Politicas macroeconomicas, handout, Miguel Lebre de Freitas

Transcription

1 6 Debt overhang Index: 6 Debt overhang Introducton When the soveregn s nsolvent Why lqudty problems? Man assumptons The determnstc case Maxmum expected repayment under uncertanty Expected to be solvent Expected to be nsolvent Defensve lendng Incentve problems Debt reducton schemes Debt forgveness Thrd party buy backs Self-fnanced Debt buy-back Debt swap The debt-relef Laffer curve Endogenous probablty Debt forgveness under endogenous probablty Lmts on debt forgveness Debt Laffer Curve Debt restructurng: practcal dffcultes Man deas...7 Further readng...8 Revew questons and exercses...9 Revew questons...9 Problems...9 5//07,

2 6. Introducton Ths note addresses the case of a soveregn that s expected to fal ts debt oblgatons. When credtors beleve that the soveregn wll not be able to servce ts debt, the market value of that debt wll fall short ts contractual (face) value. Ths stuaton s labelled debt overhang. In ths note, we address the problem of debt overhang and the avenues that can be explored to get rd of t. The analyss s restrcted to debt that s denomnated n foregn currency, that s, debt that the soveregn cannot get rd off by prntng money. Ths note s organzed as follows: In Secton 6., we dstngush the case n whch the soveregn s expected to be nsolvent from the case n whch the soveregn s expected to be solvent, even f some probablty exsts of not beng so. In Sectons 6.3 and 6.4 we revew alternatve mechansms through whch a country debt can be szed down, accountng for an eventual mpact on the probablty of repayment. Fnally, n Secton 6.5 we dscuss the coordnaton falure underlyng debt restructurng deals, and the role of collectve acton clauses n mtgatng that falure. 6. When the soveregn s nsolvent 6.. Why lqudty problems? Lqudty concerns the ablty of a country to attract new borrowng. A lqudty problem arses when, n face of some new nformaton, a country solvency comes nto queston. The followng examples llustrate ths. 6.. Man assumptons Consder a two perod economy. In ths economy, there s a soveregn that nherts some postve debt, D 0, whch matures at the begnnng of perod. To servce ts debt, the government reles on prmary surpluses (defct f negatve), s, and s. Dependng on the framework, the prmary surplus n perod may be determnstc or stochastc. 5//07,

3 In case s D0, a new loan L, wll be needed n perod. Snce there are only two perods, there wll be no new loan at the end of perod. It s further assumed that the opportunty cost of funds for credtors s equal to. For smplcty, t s assumed that all government debt takes the form of dscount bonds that s, the yeld s mpled by the dfference between the prce at whch debt s purchased n the prmary market and the redempton value The determnstc case s In a context wth certanty, the condtons for solvency s D 0 s 0. Thus, as long as s, () Max D0 s L the soveregn wll be solvent. In ths case, t wll be easy to hre a new loan, equal to L D0 s. Snce the soveregn s solvent, the nterest rate n the new loan wll be the rsk free one. The face value of the new debt wll be D L (remember that the debt s sold at dscount). The market value of the new debt wll be equal to the present value of the promsed repayment: V D L. () Hence, the secondary market prce of each ndvdual bond wll be equal to: q V D. (3) Ths dscount delvers exactly a yeld equal to the opportunty cost of captal. The case n whch the soveregn s nsolvent arses when: s (4) Max D0 s L In ths case, the country wll not be able to roll over the remanng debt. Holders of the prevous debt have to accept an mmedate wrte off. The new lendng shall be, at most 5//07, 3

4 s L, because ths s the maxmum loan the government can serve. Hence, holders of the s ntal debt wll face an har cut amountng to D0 s. Once the debt reducton s acheved, the soveregn becomes exactly solvent. Thus, the nterest rate n the new loan wll be the rsk free rate. The face value of the new debt wll be D L s. As before, the secondary market prce of ths debt wll be (3), delverng a yeld equal to the opportunty cost of captal Maxmum expected repayment under uncertanty The more nterestng case arses n a context of uncertanty. Expected nsolvency arses when debt s so large relatve to future revenue prospects that lenders no longer expect to be fully repad. To examne ths case, assume that the government future surplus can be hgh or low, dependng on the materalzaton of two alternatve states of nature. Let s be the prmary surplus n the good state, s the prmary surplus n the bad state, and p the probablty of bad state. In ths case, the present value of the maxmum amount of resources the country s expected to generate n the future s s ps p Max E s L. (5) Even n ths stochastc context, there are two trval cases: the country wll not be solvent for sure f: s D0 s (6) The country wll be solvent for sure f: s D0 s. (7) Otherwse, we don t know Expected to be solvent 5//07, 4

5 Assume that the government s nsolvent n the bad state, but s expected to be solvent on average. That s, condton (7) does not hold, but E s D0 s. (8) In ths case, rsk neutral lenders wll be wllng to roll over the exstng debt, even knowng that the country wll be unable to meet ts oblgatons n case the bad state materalzes. The only ssue s to set out a hgh enough nterest rate n the new loan,, to compensate lenders for the rsk of default. The face value of the new debt D L wll be such that the current value of expected repayments s equal to the amount lent today: V p D ps s L. Implyng pss L g (9) p Thus, the requred yeld wll depend on the probablty of the bad state and also on the dmenson of the har cut n the prncpal, n case the bad state materalzes. Reflectng the hgher promsed yeld, the secondary market prce of each ndvdual bond wll be equal to: V q. (0) D As for a numercal example, consder the followng: D s 00, =%, s 0, s 75, p=/3. 0 In ths case, E s L Max Hence, the soveregn s expected to be solvent, even f t wll not be n case the bad scenaro materalzes. The nterest rate n the new loan, has to be such that the promsed repayment (the face value of the new debt, D L ), obeys to the arbtrage condton 5//07, 5

6 pd p75 V L 00. Ths gves 4 D. That s, the government hres a loan amountng to 00 today, promsng to repay 4 n one year tme. The expected repayment of these bonds s 0, whch present value (market value of the new debt) s exactly V 00. The new debt wll be sold at dscount: V q D 00 4 Implyng the promsed yeld of 4%. Note however ths yeld wll hold wth the probablty of /3, only. Wth probablty /3 the yeld wll be -5%. On average, the expected yeld exactly matches the opportunty cost of captal, % Expected to be nsolvent Consder now the case n whch condton (6) does not hold, but E s D0 s, () In ths case, full repayment s possble but not lkely. In other words, the country s expected to be nsolvent, even f there s some probablty that the debt s fully repad. That s : D L s. The maxmum possble nterest rate n the new loan s such that s () L In ths case, credtors get all the reward n the good state. Note that the nterest rate n the new loan may be lower than the rsk free rate. 5//07, 6

7 ecause the market prce of the new debt s less than the amount lent, the new lendng wll come along wth an expected loss. The wrte off does not occur mmedately, however, because t s the nterest of credtors to lend agan and be enttled wth full repayment n case the good scenaro materalzes. Example: D s 00, =%, s 0, s 30, p=/3. In ths case, 0 E s L Max D s 0 D 0 ). The maxmum achevable nterest rate n the new loan, s 0% (that s, p0 p30 Max The market value of the new debt wll be V L 0.0 new loan L wll nvolve a market value loss equal to 0.9 to credtors. The secondary market prce of the new bond wll be:. Hence, the V q D The mpled yeld s 34.6%, but ths wll happen wth probablty /3. Wth probablty /3 the buyer of ths bond wll get 30 out of an nvestment of 89.09, whch delvers a yeld of -66.3%. On average, the expected yeld s only %. Note that the maxmum possble nterest rate n the new loan can be lower than the rsk free rate. If, for nstance, s zero, whle the rsk free rate s %. 00, the maxmum nterest rate n the new loan wll be 6..7 Defensve lendng We just saw that lendng to a country that s expected to be nsolvent nvolves a loss. Hence, no lender wll voluntarly engage n new lendng, unless t has a stake n the old debt. Old credtors, however, wll have an ncentve to roll over the exstng debt, so as to avod an mmedate default. If no lendng takes place, the country wll fnd mpossble to meet all ts oblgatons wth the current resources, s, and wll default mmedately. A 5//07, 7

8 dsordered default s not of the nterest of exstng credtors. Those wth a stake n the old debt have ncentve to keep lendng n order to protect ther clams. y rollng over the exstng debt, current debt holders preserve the possblty of gettng pad, n case the favourable outcome materalzes. Ths s called defensve lendng : by lendng enough to avod an mmedate default and acceptng a loss, credtors actually rase the value of the clams they already have. Note however that each credtor wll be wllng to engage n a new loan provded the others do the same. Any ndvdual lender would beneft f she could drop out (free rdng). Defensve lendng nvolves a coordnaton falure. A collectve acton s therefore needed n order to avod the mmedate default Incentve problems Settng the nterest rate at the maxmum possble level D L s rases a problem of ncentves: f the good state materalzes, all the reward accrues to credtors. Hence, f effort (unpopular measures) s needed for the good state to materalze, the debtor wll have no ncentve to do so. In general, as long as the debtor has the capablty to nfluence the probablty of the good state, t s a good dea to let hm share the benefts. Credtors may wsh to forgve part of a country s debt to ncrease the lkelhood of the good scenaro. Ths can be done settng an nterest rate such that D L s. To keep the ncentves rght, t may also be a good dea to make the payment oblgaton contngent on events that are out of the country control. 6.3 Debt reducton schemes When the soveregn debt s denomnated n foregn currency, t s not possble to reduce t usng nflaton or fnancal represson. Hence, when the tme comes that t becomes the nterest of credtors and debtors to reduce a country debt, alternatve mechansms have to be found. 5//07, 8

9 A debt restructurng s a process through whch the stressed debtor reduces ts debt oblgatons or renegotates the oblgatons n the contract, so as to have fnancal condtons to proceed. In general, one can dstngush two types of debt-restructurng: Market based debt-reducton schemes: debt buy-backs, securtzaton, debtequty swaps. Concerted actons: debt forgveness, concessonal rates, debt reschedulng. The dfference s that the former can be mplemented through voluntary actons by ndvdual lenders, wthout the need for collectve arrangements. We wll see that, the condtons n whch market based debt reducton schemes are benefcal are the same as for concerted debt relef Debt forgveness Consder the followng example: D 0, 30 s, p=/3, =0%. In ths case the expected repayment of the debt wll be V V 60 debt wll be sold n secondary markets at dscount: q D 0 Suppose now that lenders agree to forgve 5. Then: D ' 05. The secondary market prce of the remanng debt wll be: 3 3. The V ' q ' D Thus, bonds apprecate n the secondary markets. Was ths a good deal for credtors? The expected repayment declned by 5, so credtors are defntely worse off. The reason s that debt forgveness deprves credtors from an opton value, of sharng the benefts n the case of good fortune Thrd party buy backs 5//07, 9

10 Consder, n alternatve a debt buy-back fnanced by cash donated by a thrd party (say, the World ank). Let s start wth D 0, 60 s 30, p=/3. In ths case q Suppose the World ank buys =5 and then destroys the paper. After the buy back, D ' 05, 3 55 q The debt apprecates n the secondary markets - The W spends 0.5*5=7.8 - Total expected payments to prvate bond-holders are now =6.8>60 (the prvate sector gets better by.8) - Expected repayment declned to 55<60 (the soveregn borrower s better). All n all, the operaton comes along wth a net loss, because 7.8 of cash reduced expected repayments by 5 only. The dfference s approprated by the prvate sector. Snce the beneft of ths debt reducton scheme accrues to prvate credtors, there s no pont for the World ank to partcpate, unless there are rsks of ths crss to spll over to other countres (externalty) Self-fnanced Debt buy-back Consder the followng example: D 0, 30 s, p=/3, =0. In plus, the government has 30 of cash that could be used n case the bad state materalzed (for nstance, gold reserves at the central bank). 5//07, 0

11 V 3 In ths case, the expected repayment of the debt n the base-lne scenaro wll be Hence, bonds wll be prced n secondary markets at 80 q /3. 0 Suppose the government used the cash to buy back ts debt n the secondary markets. The problem s to fnd out how much of the debt the government can purchase wth 30 of cash. Ths wll be 30 / q' where q s the secondary market prce of the these bonds after the buy-back. After the buy back, the remanng debt wll be D ' 0 30 / q', worthng 30 0 V V' Hence, q' ', whch solves for q ' q' 3 q' 0 30 q' Substtutng back, the amount of debt purchased wll be =48.83, D ' 7. 69, V ' Note that the secondary market prce declned wth the buy-back. The reason s that payments to credtors n the bad state reduced by 30. Wth the buy-back, the total expected repayment to credtors declnes to 73.73<80. Hence, credtors got worse. Dd the borrower stuaton mprove? The country spends 30 to have the expected repayment reduced by (pocketng 8.83 n the good state). So the country s defntely better off. Debtors are normally prohbted to repurchase ther debt at dscount. One reason s that ths gves soveregns the ncentve to sgnal low commtment, so as to acheve low secondary market prces just before the buy back Debt swap Debt buy backs are only possble when governments have cash (foregn exchange) enough. An alternatve possblty s to ssue new debt and use the proceeds to buy old debt n the secondary markets, or even to drectly swap the two bonds. As long as the new debt s senor relatve to the old debt, ts market prce wll be hgher and the swap wll nvolve a net debt reducton. Consder the followng example: 5//07,

12 V 3 D 0, s 30, p=/3. In ths case, the expected repayment of the debt s , so the debt wll be prced n secondary markets at dscount 60 q Suppose the government ssues a new bond (A), senor relatve to the old bond, to be exchanged for old bonds. The amount to be ssued s 30. How much wll worth the new bonds? Snce the government can repay the new bonds whatever the scenaro s (note that s 30 ), the prce of the senor bond wll be. How much wll worth the old bonds? Snce the old bonds are only repad n the good scenaro, ther prce s q=/3. Ths means that: - The bond-holders wll lose (/3</). - The swap wll consst n exchangng 30 new bonds by 90 old bonds - After the swap, there wll be 30 old bonds prced at 0 and 30 new bonds prced at The total expected repayment wll be 40, whch s less than the ntally 60. In concluson, a debt buy back fnanced wth the ssuance of senor debt benefts the debtor at the expense of credtors. Wth no surprse, many lendng contracts protect credtors aganst the ssuance of bonds wth hgher senorty. As wll see next ths concluson may change f the probablty of the good scenaro ncreases wth the debt swap. 6.4 The debt-relef Laffer curve 6.4. Endogenous probablty The assumpton that the probablty of the good state s exogenous s not entrely reasonable: governments have the potental to nfluence budgetary outcomes, engagng n hgher or lower adjustment efforts. So when the government s commtted, the probablty of default s expected to be lower. In the debt relef debate, t s frequent to assume that the 5//07,

13 government effort declnes when the debt level gets too hgh. The reason s that the effort s perceved to be useless. On the other hand, a hgher level of debt may mpact negatvely on prvate nvestment: the reason s that, when the debt level s very hgh, a sgnfcant fracton of the output gan acheved wth the nvestment wll be devated to debt repayment, through hgh taxes. Hence, from an nvestor s pont of vew, a hgh level of debt acts lke a tax on nvestment, reducng the after tax return on captal. Hgh ndebtedness can then lead to low nvestment, low output and ultmately a lower probablty of repayment. In general, when the debt level s very hgh, the mpled fscal effort wll come along wth a depressed economy, and eventually wth socal and poltcal nstablty, further reducng the country growth prospects. Another reason why the probablty of repayment may ncrease when the debt level declnes s that, when nternatonal help s called for, a deal s typcally made, whereby the country commts to some adjustment n exchange for some form of debt relef (harcuts, restructurng, concessonal nterest rates, or other). Ths s equvalent to assume that the probablty of repayment ncreases when the debt gets smaller. To account for all these effects, n the followng, we dscuss the case n whch p d D, wth d >0. That s, the hgher the debt, the hgher the probablty of default Debt forgveness under endogenous probablty We now return to the prevous numercal example, but assumng nstead that the probablty of the bad scenaro rses proportonally to the level of debt. That s: D 0, 30 s, =0, but replace the probablty of default by the followng lnear rule: p D In the ntal state, the expected repayment of the debt s V V 60 the secondary markets s q D 0 3, so 5//07, 3

14 Now, suppose that a wrte-off of 5 comes along wth a hgher effort, so that the probablty of full repayment ncreases to p In ths case, after the wrte off, the market value of the remanng debt wll be: 5 7 V q Note that n ths case there s a free lunch: - The expected repayment ncreased by.5: credtors are better off. - The government s only commtted to pay 05 n case the god state materalzes (t saves 5). Ths provdes the proper ncentve for the government to engage n hgher effort. Hence, t s the nterest of both the soveregn borrower and ts credtors to negotate a certan amount of debt forgveness, under condtonalty. Note however that no solated credtor wll gan wth a unlateral wrte off. On the contrary, t wll pay to free rde on the others efforts. In general, debt forgveness requres a concerted acton Lmts on debt forgveness In the example above, we saw that a debt level of 05 delvers a hgher expected repayment than a debt level of 0. Hence, t pays for credtors to wrte off 5. The queston s whether t would be the nterest of credtors to engage n a second wrte off amountng5, so that the amount of debt outstandng reduced to 90. In that case, the probablty of default would reduce to p=90/80=0.5. Hence, the market value of the remanng debt would be V Ths example shows that t doesn t pay to forgve any amount of government debt, even when the probablty of repayment depends negatvely on the stock of debt. At some 5//07, 4

15 pont, the beneft to nvestors of nducng a hgher effort s more than offset by the fact that nvestors lose the opton of recevng the full amount n case the good state materalzes Debt Laffer Curve In general, the expected repayment wth endogenous probablty s gven by: Ds pd V p D Ths equaton mples an nverted U-shape relatonshp between the level of debt and expected repayment. Ths relatonshp s descrbed n Fgure, and s known as the debt Laffer curve. Pont n Fgure corresponds to the level of debt that maxmzes ts market value, V (not ts prce, q). Analytcally, t may be found solvng V D 0. The debt Laffer curve results as the balance between two opposng effects: - Debt forgveness deprves credtors from the opton value of sharng the good fortune. - Debt forgveness may ncrease the probablty of the good scenaro, by mprovng the ncentves to the government and prvate nvestors. When D s low (on the left hand sde of pont ) the frst effect domnates the second: a declne n D wll come along wt a fall n the value of expected repayment. When D s hgh (on the rght hand sde of ), the second effect domnates the former: addtonal amounts of debt actually lower expected repayments, because the country s so ndebted that the lkelhood of the good scenaro s very small In that case, a country s sad to be lyng on the wrong sde of the Laffer curve. In such condtons, a reducton n the sze of government debt, by easng the government budget constrant and also the tax rates on entrepreneurs, wll mpact postvely on the market value of the remanng debt. Note that, along the debt Laffer curve, the bonds market prce, q, also depends on the level of debt: V s q p p D D. Fgure : The debt Laffer Curve 5//07, 5

16 6.5 Debt restructurng: practcal dffcultes We saw that n some crcumstances t may be the nterest of both credtors and soveregns to restructure a gven debt. Ths happens when the debt reducton ntatve comes along wth an ncrease n the probablty of repayment, so that the expected value of repayment actually ncreases wth the debt relef. In other words, the soveregn must be n the wrong sde of the Laffer curve. In practce however, achevng a debt reducton deal s not easy. The reason s that such a deal nvolves a negotaton wth a large number of credtors. Whle ts s the collectve best nterest of all credtors to agree n the restructurng process, t s the nterest of each ndvdual credtor not to partcpate n the deal, free rdng on the other credtors losses. Indvdual credtors that decde not to partcpate n a debt restructurng n the hope that they wll be able to recover the full value of ther clams are labeled hold out credtors. When hold out credtors face a hgh probablty of success, ths wll reduce the ncentve for other credtors to partcpate n a debt restructurng deal. Ths problem has been a source of delays n debt restructurng process. In ths respect, a recent case nvolvng the Argentne debt dd not help: when called to decde whether holdout credtors of Argentne debt should get pad, the New York courts nvoked the Par Passu provson. The Par Passu states that all credtors are enttled wth equal treatment. The Par Passu provson makes sense to prohbt actons that result n subordnaton of some credtors over others, such as the ssuance of new senor bonds. 5//07, 6

17 ut the New York courts nterpreted ths provson as applyng to all holders of Argentnean debt, rrespectvely as to whether they had agreed n the prevous re-structurng or they were opportunstc holdouts. Wth such decson, Argentna could not servce the new debt wthout honorng the old un-restructured debt. Ths decson surprsed the markets and created an ncentve problem: by enhancng the expected benefts of holdng out, t made future restructurng agreements more dffcult to acheve. To address the hold out problem, debt contracts often nclude collectve acton clauses. Collectve acton clauses enable a qualfed majorty of credtors to take a decson regardng the terms of a debt restructurng that become bndng to all bond-holders. Thus, for nstance, f 90% of the credtors agree n a debt-restructurng, the remanng 0% are bound to accept the decson. A problem however s that these the actvaton of collectve acton clauses requre a vote on a per-seres bass: that s, bond ssuance by bond ssuance. Thus, f for nstance most holdout credtors are concentrated n a partcular bond seres, they may well block the restructurng n that seres. Ths, n turn, wll reduce the wllngness of other credtors n other bond seres to consent the restructurng. To address ths problem, the IMF recently proposed the ntroducton of a unque collectve acton clause that works for all bond-holders and across all bond ssuances, thus not dependng on a ssuance-by-ssuance vote. Of course, such a change wll be welcome, but t wll take a long tme untl t becomes domnant n debt contracts. Meanwhle, dealng wth hold outs wll be a major dffculty n debt restructurng. 6.6 Man deas If a country s expected to be solvent, there should be no lqudty problem. If a scenaro of non-repayment exsts, ths wll be reflected n a hgher nterest IMF Survey, IMF Supports Reforms for More Orderly Soveregn Debt Restructurngs, October //07, 7

18 rate, only. As long as the soveregn s expected to be solvent, there wll always be rsk-neutral nvestors wllng to buy that debt. When the present value of expected repayments falls short the outstandng debt, a debt overhang s sad to occur. In ths case, no new lender wll buy the soveregn debt. Expectatons of nsolvency do not necessarly prevent, however, new lendng: old credtors have an ncentve to keep lendng, even at an expected loss, so as to avod an mmedate default and protect ther clams (defensve lendng). Although t s the collectve nterest of credtors to avod the mmedate default, each credtor ndvdually would beneft by optng out (free rdng). So a collectve acton s needed. Settng the nterest rate at ts maxmum possble level may not be the best choce for credtors. In some cases, concessonal rates or whch s the same partal debt forgveness, may help get the ncentves rght. Debt-buy backs are not n general of nterest of debtors. A debt swap mplyng a subordnaton of exstng bonds may be the nterest of debtors, but hurt exstng credtors. In general, t s not the nterest of credtors to forgve a country debt, unless ths mproves the probablty of repayment of the remanng clams beyond a certan level. Ths happens when a country s on the wrong sde of the Laffer curve. Free rdng problem Further readng Krugman, Currences and Crss Urbe, M., Scmtt-rohé, 03. Internatonal Macroeconomcs. 5//07, 8

19 Revew questons and exercses Revew questons 6.. Comment: Lqudty and solvency are two sdes of the same con. 6.. What s meant by fnancal represson? Whch measures are ncluded? 6.3. Explan why sometmes t may be the nterest of lenders to gve up part of ther clams on a hghly ndebted soveregn If you were a lender negotatng a swap of old debt by a new bond, whch type of covenants you would lke the new bond to have? Under whch law? 6.5. Why sn t the current legal framework regardng collectve acton clauses consdered nsuffcent to dscourage holdout credtors? What s the IMF proposng to solve ths problem? 6.6. Why s the recent nterpretaton of the Par Passu clause by the New York courts n the case of Argentna debt challengng future agreements n debt reducton schemes? What could be done about ths? Problems 6.7. Consder a soveregn borrower wth nfnte lve whose current debt amountng to pesos 00bn matures today. Further assume that the opportunty cost of funds for (rsk-neutral) lenders s 0%. a) If, from now on, the maxmum surplus ths government could generate each year was 8bn, would t be solvent? What should credtors do n ths case? (A:80<00) b) Now suppose that ths government s perceved to be able to generate a 8bn surplus each year wth 75% probablty and 0bn surpluses wth 5% probablty. (b) would the soveregn face a lqudty problem? (b) What would be the nterest rate a rsk neutral lender would set n a new loan? (A: 0; =6%) c) Fnally, consder the case n whch the two scenaros were: 8bn surplus per year wth 75% probablty and bn surplus wth 5% probablty. (c) Explan why n ths case credtors would have an ncentve to engage n defensve lendng. (c) How much would be the maxmum nterest rate n the new loan? (c3) If there was a secondary market for these new bonds, at whch prce were they expected to be sold? (A: =%; q=90) 5//07, 9

20 6.8. Consder an economy where the government debt, amounts to 00% of DP. Further assume that there s no growth and that the nflaton rate s zero. The opportunty cost of funds to nvestors s =0%. a) Assume the government approves a fscal rule, accordng to whch the prmary surplus has to be at least 4bn each year. Is ths surplus enough to stablze the debt rato? Explan wth the help of a graph. b) What yeld should the government pay to roll over ts debt? [A: 0%]. c) Now suppose that nvestors beleved the ntended fscal adjustment to succeed wth 50% probablty, only. If t fals, nvestors guess the maxmum achevable annual surpluses wll be 8bn each year. In that case, how much wll be D-Max? [A: 0]. d) In the condtons of c), how much should the government pay n the new borrowng? [A:%]. e) In case the good scenaro materalzed, how would the debt rato evolve? 6.9. The soveregn debt of country A amounts to $480 mllon and hs dspersed by a large number of prvate agents. The followng fgure descrbes the Debt-Relef Laffer curve for ths country. a) Explan the confguraton of the debt Laffer curve. How much s the country able to pay n the worst case scenaro? b) What s the ntal secondary market prce of ths debt? c) Would t pay for lenders to jontly wrte-off $80 mllon of ths country debt? Explan. d) Explan why the debt relef rases a coordnaton problem Consder a soveregn borrower whch future prmary surplus ( s ) s expected to be 00 wth probablty ¾ and 0 wth probablty ¼. To smplfy, also assume that the rsk free nterest rate s =0% and that ths government bonds are coupon free (ssued at dscount). a) What s the maxmum loan (L) ths government can attract? 5//07, 0

21 b) If such loan materalzed, how much should be the face value of the correspondng securty (D)? What would be the yeld and the ntal secondary prce (q) of ths bond? [D=00; g=5%; q=0.8]. c) Represent n a graph the relatonshp between the market value (V) and the face value of debt for ths country. In partcular, consder the cases n whch: D=0; D=40; D=80; D=00, D=5. Is there a Laffer curve n ths case? [A: 0,35,65,80,80]. d) Suppose the ntal debt was D=0. Would the government be able to convnce nvestors to forgve 0? Was ths soluton easy to coordnate? What would be the costs and benefts? [A: no loss for credtors altogether, free rdng problem]. e) Now suppose that the ntal debt was D=00. Would the government be able to convnce nvestors on a wrte off amountng to 0? [V =65<80]. f) Stckng wth the case n whch D=00, suppose the government ssued a new bond (A=0), senor n respect to D, to be exchanged for old bonds. What would be the market prce of the old bonds? Who benefted wth ths swap? [q=0.75; V +0=75<80 ov]. 6.. Suppose that the government surplus n the bad state s s 0, and that ths wll happen wth probablty p D 50. In the good state, the government can always honor ts debt, D. a) Explan the equaton descrbng the probablty of bad state. b) Wth the assumptons above, what s the level of D that maxmzes the secondary market prce, q? [A:0]. c) What s the level of D that maxmzes ts total market value, V? What wll be the secondary market prce n ths case? [A: 8, 0.6] d) Descrbe the debt-relef Laffer curve dentfyng the followng cases: D=0; D=0; D=30; D=40; D=50; D=60 [0, 6, 8, 0, 0]. e) Assume that the ntal debt was D=40. Would credtors agree n a debt relef amountng to 0? [V =8>6]. f) In alternatve, departng from D=40, assume that the W purchased ¼ of the outstandng debt n the secondary markets, to subsequently destroy t. How much would that measure cost? Who would be the benefcares? [A: 6]. g) Fnally, stll assumng D=40 ntally, consder the possblty of the government ssung new senor bond amountng to 0, to be swapped for old bonds. What would be the new market prce for the old debt? Would the prvate sector beneft wth the operaton? [A: q =0.558;.330>6]. 6.. Consder a soveregn borrower whose future prmary surplus s expected to be: s 0 wth probablty p=0.6 and s 60 wth probablty -p=0.4. Further assume that the opportunty cost of funds to credtors s =0%. a) (Yeld n the new loan): Suppose that the government needs to rollover a loan amountng to L=40, that s equally shared by a large number credtors. Is ths government expected to be solvent? Who would be wllng to lend? Why? What 5//07,

22 would be the maxmum feasble nterest rate n the new loan, g, and the mpled face (maturty) value, D? b) (Secondary market prce): Assume that the face value of the negotated debt was D=60. ven the probabltes above, how much should be ts secondary market prce? c) (Debt Swap) Stckng wth D=60 and wth the ntal assumptons, assume that the government s consderng ssung a new, senor bond, amountng to A=0, to be swapped for old bonds. c) How much should be the secondary market prces of the new bond and of the old bond after the swap? c) How much of the old debt would be swapped that way? Would credtors beneft wth the operaton? d) (Concesson): Assume now that the probablty of the bad state, s 0, was gven by p=0.0d. d) Explan the ntuton. d) In ths case, would t pay for credtors to agree n settng D less than 60? How much should that be? What would be the secondary market prce n that case? Explan, wth the help of a graph. d3) Explan why such a move nvolves a coordnaton problem Consder a soveregn borrower wth nfnte lfe whch debt, amountng to D=00bn, matures today. The opportunty cost of funds to nvestors s constant and equal to =5%. a) If the soveregn was perceved to be solvent, what would be the prmary surplus each year needed to exactly stablze ths debt, n nomnal terms? What would be the total nterest payment each year, and the government total defct? Represent n a graph. b) Now assume that the new loan took the form of perpetual bonds wth face value totallng 00bn, and nterest rate n the annual coupon equal to g. If nvestors perceved ths government to be able to generate prmary surpluses each year equal to s=bn wth probablty -p=/3, and s=0 wth p=/3: (g) would the soveregn be expected to be solvent? (g) How much would be the maxmum possble nterest rate, g, nvestors could set n ths 00bn debt? (g3) What would be the market prce, q, of ths debt? c) Why would nvestors lend to ths government? d) Returnng to (g), assume now that p 00 g / 8. () Explan the ntuton. () In ths case, what would be the optmal nterest rate to set n the rollng over of ths 00bn debt? (3) What would be the mpled market value, V, of ths debt? (4) Compare wth (g) usng a graph and explan. 5//07,