Optimal Federal Public Debt Composition: Definition of a Long-Term Benchmark

Transcription

1 Opimal Federal Public Deb Composiion: Definiion of a Long-Term Benchmark Brasília 2011

2 MINISTER OF FINANCE Guido Manega EXECUTIVE SECRETARY Nelson Henrique Barbosa Filho NATIONAL TREASURY SECRETARY Arno Hugo Augusin Filho NATIONAL TREASURY UNDERSECRETARIES Cleber Ubiraan de Oliveira Eduardo Couinho Guerra Gilvan da Silva Danas Líscio Fábio de Brasil Camargo Marcus Pereira Aucélio Paulo Fonoura Valle TECHNICAL STAFF Undersecreary of he Public Deb Paulo Fonoura Valle General Coordinaor of Public Deb Operaions Fernando Eurico de Paiva Garrido General Coordinaor of Public Deb Sraegic Planning Oavio Ladeira de Medeiros General Coordinaor of Public Deb Conrol Anônio de Pádua Ferreira Passos Informaion: Invesor Relaions - GERIN Phone: (61) Fax: (61) Naional Treasury Secrearia Edifício Sede do Minisério da Fazenda Esplanada dos Minisérios, Bloco P, 2º Andar Brasília, DF sndivida@fazenda.gov.br Home page: hp:// 1

3 Index EXECUTIVE SUMMARY... 3 Uni I: The Process of Federal Public Deb Sraegic Planning...3 Uni II: The Analyical Framework of he Federal Public Deb Benchmark...4 UNIT I: THE PROCESS OF FEDERAL PUBLIC DEBT STRATEGIC PLANNING Insiuional Srucure of he Public Deb Undersecrearia FPD Sraegic Planning Annual Planning Federal Public Deb Opimal Composiion Model Elaboraion of Medium-Term Transiion Sraegy Risk Evaluaion: Brazilian Experience References UNIT II: THE ANALYTICAL FRAMEWORK OF THE FEDERAL PUBLIC DEBT BENCHMARK Lieraure and Inernaional Experience The Brazilian Opimal Composiion Model Some Mehodological Issues The Opimal Composiion Model Dynamics of he Economy Dynamics of he Deb Opimal Composiion Model Simulaions Final Consideraions References Appendix Dynamics of he Economy Macroeconomic Consisency Bond Prices

4 EXECUTIVE SUMMARY Uni I: The Process of Federal Public Deb Sraegic Planning In Brazil, Federal Public Deb (FPD) sraegic planning involves various aspecs ha can be grouped ino hree sages for didacic purposes: Definiion of he desired long-erm srucure (benchmark); Medium-erm planning (ransiion sraegy); and Elaboraion, publicaion and implemenaion of shor-erm sraegy (Annual Borrowing Plan - ABP, firs published in 2001). The saring poin and primary reference for he enire public deb planning process is a clear definiion of is objecives. The objecive defined for Federal Public Deb managemen is ha of efficienly meeing federal governmen borrowing requiremens a he lowes possible long-erm financing cos, while ensuring pruden risk levels. Addiionally, he aim is o he smooh operaion of he Brazilian governmen securiies marke. Considering he objecive defined above as reference, he ABP presens a series of guidelines ha orien he elaboraion of FPD borrowing sraegies. They are as follows: Increase he average mauriy of he ousanding deb; Smooh he mauriy profile, wih special aenion given o shor-erm mauriies; Gradual replacemen of floaing-rae securiies by fixed-rae and inflaion-linked insrumens; Improvemen in he Exernal Federal Public Deb (EFPD) profile hrough issuances of benchmark securiies, buyback and srucured operaions; Developmen of he of he yield curve on boh domesic and exernal markes and growh in he liquidiy of federal governmen securiies on he secondary marke; Broadening of he invesor base. Taking ino accoun he objecive and guidelines se ou in he ABP, macroeconomic scenarios, esimaes of federal governmen borrowing requiremens and he various public deb bond issuance sraegies, each year he Naional Treasury calculaes he expeced values for he major FPD indicaors: ousanding volume, composiion by indexing facor, average mauriy and percenage mauring in 12 monhs. On his basis, he ABP is used o announce he indicaive limis of he upper and lower values ha each of hese indicaors is expeced o reach a he end of he year. As he basis for ABP elaboraion, sraegic FPD planning defines a "ransiion sraegy" from he curren public deb composiion o he long-erm benchmark. The ransiion sraegy seeks o respond o he following quesion: duly respecing he iniial condiions (in oher words, he curren deb profile) and shor and medium-erm resricions (paricularly, macroeconomic resricions and hose implici in he developmen of local financial markes), wha should be he rajecory and speed of convergence o he 3

5 desired long-erm composiion? The choice of ransiion sraegies o he long erm also explores he rade-offs beween public deb coss and risks. In is urn, he opimal long-erm composiion (benchmark) is he firs sage o be discussed and approved by he Public Deb Commiee, becoming he foundaion for elaboraion of he ransiion sraegy and Annual Borrowing Plan approved for each year. In Brazil, developmen of he opimal public deb composiion model was a naural consequence of a long process of improvemen in he insiuional framework used o evaluae FPD coss and risks. Iniially, he governmen asse and liabiliy managemen model was implemened. Afer ha, he risk managemen insrumens used by he Naional Treasury in FPD managemen were adoped. I was only a ha poin ha sudies were iniiaed on an opimal public deb composiion model ha would consider all of he relevan variables. Uni II: The Analyical Framework of he Federal Public Deb Benchmark Wih regard o defining an opimal long-erm public deb composiion (benchmark), i represens he desired profile for he deb srucure and consiues a guide for delineaing he governmen's shor and medium-erm financing sraegies. In he Brazilian case, he benchmark is expressed by a se of relevan deb indicaors, including composiion of he ousanding deb by ype of index, average mauriy and mauriy srucure, paricularly he percenage of he deb mauring in he coming 12 monhs. In defining he opimal public deb composiion (benchmark), a se of models describes how relevan macroeconomic and financial variables o he public deb rajecory (ineres raes, exchange raes, inflaion and GDP) evolve over ime. Based on simulaed scenarios, evoluion of he deb/gdp raio is evaluaed in order o derive cos and risk measuremens of a given deb srucure. Thus, following examinaion of muliple possible alernaives, one obains he efficien fronier in erms of public deb coss and risks. On ha basis, one chooses he srucure in he fronier ha possesses he desired profile for he long-erm, complying wih sociey's preferences beween coss and risks. An imporan quesion in he model is wha should be he relevan concep of deb size in order o evaluae coss and risks. In he Brazilian case, we considered he Ne Public Secor Deb/GDP raio (NPSD/GDP) as he mos relevan measuremen, since i is he indicaor mos commonly uilized boh by he federal governmen, o define is indebedness arges and he primary surplus required o achieve hem, and by analyss for he purpose of evaluaing fiscal susainabiliy. Though he FPD is he Naional Treasury's work insrumen, clear communicaion is sough beween his deb and NPSD, he laer of which is a broader concep and an economic policy reference. In he Brazilian case, he iniial opimal composiion proposal was published in he 2007 ABP. Simulaions of his model suggesed ha efficien FPD managemen would resul in growh in he proporion of fixed rae and inflaion-linked securiies, in derimen o he deb linked o floaing ineres raes or he exchange rae. More recenly, refinemen of he sudies led o a definiion of he desired composiion, as presened in he 2011 ABP in he form of indicaive long-erm limis, as shown in he following able: 4

6 Opimal Long-erm FPD Composiion Lower limi Upper limi Fixed rae 40% 50% Inflaion-linked 30% 35% Floaing rae 10% 20% Exchange rae 5% 10% Source: Naional Treasury The prescripion ha calls for seeking he composiion described above should be qualified. Firs of all, i should be viewed as a guideline o be aained gradually, wihou generaing pressures ha could resul in excessive ransiion coss. Secondly, one mus avoid seeking FPD composiion in any manner ha is no coordinaed wih is mauriy srucure. Thirdly, he cos of alering he composiion mus be permanenly moniored, since changes in he relaive prices of public securiies can resul in adjusmens in he FPD benchmark porfolio. Finally, hough hese limis provide up-o-dae orienaion for defining sraegies, hey mus also reflec possible resricions relaed o he developmen sage of Brazil s financial markes, he invesor base profile and he oulook for fuure public securiy demand and liquidiy. 5

7 UNIT I: THE PROCESS OF FEDERAL PUBLIC DEBT STRATEGIC PLANNING Federal Public Deb FPD sraegic planning in Brazil involves various aspecs ha can be grouped ino hree sages: Definiion of he desired long-erm srucure (benchmark srucure); Medium-erm planning (ransiion sraegy); and Elaboraion, publicaion and implemenaion of he shor-erm sraegy (Annual Borrowing Plan ABP, firs published in 2001). The objecive of his uni is o describe he FPD planning process, highlighing Brazilian experience in deb risk evaluaion 1. This uni is organized ino six secions aimed a clarifying he differen elemens of he planning process: Secion 1 describes he insiuional srucure of he Public Deb Undersecrearia (SUDIP), charged wih FPD managemen. Here, one should highligh he Deb Managemen Commiee; Secion 2 presens a broad explanaion of he FPD sraegic planning process; Secion 3 breaks down he process of discussing and approving shor-erm FPD planning, se ou in concree form in he Annual Borrowing Plan; Secion 4 presens a brief explanaion of how he benchmark model aids in defining quaniaive guidelines for he FPD srucure over he long-erm; Secion 5 conains a discussion on how he sraegy of ransiioning from he curren FPD composiion o is benchmark is elaboraed, wih paricular emphasis on he imporance of he macroeconomic scenarios and he degree of deb marke developmen o deermining he speed of FPD convergence o he long-erm srucure; Finally, he final secion deails he hisorical evoluion of he Brazilian sraegic planning model, he risk indicaors uilized for public deb managemen in he iniial sages of his process and he more perinen merics currenly used by deb managers. 1 Based on SILVA, CARVALHO & MEDEIROS (2009) and also on he various Annual Borrowing Plans ( ABP), released since 2001 by he Naional Treasury Secrearia. 6

8 1. Insiuional Srucure of he Public Deb Undersecrearia The Naional Treasury Secrearia was creaed in 1986 wih he objecive of improving public finance managemen in Brazil. The Naional Treasury is a componen of he insiuional srucure of he Minisry of Finance and is currenly composed of six disinc undersecrearias (see figure 1 below). The firs sage of his process occurred in 1988, when he funcions of federal securiies deb planning, supervision, regulaion and conrol were ransferred o he Naional Treasury. Previously, hese funcions had been scaered abou various federal governmen organs and he Cenral Bank (BACEN). Figure 1. Adminisraive Srucure of he Federal Presidency of he Republic Minisry of Planning Minisry of Finance Oher Minisries Cenral Bank of Brazil Federal Revenue of Brazil Naional Treasury Secrearia Oher Secrearias* Undesecrearia of Inergovernmenal Financial Relaion Undesecrearia of Fiscal Planning and Saiscs Undesecrearia of Public Accouning * Execuive Secrearia (SE) Secrearia of Economic Policy (SPE), Secrearia of Inernaional Affairs (SAIN), Secrearia of Economic Monioring (SEAE), Office of he General Prosecuor of he Naional Treasury (PGFN) and he College of Treasury Managemen (ESAF) Undesecrearia of Corporae Affairs Undesecrearia of Fiscal Policy Undesecrearia of he Public Deb Source: Naional Treasury 7

9 The pracice of concenraing public deb managemen funcions in a single governmen eniy has become widely acceped inernaionally, since his insiuional arrangemen ends o resul in more efficien and coordinaed managemen 2. In line wih inernaional experience, he Naional Treasury is currenly responsible for managemen of he enire Federal Public Deb (domesic and exernal debs, securiies deb and conracual deb), a pracice ha has resuled in enhanced synergy for shor and medium-erm planning, operaions in a diversiy of markes, ransparency and communicaion wih differen invesor groups and risk classificaion agencies. In his regard, in 1999 he Naional Treasury implemened a new managemen model based on he Deb Managemen Office DMO philosophy. The Figure wih he new Naional Treasury organizaional srucure is shown below. In his framework, he hree SUDIP general coordinaion saffss paricipae in various segmens of he public deb planning, issuance, regisraion, conrol and paymen process: (i) Back-office (CODIV - General Coordinaion of Public Deb Conrol) is in charge of regisraion, conrol, paymens and budge monioring of he domesic and exernal debs; (ii) Middle-Office (COGEP - General Coordinaion of Public Deb Sraegic Planning), responsible for medium/long-erm planning, risk managemen, macroeconomic monioring and insiuional relaions; and (iii) Fron-Office (CODIP - General Coordinaion of Public Deb Operaions), which is responsible for shor-erm planning and bond issuances on domesic and exernal markes. Figure 2. Srucure of he Public Deb Undersecrearia Undersecrearia of he Public deb CODIV (Back-Office) COGEP (Middle-Office) CODIP (Fron-Office) Regisraion, conrol, paymen and budge monioring of he domesic and exernal debs Medium/Long-erm planning, risk managemen, macroeconomic monioring and insiuional relaions. Shor-erm planning and bond issuances on domesic and exernal markes Source: Naional Treasury Wihin his insiuional srucure, FPD sraegic managemen demands close coordinaion of proposed measures and monioring of resuls during execuion. In 2002, he Public Deb Managemen Commiee 2 In hose counries in which public deb managemen responsibiliies are disribued among various insiuions, one can observe inconsisencies in processes and sraegies, as well as duplicaion of funcions. 8

10 was creaed and is composed of represenaives of he hree coordinaion saffs of he Undersecrearia of he Public Deb, ogeher wih he Undersecreary who presides over he Commiee. The Commiee mees annually in order o analyze and approve he resuls of he opimal FPD composiion model and o evaluae possible medium-erm sraegies for he deb. These discussions are he jumping off poin for elaboraion of he Annual Borrowing Plan, which is laer discussed and agreed upon wihin he Commiee before being sen o he Naional Treasury Secreary for final approval. The Annual Borrowing Plan is revised every four monhs in such a way as o evaluae wheher changes in economic condiions may require significan aleraions in iniial planning. The Commiee mees in he final week of each monh in order o define he shor-erm sraegy o be adoped in order o achieve he arges se ou in he Annual Borrowing Plan and o elaborae he official schedule of aucions in he coming monh. These meeings are an opporuniy for managers and analyss of he Naional Treasury Undersecrearia of he Public Deb o share heir poins of view and informaion regarding he curren siuaion, markes and he fuure oulook for FPD financing. Finally, one should sress ha represenaives of SUDIP s hree coordinaion saffs, ogeher wih he Naional Treasury Secreary and Undersecreary, paricipae in he sraegic planning process (including boh shor and long-erm planning). 2. FPD Sraegic Planning The saring poin for sraegic planning is a clear definiion of he objecive of deb managemen. This objecive may vary from one counry o anoher. However, in general, i reflecs an effor o aain adequae balancing beween deb porfolio coss and risks and concerns regarding developmen of he governmen bond marke. Objecive of he FPD Managemen The objecive defined for Federal Public Deb managemen is ha of efficienly meeing federal governmen borrowing requiremens a he lowes possible long-erm financing cos, while ensuring pruden risk levels Addiionally, he aim is o he smooh operaion of he Brazilian governmen securiies marke. The objecive described above is he saring poin and major reference for he enire process of Brazilian public deb planning and managemen, as shown in Figure 1. This process will be discussed in deail in he following secions. 9

11 In summary, he process begins wih he elaboraion of analyical sudies o be used as he foundaion for discussion of he public deb benchmark choice. The nex sep is he design of a ransiion sraegy ha allows for more complee mapping of risks, opporuniies and resricions ha may appear over he medium-erm during he gradual shif oward he desired long-erm deb porfolio. These elemens are of criical imporance o defining and developing he shor-erm sraegy presened in he ABP, in erms of he acical decisions aken by he Public Deb Managemen Commiee. Figure 3. Process of FPD Sraegic Planning Objecive of Federal Public Deb Managemen Benchmark Definiion of Desired Long-Term FPD Srucure Transiion Sraegy Medium-Term FPD Planning Annual Borrowing Plan Shor-Term FPD Planning Deb Managemen Commiee Definiion of arges, Tacical Planning and Monioring Source: Naional Treasury 3. Annual Planning Since 2001, he Naional Treasury has published an Annual Borrowing Plan (ABP) for he Federal Public Deb 3. In he las decade, he ABP has become an insrumen for srenghening he ransparency and predicabiliy of public deb managemen, while considerably improving Naional Treasury performance on 3 Aside from he ABP, he Naional Treasury has also published he Annual Deb Repor (ADR) since This Repor presens he resuls achieved and he major evens ha marked public deb managemen in he previous year. Boh he ABP and he ADR are available in Poruguese and English on he Naional Treasury websie a: hp:// 10

12 he governmen bond marke. The ABP is designed o serve he objecive of Brazilian deb managemen and conains a series of guidelines ha orien formulaion of shor-erm sraegy 4. Aside from he FPD objecive, hese guidelines give due consideraion o he benchmark and he ransiion sraegy. In general, hey encompass lenghening of he average mauriy, smoohing of he mauriy profile, increased paricipaion of fixed rae and inflaion-linked bonds, broadening of he invesor base and governmen bond marke liquidiy and developmen of he erm srucure of ineres rae. FPD Managemen Guidelines Increase he average mauriy of he ousanding deb Smooh he mauriy srucure, wih paricular aenion o he shor-erm deb Gradual replacemen of floaing rae bonds by fixed rae or inflaion-linked insrumens Improvemen in he exernal Federal Public Deb (EFPD) profile hrough issuances of benchmark mauriies, buybacks and srucured operaions Developmen of he yield curve on boh domesic and exernal markes and growh in he liquidiy of federal governmen securiies on he secondary marke Broadening of he invesor base. Various alernaive macroeconomic scenarios are considered during he annual planning elaboraion. These scenarios are consruced on he basis of a se of relevan macroeconomic variables (shor-erm ineres rae, exchange rae and inflaion, mainly) and he hypohesis of preserving he main pillars of he economic policy adoped as of 1999 (inflaion argeing sysem, floaing exchange rae and robus primary surpluses). Based on he esimae of Federal Governmen borrowing requiremens for he year, he ABP guidelines, he various macroeconomic scenarios and differen bond issuance sraegies, he Naional Treasury calculaes he values expeced for he major Federal Public Deb FPD indicaors: amoun ousanding, composiion broken down by indexing facor, average mauriy and percenage mauring in 12 monhs. A ha poin, he ABP presens he indicaive upper and lower limis expeced for each one of hese indicaors a he end of he year, as shown in Table 1. 4 Alhough he curren framework of FPD managemen calls for definiion of he benchmark and design of a mediumerm plan, is iniial sages focus exclusively on he design of he shor-erm sraegies ha were se ou in he annual borrowing plans 11

13 Table 1. Federal Public Deb Targes in 2011 Indicaors 2010 Limis for 2011 Minimum Maximum Sock of FPD (R$ billion) 1, , ,930.0 Profile (%) Fixed rae Inflaion-linked Floaing Rae Exchange rae Mauriy Srucure Average mauriy (years) % Mauring in 12 Monhs Noe: In he 2011 ABP, he Naional Treasury gahered under Floaing Rae all bonds ied o ineres raes subjec o periodical reseing (e.g. Selic, TR and TJLP). Source: Naional Treasury Execuion of he annual FPD planning demands rigid coordinaion beween acions derived from planning and monioring of resuls during he implemenaion sage. To avoid inconsisencies in ABP execuion - and propose correcive measures, should ha become necessary - he Deb Managemen Commiee mees a he end of each monh. During hese meeings, quesions relaed o he macroeconomic scenario are discussed, borrowing requiremens and financial marke condiions are evaluaed, bond issuance sraegy for he coming monh is proposed and approved and is impacs in relaion o he limis proposed in he ABP for he end of he year are assessed. The sraegy includes such characerisics as he ime o mauriy and ype of index (fixed-rae, floaing rae, exchange variaion or price index) of he financial insrumens o be issued. This process also resuls in a definiion of he public bond issuance schedule, specifying daes and ypes of aucions, coupled wih he characerisics of he bonds o be issued. 4. Federal Public Deb Opimal Composiion Model 5 Definiion of a financing sraegy involves choices regarding he balancing of expeced coss and risks ha can be generaed by a specific public deb srucure. In his sense, based on social preferences beween coss and risks, he deb manager mus define he desired profile for long-erm liabiliies or, in oher words, he benchmark, in such a way ha financing of hese liabiliies can be done in he leas burdensome manner possible wihou, however, resuling in increased risk exposure. 5 See Uni II of his documen for a deailed descripion of he model. 12

14 Brazil is no alone in he pursui of a long-erm public deb benchmark porfolio. Various counries, including Porugal, Sweden, Ireland, Denmark and Souh Africa, have used similar heoreical frameworks. Parallel o his, inernaional organizaions such as he World Bank and Inernaional Moneary Fund recommend ha sovereign deb managers adop benchmark models as a risk managemen and sraegic planning ool. In recen years, he Naional Treasury has developed a model o aid in evaluaion of he cos and risk ha differen deb srucures may generae for FPD, focusing specifically on he choice of is benchmark. The analyical framework of he model, which will be discussed in Uni II, is founded upon a se of simulaions ha make i possible o evaluae he behavior of alernaive FPD porfolios in ligh of varied scenarios for he evoluion of he variables ha define he financing coss of he deb. Based on hese simulaions, cos and risk indicaors are derived for each porfolio evaluaed. The lowes cos porfolio for a specific risk level is considered efficien. As he final produc of he model, he bringing ogeher of all of he porfolios ha saisfied his condiion for he differen risk levels is denominaed he efficien fronier, which expresses he rade-off in erms of coss and risks wih which he deb manager has o cope. In he sochasic fronier, each porfolio is differen in erms of composiion, average mauriy and percenage mauring in 12 monhs. The final resuls are he subjec of debae among deb managers, giving due consideraion o he feasibiliy of aaining he possible benchmark porfolios. Finally, in choosing he benchmark, he public deb manager presens he resuls of he efficien fronier o he fiscal policy manager, who may be he Miniser of Finance, Treasury Secreary or some ype of Execuive Commiee. As he represenaive of sociey, he fiscal policy manager will be charged wih choosing an accepable risk level and, consequenly, he borrowing cos desired by he governmen. In his process of choosing he benchmark, i is imporan o highligh ha quesions relaed o susainabiliy of he deb mus also be given consideraion. In his way, opimal composiions ha have he poenial for making he deb unsusainable, as a resul of he projeced financing cos or assumpion of excessive risk, mus be eliminaed. For a diversiy of reasons, convergence of he curren public deb composiion o is benchmark may vary over ime. Such facors as an adverse macroeconomic environmen or he absence of a developed local deb marke - which could resul in shorfalls in demand for some preferred deb insrumens - may reduce he speed of he convergence process. Under such circumsances, more robus heoreical analysis, simulaions of he dynamics of he deb in alernaive scenarios and deepening of debaes on he definiion of long-erm objecives may be as or even more imporan o deb managemen han concenraing effors on he idenificaion of possible opimal composiions. The iniial proposal of he Brazilian opimal composiion model was published in he 2007 ABP. Simulaions of his model indicaed ha efficien FPD managemen would be ha which resuled in greaer paricipaion of fixed-rae bonds 6 and inflaion-linked bonds, in derimen o floaing rae or exchange- 6 Among he advanages of fixed-rae bonds, menion should be made of he following: (i) hey ensure greaer predicabiliy regarding deb coss; and (ii) hey conribue o developmen of he counry's fixed income marke. 13

15 rae-indexed bonds 7. Following he guidelines above, he recen evoluion of he FPD profile has resuled in greaer equilibrium beween FPD coss and risks. Annually, as shown in Table 2, discussions have moved forward o refining of he long-erm FPD quaniaive guidelines, including definiion of indicaive limis o be sough in he period. Alhough hese limis provide guidance for defining sraegies, i is imporan o emphasize ha hey also reflec possible consrains relaed o he Brazilian macroeconomic scenario and he developmen sage of local financial markes. The speed of convergence from he curren FPD composiion o ha indicaed in Table 3 will depend on surmouning some of hese consrains. Table 2. Indicaive Inervals of he Desired FPD Composiion over he Long-Term Lower limi Upper limi Fixed rae 40% 50% Inflaion-linked 30% 35% Floaing rae 10% 20% Exchange rae 5% 10% Source: Naional Treasury 5. Elaboraion of Medium-Term Transiion Sraegy Aside from informing sociey wih regard o he shor-erm (one year) sraegy and opimal long-erm composiion (benchmark) hrough publicaion of he ABP, sraegic FPD planning annually defines a ransiion sraegy from he curren public deb composiion o he long-erm benchmark. The ransiion sraegy seeks o respond o he following quesion: duly respecing iniial condiions (he curren deb profile) and shor and medium-erm resricions (paricularly, macroeconomic resricions and developmen of local financial markes), wha should be he convergence rajecory and speed oward he desired long-erm composiion? Developmen of he ransiion sraegy demands elaboraion and discussion of qualiaive and quaniaive macroeconomic scenarios for he variables (mainly, he Selic rae, exchange rae, inflaion and GDP) ha impac FPD coss and risks. In each of he proposed scenarios, differen sraegies are evaluaed in ligh of 7 As regards he deb ied o exchange rae (currenly resriced o he exernal deb), simulaions demonsrae ha, hough his deb ends o have lower average coss, is risk level is exremely high, paricularly in sress scenarios. Despie his and in ligh of he proecion provided by inernaional reserves in he case of exchange rae flucuaions, aking some degree of exchange rae risk in he FPD can be considered ineresing from he poin of view of he Ne Public Secor Deb (NPSD). A he same ime, sovereign bonds are imporan o he developmen of he Brazilian yield curve on he inernaional marke, and serve as a reference for he privae secor in Brazil. 14

16 he speed of convergence o he long-erm benchmark. In pracical erms and respecing he borrowing condiions se down for each scenario during he ransiion period, he speed of convergence oward he benchmark is he main difference among he alernaive sraegies. The choice of ransiion sraegies for he long-erm also akes advanage of he rade-offs beween public deb coss and risks. The resuls for he cos, risk, mauriy profile and deb composiion indicaors are simulaed for each sraegy. For example, a public deb manager could choose o limi issuances essenially o fixed-rae deb, while anoher may aribue greaer imporance o issuance of inflaionlinked bonds. Alernaive choices such as hese aid daa managers in he decision-making process, since hey show he consequences of heir choices for he major deb indicaors. In conclusion, elaboraion of he ransiion sraegy involves inegraion of he processes of benchmark simulaion and definiion of he convergence sraegy. While he benchmark model is based on he assumpion ha he economy is in a seady-sae 8, he ransiion sraegy is defined on he basis of possible scenarios for he coming years. For his reason, discussions on macroeconomic scenarios and evoluion of public deb markes are vial o deermining how he economy will converge o is saionary sae and, herefore, how public deb managemen mus be implemened in order o aain he benchmark Risk Evaluaion: Brazilian Experience Evaluaion of risk exposure is an imporan elemen of he planning process and one of he foundaions for defining FPD sraegic guidelines 10. Inegraion of risk managemen ools ino FPD risk evaluaion insrumens mus be viewed ogeher wih he economic evoluion of he counry, which has favored developmen of he public deb markes, hus expanding he array of financing alernaives. Economic sabiliy and marke improvemens were condiions of essenial imporance o he evoluion of public deb planning and analysis insrumens. 8 In he public deb benchmark model, he seady sae has wo meanings. In he firs place, i means ha all of he economic variables are flucuaing around heir long-erm equilibrium values. In pracical erms, he saionary sae scenario encompasses he following characerisics: sabiliy of he economic environmen, reduced fiscal vulnerabiliy, lower ineres raes, conrolled inflaion and susainable economic expansion. The second meaning found in he idea of a seady sae is ha each deb composiion is associaed o an issuance sraegy ha mainains consan he longerm FPD porfolio characerisics. 9 The alernaives for he ransiion sraegy are simulaed in a deerminisic conex. I is possible o design dynamic sochasic simulaion sysems wih he aim of also opimizing he ransiion sraegy. This approach is expeced o be he nex sep in applicaion of opimizaion models. However, since i is sill incipien and highly complex, we have been unable o find any sovereign deb manager who has successfully used i. 10 More deailed informaion can be encounered in ALVES & SILVA (2009) and SILVA, CABRAL & BAGHDASSARIAN (2009). 15

17 The major risks involved in FPD managemen are refinancing and marke risks, hough due aenion should also be given o sraegic, operaional and legal risks. A more deailed descripion of hese ypes of risk is found in he following char. Major Risks Moniored in FPD Managemen Refinancing Risk Refinancing risk is based on he possibiliy of having o cope wih higher coss in order o obain shor-erm financing or, in an exreme siuaion, of being unable o refinance he deb mauring over he shor-erm. This risk is relaed o he deb mauriy profile, as well as o is shor-erm sensiiviy o shocks in he major variables.. Make Risk Marke risk (or financial risk) is derived from variaions in he financing coss resuling from movemens in he shor-erm ineres raes, he yield curve, he exchange or inflaion. In oher words, his risk is relaed o flucuaions in he deb sock on he marke. Sraegic Risk Sraegic risk resuls from he possibiliy of a sraegy no achieving is objecives. For he naional Treasury, his risk is presen, for example, in he possibiliy of no achieving he limis se down in he ABP for FPD composiion by indexing facor, due o he choice of an inadequae sraegy. Operaional Risk The Concep of Operaional Risk is quie broad and encompasses he possibiliy of failures caused by persons, inernal processes or sysems or, furhermore, exernal evens ha generae losses for insiuions. In he case of he Naional Treasury, his risk may be perceived by he exernal public, mainly hrough governmen bond aucions. For example, an inerrupion in elecriciy ransmission could make i unfeasible o sell bonds a he programmed momen of he aucion. Legal Risk Legal Risk resuls from he possibiliy of no respecing he limis for deb indicaors as expressed in legislaion (annual volume of issuances, for example). 16

18 In Brazil, he developmen of he public deb opimal composiion model was a naural consequence of a long process of improvemen in he insiuional framework i uilized o evaluae FPD coss and risks. Iniially, he governmen s asse and liabiliy managemen model was implemened. Following ha, he risk managemen insrumens used by he Naional Treasury were adoped in FPD managemen. A ha poin, sudies were iniiaed on use of he opimal composiion model for he public deb. To faciliae undersanding of his evoluion over ime, one can divide i ino hree differen sages. In he firs sage, he Naional Treasury adoped guidelines for FPD managemen using he Asse and Liabiliy Managemen - ALM model as he basic reference. The objecive of his model is o combine he characerisics of governmen asses and liabiliies in such a way as o proec he ne deb agains marke risks and hereby smooh ou oscillaions in he governmen asse balance. Wih his in mind, ALM considers he public deb managemen sraegy and oher macroeconomic policies. The 2002 ABP 11 was he firs repor o menion he ALM model. The resul of he implemenaion of he ALM model by he Naional Treasury was he elaboraion of periodical monioring repors on he asses and liabiliies for which he Cenral Governmen was responsible. These repors made i possible o develop more effecive financing sraegies in erms of he balance beween hese asses and liabiliies. The repors in quesion idenified he mismaches beween asses and liabiliies in erms of indexing facors, average mauriies, cash flows and he percenage of deb in he following 12 monhs, and included simulaions of he fuure evoluion of hese mismaches. The objecive of he ALM model is o creae a porfolio of liabiliies wih risk characerisics similar o hose of he governmen's asses and, in his way, reduce he sensiiviy of he public secor asse balance o shocks in economic and financial variables. Considering he pariculariies of he public secor, i is imporan o adequaely map he asses o be included in he balance used for ALM purposes. The fac ha he governmen does no seek o maximize profis and is able o charge axes resuls in a siuaion in which he ALM srucure differs from he public o he privae secor. Normally, one sars wih an accouning balance, which is adaped o he "economic balance", which includes only hose iems ha represen poenial financial liabiliies and hose ha will conribue o paying hem. In oher words, one should consider only asses/liabiliies ha inerfere in sovereign risk. This rule may resul in exclusion of asses ha did no generae financial flows for deb managemen purposes and inclusion of coningen liabiliies in he governmen balance. On he oher hand, illiquid asses such as naional parks, miliary equipmen, governmen buildings are included in he accouning balance, bu may be considered irrelevan o analysis in he framework of he governmen s ALM. However, should hese iems be incorporaed ino a privaizaion program, hey would be included in he asse map. Finally, one should sress ha he major asse of a governmen is is capaciy o collec axes. In conras o his, here are cerain expendiures ha are ypically he responsibiliy of he public secor. From he ALM poin of view, he deb manager mus be capable of perceiving he characerisics of revenues or of 11 hp:// 17

19 fuure primary surpluses and, whenever possible, esimae hem wih he objecive of "maching" he balance shee. Over he long-erm, he curren value of he deb mus be financed by he presen value of he sum oal of fuure primary surplus flows. In he second sage of he process of improving he FPD risk managemen mechanisms, approaches were aggregaed seeking o measure he impac of adverse shocks in deb indexing facors on FPD. This was he case of he sress es, which simulaes he negaive impac on he ousanding volume (or cos) of FPD as a resul of srong and persisen pressure on he real ineres rae or on he exchange rae. Anoher example was he iniial use of sochasic indicaors 12, such as Cash-flow-a-risk (Cfar) 13 and Cos-a-risk (CaR) 14. These indicaors are obained on he basis of simulaions uilizing he Mone Carlo mehod for key variables (ineres, exchange and inflaion raes, in he Brazilian case), calibraed by hisorical daa or deerminisic parameers. As a resul of hese simulaions, probabiliy disribuions of cash flow (CfaR) or ousanding deb (CaR) are obained. This class of indicaors made i possible o esimae losses expeced in he deb as a resul of negaive evens and were iniially presened in he 2004 ABP 15. Table 3 below presens a brief descripion of he major indicaors used o monior FPD risks in Brazil. 12 Risk indicaors based on sochasic simulaions ha have he advanage of indicaing a probabiliy disribuion of he value of paymen flows or he value of ousanding deb. This ype of risk measuremen makes i possible o esimae losses for he public deb consequen upon negaive evens ha may occur in he economy, aside from quanifying he probabiliy of such evens. 13 Cash-flow-a-risk indicaes he maximum increase ha may occur in FPD paymens flows for a given period, in relaion o he expeced value of such paymens, wih a given probabiliy (e.g. 95% confidence level). 14 In Brazil, Cos-a-risk is used o measure uncerainy in relaion o he volume of deb a he end of a period. I indicaes he maximum value ha he deb can reach, for a given probabiliy. Differenly from he case of Denmark, in which he measuremen is defined in erms of deb coss, he Brazilian CaR is deermined on he basis of ousanding deb. However, he wo approaches are equivalen, since, he greaer he cos, he greaer will be he ousanding deb for a given governmen primary resul. 15 hp:// 18

20 Table 3. Major public deb risk indicaors used in Brazil Type of Risk Indicaor Descripion Commens A complee descripion of he deb mauriy profile can Percenage of FPD mauring in 12 monhs Indicaes he shor-erm concenraion of deb mauriies. be drawn up on he basis of an analysis of he enire FPD mauriy srucure (ha is, also evaluaing he percenage of deb mauring over he medium and long-erm) Refinancing risk Average FPD mauriy Indicaes he average period of ime in which he deb should be paid or refinanced. In Brazil, he resen value of deb flows (principal and ineres) is used as he weighing facor of he erms of each flow (concep of duraion) in calculaing he average FPD mauriy. CfaR and CaR (see below) are risk indicaors based on Cash-Flow-a-Risk (CfaR) Indicaes he maximum increase ha may occur in FPD paymen flows projeced for a given period, considering a given confidence inerval (e.g. 95% probabiliy) sochasic simulaions, wih he advanage of indicaing a disribuion of probabiliies of he value of paymen flows or of he value of he ousanding deb. This ype of risk measuremen makes i possible o esimae public deb losses consequen upon negaive evens ha occur in he economy, as well as o quanify he probabiliy of such evens. The ypes of index ha caegorize ousanding FPD in his FPD Composiion Indicaes he percenage of he ousanding deb by ype of index indicaor are defined according o classes of risk which, in urn, depend on deb indexing facors. In he case of FPD, here are 4 classes: Fixed Rae, Floaing rae, Inflaion-Linked (Price Indices), Exchange-rae Corresponds o he deb exposed o ineres rae flucuaions, caused by he fac ha he deb mus be Refixing Risk (or ineres rae risk) Indicaes he share of FPD subjec o cos increases caused by shor-erm ineres rae flucuaions. refinanced (a new raes) or because earnings on he deb are generaed by floaing rae(e.g. Selic rae). Thus, he indicaor is given by he sum oal of percenages of FPD mauring over 12 monhs and he percenage wih floaing rae mauring afer 12 monhs. Marke Risk FPD Sensiiviy Analysis Indicaes he increase in he ousanding deb (cos) as a resul of a 1% variaion in a specified indexing facor (shor-erm ineres rae or exchange rae). This analysis seeks o respond o he following quesion: "Wha happens if a specific shock occurs?". Alernaively, his indicaor may be calculaed by assuming a variaion equivalen o one sandard deviaion in he benchmark indexing facor. Sress Tes Measures he negaive impac on ousanding FPD (or on is cos) due o srong and persisen pressure on real ineres rae or real exchange rae. This is equivalen o he sensiiviy analysis. However, in his case, one applies a shock equivalen o 3 sandard deviaions of he real ineres rae or real exchange devaluaion accumulaed over 12 monhs o ousanding FPD. In Brazil, cos-a-risk is used o measure uncerainy wih Cos-a-Risk (CaR) Indicaes he maximum value ha ousanding FPD may reach a he end of a specified period of ime (e.g. 1 year) for a given confidence inerval (e.g. 95% probabiliy). respec o he volume of deb a he end of he period. Despie being defined in erms of ousanding volume, insead of cos (ineres), hese wo approaches are direcly relaed, since, he greaer he cos, he greaer will be he deb sock for a given primary governmen resul. Source: Naional Treasury 19

21 Having defined risk managemen insrumens, he final sage of insiuional developmen resuled in effors o elaborae a model ha would furher refine general FPD guidelines quaniaively. In oher words, definiion of an opimal long-erm composiion model for FPD was sough, wih he purpose of minimizing impacs of public deb shocks on he fiscal resul. The iniial proposal of he model was published in he 2007 Annual Borrowing Plan 16 and laer in CABRAL e. alli. (2008). A more deailed descripion of he analyical framework used by he Naional Treasury o aid in defining he FPD benchmark will be discussed in Uni II of his documen. In conclusion, hough uilizaion of sophisicaed financial insrumens in FPD managemen has ransformed he Naional Treasury of Brazil ino a reference for like insiuions in he world, here is sill room for improvemen in he model. By way of example, one could include uilizaion of macrosrucural models for generaion of scenarios, in which macroeconomic and financial models are conjugaed in he generaion of sochasic scenarios, and use of differen approaches o modeling of he yield curves 17, inflaion and exchange raes. 16 hp:// 17 Currenly, a COX, INGERSOLL & ROSS (1985) - based model is uilized, known as CIR models, wih jus one facor (ineres rae level) o explain he forward ineres rae srucure (ETTJ). In he fuure, one expecs o work wih models ha include he dynamics of more yield curve facors (for example, level and inclinaion), wheher hey be derived from he CIR family or based on oher specificaions such as hose derived from NELSON & SIEGEL (1987). 20

22 7. References ALVES, L. F.; SILVA, A.C. Federal Public Deb Sraegic Planning. In Public Deb: The Brazilian Experience. Secrearia do Tesouro Nacional. Par 2, Chaper 2, pg Available a: < hp:// >. CABRAL, R.S.V; LOPES, M.L.M; BAGHDASSARIAN, W.; ALVES, L.F., de SOUZA JR., P.I.F; dos SANTOS; A.T.L. A Benchmark for Public Deb: The Brazilian Case Working Paper. Available a: <hp://papers.ssrn.com/sol3/papers.cfm?absrac_id= >. COX, J.; INGERSOLL, J.; ROSS, S. A Theory of he Term Srucure of Ineres Raes. Economerica 53, pg , MINISTERIO DA FAZENDA. SECRETARIA DO TESOURO NACIONAL. Plano Anual de Financiameno (Annual Borrowing Plan) (various years: ). Available a: < hp:// >. NELSON, C.; SIEGEL, A. Parsimonious Modeling of Yield Curves. Journal of Business, 60, VOL. 4, pg , SILVA, A.C.; CABRAL, R.; BAGHDASSARIAN, W.; Federal Public Deb Risk Managemen. In Public Deb: The Brazilian Experience. Secrearia do Tesouro Nacional. Par 2, Chaper 3, pg Available a: < hp:// >. 21

23 UNIT II: THE ANALYTICAL FRAMEWORK OF THE FEDERAL PUBLIC DEBT BENCHMARK As we saw in Uni I, he definiion of he opimal public deb composiion is one elemen of he sraegic planning process. Opimal composiion (benchmark) represens he profile desired for he long-erm deb srucure and acs as a guide for elaboraing he governmen's shor and medium-erm financing sraegies. In he Brazilian case, he benchmark is expressed by a se of indicaors of relevance o he deb, including composiion of ousanding deb by ype of index, mauriy srucure, paricularly he percenage of deb o maure in he nex 12 monhs, and he average mauriy of he ousanding deb. Implemenaion of he benchmark can be achieved hrough definiion of arges for he values o be aained by hese indicaors over a specific emporal horizon. This Uni is an effor o describe he model uilized by he Naional Treasury in evaluaing he rade-offs beween coss and risks derived from alernaive profiles for he Federal Public Deb (FPD) srucure over he long-erm, based on he objecives and guidelines defined for managemen of ha deb 18. This uni is organized ino four secions: Iniially, we will presen he main heoreical argumens in favor of he adopion of a benchmark, ogeher wih informaion on inernaional experience in his area; In secion 2, we will describe he simulaion model used by he Naional Treasury; Applicaion of he model for defining he FPD benchmark is illusraed in secion 3; Finally, secion 4 presens FPD composiion desired for he long-erm, in he form of upper and lower limis. 18 Definiion of a FPD benchmark was discussed in such previous sudies as CABRAL & LOPES (2005), SILVA, CABRAL & BACHDASSARIAN (2006), CABRAL e alli. (2008) and ALVES (2009). 22

24 1. Lieraure and Inernaional Experience The imporance of he opimal composiion (benchmark) is clearly suppored by heoreical lieraure, which sresses he relevance of public deb managemen o economic aciviy 19. This is paricularly rue regarding he lieraure on ax smoohing and emporal consisency, which suppors acive deb managemen. The heoreical argumens in favor of seeking an adequae deb composiion ake on even greaer relevance when one considers he elemens discussed in lieraure on he credibiliy of macroeconomic policies, signaling and real effecs of a sovereign defaul, among ohers 20. In his debae, one should also menion he conribuion made by mulilaeral insiuions, including he World Bank and Inernaional Moneary Fund. In heir publicaion Guidelines for Public Deb Managemen (WB; IMF, 2001), hese wo insiuions describe he benchmark as a powerful ool for represening he deb profile ha he governmen desires o aain, based on is preferences as defined by he rade-off beween coss and risks. Finally, inernaional experience has documened ha various counries have aken measures o define an opimal composiion for heir debs. A case in poin is Porugal, one of he pioneers in he formulaion and adopion of opimal long-erm composiion for quanifying he objecive of is public deb managemen, as well as for enhancing he consisency beween daily decisions and he long-erm objecive. Denmark, Sweden, Canada and he Unied Kingdom have also developed models designed o aid in defining a benchmark porfolio o be used as a guide in elaboraion of financing sraegies. The following char summarizes aspecs of he experience of hese counries. 19 The Hypohesis of Ricardian Equivalence is an imporan poin of deparure in his debae, hough i does no provide subsidiary informaion for an acive defense of public indebedness. One consequence of he Hypohesis of Ricardian Equivalence is he neuraliy of he deb wih respec o economic aciviy, since deb and axes are equivalen from he ineremporal poin of view. However, Ricardian Equivalence is basically founded upon he following supposiions: 1) an infinie planning horizon; 2) complee markes; and 3) axes ha do no cause disorions (BARRO, 1974; 1979; 1989). Wih relaxaion of hese presupposiions, new heories have drawn conclusions regarding he imporance of adequae deb managemen. 20 See GOLDFAJN & DE PAULA (1999). 23

25 Tabela 1. Inernaional Experience Counry Relevan indicaor Summary of he model Source The model assumes a consan nominal deb in a saionary sae and has hree inpus: 1) sochasic Porugal Cos and risk of cash flows, wih resricions regarding refinancing risk ineres raes; s) financing sraegies; and 3) deerminisic scenarios for oher macroeconomic variables. A subse of he bes soluions of he model is presened o he auhoriies charged wih he final decision. IGCP (1999). Running Yield: probabiliy disribuion of he model is Sweden Targes for he paricipaion of each ype of deb, based on cash flows and duraion calculaed hrough dynamic simulaion of he ineres (shor and long-erm), inflaion, exchange rae and GDP curves. A measuremen of dispersion of his disribuion is used as risk indicaor. RIKSGÄLDEN (2008); RIKSGÄLDEN (2009) The curren ne value is used as a cos measuremen, and fiscal volailiy as a risk measuremen. Since i reflecs he srucural condiions of he economy and Ireland Curren ne value and fiscal volailiy he final objecive of fiscal policy, he benchmark should no be alered significanly over ime. In his sense, revisions in he benchmark can be implemened o reflec srucural changes in he economy, bu no in response o shor-erm movemens. NTMA (2006); NTMA (2011) In order o define he duraion arge, a long-erm analysis of he evoluion of expeced coss is carried Denmark Duraion of he porfolio ou. The model considers only he domesic deb. Ineres rae risk is deal wih in he ALM approach and he rade-off beween coss and risks is evaluaed by a Cos-a-Risk model. The model combines sochasic and deerminisic scenarios. DANMARKS NATIONALBANK (2007) England The benchmark is no uilized. However, models are uilized o illusrae he impac of differen issuance sraegies and indicaors for risk managemen. Longerm analysis of financing sraegies is done hrough Deb Service Cos (in erms of cash flows) as a proporion of GDP he use of sochasic scenarios based on he combinaion of a macroeconomic model wih specificaions for ineres curves. Cos is measured by cash flows and risk by he dispersion of paymens. UK-DMO (2011) e PICK AND ANTHONY (2006) Canada Cos measuremen: annual average deb service burden as a percenage of oal ousanding deb Measuremen of risk: cos of volailiy or consideraion of impac on he budge Combines a macroeconomic model wih ineres curves o simulae coss and risks of alernaive financing sraegies. In order o aggregae more han one objecive ino he analysis, he model offers a ool for minimizing he weigh of he deb service wih resricions on oher objecives. BOLDER (2008) Elaboraion: Naional Treasury 24

26 2. The Brazilian Opimal Composiion Model 2.1. Some Mehodological Issues The analyical framework uilized in he sudy of opimal FPD composiion is based on sochasic simulaions derived from finance and efficien porfolio heories. However, before proceeding o a descripion of he model iself, some commens mus be made regarding he direc applicaion of he insrumens of radiional financial analysis o governmen policies. In general, he governmen, wih he condiion of preserving pruden risk levels, may have more complex objecives han reducing coss. Aside from his, evoluion of is cash flows and indicaors of budge impacs may have implicaions for he choice of he opimal deb srucure. One should also consider ha, given he naure of he public deb, governmen measures have a srong impac on bond prices and, consequenly, on he cos and risk of is financing sraegies. As a resul, hese peculiariies may lead economic policy managers o define a deb composiion as benchmark ha is differen from hose on he efficien fronier, obained from he sricly financial poin of view. One imporan quesion in he model refers o wha should be he relevan deb concep for evaluaing coss and risks. In he Brazilian case, he Naional Treasury only has direc conrol over he Federal Public Deb, which encompasses all domesically and inernaionally issued bonds, as well as he federal governmen's exernal conracual deb. Noneheless, he mos commonly used indicaor, boh by he federal governmen, o define is deb arges and he primary surplus required o achieve hose arges, and by analyss, wih he aim of evaluaing fiscal susainabiliy, is he raio beween he Ne Public Secor Deb and GDP (NPSD/GDP). This concep is more inclusive since i encompasses all public secor liabiliies, deduced from is asses agains oher economic agens. Public secor is undersood as he federal governmen (including he Social Securiy Sysem), Cenral Bank, sae and municipal governmens and public secor companies. The reducion in NPSD volailiy (risk) is imporan o he exen in which he occurrence of shocks wih poenial o jeopardize is susainabiliy requires a fiscal policy response. In his sense, unforeseen NPSD flucuaions may resul in ax surprises ha would affec he available income of he populaion, generaing inefficiencies from he social welfare poin of view 21. Despie he fac ha he Naional Treasury's work insrumen is he FPD, here is clear communicaion beween his deb and he NPSD, which is much broader and used as an economic policy reference. For he reasons se ou above, a decision was made o use he NPSD/GDP indicaor for choosing he opimal composiion in Brazil. This choice was based on he idea ha, in an analysis of governmen ineremporal budge resricions aimed a evaluaing he susainabiliy of he public deb, all public secor asses and liabiliies should be considered. As a maer of fac, many economic analyss and 21 Lieraure on opimal axaion suggess ha if axes cause dead weigh losses, he governmen should smooh hem over ime, hus minimizing disorions consequen upon revenue inflows. In his case, he deb profile and is risks are relevan for public policy purposes, since flucuaions in deb coss would resul in aleraions in he ax load. See BOHN (1990). 25

27 financial marke paricipans, including inernaional organizaions (e.g., he World Bank and IMF) and raing agencies (e.g., Sandard & Poor's), consider NPSD/GDP as he relevan indicaor for evaluaing he susainabiliy of he Brazilian deb. Anoher imporan aspec refers o he fac ha he benchmark sudy is based on he premises of he seady-sae. This has wo meanings for he model. In he firs place, i presupposes ha he economy is already in a seady sae or, in oher words, ha all variables are flucuaing around heir long-erm equilibrium values. The fac of he maer is ha his supposiion is appropriae o a discussion of a deb profile desired for he long-erm, avoiding he possibiliy of he decision being conaminaed by ransiory flucuaions in economic scenarios. In pracical erms, he reference o he seady sae scenario includes he following characerisics: sabiliy of he economic environmen, low fiscal vulnerabiliy, real ineres raes already in a sae of equilibrium, conrolled inflaion and susainable economic growh. The second meaning found in he idea of a seady-sae is ha each issuance sraegy implicily preserves consan he characerisics in he long-erm FPD porfolio. In oher words, he sraegy iself and, herefore, deb managemen guidelines mus be sable over ime, wih no sharp flucuaions caused by emporary shocks in he economy, coupled wih avoidance of nearsighed behavior guided by shor-erm parameers The Opimal Composiion Model The sudy of he opimal composiion (benchmark) for he Brazilian deb is based upon he applicaion of sochasic simulaion mehods, wih he objecive of deriving an efficien fronier of deb composiions, expressing poenial rade-offs beween coss and risks in FPD managemen. In his sense, a composiion is viewed as efficien when i has he lowes risk for a specified cos level or, alernaively, when he cos is he lowes for a specified risk level. The enire se of composiions ha saisfied his condiion defines he efficien fronier, while i is he deb manager's ask o choose which composiion is desirable, since i is no possible o obain simulaneous cos and risk reducions among he fronier porfolios. The following Figure illusraes he general idea of he model used for analysis of he rade-off beween coss and risks. 26

28 Figure 1. Schemaic Summary of he Model Source: Naional Treasury Iniially, various sochasic scenarios are generaed for he principal macroeconomic and financial variables oupu, inflaion, exchange raes, shor-erm ineres raes and public bond prices wih he objecive of simulaing evoluion of he major facors ha influence he rajecory and cos of he public deb over ime. A ha poin, a deb composiion is chosen ha involves a baske of securiies, wih varied ypes of indexes and differen mauriies. By way of example, we will look a a porfolio composed equally of one year fixed rae bonds and five-year floaing rae bonds. Over he course of each simulaed scenario, he FPD financing cos is calculaed for he chosen deb composiion. The nex sep of he simulaion process involves calculaion of FPD and NPSD evoluion which depends on he previously obained FPD financing cos, as well as on oher parameers ha define he public secor primary resul and evoluion of oher asses and liabiliies 22 ha make up he NPSD. Finally, cos and risk indicaors are derived from analysis of he behavior of NPSD in he face of sochasic shocks. Since housands of scenarios are simulaed and he value of he NPSD is calculaed for each one of 22 FPD includes only he domesic and exernal debs for which he Naional Treasury is liable. In calculaing NPSD, he definiion of public secor used o measure indebedness is ha of he nonfinancial public secor plus he Cenral Bank. Consequenly, i encompasses he direc federal, sae and municipal adminisraions, indirec adminisraions, he public social securiy sysem, nonfinancial federal, sae and municipal governmen companies, as well as he Cenral Bank of Brazil. In his concep, inragovernmenal debs are excluded, so as o measure only he public secor deb wih privae agens. Since NPSD is a ne deb concep, public secor liabiliies are deduced from is asses wih oher economic agens. 27

29 hem for a given poin in ime, in pracical erms he resuls provide a disribuion of probabiliies of he value of NPSD, from which he coss and risk merics are exraced. In he simulaions, he iniial FPD srucure, sochasic scenarios, primary resul parameers and "oher asses and liabiliies" are he same for any deb composiion chosen. As a resul, he only reason for he resuling rajecory of NPSD simulaions o vary among differen deb composiions is he seleced composiion iself. Afer performing he simulaions, he merics obained for each evaluaed composiion are ploed on a graph in which he axes are NPSD/GDP cos and risk, in such a way ha he efficien fronier is obained as a curve composed of he poins ha represen he lowes cos for a specified risk level. The fronier porfolios are efficien because i is no possible o alernae among hese porfolios in order o obain cos and risk reducion gains simulaneously. Finally, given he governmen's posiion on risk (which should reflec ha of sociey), i is possible o choose a specific fronier porfolio ha will define he deb benchmark. The following figure illusraes his concep. Porfolios over he lengh of he fronier (A, B and C) are efficien because he risk necessarily increases when one seeks o reduce he cos of he deb alernaing beween hese composiions (from A o B; or from B o C). Composiions above and o he righ of he fronier are inefficien because hey increase risk, given he level of coss (D compared o A), or increase he cos for a given risk level (D compared o C), or increase boh he cos and he risk, in comparison o an efficien composiion (D compared o B). Figure 2. Illusraion of he Efficien Fronier Source: Naional Treasury In operaional erms, he efficien fronier depends on he average cos and sandard deviaion of each bond, jus as occurs wih he cos correlaion marix of hese securiies. In he firs place, simulaions based on deb composiions wih 100% of a specified bond provide he average cos and sandard deviaion. Secondly, simulaions based on porfolios wih 50%-50% pairs of bonds aid in calculaing he cos 28

30 correlaion marix 23,24. Consequenly, wih hese daa in hand, a numerical procedure is employed in order o discover he lowes cos porfolio for each possible risk level, concluding wih he obaining of he analyical efficien fronier. In he case of he FPD benchmark, porfolios can be composed of four basic insrumens which differ wih respec o heir characerisics: fixed rae bonds, floaing rae bonds, inflaion-linked bonds and bonds denominaed in foreign currencies. Each one of hese caegories also differs in erms of mauriies, hus making i possible o specify a baske of represenaive shor, medium and long-erm bonds. More specifically, he financing insrumens considered are as follows: Fixed rae : 1, 3, 5 and 10 years; Floaing-rae (indexed o he Selic rae): 5 years; Inflaion-linked : 10 and 30 years; Denominaed in foreign currency (exchange rae): 10 and 30 years. Alhough he bond lising above seeks o reflec he financing opions currenly available for FPD financing, he simulaion framework has he flexibiliy needed for inclusion of oher securiies, currencies and mauriies. Besides his, in generaing he efficien fronier i is possible o include such echnical resricions as a minimum (or maximum) percenage for paricipaion of a securiy or caegory in he deb porfolio, or a minimum average mauriy for he opimal porfolio. Nex, wo large ses of procedures used o simulae he model are emphasized. In he firs place, he generaion of scenarios for simulaing he dynamics of he economy and calculaing he cos of deb financing are shown. Righ afer ha, he dynamics of he deb from which he cos and risk indicaors resul in he model will be presened Dynamics of he Economy The se of simulaions depends on he generaion of scenarios for he economic variables ha deermine he cos of deb financing and he dynamics of he NPSD/GDP raio. Wih his, he model requires specificaion of a se of equaions used o describe how hese variables evolve over ime. 23 The correlaion beween he cos of wo bonds is exraced hrough he following raio: cos variance (σ p 2 of a porfolio wih wo securiies is σ p 2 w 1 2 σ w 1 2 σ 2 2 2ρ 12 σ 1 σ 2, in which σ 1 is he cos variance of securiy 1; σ 2 is he cos variance of securiy 2; ρ 12 is he correlaion beween he coss of securiies 1 and 2; 0 w 1 1 is he relaive weigh of securiy 1 in he porfolio. 24 The correlaion marix mus be semi-defined posiive. When his does no occur, a specral decomposiion is uilized o obain a semi-defined posiive marix ha is close o he original. This decomposiion considers ha when a marix is no semi-defined posiive, i has a leas one negaive eigenvalue. The procedure for decomposiion uilizes he posiive eigenvalues of he original marix and subsiues he negaive values for zero in order o recompose he marix. This mehod provides a reasonable approximaion for he correlaion marix. The seps for specral decomposiion can be seen in JÄCKEL (2002). 29

31 In his sense, he basic processes of he model cover he following variables: Basic ineres rae (Selic); Term srucure of ineres raes for:; o o o fixed-rae securiies; IPCA-linked securiies; securiies denominaed in foreign currency; Inflaion raes (domesic and foreign); Exchange rae (real and nominal 25 ); Gross Domesic Produc (GDP). Aside from he deerminisic componen, he equaions ha describe he evoluion of he variables above add a sochasic erm wih he objecive of simulaing random shocks in heir rajecories. One assumes ha hese sochasic shocks follow a correlaion srucure, hus conferring macroeconomic consisency on he simulaions. Paricularly in relaion o he yield curves, he scenarios are necessary in order o obain he cos of each financing opion. Alhough he cos of FPD financing depends primarily on he prime ineres rae of he economy, each deb insrumen has pariculariies, especially wih regard o indexing facors, mauriy and degree of liquidiy. The mos basic case applies o floaing rae bonds (Selic rae). The model presumes ha hey are sold a par or, in oher words, heir price is equal o face value. The cos is hen defined by he Selic rae composed on a daily basis hroughou he period, independenly of is mauriy. Given he oher alernaives available for FPD financing, he model has specific yield curves for each ype of insrumen. Alhough cos is based on he shor-erm ineres rae, each deb insrumen has is own pariculariies, for example, wih respec o mauriy and degree of liquidiy. In his sense, a yield curve model is specified o obain he nominal ineres rae ha will define he cos of fixed rae bonds, according o he mauriy of he insrumen o be issued, as shown in Figure Nominal exchange rae is obained by aggregaing he differenial beween domesic and foreign inflaion ino real exchange rae. 30

32 Figure 3. Fixed-rae Curve Yield r Mauriy (in year) Nominal Ineres rae (fixed rae securiies) Prime rae (Selic) Source: Naional Treasury In he Brazilian case, aside from fixed rae bonds, one should also specify yield curves for inflaion-linked bonds and for hose wih linked o exchange rae variaions (in he case of he exernal deb). The model is specified in such a way ha he cos of hese alernaives is relaed o he cos of fixed rae bonds wih equivalen mauriies, adjused by a risk premium ha will be explained below. The risk premium srucure of he model reflecs how lower he reurns on a securiy linked o inflaion or exchange rae variaions should be, compared o bonds wih nominal fixed rae yield and equivalen mauriies. The idea here is ha he exisence of a facor ha proecs real reurns on he bond should be provided o he issuer hrough a lesser risk premium. Figure 4 illusraes how yield curves are relaed in he model. The expeced cos of inflaion-linked securiies is composed of he sum of he real ineres rae given by he specific yield curve used o price hese securiies plus inflaion expecaions. This expeced cos will be less han he average cos of fixed rae bonds in he presence of a posiive inflaionary risk premium, since he real reurns of he holder of he indexed securiy are proeced agains unexpeced ineres rae variaions. 31

33 Figure 4. Inflaion Risk Premium Yield Mauriy (in years) Nominal ineres rae Real ineres rae Real ineres rae + Inflaion expecaions Source: Naional Treasury In a similar manner, as shown in Figure 5, here is also a direc relaion beween he yield curve in foreign currency and he curve for fixed rae securiies. Wih respec o bonds denominaed in foreign currency, he reason for he risk premium originaes in he fac ha he exernal invesor desires a hedge agains exchange rae flucuaions. Figure 5. Exchange Risk Premium Yi e l d Mauriy (in years) Ineres rae (domesic currency) Ineres rae (foreign currency) Ineres rae (foreign currency) +Expeced Exchange Rae Variaion Source: Naional Treasury 32

34 Following simulaion of he scenarios for financial and macroeconomic variables, he cos of FPD financing is calculaed, which depends on he issuance cos of each public bond plus variaion of is indexing facor, when appropriae. Appendix 6.4 explains how his calculaion is done Dynamics of he Deb Once he scenarios have been defined, he following accouning ideniy is used as he saring poin for deriving he dynamics of he NPSD and is relaion o he FPD. (1) In his ideniy, he asses and liabiliies included in NPSD (D) are grouped ino four caegories: FPD (X), moneary base (M), inernaional reserves (F) and oher ne public secor liabiliies 26 [indexed o floaing raes ( ), inflaion ( ), and exchange rae variaion ( )]. Ousanding FPD in period is equal o he ousanding volume in he previous period plus is carrying cos (c ), less he primary fiscal resul, less variaion of he moneary base. Consequenly, FPD evolves according o he following equaion: (2) 1 Wih respec o he oher componens of NPSD, i is presumed ha he moneary base remains consan as a proporion of GDP over ime, while inernaional reserves (equaion 3) 27, as well as oher ne public secor liabiliies (equaions 4-6) sar from an iniial volume and evolve according o heir reurns. (3) 1 1 â (4) 1 Selic (5) 1 (6) 1 26 FPD encompasses only federal governmen liabiliies. To shif o he NPSD concep, one mus consider ha his deb includes nonfinancial public secor liabiliies plus he Cenral Bank. Therefore, his concep includes he direc federal, sae and municipal adminisraions, indirec adminisraions, he public social securiy sysem, nonfinancial governmen companies, as well as he Cenral Bank of Brazil. Addiionally, as a ne concep, NPSD deducs public secor financial asses (for example, inernaional reserves, funds such as he Worker Suppor Fund and credis wih financial insiuions) from liabiliies. Finally, inragovernmenal debs (crossed relaions) are excluded, in such a way ha only he public secor deb wih privae agens is measured. 27 The rae of reurn on inernaional reserves (r eserv s in he model may be differen from he average cos of he exernal deb. 33

35 In which c IP and c FX are he carrying cos of he bonds indexed o inflaion and denominaed in foreign currency; and r reserv s represens he rae of reurn of inernaional reserves. Afer subsiuing (2) (6) in (1) and dividing he new equaion by GDP, algebraic manipulaions lead o he following formula o describe he rajecory of he NPSD/GDP raio over ime: (7) In which: reserves 1 reserves 1 Δ â 1 3. Opimal Composiion Model Simulaions By means of an exercise, his secion will demonsrae he applicaion of he model described above o FPD. The following daa and resuls are merely illusraive. In acual pracice, aside from he simulaions based on a fundamenal se of parameers, he robusness of he conclusions is esed when analyzing he sensiiviy of he model o variaions in benchmark parameers. A he same ime, hough he definiion an opimal composiion (benchmark) is based on inpus derived from simulaions, i will depend on a wide-ranging discussion ha gives due consideraion o he feasibiliy of adoping a specific deb profile in a given emporal horizon, as well as an undersanding of he ineracions beween deb managemen and such oher economic policies as fiscal and moneary policy. The firs sep in he simulaion is o obain he parameers and iniial values 28 for he sochasic models and, wih his, generae he macroeconomic scenarios. These parameers depend on he sochasic model adoped bu, in general, can be described in erms of he average and volailiy of he scenarios for each variable. The following ables show he scenarios generaed by he models for he macroeconomic variables 29 : 28 Since he model presupposes work in he saionary sae, all of he macroeconomic variables remain in he range of heir long-erm averages. For his reason, he iniial values are he same as he long-erm values. 29 The sochasic processes currenly employed by he Naional Treasury are deailed in Appendix

36 Table 2. Scenarios Generaed (cumulaive in 12 monhs) Per Year SELIC IGP-M CPI Nominal Exchange Rae Libor GDP Average 7.45% 2.98% 2.99% 2.84% 4.69% 4.50% Sandard Deviaion 1.80% 1.11% 0.70% 14.28% 1.52% 2.33% Percenile 5º 4.79% 1.16% 1.84% % 2.51% 0.72% Percenile 95º 10.67% 4.83% 4.15% 22.77% 7.48% 8.39% Source: Naional Treasury Calculaion of he cos of FPD financing also depends on simulaion of yield curves. In average erms, he figure below shows he cos of fixed rae bonds, he real yield curve (for inflaion-linked bonds) and he yield curve in dollars (for bonds denominaed in foreign currency). As already described, once he prices and, consequenly, he cos of he fixed rae bonds have been defined, he cos of he inflaion-linked bonds is ha of he fixed rae bonds less inflaion expecaions, less an inflaion risk premium. Analogously, he cos of exchange rae-indexed bonds is ha of fixed rae bonds, less expecaions of currency devaluaion, less an exchange risk premium. Figure 6. Fixed Rae Curve, Inflaion Coupon and Exchange Rae Coupon Source: Naional Treasury] Table 3 shows he carrying cos of each financing operaion for he seleced insrumens. In his case, aside from he rae of reurn indicaed by he yield curve, he cos is calculaed by adding in he variaion of he indexing facor of he bond hroughou he period. Considering a 10-year horizon, dispersion of he cos is also explained by he dynamics of deb refinancing during he simulaions. 35

37 Table3. Financing Cos in 10 Years (cumulaive in 12 monhs) Per Year Average Sandard Deviaion Percenile 5 Percenile 95 Fixed 1 year 7.77% 1.40% 5.55% 10.43% Fixed 3 years 8.14% 0.84% 6.78% 9.75% Fixed 5 years 8.40% 0.52% 7.55% 9.39% Fixed 10 years 8.76% 0.16% 8.50% 9.06% Inflaion 10 years 8.21% 2.41% 4.07% 12.50% Inflaion 30 years 8.37% 2.40% 4.24% 12.66% Exchange rae 10 years 8.24% 68.80% % % Exchange rae30 years 9.24% 68.91% % % Selic 5 years 7.51% 1.83% 4.63% 10.99% Source: Naional Treasury Once he coss of each insrumen are obained, he dynamics of he FPD and, afer ha, of he NPSD, are calculaed for porfolios composed 100% of a specific insrumen and for porfolios wih pairs of securiies in a proporion of 50%-50%. The figure below shows he rajecories of 3000 simulaions of NPSD/GDP for a porfolio composed 100% of bonds linked o he Selic rae, ogeher wih a hisogram wih he disribuion of he variaion of he NPSD/GDP in hese simulaions. Figure 7. Dynamics of he NPSD/GDP 1200 Variaion of NPSD/GDP Frequency % -15% -10% -5% 0% 5% 10% 15% 20% Mais %GDP Source: Naional Treasury In a manner similar o ha presened above, for each simulaed porfolio here are he disribuion of he NPSD/GDP in he analysis period, is average, he sandard deviaion and he correlaion marix of he porfolios. Cos is defined as he average of he NPSD/GDP variaion and he risk as is sandard deviaion. Wih his informaion, he efficien fronier is generaed. 36