Nonlinearities in Brazilian Yield Curve

Transcription

1 Nonlineariies in Brazilian Yield Curve Luiz Albero D Ávila de Araújo Banco do Brasil Joaquim Pino de Andrade Universidade de Brasília UnB Absrac This aricle invesigaes he effec of macroeconomic condiions on he Brazilian erm srucure represened by he spreads of 1, 5 and 10 years erm bonds. The resuls indicae he presence of srong nonlineariies ha may compromise he effeciveness of moneary policy. On he oher hand he effecs of key macroeconomic variables, such as ineres rae, oupu, inflaion, and exchange raes, in normal imes, on he spreads, are consisen wih expecaions of coheren moneary policies. JEL: E31, E43, E50 Keywords: inflaion, yield curve, moneary policy

2 Nonlineariies in Brazilian Yield Curve Absrac This aricle invesigaes he effec of macroeconomic condiions on he Brazilian erm srucure represened by he spreads of 1, 5 and 10 years erm bonds. The resuls indicae he presence of srong nonlineariies ha may compromise he effeciveness of moneary policy. On he oher hand he effecs of key macroeconomic variables, such as ineres rae, oupu, inflaion, and exchange raes, in normal imes, on he spreads, are consisen wih expecaions of coheren moneary policies. JEL: E31, E43, E50 Keywords: inflaion, yield curve, moneary policy 1. Inroducion The conduc of moneary policy is a recurring heme in sudies and economic cener of imporan heoreical divisions in he hisory of economic hough. Mos of he modern moneary policy models are based on he assumpion ha he economy presens a sable erm srucure. This is a key elemen for he coheren moneary policy based on he conrol of he shor ineres rae. In some cases, he moneary auhoriies seek o creae an effecive and direc communicaion wih he agens who work in he financial marke, o reduce he uncerainy of is effec on ineres raes for shor-erm and provide a clear undersanding of he rajecory of ineres raes shor, medium and long erm. The hope is ha he ineres raes on shor-erm, which is he insrumen of moneary policy, have he capaciy o affec he long-erm rae and hus affec aggregae demand. I has been he case in Brazilian economy ha he risk of defaul due o confidence and exernal demand shocks has raised he long erm ineres rae independenly of moneary policy. This is noeworhy during he currency crisis of he year 1999 and elecion cycle expecaions in he year In boh cases he shor run ineres raes jumped subsanially wihou much effec on he long 1

3 run raes. During hese evens here is an indicaion ha moneary policy was endogenous, i.e. he long erm may have affeced he shor erm and no he oher way around. The aim of his paper is o examine he role of macroeconomic variables in deermining he yield curve of he Brazilian economy. Considering ha he economy has suffered considerable confidence and exernal demand shocks in recen decades he economeric mehodology employed will consider he presence of non-linear relaionships beween he variables. This aricle is divided ino four secions, besides his inroducion, secion 2 moivaes he work showing he relaionship beween macroeconomic variables and ineres raes in he financial marke, secion 3 presens he smooh ransiion regression model of he behavior of Brazilian ineres raes and, finally, secion 4 presens he main conclusions. 2. Relaionship beween macroeconomic variables and ineres raes in he financial marke The sudy of he erm srucure of ineres raes used o focus solely on he behavior of demand and supply of bonds in he financial marke, as an example we can menion Meron (1973, p.163) and Vasicek (1977). A new line of research aemps o idenify he macroeconomic forces ha affec he movemen of erm srucure. I analyzes, he role of he moneary auhoriy as influencing effecively and efficienly marke expecaions abou he presen and fuure rajecory of ineres, such as Diebold, Rudebusch and Aruoba (2006). To clarify he saemen of he preceding paragraphs, noe ha possible explanaions for he yield curve, paricularly for movemens in long-erm raes, have opposie implicaions for he conduc of moneary policy. These explanaions are, on he one hand a radiional analysis of he erm srucure of 2

4 ineres cenered on he risk premium and, secondly, a new chain ha cares abou economic condiions and heir effec on he ineres rae pah. The possibiliy of subsiuion beween bonds wih differen mauriies ensures arbirage condiion according o which he rae of reurn on hese bonds is equal. This condiion is called by Campbell (1995) as he pure expecaions hypohesis. Accordingly he rae of reurn of a bond of n periods mauriy is equal o he average of curren and expeced raes of bonds of mauriies of one period. i n 1 n (i e e 1 + i i 1+2 e +...i 1+n 1 )+ε i Where n corresponds o he rae of reurn of n periods bond, is for he rae of reurn of a one period bond. The spread is he difference beween he longerm ineres rae and curren shor-erm ineres rae as follows: spread 1 n e e e [( i i ) ( i i ) + ( i i ) +...( i i ] + ε n n 1 1 ) If he marke expecs he rae of reurn on shor-erm securiies rise in he near fuure, hen he long-erm rae will end o rise. The difference beween he longerm rae and he shor rae, i.e. he spread, can be considered as an approximaion of he slope of he yield curve. This means ha he slope of he yield curve depends on he behavior of shor-erm raes expeced. The opposie occurs when i is expeced ha he rae of reurn will be reduced in he shor erm fuure. I can be seen herefore ha he role of expecaions is key o deermining he rae of long-erm reurn and consequenly he spread. In addiion o he average of he shor erm of ineres here is an addiional elemen o explain he long-erm rae. The long-erm bonds, as long as heir face value is only available over he fuure, are subjec o risks, such as defaul and inflaion. Thus he yield of hese bonds can embed a risk premium. This is represened as he facor ε. 3

5 The objecive of his work is o explain he behavior of spread by macroeconomic condiions, hrough heir effecs on he shor-erm ineres raes and on he risk premium. Sock and Wason (1989), Dombrosky and Haubrich (1995), Sock and Wason (2001), Hamilon and Kim (2002), used he informaion of he erm srucure o anicipae economic cycles. Evans (1985) sudied he effecs of fiscal policy and showed ha large deficis affec ineres raes of long and shor erm, changing he behavior of he yield curve. In anoher sudy, Evans (1987) found ha he announcemen of defici has a emporary effec on shor erm ineres raes. In Brazil, Rocha, Moreira and Magalhães (2002) idenified he imporance of foreign deb on he spread of foreign securiies, Masumura and Moreira (2005) sudied he imporance of macroeconomic variables in he deerminaion of he spread. The inclusion of macroeconomic variables followed in his work comes from Diebold, Rudebusch and Aruoba (2006) ha relaes he level, slope and curvaure of he yield curve wih macroeconomic variables: Capaciy Uilizaion insalled (UC), Selic 1, shor-erm ineres ( i m ) and inflaion rae ( π ). 3. Modeling he erm srucure of ineres raes for he Brazilian economy The models of he erm srucure exhibi nonlineariy as shown by Tabak and Andrade (2001). The objecive of his work differs, however, and i is no o esimae he yield curve model bu assess he imporance of he macroeconomic variables in he erm srucure represened by he spread. 1 Ineres rae is conrolled by Banco Cenral do Brasil. 4

6 The firs aspec ha can be observed in he behavior of he spread in he Brazilian economy is he presence of subsanial and rapid changes in he erm srucure Spread1y Spread5y Spread10y Figure 1: Spread of he Term Srucure in Brazil. The spread behavior in Brazil can be seen in Figure 1. We can observe ha he erm srucure of ineres raes in Brazil does no presen always a posiive slope. Abrup changes in he spread are noorious reflecing possibly confidence and demand shocks affecing he risk of defaul of public bonds. Noe ha he spread of he 1 year, 5 years and 10 years bonds, presen negaive values in some years. Thus, he Brazilian economy displays some characerisics ha may indicae he presence of non-lineariy (regime change) in he erm srucure. The model used is based on he idea of "hreshold", he dependen variable is a funcion of he independen variables in a peculiar way: he dependen variable is described by a linear process o a cerain hreshold, from which he coefficien of he variables changes. The "hreshold" approach is based on Hansen (2000), which provided he possibiliy o spli he sample and use an indicaor funcion wih observable variables. The "hreshold" variable has is use linked o he division of he sample ino subgroups ha can be considered as classes or arrangemens of economic policy. 5

7 Teräsvira (2007) showed ha nonlinear models have gained imporance in macroeconomics and financial modeling. Among he caegories of nonlinear models i is well known he Swiching, Markov-swiching and he Smooh Transiion Regression (STR) models. The STR model can be seen as an evoluion of swiching regression model. The ypical STR model is defined as: / [ + θg( γ, c, s )] z u y = φ + (1) Where z = ( w /, x/ ) is a vecor of explanaory variables ha conains a vecor of / lags of he dependen variable w (, y,, y ) / variables x ( x L x ) / 1,, k = L and a vecor of exogenous 1 1 p =. Noe ha ϕ is he vecor of parameers of he linear par and θ is he parameer vecor of he non linear. The ransiion funcion G (, c, ) γ has a slope parameer γ, a vecor of locaion s parameers c, where c1 L ck, and a limi s. The ransiion funcion is a logisic of he general ype: 1 K G ( γ, c, s ) 1 exp ( ) = + γ s ck, γ > 0 (2) k= 1 Where γ > 0 is a consrain for idenificaion. The esimaed model for he Brazilian economy follows he equaion (1) where = and z is he vecor conaining he exogenous macroeconomic variables ( RBrazil UCI Selic IPCA ) variable ( y ) z = and he lagged dependen = 1 w. Noe ha he lineariy is esed agains a STR model wih ransiion variable predeermined. As he heory does no specify he ransiion variable, he es is repeaed for each variable in he se of poenial ransiion variables. Thus, he 6

8 model STR has he propery of being idenified under he alernaive hypohesis, insead of he null hypohesis of lineariy. When γ = 0 we have he ransiion funcion G( γ, c, ) 1/ 2 s and he model is linear. Oherwise, being nonlinear, we have o choose K resriced o K = 1 or K = 2. For K = 1, he parameers φ + θg ( γ, c, ) s change monoonically as a funcion of s from φup o φ + θ. For K = 2, hey change symmerically around he midpoin ( c + )/ 2 1 c 2, where he logisic funcion reaches is minimum value. The minimum value is beween zero and ½, reaching zero when γ and ½ when c 1 = c 2 e γ <. The parameer γ conrols he iling and c1 e c2 provide he locaion of he ransiion funcion. Similarly o he linear models, in STR have o reduce heir size by eliminaion of redundan variables in y = [ + θg( γ, c, s )] z + u ϕ. 3.1 Esimaion of he Smooh Threshold Model STR The daabase used conains monhly daa for he period Augus 1997 o Sepember 2011 (169 observaions). The hisorical series of ransacions of Fuure Pre x DI were obained from he BM&F and were used for he consrucion of he erm srucure of ineres raes; he capaciy uilizaion of he Brazilian indusry (UCI) in he las welve monhs was obained from he Naional Confederaion of Indusry - CNI; he rae of inflaion measured by he Naional Index of Consumer Prices (IPCA) for 12 monhs was obained from he IBGE and he Selic rae was obained from he Cenral Bank of Brazil. The evoluion of he EMBI + Brazil (Emerging Markes Bond Index) was obained from Bloomberg and corresponds o RBrazil. Considering he assumpions of economic heory some resuls are expeced. Inflaion (IPCA) is expeced o have a posiive effec on he ineres rae erm srucure, due o he risk of inflaion embedded in he yield curve. Besides his 7

9 risk premium here is ye anoher elemen which is he expeced increase in shor erm ineres raes bonds driven by he moneary policy. Boh facors end o reinforce he posiive effec of inflaion on he long-erm ineres rae. The coefficien of he annualized overnigh rae of ineres (Selic), in he spread equaion depends on marke expecaions. If marke believes ha he increase in he Selic rae is permanen he effec on he long erm rae will be close o one and so will no affec significanly he spread. This resul is crucial for he effeciveness of moneary policy. When he coefficien is equal or greaer han zero i means ha he Selic rae changes will affec he long-erm rae in equal or greaer measure. However, when an increase in he Selic is undersood by he marke as a emporary he effec on he long-erm rae will be small and he spread will fall. In his sense i is imporan o analyze he sign and value of he coefficien of he Selic rae in he spread equaion. The level of capaciy uilizaion (UCI) is he raio of he volume produced and he ceiling ha he machines and equipmen are able o produce. I can be considered as a proxy for he oupu gap. I is imporan o noe ha a posiive sign may indicae increase in expeced shor erm ineres raes (long-erm yield curve). This can be undersood as he expeced response of he moneary auhoriies ha dislike inflaion hreas. Somehing similar can happen from he devaluaion of he exchange rae (Dollar). An increase in he exchange rae indicaes an improvemen in expor compeiiveness leading o fuure expansion. Anoher possibiliy is ha devaluaion may signal a fuure ighening of liquidiy. In boh cases an increase of he shor erm ineres raes is expeced. This means a posiive coefficien of exchange rae on spread. To pursue he empirical research on he Brazilian erm srucure, based on he smooh ransiion regression model, STR, i is necessary o idenify which is he variable responsible for regime changes and wha are he signs and magniudes of he effecs of macroeconomic and financial variables o explain movemens in spreads measured by 1, 5 and 10 years bonds. 8

10 STR model is esimaed using he condiional maximum likelihood, hrough he sofware Muli-J. The specificaion began wih a linear model suggesed by Diebold e al (2006) including wo addiional variables, he exchange rae (Dollar), which accouns for he Brazilian dependence on foreign rade, and he so called Brazil Risk (RBrazil) as proxy for dependence on inernaional capial. RBrazil is he level of counry risk measured by he EMBI + Brazil 2, he higher is he price index of his bundle of asses he higher is he risk percepion by he inernaional financial marke of he direcions of he Brazilian economy. The specificaion of he models was parsimonious, considered he problems of auocorrelaion and heeroscedasiciy in residuals, and obeyed he minimizaion of he Akaike informaion crierion (AIC), Schwarz (SC) and Hannah-Quinn (HQ). Using he usual ess for uni roo in paricular he DF-GLS es of Ellio, Rohenberg and Sock, he exisence of uni roo was rejeced for all variables excep he nominal exchange rae, Brazil Risk and he rae of inflaion measured by IPCA. These variables, ha presened uni roo, were considered in firs differences. The nex sep is o apply economeric ess ha seek o ensure he correc specificaion of he model. Accordingly, he firs sep is o es for he exisence or non-lineariy of he esimaed model. If lineariy is rejeced, he choice is he correc value K (K = 1 or K = 2). Table 1 indicaes ha he model is non-linear and corresponds o he smooh logisic regression model LSTR1 wih ransiion variable defined as he RBrazil. Table 1: Lineariy Tes agains STR. 2 The EMBI + Brazil measure he price movemen of securiies from one day o he oher. Is uni is he base poin, i.e. 500 basis poins imply ha Brazilian bonds pay 5% more han he U.S., considering periodic ineres paymens, purchase price, redempion value and he ime remaining unil mauriy obligaions, is used by domesic and inernaional invesors 9

11 p-values of F-ess (NaN - marix inversion problem): ransiion variable F F4 F3 F2 suggesed model erm model RBRAZIL_d1()* 4.29E E E E-34 LSTR1 Spread1y RBRAZIL_d1()* 2.72E E E E-17 LSTR1 Spread5y RBRAZIL_d1()* 7.35E E E E-10 LSTR1 Spread10y The grid was calculaed, indicaing he value of he variable range ha represens he ype of gradien vecor and he locaion represened by he variable c1 whose resuls are deailed in Table 2. Table 2: Grid. SSR gamma c1 erm model Spread1y Spread5y Spread10y ransiion funcion: LSTR1 grid c { , , 30} grid gamma { 0.50, 10.00, 30} ransiion variable: RBRAZIL_d1() Having he specificaion of he model, in he case LSTR1, he ransiion variable RBrazil, he variable grid ha is c { , , 30} and he funcion ha corresponds o he range {0, 50, 10,00, 30}, i is possible o run he esimaion algorihms and, hrough an ieraive process, o esimae he nonlinear model o evaluae he behavior of he yield curve. The ess for heeroscedasiciy and auocorrelaion of he residuals are shown in Tables 3 and 4. The es for absence of auocorrelaion corresponds o he applied es used by Teräsvira (1998) and corresponds o a special case of he general es Godfrey (1988). The procedure corresponds o regress he esimaed residuals on he lagged ones and on he parial derivaives of he log -likelihood funcion wih respec o he parameers of he model. The deailed resuls, in Table 3, show he null hypohesis of no auocorrelaion of he esimaed residuals of he models for spreads of 1, 5 and 10 years. Table 3: Model Specificaion - Tesing Absence of Correlaion. 10

12 Spread1y Spread5y Spread10y lag F-value p-value F-value p-value F-value p-value The es of Heeroscedasiciy corresponds o he ARCH-LM es ha represens a similar saisics o ha described by Doornik and Hendry (1997), cenered on a mulivariae LM saisics. Table 4 shows ha he null hypohesis of homoscedasiciy of he residuals was no rejeced for models esimaed for erms of 1 and 10 years. For he erm of five years, here is some probabiliy of incurring in his ype of problem. Table 4: Model Specificaion - Tes of Heeroscedasiciy. Spread1y Spread5y Spread10y lag F-value p-value F-value p-value F-value p-value The proper fi of he model o esimae Spread of 1 year is suggesed in figure 2, when i is shown he almos impercepible difference beween he original series and he series adjused by linear and nonlinear componens. Figure 2: Se he STR model for he spread of 1 year. 11

13 The version of he STR model esimaed is a generalizaion of he sandard auoregressive model where he auoregressive coefficien is a logisic funcion, = + k= 1 where G ( γ, c, s ) 1 exp γ RBrazil c, γ > 0 k. Noe ha is he smoohing parameer. For he spread of 1 year, 5 years and 10 years, values found were , and , respecively, noing ha he higher he value of sharper is he S shape of he ransiion variable. Analyzing he behavior of he ransiion funcion - he logisic ype, i is considered a range of -800 o +1,000 poins of variaion in risk Brazil (RBrazil) and varying values 0 o 1 of he funcion G. I is noorious he S shape of he ransiion for he highes values of γ for he spreads of 5 and 10 years, as shown in Figure 3. Figure 3: Values of γ (gamma) in he model LSTR. Brazilian economy has suffered in he las wo decades severe shocks of confidence ha affeced mainly he foreign currency and long erm governmen bonds. The variable chosen o define he ransiion and he hreshold for he non linear model is he RBrazil. I saisfies he ess as ransiion variable accordingly, as explained earlier. Noe ha RBrazil is measured by he weighed average of he Brazilian securiies raded abroad in relaion o securiies of he same characerisic of he Unied 12

14 Saes governmen and as such i is a very good proxy of counry risk. I may affec direcly he ineres of he long erm bonds; however is main imporance is in explaining he main shifs of he whole erm srucure. The esimaed hresholds of he change of he RBrazil are , and for he spreads of 1, 5 and 10 year bonds respecively (see Table 5 below). Is relaionship wih he non linear behavior of he erm srucure is illusraed in he Figure 4 ha presens he drbrazil (firs differences of RBrazil), and he spreads of 1 and 10 year bonds ,00 6,00 4,00 2,00 0,00-2,00-4,00-6,00-8,00 drbrazil Spread1y Spread10y Figure 4: Risk Brazil vs. Spread. 3.2 Main Resuls of he Economeric Experimen The esimaion of he spread of he erm srucure of ineres raes suppor he conclusion of Diebold, Rudebusch and Aruoba (2004) and i indicaes ha macroeconomic variables have significan explanaory power for he volailiy of he spread of he erm srucure of ineres raes observed in he Brazilian financial marke. The imporance of he spread of he previous period in he formaion of he spread of he curren period is posiive and significan in all hree erms 13

15 analyzed (1, 5 and 10 years), as can be seen in he linear par of he esimaes described in Table 5. The coefficien reduces by half when he erm goes from 1 o 5 and 10 years, being 1.34, 0.77 and 0.72 respecively. I means ha he memory of shor erm mauriy (1 year) ends o increase volailiy while longer erm mauriies (5 and 10 years) end o smooh he spreads. Spread1y Spread5y Spread10y variable esimae p-value esimae p-value esimae p-value linear par CONST Spread(-1) Selicef() DOLLAR_d1() UCI(-1) DOLLAR_d1(-1) ND ND IPCA_d1(-2) ND ND ND ND IPCA_d1(-3) ND ND RBRAZIL_d1(-4) ND ND ND ND UCI(-4) nonlinear par CONST Spread1y(-1) Selicef() DOLLAR_d1() UCI(-1) DOLLAR_d1(-1) ND ND IPCA_d1(-2) ND ND ND ND IPCA_d1(-3) ND ND RBRAZIL_d1(-4) ND ND ND ND UCI(-4) Gamma C AIC: SC: HQ: R2: adjused R2: variance of ransiion variable: SD of ransiion variable: variance of residuals: SD of residuals: ransiion funcion: LSTR1 sample range: [1998 M2, 2011 M9], T = 164 Models: Spread1y() = CONST Spread1y(-1) Selicef() DOLLAR_d1() UCI(-1) IPCA_d1(-3) RBRAZIL_d1(-4) UCI(-4) Spread5y() = CONST Spread5y(-1) Selicef() DOLLAR_d1() UCI(-1) DOLLAR_d1(-1) IPCA_d1(-3) UCI(-4) Spread10y() = CONST Spread10y(-1) Selicef() DOLLAR_d1() UCI(-1) DOLLAR_d1(-1) IPCA_d1(-2) UCI(-4) Table 5: Model STR Esimae. The shor erm ineres rae Selic rae presened significan negaive coefficien, as observed in he linear par, an indicaion of a emporary impac on CDI's financial marke. However, in he non-linear esimaion, he signal is posiive, indicaing ha he increase in he Selic rae has a posiive effec on long erm raes. In oher words, he negaive effec on he spread of he Selic is cushioned 14

16 and may even become posiive in he periods ha he Brazil risk exceeds he hreshold. This may indicae ha agens expec he Selic rae will coninue increasing in he fuure o circumven he impac of shocks. The exchange rae (U.S. dollars) had he expeced posiive sign, indicaive of improved expor compeiiveness or devaluaion involving a ighening of liquidiy, boh indicaing increased rae of long-erm (increased ineres rae of shor- expeced erm). The analysis of he inflaion rae is imporan because i is associaed wih he influence he yield curve hrough he inflaion risk premium. The expeced resul of a posiive effec is observed, bu for longer erms he effec is reduced subsanially, reflecing possibly he credibiliy of he Brazilian moneary auhoriies o conrol inflaion. An alernaive inerpreaion, however, is ha an increase in inflaion indicaes ha he cenral bank will gradually increase he rae of shor-erm ineres. On he non-linear behavior here is a negaive cushioning effec as before. The coefficien of capaciy uilizaion of he Brazilian indusry presened a posiive coefficien in he linear par, showing ha he yield curve has a behavior aached o he cyclical dynamics of he Brazilian economy Brazil risk is exremely relevan as he ransiion variable esablishing he hreshold of he non linear behavior of he Brazilian financial marke. Is relevance o explain he level of he spread in he nonlinear par of he model is noeworhy. Tha may explain why is conribuion as an addiional variable wihin he equaion is weak. 4. Conclusion The sudy of he erm srucure of ineres raes and he behavior of he erm spread, he difference beween long-erm raes minus he shor erm, has puzzled moneary policy researchers, because no always is he expeced effec 15

17 of he acions of he moneary auhoriy on long raes prevailing in he financial marke. The presence of srong nonlineariy in he erm srucure largely explains he pifalls of moneary policy. Tha is, he lack of effeciveness of his policy in cerain periods, paricularly in hose wih non-linear behavior. The posiive correlaion of inflaion wih he spread, is coheren wih growing uncerainy, bu also seems o indicae ha he financial communiy believes in he moneary policy of he Cenral Bank. The same happened wih he rae of capaciy uilizaion and exchange rae. Las bu no leas i is possible o consider ha inflaion rae, capaciy uilizaion and exchange rae could be aken as proxies for he fuure expansionary cycles and in ha sense he spread could be considered as a predicive facor of fuure expansion. This, however, shall be objec of a new research. Therefore, he Brazilian economic policymakers mus wach he movemens of he yield curve and analyze he informaion frequenly, o guide he analysis and acions o be aken, o inerfere in a beneficial way on he rajecory of he Brazilian economy. 16

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