be in the

wrong side of the Laffer curve.

In practice however, achieving a debt reduction deal is not easy. The reason is that

such a deal involves a negotiation with a large number of creditors. While its is the collective

best interest of all creditors to agree in the restructuring process, it is the interest of each

individual creditor not to participate in the deal, free riding on the other creditors’ losses.

Individual creditors that decide not to participate in a debt restructuring in the hope

that they will be able to recover the full value of their claims are labeled “hold out creditors”.

When hold out creditors face a high probability of success, this will reduce the incentive for

other creditors to participate in a debt restructuring deal. This problem has been a source of

delays in debt restructuring process.

In this respect, a recent case involving the Argentine debt did not help: when called

to decide whether holdout creditors of Argentine debt should get paid, the New York courts

invoked the “Pari Passu provision”. The Pari Passu states that all creditors are entitled with

equal treatment. The Pari Passu provision makes sense to prohibit actions that result in

subordination of some creditors over others, such as the issuance of new –senior – bonds.


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But the New York courts interpreted this provision as applying to all holders of Argentinean

debt, irrespectively as to whether they had agreed in the previous re-structuring or they were

opportunistic holdouts. With such decision, Argentina could not service the new debt without

honoring the old un-restructured debt. This decision surprised the markets and created an

incentive problem: by enhancing the expected benefits of holding out, it made future

restructuring agreements more difficult to achieve.

To address the hold out problem, debt contracts often include “collective action

clauses”. Collective action clauses enable a qualified majority of creditors to take a decision

regarding the terms of a debt restructuring that become binding to all bond-holders. Thus, for

instance, if 90% of the creditors agree in a debt-restructuring, the remaining 10% are bound

to accept the decision. A problem however is that these the activation of collective action

clauses require a vote on a per-series basis: that is, bond issuance by bond issuance. Thus, if

for instance most holdout creditors are concentrated in a particular bond series, they may well

block the restructuring in that series. This, in turn, will reduce the willingness of other

creditors in other bond series to consent the restructuring. To address this problem, the IMF

recently proposed the introduction of a unique collective action clause that works for all

bond-holders and across all bond issuances, thus not depending on a issuance-by-issuance

vote2. Of course, such a change will be welcome, but it will take a long time until it becomes

dominant in debt contracts. Meanwhile, dealing with hold outs will be a major difficulty in

debt restructuring.

18.6 Main ideas

If a country is expected to be solvent, there should be no liquidity problem. If

a scenario of non-repayment exists, this will be reflected in a higher interest

2 IMF Survey, “IMF Supports Reforms for More Orderly Sovereign Debt

Restructurings”, October 6 2014.


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rate, only. As long as the sovereign is expected to be solvent, there will always

be risk-neutral investors willing to buy that debt.

When the present value of expected repayments falls short the outstanding

debt, a debt overhang is said to occur. In this case, no new lender will buy the

sovereign debt.

Expectations of insolvency do not necessarily prevent, however, new lending:

old creditors have an incentive to keep lending, even at an expected loss, so as

to avoid an immediate default and protect their claims (defensive lending).

Although it is the collective interest of creditors to avoid the immediate

default, each creditor individually would benefit by opting out (free riding). So

a collective action is needed.

Setting the interest rate at its maximum possible level may not be the best

choice for creditors. In some cases, concessional rates or – which is the same –

partial debt forgiveness, may help get the incentives right.

Debt-buy backs are not in general of interest of debtors. A debt swap implying

a subordination of existing bonds may be the interest of debtors, but hurt

existing creditors.

In general, it is not the interest of creditors to forgive a country’ debt, unless

this improves the probability of repayment of the remaining claims beyond a

certain level. This happens when a country is on the wrong side of the Laffer

curve.

Free riding problem

Further reading

Krugman, Currencies and Crisis

Uribe, M., Scmitt-Grohé, 2013. International Macroeconomics.


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Review questions and exercises

Review questions

18.1. Comment: “Liquidity and solvency are two sides of the same coin”.

18.2. What is meant by “financial repression”? Which measures are included?

18.3. Explain why sometimes it may be the interest of lenders to give up part of their claims on a highly indebted sovereign.

18.4. If you were a lender negotiating a swap of old debt by a new bond, which type of covenants you would like the new bond to have? Under which law?

18.5. Why isn’t the current legal framework regarding collective action clauses considered insufficient to discourage holdout creditors? What is the IMF proposing to solve this problem?

18.6. Why is the recent interpretation of the Pari Passu clause by the New York courts in the case of Argentina debt challenging future agreements in debt reduction schemes? What could be done about this?

Problems

18.7. Consider a sovereign borrower with infinite live whose current debt amounting to pesos 100bn matures today. Further assume that the opportunity cost of funds for (risk-neutral) lenders is 10%.

a) If, from now on, the maximum surplus this government could generate each year was 8bn, would it be solvent? What should creditors do in this case? (A:80<100)

b) Now suppose that this government is perceived to be able to generate a 8bn surplus each year with 75% probability and 20bn surpluses with 25% probability. (b1) would the sovereign face a liquidity problem? (b2) What would be the interest rate a risk neutral lender would set in a new loan? (A: 110; i=16%)

c) Finally, consider the case in which the two scenarios were: 8bn surplus per year with 75% probability and 12bn surplus with 25% probability. (c1) Explain why in this case creditors would have an incentive to engage in “defensive” lending. (c2) How much would be the maximum interest rate in the new loan? (c3) If there was a secondary market for these new bonds, at which price were they expected to be sold? (A: i=12%; q=90)


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18.8. Consider an economy where the government debt, amounts to 100% of GDP. Further assume that there is no growth and that the inflation rate is zero. The opportunity cost of funds to investors is i=10%.

a) Assume the government approves a fiscal rule, according to which the primary surplus has to be at least 14bn each year. Is this surplus enough to stabilize the debt ratio? Explain with the help of a graph.

b) What yield should the government pay to roll over its debt? [A: 10%].

c) Now suppose that investors believed the intended fiscal adjustment to succeed with 50% probability, only. If it fails, investors guess the maximum achievable annual surpluses will be 8bn each year. In that case, how much will be D-Max? [A: 110].

d) In the conditions of c), how much should the government pay in the new borrowing? [A:12%].

e) In case the good scenario materialized, how would the debt ratio evolve?

18.9. The sovereign debt of country A amounts to $480 million and his dispersed by a large number of private agents. The following figure describes the Debt-Relief Laffer curve for this country.

a) Explain the configuration of the debt Laffer curve. How much is the country able to pay in the worst case scenario?

b) What is the initial secondary market price of this debt?

c) Would it pay for lenders to jointly write-off $80 million of this country debt? Explain.

d) Explain why the debt relief raises a coordination problem.

18.10. Consider a sovereign borrower which future primary surplus ( 2s ) is expected to be 100 with probability ¾ and 20 with probability ¼. To simplify, also assume that the risk free interest rate is i=0% and that this government’ bonds are coupon free (issued at discount).

a) What is the maximum loan (L) this government can attract?


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b) If such loan materialized, how much should be the face value of the corresponding security (D)? What would be the yield and the initial secondary price (q) of this bond? [D=100; ig=25%; q=0.8].

c) Represent in a graph the relationship between the market value (V) and the face value of debt for this country. In particular, consider the cases in which: D=20; D=40; D=80; D=100, D=125. Is there a Laffer curve in this case? [A: 20,35,65,80,80].

d) Suppose the initial debt was D=120. Would the government be able to convince investors to forgive 20? Was this solution easy to coordinate? What would be the costs and benefits? [A: no loss for creditors altogether, free riding problem].

e) Now suppose that the initial debt was D=100. Would the government be able to convince investors on a write off amounting to 20? [V’=65<80].

f) Sticking with the case in which D=100, suppose the government issued a new bond (A=20), senior in respect to D, to be exchanged for old bonds. What would be the market price of the old bonds? Who benefited with this swap? [q=0.75; V’+20=75<80 Gov].

18.11. Suppose that the government surplus in the bad state is 102 Bs , and that this

will happen with probability 50Dp . In the good state, the government can always honor its debt, D.

a) Explain the equation describing the probability of bad state.

b) With the assumptions above, what is the level of D that maximizes the secondary market price, q? [A:10].

c) What is the level of D that maximizes its total market value, V? What will be the secondary market price in this case? [A: 18, 0.6]

d) Describe the debt-relief Laffer curve identifying the following cases: D=10; D=20; D=30; D=40; D=50; D=60 [10, 16, 18, 10, 10].

e) Assume that the initial debt was D=40. Would creditors agree in a debt relief amounting to 10? [V’=18>16].

f) In alternative, departing from D=40, assume that the WB purchased ¼ of the outstanding debt in the secondary markets, to subsequently destroy it. How much would that measure cost? Who would be the beneficiaries? [A: 6].

g) Finally, still assuming D=40 initially, consider the possibility of the government issuing new senior bond amounting to 10, to be swapped for old bonds. What would be the new market price for the old debt? Would the private sector benefit with the operation? [A: q’=0.5582; 22.330>16].

18.12. Consider a sovereign borrower whose future primary surplus is expected to be: 10Bs with probability p=0.6 and 60Gs with probability 1-p=0.4. Further assume

that the opportunity cost of funds to creditors is i=0%.

a) (Yield in the new loan): Suppose that the government needs to rollover a loan amounting to L=40, that is equally shared by a large number creditors. Is this government expected to be solvent? Who would be willing to lend? Why? What


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would be the maximum feasible interest rate in the new loan, gi , and the implied face

(maturity) value, D?

b) (Secondary market price): Assume that the face value of the negotiated debt was D=60. Given the probabilities above, how much should be its secondary market price?

c) (Debt Swap) Sticking with D=60 and with the initial assumptions, assume that the government is considering issuing a new, senior bond, amounting to A=10, to be swapped for old bonds. c1) How much should be the secondary market prices of the new bond and of the old bond after the swap? c2) How much of the old debt would be swapped that way? Would creditors benefit with the operation?

d) (Concession): Assume now that the probability of the bad state, 10Bs , was given by p=0.01D. d1) Explain the intuition. d2) In this case, would it pay for creditors to agree in setting D less than 60? How much should that be? What would be the secondary market price in that case? Explain, with the help of a graph. d3) Explain why such a move involves a coordination problem.

18.13. Consider a sovereign borrower with infinite life which debt, amounting to D=100bn, matures today. The opportunity cost of funds to investors is constant and equal to i=5%.

a) If the sovereign was perceived to be solvent, what would be the primary surplus each year needed to exactly stabilize this debt, in nominal terms? What would be the total interest payment each year, and the government total deficit? Represent in a graph.

b) Now assume that the new loan took the form of perpetual bonds with face value totalling 100bn, and interest rate in the annual coupon equal to gi . If investors

perceived this government to be able to generate primary surpluses each year equal to s=12bn with probability 1-p=1/3, and s=0 with p=2/3: (g1) would the sovereign be expected to be solvent? (g2) How much would be the maximum possible interest rate, ig, investors could set in this 100bn debt? (g3) What would be the market price, q, of this debt?

c) Why would investors lend to this government?

d) Returning to (g), assume now that 18/100 gip . (i1) Explain the intuition. (i2) In this

case, what would be the optimal interest rate to set in the rolling over of this 100bn debt? (i3) What would be the implied market value, V, of this debt? (i4) Compare with (g) using a graph and explain.

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