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
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,D0, which matures at the beginning of period 1. To service its debt, the government relies on primary surpluses (deficit if negative), s1, and s2. Depending on the framework, the primary surplus in period 2 may be deterministic or stochastic.
In case s1D0, a new loan L1, 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 0 1
2 1
0
i
s s
D . Thus, as
long as
LMax
i s s
D0 1 2 1
1
, (1)
the sovereign will be solvent. In this case, it will be easy to hire a new loan, equal to
1 0
1 D s
L . 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 D1L1
1i (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:
1 1
1 1 L
i
V D
. (2)
Hence, the secondary market price of each individual bond will be equal to:
i D
q V
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:
LMax
i s s
D0 1 2 1
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
i L s
1
2
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 s s D
1
2 1
0 .
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
21
1 L 1 i s
D . 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 s2G be the primary surplus in the good state, s2B 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 s p ps
i s L E
G B
Max
1 1 1
2 2
2
1 . (5)
Even in this stochastic context, there are two trivial cases: the country will not be solvent for sure if:
i s s D
G
1
2 1
0 (6)
The country will be solvent for sure if:
i s s D
B
1
2 1
0 . (7)
Otherwise, we don’t know.
18.2.5 Expected to be solvent
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 s s E D
1
2 1
0 . (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, iG, to compensate lenders for the risk of default. The face value of the new debt D1L1
1iG
will be such that the current value of expected repayments is equal to the amount lent today:
1 1
1 1
1 L
i ps D V p
B s
.
Implying
p
L ps i i
B s
g
1
1 1 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:
iG
D q V
1
1
1
1 . (10)
As for a numerical example, consider the following:
1 100
0s
D , i=1%, s2G 120, 75s2B , p=1/3.
In this case,
103.96 100 01. 0 1
80 25 1
2
1
i s LMax E
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, iG has to be such that the promised repayment (the face value of the new debt, D1L
1iG
), obeys to the arbitrage condition
1 100 75
1 1
1
L
i p D
V p . This gives D1114. 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 V1 100.
The new debt will be sold at discount:
114 100
1 1
D q V
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 s s E D
1
2 1
0 , (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 D1L1
1iG
s2G. That is1:1
1 2
L i s
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.
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:
1 100
0s
D , i=1%, s2G 120, s2B30, p=1/3. In this case,
1 0 2
1 89.109
01 . 0 1
80 10
1 D s
i s
LMax E
The maximum achievable interest rate in the new loan, iG is 20% (that is,
1 120 D ).
The market value of the new debt will be
Maxp L
V1 p 1
01 . 0 1
30 120
1
. 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 . 120 0
109 . 89
1
1
D q V
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, s2G 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, s1, and will default immediately. A
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 D1L
1iG
s2G 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 D1L
1iG
s2G. 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.
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:
1120
D , 30s2B , p=2/3, i=0%.
In this case the expected repayment of the debt will be
30 60 3120 2 3 1
1
V . The
debt will be sold in secondary markets at discount: 0.5 120
60
1
1
D
q V .
Suppose now that lenders agree to forgive 15. Then: D1'105. The secondary market price of the remaining debt will be:
52 . 105 0
55 105
330 105 2 3 1 ' '
1
1
D
q V
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
Consider, in alternative a debt buy-back financed by cash donated by a third party (say, the World Bank).
Let’s start with
1120
D , s2B30, p=2/3. In this case 0.5 120
60
q .
Suppose the World Bank buys B=15 and then destroys the paper.
After the buy back,
105
1'
D , 0.52
105 55 105
330 105 2 3 1
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
Consider the following example:
1120
D , 30s2B , 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).
In this case, the expected repayment of the debt in the base-line scenario will be
60 80 3120 2 3 1
1
V . Hence, bonds will be priced in secondary markets at
3 / 120 2
80
q .
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 B30/q' where q’ is the secondary market price of the these bonds after the buy-back.
After the buy back, the remaining debt will be D1'12030/q' , worthing
'60 10 3 30
2 ' 120 30 3 ' 1
1 q q
V
. Hence,
' 30 120
' 1'
q q V
, which solves for q'0.6143. Substituting back, the amount of debt purchased will be B=48.831, D1'71.169 ,
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.
Consider the following example:
1120
D , 30s2B , p=2/3. In this case, the expected repayment of the debt is
30 60 3120 2 3 1
1
V , so the debt will be priced in secondary markets at discount
5 . 120 0
60
q .
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 thats2B30), 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
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
D1 dp , 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:
1120
D , 30s2B , i=0, but replace the probability of default by the following linear rule: pD1 180.
In the initial state, the expected repayment of the debt is
30 60 3120 2 3 1
1
V , so
the secondary markets is 0.5 120
60
1
1
D
q V .
Now, suppose that a write-off of 15 comes along with a higher effort, so that the probability of full repayment increases to 1p1105180512. In this case, after the write off, the market value of the remaining debt will be:
60 25 . 12 61 30 7 12 1055
1
V
583 . 105 0
25 .
61
q
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 . 61 2 60
301 2 901
1
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
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:
D s
p
D
Dp
V1 2B 1
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, V1 (not its price, q). Analytically, it may be found solving V1 D0.
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: p
D ps D q V
B
1 2 1 .
Figure 1: The debt Laffer Curve
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.
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.
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.
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)
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 (s2) 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?
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 s2B 10, and that this will happen with probability pD 50. 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:
10
sB with probability p=0.6 and sG 60 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
would be the maximum feasible interest rate in the new loan, ig, 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, sB 10, 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 ig. 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 p100ig/18. (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.
