Puttable and Extendible Bonds: Developing Interest Rate Derivatives for Emerging Markets

Transcription

1 WP/03/01 Puable and Exendible Bonds: Developing Ineres Rae Derivaives for Emerging Markes Salih N. Nefci and André O. Sanos

2 003 Inernaional Moneary Fund WP/03/01 IMF Working Paper IMF Insiue Puable and Exendible Bonds: Developing Ineres Rae Derivaives for Emerging Markes Prepared by Salih N. Nefci and André O. Sanos 1 Auhorized for disribuion by Enzo Croce Ocober 003 Absrac The views expressed in his Working Paper are hose of he auhor(s) and do no necessarily represen hose of he IMF or IMF policy. Working Papers describe research in progress by he auhor(s) and are published o elici commens and o furher debae. This paper analyzes he price sabilizing properies of puable and exendible bonds, heir poenial o help develop ineres-rae derivaive markes, and heir use by governmens. Their sabilizing properies imply ha, when bond prices fall, prices for puable and exendible bonds fall by less. Their embedded opions work as a cushion and replicae he rading gains from hedging long-erm bonds wih ineres rae derivaives. These bonds can help develop ineres-rae derivaive markes in developing counries and evenually increase demand for long-erm governmen bonds. Informal evidence from OECD counries suggess ha hese bonds were useful in he 1980s, when ineres raes were volaile. JEL Classificaion Numbers: G13, G15 Keywords: Fixed income securiies, opion pricing heory, financial markes Auhors Addresses: snefci@wwc.com; asanos@imf.org 1 The auhors are affiliaed wih he Ciy Universiy of New York and Inernaional Moneary Fund, respecively. They would like o hank Carlos Hamilon V. Araujo, Adolfo Barajas, Ralph Chami, Enzo Croce, Connel Fullenkamp, Angela Gaviria, Hugo Juan-Ramon, and Sunil Sharma for insighful commens.

3 - - Conens Page I. Inroducion...3 II. The Sabilizing Properies of Puable and Exendible Bonds...5 A. Hedging Long Posiions in Long-Term Bonds...5 B. Puable and Exendible Bonds Wrien on Discoun and Coupon Bonds...7 C. Credi Risk Aspecs...10 III. IV. Mimicking Markes for Ineres Rae Derivaives on Governmen Bonds...11 A. The Brazilian Governmen Bond Markes...1 B. Some Weaknesses of Emerging Bond Markes...15 C. Measuring he Effec of C-Bond Volailiy...16 D. The Effec of Puable Bonds...17 Experience wih Puable and Exendible Bonds...19 V. Conclusion...1 Appendix: Pricing Governmen Bonds... References...7 Figures 1. Use of Ineres Rae Derivaives by Emerging Markes...6. Brazil: Composiion of Governmen Securiies, June 1994 December Brazil: Average Mauriy of Ousanding Discoun Bonds, July 1996 December Discoun Bond Prices as a Funcion of Ineres Rae Volailiy Brazil: C-Bond Price, January 1, 1997 Ocober 30, Brazil: Puable Bond Price, January 1, 1997 Ocober 30, Tables 1. Puable and Exendible Bonds in Seleced OECD Counries Belgium: Ousanding Sae Noes, Belgium: Descripive Saisics for Price Changes of 1998 Sae Noe and 1999 Linear Bond, Sepember 14, 000 Ocober 5, Sovereign Puable Bonds and Loans by Emerging Markes,

4 - 3 - I. INTRODUCTION To ap financial markes, borrowers have a broad range of insrumens from which o choose. Puable and exendible bonds are one example. These bonds give invesors he righ o sell hem back a par o he borrower a a predeermined dae or o exend heir erm beyond a specified dae. They are common among privae secor issuers in developed counries and in inernaional financial markes, bu no among public secor issuers boh in developed and emerging markes. In his paper, we analyze key characerisics of puable and exendible bonds: he price sabilizing properies of he bonds, he poenial of he bonds o sar ineres rae derivaive markes, and he use of he bonds by governmens. We argue ha such bonds have ineresing price sabilizing properies. Meron (1995) shows ha puable bonds are economically equivalen o a porfolio of discoun bonds and a risk-free shor-erm bond. When discoun bond prices fall, he pu opion kicks in and reduces he ineres rae risk exposure incurred by invesors. By conras, when discoun bond prices increase, he pu opion has no value and invesors increase heir risk exposure. Therefore, heir price change is limied o a riskfree shor-erm bond when he pu opion is in-he-money and racks a discoun bond when he pu opion is ou-of-he-money. We exend Meron s insigh by examining oher underlying bonds, such as coupon bonds and bonds subjec o credi risk. We find ha Meron s resul remains inac: When prices of coupon bonds or bonds subjec o credi risk fall, prices of puable and exendible bonds wrien on hese bonds fall less. Due o hese price sabilizing properies, we claim ha puable and exendible bonds can ake advanage of he convexiy gains from volailiy in emerging markes. The embedded pu and call opions work as cushions and replicae he rading gains from convexiy when invesors hedge heir long posiions in long-erm bonds by shor selling shor-erm bonds and fuures conracs. As IOSCO (00) shows, hese ineres rae derivaive insrumens are no available o invesors in emerging markes and mos invesors are hence deprived of benefiing from he convexiy gains. Using puable and exendible bonds would hus be a way o emporarily overcome obsacles in he developmen of long-erm governmen bond markes. We sugges ha governmens can consider using puable and exendible bonds as par of a deb managemen sraegy ha also includes he developmen of ineres rae derivaive markes for governmen bonds. 3 The informal hisorical evidence from OECD counries shows ha some counries used puable and exendible bonds in he 1980s when shor-erm ineres raes were high and volaile, he deb-o-gdp raio was high, and bond fuures and Puable bonds are also known as pu bonds or reracable bonds. 3 See De Broeck, Guillaume, and Van der Sichele (1998) for a discussion of he inroducion of fuures on governmen bonds in maure markes.

5 - 4 - shor selling bonds were no common. Favero and Giavazzi (00), for example, menion he use of puable bonds by Ialy in he 1980s and also sugges hem for lenghening he deb mauriy in Brazil. This does no mean ha all governmen bonds should be puable. We should cauion ha raders may be emped o increase he price volailiy of he underlying bond so ha hey increase he probabiliy of exercising he opion embedded in he bond. An analogous example is he sock opions given o managers in he 1990s. Managers had an implici ineres in he increase of price volailiy so ha hey could exercise heir sock. 4 In addiion, if all bonds were puable or exendible, he exercise of he pu or call opion could lead o serious liquidiy problems for governmens. Even hough some would argue ha he fiscal implicaion of early redempion in he case of puable or exendible bonds is imporan, we do no hink ha i is significanly differen from ha generaed when he governmen is obliged o buy back is opion-free deb before mauriy. The Brazilian experience in 00 is an example of governmen concern for sabiliy in he secondary markes for bonds and of inervenion o buy back deb before is mauriy. Therefore, he embedded pu and call opions make explici wha is already assumed o be an implici guaranee ha he governmen will buy back is paper. This should help reduce marke jiers and avoid overshooing or overreacion of bond markes o price shocks. We also believe ha puable and exendible bonds can signal o he privae secor ha he governmen is commied o macroeconomic sabiliy and fiscal discipline since i is no in he governmen s ineres for he privae secor o exercise he embedded opion. For example, when he governmen sells such bonds, i knows ha hey may be redeemed a someime in he fuure when i is leas convenien for he governmen. Governmens would hen need o make sure ha, ex ane, heir fiscal posiion is in order or ha hey have he fiscal resources o pay for he exercise of he opions. This paper conains four secions. The nex secion describes dynamic hedging and characerizes puable and exendible bonds wrien on discoun and coupon bonds wih and wihou credi risk. Secion III describes evens in Brazil during ha led o a reducion in he share of ousanding discoun bonds in he oal sock of public deb and simulaes puable bonds wrien on he Brazilian C-Bond. Secion IV looks a he inernaional experience wih he public issues of puable and exendible bonds. The las secion concludes wih direcions for fuure research. 4 See Tufano (1996) for he argumen in he gold mining indusry.

6 - 5 - II. THE STABILIZING PROPERTIES OF PUTTABLE AND EXTENDIBLE BONDS As noed, markes for shor selling bonds and fuures conracs are no available o invesors in emerging markes, and invesors are deprived of benefiing from he convexiy gains. How can puable and exendible bonds replicae he convexiy gains when invesors hedge heir long posiions in long-erm bonds by shor selling shor-erm bonds and fuures conracs? This secion answers his quesion by analyzing dynamic hedging sraegies and he sabilizing properies of puable and exendible bonds. We also incorporae he credi risk aspecs of bonds. A. Hedging Long Posiions in Long-Term Bonds Le P dollars be invesed in a porfolio consising of a long-erm bond, B L, and a shor-erm bond, B S : P = θ B + θ B, ( 1 ) L S 1 where B L and B S are he prices for he long-erm and shor-erm bonds, and θ 1 and θ are heir respecive number of unis. The value of he porfolio P changes as ime passes because of changes in B L and B S : dp = θ db + θ db. ( ) L S 1 We assume ha a one-facor ineres rae model describes he dynamics of he shor-erm ineres rae. 5 This assumpion implies ha here is only one source of randomness in equaion () since he sochasic differenial equaions for he shor- and long-erm bonds have diffusion erms wih he same Wiener process. 6 So we can eliminae all he randomness in equaion () by selecing he appropriae quaniies of each asse in he porfolio. We se hem equal o: σ S σ L θ1 = P L and θ = P S, ( 3 ) σ σ B σ σ B ( ) S L ( ) S L where σ L and σ S are he diffusion parameers for he long-erm and shor-erm bonds, respecively. 5 See Nefci (000a) and Rebonao (1998) for a review of one-facor ineres rae models. Appendix I shows how he parameers describing he dynamics for discoun bonds are a funcion of he parameers characerizing he dynamics for he shor-erm ineres rae. 6 See Nefci (000b) for a jusificaion for a one-facor model o describe he shor-erm srucure of ineres raes in emerging markes.

7 - 6 - The posiions in each asse are hen long in he long-erm bond and shor in he shor-erm bond. This porfolio is hen risk-free and should also yield a reurn equal o a risk-free invesmen o avoid arbirage: ( ) r θ B + θ B d = θ db + θ db, ( 4 ) L S L S 1 1 where r is he risk-free shor-erm ineres rae. Dividing boh sides of expression (4) by θ 1, we can rewrie i as: r B θ + B d = db θ + db L S L S θ1 θ1. ( 5 ) In Appendix I we show ha he relaive quaniy raio θ /θ 1 can be approximaed by he firs derivaive B y L, which measures how much he price for he long-erm bond changes as is yield-o-mauriy changes by 1 percenage poin. This approximaion allow us o rewrie expression (5) as: ( ) where B y L is also known as he hedge raio. r B + B B d = db + B db, ( 6 ) L L S L L S y y Noe ha since here exiss a negaive and nonlinear relaionship beween he price of a bond and is yield-o-mauriy, he hedge raio B y L is negaive and changes as he yield changes. If he yield increases, he hedge raio B y L decreases and vice-versa. To keep he long-erm bond hedged, we need o rebalance he number of unis of he shor-erm bond in he porfolio as he yield changes. This rebalancing sraegy is called a dynamic hedging sraegy, requires no ne invesmen, and is self-financing. In addiion, he rebalancing sraegy allows he invesor o ge a risk-free reurn on his porfolio ha is generaed from he rading gains (or convexiy gains). Figure 1 - Use of Ineres Rae Derivaives by Emerging Markes 0 No. of counries repored Repos and reverse repos Source: IOSCO (00). Securiies borrowing and lending Shor selling Ineres rae swaps Bond fuures and opions

8 - 7 - The dynamic hedging sraegy above seems a sraighforward operaion bu canno be easily performed in many emerging markes. I is effecive only if we can shor sell he shor-erm bond. As Figure 1, compiled from IOSCO (00), shows, only 10 ou of emerging marke counries allow shor selling bonds. 7 Indeed, abou he same number of counries allow securiies borrowing and lending, which is a precondiion for shor selling. Therefore, few invesors in emerging markes can perform dynamic hedging sraegies and exrac he convexiy gains necessary o cover losses from price flucuaions on heir bond holdings. In addiion, where shor selling is allowed, invesors migh no be able o shor sell because hey are afraid of being caugh in a shor squeeze, ha is, when i is cosly o buy he collaeral (bonds) o close ou he shor posiion. The majoriy of counries surveyed in IOSCO (00) have repos and reverse repos, which can help invesors acquire he bonds. However, if hese insrumens are no acively used because of ax reamen or oher impedimens and if liquidiy in he secondary markes for he collaeral is low, invesors can be cornered. Shor selling hen becomes impracical and, as a consequence, dynamic hedging sraegies based on hem are unfeasible. Invesors can make dynamic hedging sraegies feasible no only by shor selling shor-erm bonds bu also by using bond fuures. In his case, invesors sell an appropriae number of bond fuures wrien on he underlying long-erm bond o hedge one uni of he long-erm bond. As he hedge raio changes hrough ime, he number of fuures conracs also needs o be adjused accordingly so ha he porfolio remains dela-neural or fully hedged. Even hough he dynamic hedging sraegy using bond fuures also seems simple, few emerging markes have bond fuures. Therefore, invesors canno benefi from he convexiy gains ha offse he losses invesors incur in heir long posiions when bond prices flucuae. B. Puable and Exendible Bonds Wrien on Discoun and Coupon Bonds Few governmens in he developing world are aware ha i is possible o mimic markes for shor selling bonds and bond fuures using puable and exendible bonds. Meron (1995) suggess ha governmens can issue puable and exendible bonds in addiion o he usual vanilla insrumens o mimic open marke operaions. In his secion we use Meron s analysis of he sabilizing properies of puable bonds wrien on discoun bonds o sugges heir use for mimicking markes for shor selling shor-erm insrumens. Puable bonds are bonds ha give heir holders he righ o sell hem back o he governmen for a fixed srike price, E, if he price of he underlying U-mauriy bond, B, falls below he 7 The counries in IOSCO (00) are Argenina, Bangladesh, Brazil, Taiwan Province of China, El Salvador, Hungary, India, Indonesia, Kenya, Korea, Lihuania, Malaysia, Mauriius, Pakisan, Peru, Singapore, Slovenia, Souh Africa, Thailand, Trindad and Tobago, Tunisia, and Turkey.

9 - 8 - srike price E a ime T, where T U. A ime T, when he pu opion expires, puable bonds have a price equal o: T (, ) F = Max B E. ( 7 ) A puable bond, hen, is equivalen o a porfolio of a sraigh bond and a pu opion on he underlying bond. Since he righ o pu back he bond o he governmen has posiive ime value, puable bonds have a higher price and are issued a a lower discoun or coupon han a sraigh bond. One can inerpre he price of he pu opion as wha he governmen charges he privae secor for sabilizing financial markes and selling proecion ha is no widely available. Similarly, exendible bonds give he holder he righ o exend he erm of he bond on a fixed dae a a predeermined rae. So an exendible bond can be hough of as a shor-erm bond coupled wih a call opion o buy a long-erm bond a a price E on he predeermined dae T, while he puable bond is a long-erm bond coupled wih a pu opion o sell he bond a a price E on he predeermined dae T. In case of European opions, due o pu-call pariy, he valuaion of boh bonds should be more or less equivalen. 8 As a consequence, he analysis ha follows also applies o exendible bonds. Since a puable bond conains a derivaive wrien on he underlying bond, he price F of a puable bond depends on ime and he price of he underlying bond B : F T (, ) = F B. ( 8 ) The funcional form of F is found by using replicaing rading sraegies. Le P dollars be invesed in a combinaion of he puable bond F and he underlying discoun bond B : P = θ F + θ B, ( 9 ) 1 where θ 1 and θ are unis of he puable bond F and he underlying bond B, respecively. The value of he porfolio P changes as ime passes because of changes in F and B : dp = θ df + θ db. ( 10 ) 1 We also assume ha one-facor ineres rae models describe he dynamics of shor-erm ineres raes in developing counries. So we can also eliminae he randomness in equaion (10) by selecing he appropriae quaniies of each asse in he porfolio, which are equal o: θ 1 = 1 and θ = F1 ( 11 ) 8 See Kaloay and Abreo (1999).

10 - 9 - where F 1 sands for he firs derivaive of he puable bond F wih respec o he underlying bond price B and is also known as he hedge raio. 9 As we are shor in he underlying bond and long in he puable bond wih he righ proporions, random flucuaions cancel ou and he porfolio is risk-free. To avoid arbirage, i should hen have a rae of reurn equal o a risk-free invesmen: r Pd = df F db, ( 1 ) 1 By using equaions (9) and (11) in equaion (1) and rearranging erms in he resuling equaion, we can noe ha puable bonds are economically equivalen o a porfolio of F 1 unis of he discoun bond and (F -B F 1 ) unis of he risk-free shor-erm bond: ( ) df = F db + r F F B d. ( 13 ) 1 1 This economic equivalence resuls in a paricular price dynamics for puable bonds. Since 0 F 1 1 and F is wice coninuously differeniable, wih F 11 >0, as he price B for he discoun bond falls, F 1 also falls. 10 This is equivalen o a repurchase of discoun bonds by he governmen, which decreases he ineres rae exposure incurred by invesors. The reverse is also rue. When he price B for he discoun bond increases, F 1 also increases, which is equivalen o holding more discoun bonds. Invesors are hus more exposed o ineres rae risk. Because of hese characerisics, Meron (1995) describes puable bonds as he equivalen of a dynamic, open marke, rading operaion wihou any need for acual ransacions. Wha is key o he price dynamics in equaion (13) is he auomaic cushion mechanism provided by he embedded pu opion. When discoun bond prices fall due o ineres rae increases, he value of he pu opion kicks in and offses parially he capial loss. The pu opion hen works as a cushion agains capial losses. In he exreme case, when he underlying bond price has fallen enough and he pu opion is in-he-money, a puable bond behaves like a shor-erm bond. 11 On he oher hand, when discoun bond prices rise, he pu opion is ou-of-he-money and has lile effec on puable bond price changes. In his case, puable bonds are similar o he underlying discoun bonds, wih heir price changes limied o he price changes of discoun bonds. In equaion (13), noe ha he second erm on he righ-hand side, r (F -F 1 B )d, is similar o he risk-free reurn obained from a dynamic hedging sraegy wih shor selling or bond fuures. When invesors hold a puable bond, hey do no need o buy he underlying 9 See Appendix. 10 See Hull (000) and Meron (1990). The Appendix shows ha he funcion F is found by solving a parial differenial equaion subjec o some boundary condiions. 11 See Fabozzi (001).

11 discoun bond and shor sell shor-erm bonds or bond fuures o hedge and manage ineresrae risk exposures. The puable bond is able o mimic rading in hese markes and replicae he rading gains from convexiy (or convexiy gains) used o offse losses on he long posiion in he discoun bond. Since few emerging markes allow shor selling, securiies borrowing and lending, repos, reverse repos, and bond fuures, puable bonds would overcome resricions in boosing demand for long-erm governmen bonds. In he case of coupon bonds, he no-arbirage condiion includes an exra erm ha capures coupon paymens boh on he underlying coupon and puable bonds: ( ) r Pd = df F db + C + FC d, ( 14 ) 1 F 1 B where C B and C F are he coupon paymens for he underlying and puable bonds, respecively. 1 We can rearrange he exra erms on he righ hand-side in equaion (15) and he economic inerpreaion of a puable bond would remain he same. An invesor holding a puable bond wih coupon paymens has a ne exposure (excluding coupon paymens) equivalen o F 1 unis of he underlying coupon bond and (F -B F 1 ) unis of he shor-erm bond: ( ) ( ) df = F1 db CBd + r F BF1 CF d. ( 15 ) Since he embedded pu opion has an implici value for invesors, governmens can offer puable bonds wih lower coupons han he ones for underlying coupon bonds. The hybrid naure of a puable bond wih coupons implies ha he price of a puable bond is equal o he price of a coupon bond plus he pu opion wrien on he coupon bond. In his sense, puable bonds are a cheaper source of financing for governmens. The governmen essenially charges invesors for he insurance policy provided. C. Credi Risk Aspecs The previous analysis assumed ha governmen bonds are exemp from credi risk. In his secion we incorporae he credi risk aspec of governmen bonds ino our analysis. We assume ha swap raes provide a se of defaul-free ineres raes. Hull, Predescu, and Whie (00) argue ha even hough U.S. reasury bonds do no have credi risk, oher facors such as liquidiy, axaion, and regulaion affec hem. They hus favor he use of swap raes as risk-free ineres raes. We can exend heir argumen o emerging markes, 1 See Meron (1990). The Appendix shows ha dynamics for discoun and coupon bonds are slighly differen. The laer includes he coupon rae in he drif componen. The pricing formula for he puable bond wrien on he coupon bond would also conain he coupon paymen rae.

12 where a swap could be even less risky han a reasury bond because he counerpary is a highly raed financial insiuion. Assuming differen credi risk for differen financial insrumens, we exend he previous analysis o a puable bond wrien on a risky bond. As in Duffie and Singleon (1999), we replace he defaul-free shor-erm ineres rae in he pricing formula for our puable bonds by an ineres rae adjused for he defaul risk: T Q B = E exp ( rs + hsls) ds Max( BT, E ), ( 16 ) s= where E Q is he expecaion operaor under he risk-neural probabiliies; h is he exogenous inensiy or hazard rae process; and L is he exogenous loss process given by L =1 -R, where R is he recovery process. 13 Equaion (16) saes ha he price of a puable bond is he presen value of he pu opion payoff a ime T, discouned a he defaul-adjused rae (r +h L ) insead of he shor-erm ineres rae r. If boh he puable and underlying bonds do no pay coupon and if he puable bond a ime is a funcion of he underlying bond a ime, F =F(B,), hen he no-arbirage condiion implies ha: ( )( ) df = F db + r + h L F F B d. ( 17 ) 1 1 As before, puable bonds are equivalen o a porfolio of F 1 unis of he underlying bond and (F -F 1 B ) unis of a shor-erm bond adjused by a premium for he credi risk incurred by bondholders. Price changes for puable bonds would sill be limied o he price changes for he underlying bond which includes credi risk in is dynamics when prices for he underlying bond go up, and would be limied o a defaul-adjused shor-erm ineres rae when prices for he underlying bond go down. Wih credi risk, puable bonds would sill be able o mimic markes for shor selling shor-erm bonds and bond fuures. III. MIMICKING MARKETS FOR INTEREST RATE DERIVATIVES ON GOVERNMENT BONDS In his secion, we highligh evens in Brazil ha affeced he governmen deb composiion during Our objecive is o show wha happens when markes for fuures conracs and shor selling bonds are missing. We hen simulae a puable bond wrien on Brazilian C- Bonds from January 1, 1997, o Ocober 30, 00 o show how price changes for puable bonds would be less han price changes for C-Bonds and o mimic he convexiy gains ha 13 See he Appendix for he sochasic and parial differenial equaions for he discoun bond.

13 - 1 - muual funds would have exraced if ineres rae derivaive markes had been used in A. The Brazilian Governmen Bond Markes In November 1999 he Brazilian governmen embarked on a program o lenghen he erm and duraion of is deb securiies and o reduce is financing coss. 15 The program included more han weny measures o be implemened gradually. The measures were inended o allow beer deb and cash managemen by he reasury, o inroduce new marke ransacions wih governmen securiies, o improve secondary marke liquidiy, and o increase cenral bank consulaions wih he privae secor. In addiion o he measures announced in 1999, he reasury also se objecives for deb managemen in The reasury sough o minimize coss over he long run while limiing marke and liquidiy risks. I pursued his objecive by lenghening he deb mauriy in public aucions, gradually subsiuing indexed deb by discoun bonds, developing a erm srucure of ineres raes, and sandardizing deb insrumens. As a resul of he parial implemenaion of he measures, he adopion of deb managemen objecives and sraegies, and he decreasing ineres raes afer he 1999 Brazilian crisis, he average mauriy and share of ousanding discoun bonds in he oal sock of public deb improved in 000 as can be seen in Figures and C-Bonds are he mos raded and liquid Brazilian Brady bonds in inernaional financial markes. 15 See Cenral Bank of Brazil (00d). 16 See Naional Treasury of Brazil (001) and Inernaional Bank for Reconsrucion and Developmen and Inernaional Moneary Fund (001) for deails on he design of deb managemen objecives and sraegies. 17 See Cenral Bank of Brazil (001). In he firs quarer of 000 he Brazilian reasury was able o sell six-monh and 1-year discoun bonds in public aucions.

14 Figure. Brazil: Composiion of Governmen Securiies, June 1994 December Jun-94 Dec-94 Jun-95 Dec-95 Jun-96 Dec-96 Jun-97 Dec-97 Jun-98 Dec-98 Jun-99 Dec-99 Jun-00 Dec-00 Percen Jun-01 Dec-01 Jun-0 Dec-0 Discoun bonds Exchange-rae indexed deb Source: Cenral Bank of Brazil. Ineres-rae indexed deb Oher indexed deb However, he deb managemen improvemens in 000 were negaively affeced by he Argenine crisis and he U.S. recession in 001. Wih an increase in ineres raes, he Brazilian reasury faced a dilemma in 001: Wheher o issue discoun bonds wih shorer mauriies\ or o increase he share of indexed deb wih longer mauriies. 18 Given he high liquidiy risk a he ime, he reasury mainly relied on reducing he share of discoun bonds in he oal sock of public deb. 19 Figure 3. Brazil: Average Mauriy of Ousanding Discoun Bonds, July 1996 December 00 8 Number of Monhs Jul-96 Jan-97 Jul-97 Jan-98 Jul-98 Jan-99 Jul-99 Jan-00 Jul-00 Jan-01 Jul-01 Jan-0 Jul-0 Sources: Cenral Bank of Brazil and Naional Treasury of Brazil. Afer a calm firs quarer, Brazilian financial markes suffered more urmoil in 00. The uncerainy surrounding he presidenial elecions, he difficulies in financing he balance of paymens during he year, and he implemenaion of mark-o-marke accouning rules for muual funds in May 00 led o high levels of discouns on he indexed deb and an increased volailiy in discoun bond prices. 0 Invesors reaced o his volailiy in 18 See Naional Treasury of Brazil (00). 19 See Cenral Bank of Brazil (00a). 0 See Cenral Bank of Brazil (00d).

15 governmen bond markes and he drop in earnings in muual funds by fleeing from muual funds from May 00 o Augus 00, around R$ 55 billion was wihdrawn. 1 Auhoriies in Brazil responded o he run on muual funds by shorening he deb mauriy and loosening he fair-value accouning rules. In paricular, he deb managemen sraegy for discoun bonds was o issue shorer mauriies. Given he high uncerainy in Brazilian financial markes, auhoriies also decided o exemp from he fair-value accouning rule asses wih mauriy of less han one year, making all oher reasury securiies unaracive. 3 Even hough he measures inroduced in November 1999 acknowledged he imporan role of derivaive insrumens in increasing liquidiy in secondary markes for governmen securiies, he use of derivaives by he privae secor did no occur. In December 1999, he cenral bank consolidaed all laws concerning forward, repos (and reverse repos), and opions on fixed income securiies. 4 This consolidaion was expeced o creae flexible rading condiions in governmen bond markes. However, excep for repos (and reverse repos), IOSCO (00) sill lised Brazil as a counry ha did no allow shor selling, securiies borrowing and lending, bond fuures and opions, and ineres rae swaps o enhance liquidiy in governmen bond markes. 5 Indeed, in he middle of he run on muual funds in 00, auhoriies in Brazil raised he possibiliy ha he cenral bank would sell pu opions on bonds. 6 Auhoriies fel a need o inroduce a derivaive insrumen o hedge he ineres rae risk exposure by invesors in governmen bonds. Puable and exendible bonds conain embedded opions ha work as a cushion and offse losses due o he fall in bond prices. They would hen help proec invesors from he ineres rae risk. 1 Figures are from he Naional Treasury of Brazil. See Cenral Bank of Brazil (00d). 3 See Securiies and Exchange Commission of Brazil (00). 4 See Cenral Bank of Brazil (1999). 5 One-day bond forward conracs are negoiaed in he elecronic sysem SIBEX run by he Rio de Janeiro Sock Exchange (BVRJ). Hybrid shor-erm ineres-rae fuures conracs are raded in he Brazilian Mercanile & Fuures Exchange (BMF). The objec of he fuures conracs is he average inerbank marke ineres rae. So fuures conracs are an imperfec hedge for governmen bonds. 6 See Cenral Bank of Brazil (00b) and (00e).

16 B. Some Weaknesses of Emerging Bond Markes Consider a sovereign defaul-free discoun bond wih mauriy U. Le is ime arbirage-free price be denoed by B(r, ; U). I can be shown ha he price of his discoun bond, wihou any embedded opion, will saisfy he parial differenial equaion: 7 1 B ( ( ) ( ) ) ( ) rb + a r, b r, λ B1+ b r, B11 = 0, ( 18 ) wih he boundary condiion: B( ru, U; U ) = 1. ( 19 ) Here he a(r,) and b(r,) are he drif and diffusion parameers in he sochasic differenial equaion for he shor-erm ineres rae r, and λ is he marke price of risk: ( α r ) σ = λ, ( 0 ) where α and σ are he drif and diffusion parameers in he sochasic differenial equaion for he bond price. This equaion shows an imporan source of income for sovereign bond raders if B 11 and/or b(r,) is large enough. In fac, in he above parial differenial equaion he firs hree erms can be regarded as he daily ne cos of holding he bond posiion, apar from convexiy gains. The las erm can be inerpreed as daily gains from convexiy. These laer gains are due o volailiy in he underlying shor-erm ineres rae r. Wha is imporan for us is ha hese daily gains have wo componens. One is he resul of he earnings from passing ime, and he oher is due o volailiy in he r. These laer gains are known as convexiy or Gamma gains and play a significan role in markes for highly raed sovereign bonds. Convexiy gains basically sugges he following. If he bond s second derivaive wih respec o r and he ineres rae volailiy is high enough, hen oscillaions in he shor rae will lead o significan rading gains for he long posiion holder. I may seem paradoxical, bu a sudden increase in volailiy may lead o an increase in he price of he long bond. In fac, his saemen should be qualified. Everyhing else being he same, an increase in ineres rae volailiy will increase he bond price. The criical saemen here is, ceeris paribus, because his means credi risk remains he same. There is no doub ha if he credi risk of a bond were o increase, he bond value would go down. I is possible ha increased ineres rae volailiy increases credi risk and hence has a negaive effec on he bond price. Thus, in he 7 See he Appendix.

17 discussion below we omi such effecs in order o emphasize he effec of convexiy on he bond price. C. Measuring he Effec of C-Bond Volailiy An example of convexiy gains is shown for Brazil using he daily reurns of he Brazilian C-bond from January 1, 1997, o Ocober 30, We use he Vasicek model for he shor-erm ineres rae and calculae he closed form formula for a discoun bond having he same yield srucure. The Vasicek model gives he price of a defaul-free pure discoun bond as: (, ) ( 1 exp( au ( ) )) C U = a AU (, ) = exp a BU AU CU r ( C(, U) U)( a d 1 b ) bc( U, ) (, ) = (, ) exp ( (, ) ) where a, d, and b are he parameers of he mean revering dynamics assumed for he shorerm rae r : ( ) 4a, ( 1 ) dr = a d r d + br dw. ( ) For he Brazilian C-bond we used he values: b= 0.50, a = 0.90, d = 0.11, ( 3 ) and evaluaed he discoun curve B(r, ; U) a he mean ineres rae 11 percen. We used wo levels of volailiies. In one case (absolue) volailiy was aken as 5 percen a year, and in he oher, volailiy was aken as 15 percen. The wo discoun curves are shown in Figure 4. We see ha increased volailiy leads o much higher long bond prices. In fac, he price of a 30-year bond would be abou 30 percen higher in a more volaile environmen. The price of a 10-year bond would increase by abou 10 percen. The criical poin is his: in an environmen where high volailiy does no lead o credi risk changes, an increase in ineres rae volailiy would increase bond prices and is no derimenal o porfolios ha are marked o marke. Bu for his be rue, here mus be liquid ools and markes ha bond raders can use o exrac he Gamma gains expressed by he componen 1/B 11 b(r,) in he parial differenial equaion shown above. This is done by aking posiions in liquid ineres rae fuures or in shor-erm bonds. These posiions are in 8 We use he Brazilian C-Bond for liquidiy reasons and daa availabiliy.

18 he opposie direcion o he posiion in he long bond. For example, a long bond holder will shor sell B 1 unis of he fuures conrac. Adjusmens in his dela-hedge would exrac he Gamma gains. In emerging markes here are wo major hurdles for exracing convexiy gains. Firs, here are no markes for liquid ineres rae derivaives. Second, ineres rae volailiy leads o significan increases in credi risk and lowers he bond's price. This implies ha raders in emerging markes canno benefi from he posiive effecs of volailiy increases, ye suffer from he negaive ones. Thus, changes in volailiy have significanly differen effecs on he bond porfolios. A newly inroduced mark-o-marke requiremen would lead a bond porfolio manager o lower his exposure o long-erm ineres rae movemens. This increases bond marke volailiy and a he same ime causes shorening of he mauriies on new issues. D. The Effec of Puable Bonds One advanage of puable bonds is ha he embedded opion will increase in value when volailiy increases. This increase in opion s value would play he role of Gamma rading ha is available o raders in maure markes and would balance ou he negaive effec of increased volailiy on credi risk. Hence, puable opions can be used o inroduce radable convexiy gains in emerging markes.

19 To see he effec of puable bonds on Brazilian bond porfolios, we use daily reurns daa on he Brazilian C-Bond o calculae he price volailiy of a 10-year discoun bond wih he same yield as he C-Bond. Figure 5 shows he explosive price volailiy during he recen elecion and afer he mark-o-marke requiremen in 00, when he bond decreased by abou 50 percen. Using he Black-Scholes formula we hen calculae an approximae value for he same bond ha conains a 1-year pu opion wih he srike price se a 40. Figure 6 shows how he addiion of a pu opion in his ficiious bond would have sabilized bond porfolios in Brazil and, in fac, would have led o higher overall bond values in Brazil in he laes period. 9 9 Of course a more deailed sudy would model he bond dynamics joinly wih sovereign credi dynamics for Brazil and hen simulae he effecs of adding pu opions. Bu his (coninued )

20 IV. EXPERIENCE WITH PUTTABLE AND EXTENDIBLE BONDS Wha is he hisorical evidence on he use of puable and exendible bonds by governmens? Governmens in OECD counries have used such bonds as a way o reduce heir financing coss. Table 1 repors puable and exendible bonds issued by Ausria, Belgium, Canada, France, Germany, Ialy, he Neherlands, he Unied Kingdom, and he Unied Saes. Noe ha, excep for Belgium, mos counries issued puable and exendible bonds in he 1980s, when ineres raes were high and volaile. Counries wih high deb levels such as Belgium and Ialy have used puable and exendible bonds as well. Counry Type Characerisics Issue Ausria Puable 1/ Floaing-rae noes Currenly in use Belgium Puable Floaing-rae noes Issued unil New issues afer 1994 Exendible Sae coupon bonds (Bons d'éa ); 5 years exendible o 7 years Currenly in use Canada Exendible Medium-erm coupon bonds Issued during , and raded beween France Exendible Coupon bonds (Empruns à Fenêre e Prorogeables ) Issued during Germany Puable Loans agains borrowers' noes (Schuldscheine ), ypically 3 o 10 years Ialy Exendible Treasury cerificaes wih opion (CTO ), fixed coupon; 3- and 4-year securiies exendible wih 3 and 4 years more, respecively Currenly being redeemed Issued during Neherlands Exendible Coupon bonds Issued unil 1984 Unied Kindgom Table 1. Puable and Exendible Bonds in Seleced OECD Counries Exendible Coupon bonds and inflaion-indexed bonds From early 1980s, wih las redempion in 1999 Unied Saes Puable Three coupon bond issues in 1933 Las issue redeemed in 196 Sources: Bank of England; Ausrian Naional Bank; Deusche Bundesbank, Belgian, Duch, German, and Ialian Minisries of Economy and Finance; Ahanassakos (1996); Bliss and Ronn (1995); Board of Governors of he Federal Reserve Sysem (1998); Branion (1995); McLean (1993); Missale (1999); Urich (1991). Noe: 1/ Publicly guaraneed bond. Belgium, in paricular, is an ineresing case. The Belgian reasury issues sae noes, which are long-erm securiies wih fixed coupons. Only privae individuals, nonprofi organizaions, and public insiuions have access o is primary marke. Currenly, here is one ousanding noe ha is exendible: he 5-year sae noe, which gives he righ o he deb holder of exending he mauriy for wo exra years (o 7 years). Table shows he evoluion of sae noes during Sae noes rose from 0.64 percen and 0.50 percen of he long-erm and oal domesic governmen deb, respecively, in 1996 o 3.31 percen and.85 percen in 001. would, by iself, be a major calibraion effor. Our purpose here is o look simply a an example and ge some rough idea abou he impac of puable bonds.

21 - 0 - Table. Belgium: Ousanding Sae Noes, Sae Noes In millions of Euros % of long-erm bonds % of domesic bonds , , , , , , Source: Naional Bank of Belgium. If we compare price movemens for Belgian linear bonds (he underlying asse) and sae noes (he exendible bond), we would expec Belgian sae noes o move less han Belgian linear bonds when prices fall. Equaion (15) above shows ha an invesor holding a sae noe wih coupon paymens has a ne exposure (excluding coupon paymens) of F 1 unis of he underlying linear bond and (F -B F 1 ) unis of he shor-erm bond. Since 0 F 1 1 and F is wice coninuously differeniable, wih F 11 >0, as he price of he linear bond falls, F 1 also falls. This is equivalen o a repurchase of linear bonds by he governmen, which decreases he ineres rae exposure incurred by invesors. Table 3 shows some basic saisics for he price changes (from Sepember 14, 000, o Ocober 5, 00) of he 4. percen sae noe, issued in 1998, due Sepember 4, 003 and he 4 ¾ percen linear bond, issued in 1999, due Sepember 8, 005. The evidence suggess ha price changes for he 4. percen sae noe were less han hose for he 4 ¾ percen linear bond. Table 3. Belgium: Descripive Saisics for Price Changes of he 1998 Sae Noe and he 1999 Linear Bond, Sepember 14, 000 Ocober 5, Sae Noe 1/ 1999 Linear Bond / Mean Median Maximum Minimum Sd. Dev Skewness Kurosis Observaions Source: Daasream. 1/ 4.% Sae Noe, due Sepember 4, 005. / 4 3/4 linear bond, due Sepember 14, 005. Emerging markes have also apped inernaional markes wih puable bonds. Table 4 shows ha even hough here was a decline in he issuance of puable bonds by developing counries during , hese bonds sill remained an imporan source of financing for

22 - 1 - developing counries. Therefore, puable bonds have also been used by emerging markes o smooh price changes of heir inernaional deb. Table 4. Sovereign Puable Bonds and Loans by Emerging Markes, (In millions of U.S. dollars) Puable 3,05 4,064,543 1,95,06 Of which are loans Number of ransacions Source: IMF (00). V. CONCLUSION This paper analyzes he sabilizing role ha puable and exendible bonds can play in governmen securiies markes. I finds ha hese bonds are less price sensiive han underlying bonds are o increases in shor-erm ineres raes. When he prices of he underlying bonds fall, puable and exendible bond prices fall less han hose of he underlying bonds. In addiion o heir sabilizing properies, puable and exendible bonds can also mimic markes for shor selling shor-erm bonds and fuures. These derivaives insrumens are imporan o invesors since hey allow hem o exrac he convexiy gains ha offse losses in long posiions in long-erm bonds. However, he derivaives markes ha suppor he hedging of long-erm bonds are absen in many emerging markes. Where absen, governmens can herefore issue puable or exendible bonds o help boos he demand for heir long-erm governmen bonds. I appears o us ha governmens could issue puable or exendible bonds as a ransiory financing source unil liquid and ransparen ineres rae derivaive markes are esablished and as a deb sraegy o move from indexed bonds o fixed-ineres coupon bonds. Due o heir lower price-sensiiviy o shor-erm ineres rae changes, puable and exendible bonds can be an alernaive o he issuing of indexed deb in periods of marke urbulence. Indeed, hisorical evidence in OECD counries shows ha many counries did use such bonds during he 1980s, when ineres raes were high and volaile and counries did no have well esablished ineres rae derivaive markes.

23 - - APPENDIX PRICING GOVERNMENT BONDS Discoun bonds and hedging We assume ha bond prices wih mauriy a ime U are a funcion of he shor-erm risk-free ineres rae r and ime : (, ; ) B = B r U. ( 4 ) The dynamics for he shor-erm r is given by he sochasic differenial equaion: (, ) (, ) dr = a r d + b r dw, ( 5 ) where he drif a(r,) and he diffusion b(r,) parameers are assumed o be known, and W is he sandard Brownian moion. We also assume ha he insananeous variance, b(r,), is nonsochasic or a funcion of ime. In his paper, we rely heavily on he assumpion ha one-facor ineres rae models describe movemens in he erm srucure of ineres raes in developing counries. This assumpion implies ha any change in shor-erm ineres raes is followed by a parallel shif in he whole yield curve. This migh indeed be a reasonable approximaion in emerging markes, where he erm srucure is shor. For pricing puable or exendible bonds, one-facor ineres rae models can be good approximaions. Applying Io s Lemma o B(r, ; U) and using equaion (5) yields: 1 db = Ba 1 ( r, ) + B + B11b( r, ) d+ Bb 1 ( r, ) dw, ( 6 ) where B i and B ii indicae he firs and second derivaives wih respec o he ih argumen, respecively. We can rewrie his sochasic differenial equaion for bonds, of all mauriies, as: where he drif componen, αb, equals: db = αb d + σb dw, ( 7 ) 1 α B ( ) ( ) = Ba 1 r, + B + B11b r,, ( 8 ) and he diffusion componen, σb, is: ( ) σ B = Bb r. ( 9 ) 1,

24 - 3 - APPENDIX Meron (1990) shows ha bonds of differen mauriies offer he same risk premia adjused by he corresponding volailiy. So we can define he marke price of ineres rae risk, λ(r,), as: ( α r ) σ = λ, ( 0 ) and use i in expressions (8) and (9) o obain a parial differenial equaion, which we solve for he bond price, B, as a funcion of he shor-erm ineres rae, r. Noe ha expressions (8) and (9) conain an unknown drif αb. To replace αb in he equaions, we firs rewrie he marke price of risk as: which gives: ( α r) (, ) 1 B b r B = λ, ( 30 ) (, ) 1 α B = rb + b r Bλ. ( 31 ) Then we subsiue αb in expression (8) by he righ-hand side of (31) and rearrange he resuling equaion as: 1 B ( ( ) ( ) ) ( ) rb + a r, b r, λ B1+ b r, B11 = 0. ( 18 ) This is a parial differenial equaion ha can be solved for B subjec o he boundary condiion: B( ru, U; U ) = 1. ( 19 ) To obain he hedging sraegy, le P dollars be invesed in a porfolio of long-erm bonds, B L, and shor-erm bonds, B S : P = θ B + θ B, ( 1 ) L S 1 where θ 1 and θ are unis of he long-erm and shor-erm bonds, respecively. As ime passes, he value of he porfolio P changes according o: dp = θ db + θ db, ( ) L S 1 where we describe he dynamics for each bond by a similar sochasic differenial equaion as in (7). Since we assume ha he shor-erm ineres rae is he only source of randomness in equaion ( ), we can eliminae he randomness by selecing he appropriae quaniies of each asse in he porfolio. We se hem equal o: θ = 1 σ S L S L B ( σ σ ) P and θ = σ L S S L B ( σ σ ) P. ( 3 )

25 - 4 - APPENDIX These posiions in he wo bonds are equivalen o being long in he long-erm bond and shor in he shor-erm bond. The porfolio is hen risk-free and should also yield a reurn equal o a risk-free invesmen o avoid arbirage: ( ) r θ B + θ B d = θ db + θ db. ( 4 ) L S L S 1 1 Dividing boh sides of (4 ) by θ 1, we can rewrie i as: r B θ + B d = db θ + db L S L S θ1 θ1 We can use (3 ) for θ 1 and θ o wrie he raio θ /θ 1 as: which is equivalen o: θ θ 1 σ B. ( 5 ) L L = S σsb ( 3 ) θ B θ = ( 33 ) L 1 S 1 B1 where B 1 L and B 1 S sand for he firs derivaive of he long-erm and shor-erm bond prices wih respec o he shor-erm risk-free ineres rae, respecively. If B S is he bond wih he shores mauriy available in he marke, we assume ha B 1 S = -1. In his case, any change in he shor-erm ineres rae is fully compensaed by a negaive price change for he shor-erm bond; ha is, δb S = -δr. As menioned above, one-facor ineres rae models imply ha any change in he shor-erm ineres rae ha affecs he shor end of he erm srucure also affecs he long end in he same way. We can hen approximae he changes in he shor-erm ineres rae, δr, by he changes in he yield-o-mauriy of he long-erm bond, δy L, and B 1 L by he firs derivaive B y L. This allows us o rewrie (33) as: and (5 ) as: θ L B y θ =, ( 34 ) 1 ( ) where B y L is also known as he hedge raio. r B + B B d = db + B db, ( 6 ) L L S L L S y y

26 - 5 - APPENDIX Puable discoun bonds In he case of puable bonds, heir price depends only on he value of he underlying bond B : F (, ) = F B. ( 8 ) Using Io s Lemma, we can find he sochasic differenial equaion for he puable bond o equal: 1 df = F1αB + F + F11σ B d + F1σB dw. ( 35 ) Recall ha he porfolio P is invesed in a combinaion of θ 1 unis of he puable bond and θ unis of he underlying discoun bond B : P = θ F + θ B. ( 9 ) 1 The value of he porfolio P changes as ime passes because of changes in F(B, ) and B : dp = θ df + θ db. ( 10 ) 1 Replacing he expressions for db and df from (7) and (35) in equaion (10 ) yields: 1 dp = θ1 F1αB + F + F11σ B + θαb d + [ θ1f1+ θ] σbdw. ( 36 ) If we se θ 1 = 1 unis of he puable bond and θ = -F 1 unis of he underlying discoun bond, hen we eliminae all he randomness in he porfolio: 1 dp = F + F11σ B d. ( 37 ) To avoid arbirage, he porfolio should yield he same rae of reurn as oher risk-free asses: and: Rearranging erms in (39) yields: ( ) dp = r F F B d ( 38 ) 1 1 F + F11σ B = r( F FB 1 ). ( 39 ) 1 F rf + rbf 1+ σ B F11 = 0. ( 40 )

27 - 6 - APPENDIX This equaion is he Black-Sholes-Meron differenial equaion. The funcion F =F(B,) is found by solving equaion (40) subjec o he following boundary condiions: F B 1 as B, F ( 0, ) = 0, ( ) = ( ) F B, T max 0, E B. T T ( 41 ) Puable bonds wrien on coupon bonds When he underlying bond pays he coupon C B, he drif componen of he sochasic differenial equaion needs o be adjused according o: ( α ) db = B C d + σb dw. ( 4 ) B Hence, he drif of he sochasic differenial equaion for he puable bond will also conain he coupon paymens: 1( ) 1 df = F αb CB + F + F11σ B d + F1σB dw. ( 43 ) The corresponding parial differenial equaion for he puable bond wih coupon C F is: F rb ( ) 1 + rb CB F1+ CF + σ B F11 = 0, ( 44 ) and is subjec o he same boundary condiions as in (41). Puable bonds wrien on bonds subjec o credi risk If he inensiy or hazard rae h and he loss process L are exogenous, he sochasic differenial equaion for he defaulable indexed bond is: ( ) The corresponding parial differenial equaion is: db = r + h L B d + σ B dw. ( 45 ) F ( r ) ( ) 1 + hl F + r + hl BF 1+ σ B F11 = 0, ( 46 ) subjec o he same boundary condiions as in (41).

28 - 7 - REFERENCES Ananhanarayanan, A. L., and Eduardo S. Schwarz, 1980, "Reracable and Exendible Bonds: The Canadian Experience," Journal of Finance, Vol. 35, No. 1, pp Ahanassakos, George, 1996, "On he Applicaion of he Black and Scholes Formula o Valuing Bonds wih Embedded Opions: The Case of Exendible Bonds," Applied Financial Economics, Vol. 6, No. 1, pp Bliss, Rober R., and Ehud I. Ronn, 1995, "To Call or No o Call? Opimal Call Policies for Callable U.S. Treasury Bonds," Federal Reserve Bank of Alana Economic Review, November-December, pp Board of Governors of he Federal Reserve Sysem, 1998, Trading and Capial-Markes Aciviies Manual (Washingon: Federal Reserve Sysem). Branion, Andrew, 1995, "The Governmen of Canada Bond Marke since 1980," Bank of Canada Review, Auumn, pp Bueow Jr., Gerald W., Frank J. Fabozzi, and Bernd Hanke, 001, Impac of Differen Ineres Rae Models on Bond Value Measures, Journal of Fixed Income, Vol. 11, No. 3, pp Cenral Bank of Brazil, 1998, Annual Repor 1997, Vol. 34 (Brasília: Cenral Bank of Brazil)., 1999, Resolução 675 (Brasília: Cenral Bank of Brazil)., 001, Annual Repor 000, Vol. 36 (Brasília: Cenral Bank of Brazil)., 00a, Annual Repor 001, Vol. 37 (Brasília: Cenral Bank of Brazil)., 00b, Circular 3139 (Brasília: Cenral Bank of Brazil)., 00c, Financial Sabiliy Repor, Vol. 1, No. 1 (Brasília: Cenral Bank of Brazil)., 00d, Políica Moneária Relaório de Aividades 1999 a 00 (Brasília: Cenral Bank of Brazil)., 00e, Resolução 3006 (Brasília: Cenral Bank of Brazil).