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Referencias Bibliograficas
[1] A . D . H A L L , H . M . A .; G R A N G E R , C . W . J .. A cointegration analysis of
treasury bill yields. R ev iew o f E c o n o m ic a n d S ta tistic s, v o lu m e 7 4 :116 –
12 6 , 19 9 2 .
[2 ] A M A T O , J . D .; L U IS I, M .. M acro factors in th e term structure of
credit sp reads. B IS W o rk in g P a p ers, 2 0 3 , M a rc o 2 0 0 6 .
[3 ] A N G , A .; P IA Z Z E S I, M .. A no-arbitrage v ector autoregressiv e
of term structure dynam ics w ith m acroeconom ic and latent
v ariables. N a tio n a l B u rea u o f E c o n o m ic R esea rc h , w o rk in g p a p er 8 3 6 3 :3 3 7 –
3 6 4 , J u lh o 2 0 0 1.
[4 ] B J O R K , T .; C H R IS T E N S E N , B . J .. Interest rate dynam ics and
consistent forw ard rate curv es. M a th em a tic a l F in a n ce, 9 :3 2 3 – 3 4 8 ,
19 9 9 .
[5 ] B L IS S , R . R .. T esting term structure estim ation m eth ods. F ed era l
R eserv e B a n k o f A tla n ta , 9 6 -12 a , W o rk in g P a p er, N o v em b ro 19 9 6 .
[6 ] B L IS S , R . R .. M ov em ents in th e term structure of interest rates.
F ed era l R eserv e B a n k o f A tla n ta E c o n o m ic R ev iew , Q u a rto S em estre 19 9 7 .
[7 ] B O N O M O , M .; L O W E N K R O N , A .. A term structure m odel for
em erging econom y bonds. M a io 2 0 0 6 .
[8 ] D A S ILV E IR A , G . B .; B E S S A D A , O .. Analise de com p onentes p rinci-
p ais de dados funcionais - um a ap licacao as estruturas a term o
de tax as de juros. T ra b a lh o s p a ra d isc u ssa o - B a n c o C en tra l d o B ra sil,
7 3 :1– 3 1, M a io 2 0 0 3 .
[9 ] D IE B O L D , F . X .; L I, C .. F orecasting th e term structure of gov ern-
m ent bond yields. J o u rn a l o f E c o n o m etric s, 13 0 (2 0 0 6 ):3 3 7 – 3 6 4 , M a io
2 0 0 5 .
[10 ] D U F F E E , G . R .. T erm p rem ia and interest rate forecasts in affi ne
m odels. J o u rn a l o f F in a n ce, V o lu m e LV II, n u m ero 1, F ev ereiro 2 0 0 2 .
Referencias Bibliograficas 90
[11] D U F F IE , D .; K A N , R .. A yield-factor m odel of interest rates.
M a th em a tic a l F in a n ce, v o lu m e 6 , n u m ero 4 :3 7 9 – 4 0 6 , O u tu b ro 19 9 6 .
[12 ] E . B E R N D T , B . H A L L , R . H .; H A U S M A N , J .. E stim ation and inference
in nonlinear structural m odels. A n n a ls o f S o c ia l M ea su rem en t, V o lu m e
3 :6 5 3 – 6 6 5 , 19 7 4 .
[13 ] E M A R C O S V A L L I, G . V .. M ov im entos da estrutura a term o da tax a
de juros brasileira e im unizacao. E c o n o m ia A p lic a d a , v o lu m e 5 , n u m ero
1:3 3 – 5 3 , M a rc o 2 0 0 1.
[14 ] E R IC Z IV O T , J . W .; K O O P M A N , S . J .. S tate sp ace m odeling in
m acroeconom ics and fi nance. M a io 2 0 0 3 .
[15 ] E V A N S , C . L .; M A R S H A L L , D . A .. M onetary p olicy and th e
term structure of nom inal interest rates: E v idence and th eory.
C a rn eg ie-R o c h ester C o n feren ce S eries o n P u b lic P o lic y, 4 9 :5 3 – 111.
[16 ] F A M A , E . F .; B L IS S , R . R .. T h e inform ation in long-m aturity
forw ard rates. C en ter fo r R esea rc h in S ec u rity P rices W o rk in g p a p er series,
17 0 , 19 8 7 .
[17 ] F IS H E R , M .. F orces th at sh ap e th e yield curv e. F ed era l R eserv e B a n k
o f A tla n ta E c o n o m ic R ev iew , P rim eiro S em estre 2 0 0 1.
[18 ] F R A N C IS X . D IE B O L D , C . L .; Y U E , V . Z .. G lobal yield curv e dynam ics
and interactions: A dynam ic N elson-S iegel ap p roach . J o u rn a l o f
E c o n o m etric s, 3 5 , 2 0 0 8 .
[19 ] F R A N C IS X . D IE B O L D , C . L .; Y U E , V . Z .. G lobal yield curv e dynam ics
and interactions: A dynam ic N elson-S iegel ap p roach . N a tio n a l
B u rea u o f E c o n o m ic R esea rc h , 13 5 8 8 , w o rk in g p a p er series, N o v em b ro 2 0 0 7 .
[2 0 ] F R A N C IS X . D IE B O L D , G . D . R .; A R O U B A , S . B .. T h e m acroeconom y
and th e yield curv e: A dynam ic latent factor ap p roach . J o u rn a l
o f E c o n o m etric s.
[2 1] G O N C A LV E S , R .. A crise internacional e a Am erica L atina com
referencia esp ecial ao caso do B rasil. O u tu b ro 2 0 0 8 .
[2 2 ] H U L L , J .; W H IT E , A .. P ricing interest rate deriv ativ e securities.
T h e R ev iew o f F in a n c ia l S tu d ies, v o lu m e 3 , n u m ero 4 :5 7 3 – 3 9 2 , 19 9 0 .
[2 3 ] J . C . C O X , J . E . I.; R O S S , S . A .. A th eory of th e term structure of
interest rates. E c o n o m etric a , V o lu m e 5 3 :3 8 5 – 4 0 7 , 19 8 5 .
Referencias Bibliograficas 91
[2 4 ] J O H N S O N , R . A .; W IC H E R N , D . W .. Ap p lied M ultiv ariate Analysis
4 th edition. P ren tice H a ll, 19 9 8 .
[2 5 ] J O O S T D R IE S S E N , B . M .; N IJ M A N , T .. C om m on factors in interna-
tional bond returns. J o u rn a l o f In tern a tio n a l M o n ey a n d F in a n ce, v o lu m e
2 2 :6 2 9 – 6 5 6 , 2 0 0 3 .
[2 6 ] K U R G M A N , P . R .. A crise de 2 0 0 8 e a econom ia da dep ressao. E d .
E lsev ier, 2 0 0 9 .
[2 7 ] L IO N E L M A R T E L L IN I, P . P .; P R IA U L E T , S .. F ix ed Incom e S ecurities.
V aluation, R isk M anagem ent and P ortfolio S trategies. E d . W iley,
2 0 0 3 .
[2 8 ] L IT T E R M A N A , R .; S C H E IN K M A N , J .. C om m on factors aff ecting bond
returns. T h e J o u rn a l o f F ix ed In c o m e, p . 5 4 – 6 1, J u n h o 19 9 1.
[2 9 ] L O N G S T A F F ; S C H W A R Z . Interest rate v olatility and th e term
structure: a tw o factor general eq uilibrium m odel. J o u rn a l o f
F in a n ce, v o lu m e X LV II:12 5 9 – 12 8 2 , 19 9 2 .
[3 0 ] L U N A , F . E .. Ap licacao da m etodologia de com p onentes p rincip ais
na analise da estrutura a term o de tax a de juros brasileira e no
calculo do v alor em risco. IP E A , tex to p a ra d isc u ssa o 114 6 , 2 0 0 6 .
[3 1] N E L S O N , C .; A .S IE G E L . P arsim onious m odeling of yield curv es.
J o u rn a l o f B u sin ess, 6 0 :4 7 3 – 4 8 9 , 19 8 7 .
[3 2 ] P E T E R H O R D A L , O . T .; V E S T IN , D .. A joint econom etric m odel of
m acroeconom ic and term structure dynam ics. J o u rn a l o f E c o n o -
m etric s, 13 1:p p . 4 0 5 – 4 4 4 , 2 0 0 6 .
[3 3 ] P O O T E R , M . D .. E x am ining th e N elson-S iegel class of term
structure m odels. T in b erg en In stitu te D isc u ssio n P a p er, V o l. 0 4 3 / 4 , 2 0 0 7 .
[3 4 ] R O B E R T L IT T E R M A N A , J . S .; K N E Z , P . J .. E x p loration into factors
ex p lanining m oney m ark et returns. T h e J o u rn a l o f F in a n ce, V o l. 9
N o . 5 :p p . 18 6 1 – 18 8 2 , D ezem b ro 19 9 4 .
[3 5 ] R O L L , R .; R O S S , S . A .. An em p irical inv estigation of th e arbitrage
p ricing th eory. J o u rn a l o f F in a n ce, 3 5 :10 7 3 – 110 3 .
[3 6 ] S A N G T A M , C .; W IN G Y U , I.. M odelling sov ereign bond yield curv es
of th e U S , J ap an and G erm any. W o rk in g P a p er H o n k K o n g M o n eta ry
A u th o rity, 0 9 :1– 17 (17 ), J u n h o 2 0 0 7 .
Referencias Bibliograficas 92
[3 7 ] S E U N G C H A N A H N , S . D .; P E R E Z , M . F .. E x p loring th e com m on
factors in th e term structure of credit sp reads. M a rc o 2 0 0 8 .
[3 8 ] S E U N G C H A N A H N , S . D .; P E R E Z , M . F .. E x p loring th e com m on
factors in th e term structure of credit sp reads. M a rc o 2 0 0 8 .
[3 9 ] S H O U S H A , S .. E strutura a term o da tax a de juros e dinam ica
m acroeconom ica no B rasil. R ev ista d o B N D E S , v .15 n .3 0 :3 0 3 – 3 4 5 ,
D ezem b ro 2 0 0 8 .
[4 0 ] S T A N D A R D ; P O O R S R A T IN G S D IR E C T . R atings direct. D ezem b ro
2 0 0 8 .
[4 1] S U K -J O O N G K IM , B . L .; W U , E .. D ynam ics of bond m ark et inte-
gration betw een ex isting and accession E U countries. D isc u ssio n
P a p er - In stitu te fo r In tern a tio n a l In teg ra tio n S tu d ies, D isc u ssio n P a p er 2 5 ,
M a io 2 0 0 4 .
[4 2 ] S V E N S S O N , L . E .. E stim ating and interp reting forw ard interest
rates: S w eden 1 9 9 2 - 1 9 9 4 . C en ter fo r E c o n o m ic P o lic y R esea rc h ,
D isc u ssio n P a p er 10 5 1, 19 9 4 .
[4 3 ] T O M A R N O L D , M . J . B . J . G .. A sim p lifi ed ap p roach to understand-
ing th e k alm an fi lter tech niq ue. T h e E n g in eerin g E c o n o m ist, v o l. 5 0 ,
A b ril 2 0 0 8 .
[4 4 ] V A S IC E K , O . A .. An eq uilibrium ch aracterization of th e term
structure. J o u rn a l o f F in a n c ia l E c o n o m ic s, V o lu m e 5 :17 7 – 18 8 , 19 7 7 .
[4 5 ] W E L C H , G .; B IS H O P , G .. An introduction to th e k alm an fi lter.
U n iv ersity o f N o rth C a ro lin a a t C h a p el H ill, T R 9 5 -0 4 1, A b ril 2 0 0 4 .
[4 6 ] W U , L .; Z H A N G , F . X .. A no-arbitrage analysis of econom ic deter-
m inants of th e credit sp read term structure. F in a n ce a n d E c o n o m ic s
D isc u ssio n S eries D iv isio n s o f R esea rc h a n d S ta tistic s a n d M o n eta ry A ff a irs
F ed era l R eserv e B o a rd , W a sh in g to n , D .C ., 2 0 0 5 .
[4 7 ] W U , T .. W h at m ak es th e yield curv e m ov e? F ed era l R eserv e B a n k o f
S a n F ra n c isc o (F R B S F ) E c o n o m ic L etter, 2 0 0 3 -15 , J u n h o 2 0 0 3 .
[4 8 ] Y A N G , J .. M acroeconom ic determ inants of th e term structure of
corp orate sp reads. W o rk in g P a p er - B a n k o f C a n a d a , 2 0 0 8 -2 9 , S etem b ro
2 0 0 8 .
A
Ap end ice - Analise d e Com p onentes P rincip ais
S eg u e resu m o d e a lg u m a s a n a lises d e C o m p o n en tes P rin c ip a is rea liz a d a s p o r
o u tro s a u to res p a ra d iferen tes a m o stra s d e p a ıses. T a is resu lta d o s fo ra m ex tra ıd o s
d o liv ro “ F ix ed In c o m e S ec u rities - V a lu a tio n , R isk M a n a g em en t a n d P o rtfo lio
S tra teg ies” , L io n el M a rtellin i, P h ilip p e P ria u let a n d S tep h a n e P ria u let; E d . W iley ;
2 0 0 3 .
Resultados com Analises ACP
Autores Paıses (p erıodo) Interv alo F at % de ex p licacao
L S (19 9 1) E U A(19 8 4 - 19 8 8 ) 6M -18 Y 3 8 8 ,04 / 8 ,38 / 1,9 7
K M (19 9 2) F ranca (19 8 9 - 19 9 0) 1Y -25Y 2 9 3,7 / 6,1
D Z (19 9 4 ) Italy (19 8 8 - 19 9 2) 6M -7 Y 3 9 3,9 1/ 5,4 9 / 0,4 2
K R (19 9 4 ) Alemanh a/ S uica/ E U A(19 9 0-19 9 4 ) 3M -10Y 3 T otal: 9 7 / 9 8 / 9 8
B C (19 9 6) E U A (19 8 5 - 19 9 1) 1M -20Y 3 8 0,9 3/ 11,8 5/ 4 ,36
B Z (19 9 6) Alemanh a/ S uica (19 8 8 - 19 9 6) 1M -10Y 3 7 1/ 18 / 04 e 7 5/ 16/ 3
G T (19 9 7 ) J PM org an Risk M etrics 30/ 09 / 9 6 3M -30Y 3 9 2,8 / 4 ,8 / 1,27
L (2000) Alemanh a (19 8 7 - 19 9 5) 1Y -9 Y 5 50,6/ 17 ,3/ 13,5/ 8 ,8 / 5,8U S A (19 8 4 - 19 9 5) 56,5/ 17 ,4 / 9 ,8 6/ 8 ,12/ 4 ,3
Reino U nido (19 8 7 - 19 9 5) 63,5/ 6,3/ 7 ,5/ 8 ,1/ 5,3J ap ao (19 8 7 - 19 9 5) 4 2,8 / 25,5/ 17 ,1/ 6/ 4 ,9
M P (2000) F ranca (19 9 5 - 19 9 8 ) 1M -10Y 3 66,64 / 20,52/ 6,9 6B elg ica 62/ 27 / 6F ranca 62/ 21/ 8
L PP (2003) Alemanh a (19 9 8 - 2000) 1M -30Y 3 61/ 23/ 6Italia 59 / 24 / 7
Reino U nido 60/ 24 / 9
T ab ela A.1: ACP p ara diferentes g rup os de p aıses.
B
Ap end ice - F iltro d e K alm an
U m a v ez feita a esc o lh a d o m o d elo resp o n sa v el p ela c o n stru c a o d a s estru tu ra s
a term o , e n ecessa rio u m m o d elo q u e d esc rev a a ev o lu c a o d a estru tu ra n o tem p o .
U tiliz a rem o s ta m b em o a rc a b o u c o d a s eq u a c o es d e esp a c o d e esta d o p a ra d esc rev er
essa ev o lu c a o . O m o d elo e d esc rito p o r d o is g ru p o s b a sic o s d e eq u a c o es1: eq u a c o es
d e m ed id a e eq u a c o es d e tra n sic a o . A eq u a c a o d e m ed id a rela c io n a v a ria v eis n a o
o b serv a v eis (Xt) c o m o b serv a v eis (Yt). D e fo rm a g era l a s eq u a c o es d e m ed id a
esta o n o fo rm a to :
Yt = at ∗ Xt + bt + εt (B -1)
P o d em o s sim p lifi c a r a eq u a c a o c o n sid era n d o bt ig u a l a zero e at c o n sta n te
a o lo n g o d o tem p o . P a ra εt c o n sid era rem o s m ed ia zero e v a ria n c ia rt. A eq u a c a o
B -1 resu m e-se a :
Yt = a ∗ Xt + εt (B -2)
A eq u a c a o d e tra n sic a o , p o r su a v ez , se b a seia em u m m o d elo q u e p erm ite
q u e a v a ria v el n a o o b serv a v el m u d e n o tem p o . S u a estru tu ra e d a d a p o r:
Xt+1 = ct ∗ Xt + dt + θt (B -3 )
A ssu m in d o a s m esm a s sim p lifi c a c o es, c o m m ed ia zero e v a ria n c ia st p a ra θt,
tem o s:
Xt+1 = c ∗ Xt + θt (B -4 )
A s eq u a c o es B -2 e B -4 c o m p o e u m sistem a c o n h ec id o p o r rep resen ta c a o d e
esp a c o d e esta d o . O F iltro d e K a lm a n e u m a lg o ritm o q u e itera tiv a m en te a tu a liz a
a p ro jec a o lin ea r d esse sistem a . P a ra o d esen v o lv im en to d o a lg o ritm o p o d em o s
c o m ec a r in serin d o u m v a lo r in ic ia l X0 n a eq u a c a o B -4 p a ra o v a lo r d e Xt, o n d e
X0 tem m ed ia µ0 e d esv io p a d ra o σ0. Im p o rta n te ressa lta r q u e εt, θt e X0 sa o
d esc o rrela ta d o s. T em o s, p o rta n to , a eq u a c a o B -4 ig u a l a :
X1P = c ∗ X0 + θ0 (B -5 )
1U tilizaremos a descricao encontrada na referencia “A Simplified Approach to Under-
standing the Kalman Filter Technique” , (de T om Arnold, M ark J . B ertus e J onath an G od-b ey ) p ara esclarecer o funcionamento do F iltro de K alman.
A p end ice B. A p end ice - F iltro d e K alm an 95
o n d e X1P c o rresp o n d e a p rev isa o d e X1. O v a lo r d e X1P d ev e ser in serid o
n a eq u a c a o B -2 p a ra c a lc u lo d e u m v a lo r p rev isto d e Y1 ig u a l a Y1P ,
Y1P = a ∗ X1P + ε1 = a ∗ (c ∗ X0 + θ0) + ε1 (B -6 )
C o m a o c o rren c ia d e Y1 p o d e-se m ed ir o erro Y1E d a d o p o r:
Y1E = Y1 − Y1P (B -7 )
O v a lo r d o erro p o d e ser in c o rp o ra d o a p rev isa o d e X1, g era n d o u m a p rev isa o
a ju sta d a , X1Pa j :
X1Pa j = X1P + k1 ∗ Y1E = X1P [1 − a ∗ k1] + k1 ∗ Y1 − k1 ∗ ε1 (B -8 )
o n d e k1 c o rresp o n d e a o g a n h o d e K a lm a n .
O g a n h o d e K a lm a n e d eterm in a d o m in im iz a n d o a v a ria n c ia d e X1Pa j , c o m
rela c a o a k1. U tiliz a n d o p1 c o m o a v a ria n c ia d e X1P , a v a ria n c ia d e X1Pa j e d a d a
p o r:
V ar(X1Pa j ) = p1 ∗ [1 − a ∗ k1]2 + k2
1 ∗ r1 (B -9)
M in im iz a n d o a v a ria n c ia tem o s:
∂ V ar(X1Pa j )
∂ k1
= 0 (B -10)
k1 =p1 ∗ m
p1 ∗ a2 + r1
=C o v (X1P ,Y1P )
V ar(Y1P )(B -11)
P ela eq u a c a o B -11 vem o s q u e o g a n h o d e K a lm a n e eq u iv a len te a o c o efi c ien te
β d e u m a reg ressa o lin ea r c o m X1P sen d o a v a ria v el d ep en d en te e Y1P sen d o a
v a ria v el in d ep en d en te. N a o n ecessa ria m en te ex istem d a d o s su fi c ien tes p a ra rea liz a r
essa reg ressa o , m a s a ssim c o m o o c o efi c ien te β e u sa d o p a ra red u zir o erro d a
reg ressa o , o m esm o o c o rre p a ra o g a n h o d e K a lm a n , u tiliz a d o p a ra red u zir a
v a ria n c ia d a p rev isa o a ju sta d a d e X1. O p ro x im o p a sso se d a p ela su b stitu ic a o
d e X1Pa j n a eq u a c a o B -4 . X1Pa j e esc o lh id o em lu g a r a X1P p o rq u e p o ssu i u m a
m en o r v a ria n c ia . O p ro cesso e en ta o re-in ic ia d o p a ra o tem p o t = 2.
O F iltro d e K a lm a n g era c o m o resu lta d o estim a tiv a s p a ra a v a ria v el n a o
o b serv a v el XtP a j . A v a ria v el o b serv a v el, p o r su a v ez , p o ssu i serie d e v a lo res e
d istrib u ic a o b a sea d a s n o v a lo r p rev isto YtP . O q u e o F iltro d e K a lm a n n a o p o d e
d eterm in a r sa o o s p a ra m etro s n a o c o n h ec id o s d o m o d elo , n a s eq u a c o es d e m ed id a
e tra n sic a o . S en d o eles εt e c, e ta m b em o θt, resp ec tiv a m en te. E x iste, p o rta n to ,
a n ecessid a d e d e estim a r o s p a ra m etro s e, u m a v ez feito isso , p erm itir q u e o
F iltro d e K a lm a n g ere o s resu lta d o s p a ra a v a ria v el n a o o b serv a v el d e in teresse.
S e a ssu m irm o s q u e a d istrib u ic a o p a ra c a d a YtP e seria lm en te in d ep en d en te e
d istrib u id o s n o rm a lm en te, a fu n c a o c o n ju n ta d e v ero ssim ilh a n c a e d a d a p o r:
A p end ice B. A p end ice - F iltro d e K alm an 96
T∏
t= 1
{[ 1√
2 ∗ π ∗ V ar[YtP ]
]T
∗ e−
sumTt=1(Yt−E[YtP ])2
2∗V a r [YtP ]
}
(B -12)
A id eia p o r tra s d a s fu n c o es d e v ero ssim ilh a n c a e q u e a s v a ria v eis o b serv a v eis
v em d e u m a d istrib u ic a o c o n ju n ta n o rm a l. C o n seq u en tem en te o s p a ra m etro s a
serem estim a d o s p ela d istrib u ic a o sa o esc o lh id o s d e fo rm a a m a x im iz a r o v a lo r
d a fu n c a o d e v ero ssim ilh a n c a , g era n d o a m a io r p ro b a b ilid a d e p a ra q u e a d a ta
o b serv a d a rea lm en te o c o rra . P a ra fa c ilita r o c a lc u lo e u tiliz a d o o lo g a ritm o n a tu ra l
d a fu n c a o . A d eriv a d a p a rc ia l d o lo g d a fu n c a o d e v ero ssim ilh a n c a c o m rela c a o
a c a d a p a ra m etro q u e se d eseja estim a r e ig u a la d a a zero , c o m o o b jetiv o d e
m a x im iz a r o lo g d a fu n c a o .
A p o s o g ru p o d e p a ra m etro s ser estim a d o o a lg o ritm o d o F iltro d e K a lm a n
e a p lic a d o n o v a m en te, p ro d u z in d o n o v a s series d e YtP e XtP a j c o m resp ec tiv a s
d istrib u ic o es. A fu n c a o d e v ero ssim ilh a n c a e n o v a m en te a p lic a d a , p ro d u in d o n o v o s
p a ra m etro s, en tra n d o n o v a m en te n o F ltro d e K a lm a n . E sse p ro cesso itera tiv o
c o n tin u a a te q u e n a o se a lc a n ce m a is u m a u m en to sig n ifi c a tiv a n o lo g d a fu n c a o
d e v ero ssim ilh a n c a , v er B ro c k w ell e D a v is (2 0 0 2 ).
B.1
M etod os d e O tim izacao d o E -V iew s
O s m eto d o s d e o tim iz a c a o em p reg a d o s p elo E -V iew s se b a seia m n a s p rim eira s
e seg u n d a s d eriv a d a s d a fu n c a o lo g d e m a x im a v ero ssim ilh a n c a c o m rela c a o a o s
v a lo res d o s p a ra m etro s a c a d a itera c a o , c h a m a d a s g ra d ien te o u H essia n a (a m a triz
d a seg u n d a d eriv a d a ) resp ec tiv a m en te. O a lg o ritm o d e o tim iz a c a o d esen v o lv id o
p o r B ern d t, H a ll, H a ll e H a u sm a n (19 7 4 ), c o n h ec id o p o r B H H H , a p lic a so m en te
a p rim eira d eriv a d a (c a lc u la d a n u m eric a m en te e n a o a n a litic a m en te) e c a lc u la
a p ro x im a c o es p a ra a seg u n d a d eriv a d a . N a o ten d o q u e g era r a seg u n d a d eriv a d a
a c a d a itera c a o , e a c a d a p a sso d o a lg o ritm o , a u m en ta a ra p id ez c o m p u ta c io n a l.
A a p ro x im a c a o , en treta n to , p o d e ser “ p o b re” q u a n d o o p erc u rso a te en c o n tra r
o v a lo r m a x im o d a fu n c a o e m a io r; n ecessita n d o u m m a io r n u m ero d e itera c o es
p a ra a tin g ir o p o n to o tim o . O m eto d o M a rq u a rd t e u m a m o d ifi c a c a o d e B H H H
(a m b o s v a ria c o es d o m eto d o d e G a u ss-N ew to n ), in c o rp o ra n d o u m a “ c o rrec a o ”
c o m o o b jetiv o d e a lc a n c a r o p o n to o tim o n a s estim a tiv a s d o s c o efi c ien tes a in d a
d e fo rm a m a is ra p id a . N esse tra b a lh o p a ra estim a rm o s o F iltro d e K a lm a n so b re
u m m a io r n u m ero d e p a ra m etro s, sec a o 4 .4 .2 , u tiliz a m o s o m eto d o B H H H a o
in v es d o M a rq u a rd t. N este u ltim o fo ra m en c o n tra d o s p ro b lem a s d e c o n v erg en c ia ,
p ro v a v elm en te d ev id o a o o b jetiv o d o m eto d o d e a lc a n c a r o p o n to o tim o d e fo rm a
m a is ra p id a .
C
Ap end ice - T este d e Raız U nitaria
C.1
T este d e Raız U nitaria: S overeign Bond s
E U A
S eries t ob s t(1% ) t(5% ) t(10% ) Confi g . V ar. E x og enas
E U A 3M −0, 68 1 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
E U A 6M −0, 503 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
E U A 1Y −0, 639 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
E U A 2Y −0, 7 9 3 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
E U A 3Y −1, 106 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
E U A 4 Y −1, 163 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
E U A 5Y −1, 34 5 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
E U A 7 Y −1, 9 8 5 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
E U A 8 Y −2, 216 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
E U A 9 Y −2, 205 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
E U A 10Y −2, 4 14 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
E U A 15Y −2, 9 23 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
E U A 20Y −2, 8 8 1 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
E U A 25Y −2, 8 9 9 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
E U A 30Y −2, 4 58 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
T ab ela C.1: T estes de Raız U nitaria - E U A.
A p end ice C . A p end ice - T este d e Raız U nitaria 98
B rasil
S eries t ob s t(1% ) t(5% ) t(10% ) Confi g . V ar. E x og enas
B RA 3M −2, 7 19 −3, 4 4 2 −2, 8 67 −2, 57 0 constante
B RA 6M −2, 657 −3, 4 4 2 −2, 8 67 −2, 57 0 constante
B RA 1Y −2, 64 7 −3, 4 4 2 −2, 8 67 −2, 57 0 constante
B RA 2Y −2, 64 8 −3, 4 4 2 −2, 8 67 −2, 57 0 constante
B RA 3Y −3, 024 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
B RA 4 Y −3, 24 5 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
B RA 5Y −3, 268 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
B RA 7 Y −3, 222 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
B RA 8 Y −2, 8 8 0 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
B RA 9 Y −3, 011 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
B RA 10Y −3, 250 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
B RA 15Y −2, 9 7 9 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
B RA 20Y −3, 062 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
B RA 25Y −3, 29 2 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
B RA 30Y −2, 68 3 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
T ab ela C.2: T estes de Raız U nitaria - B rasil.
C.2
T este d e Raız U nitaria: Corp orate Bond s
A p end ice C . A p end ice - T este d e Raız U nitaria 99
IN D AAA
S eries t ob s t(1% ) t(5% ) t(10% ) Confi g . V ar. E x og enas
IN D AAA 3M −0, 9 7 6 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D AAA 6M −0, 9 9 2 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D AAA 1Y −0, 8 9 5 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D AAA 2Y −1, 059 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D AAA 3Y −1, 265 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D AAA 4 Y −1, 4 4 5 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D AAA 5Y −1, 505 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D AAA 7 Y −1, 8 57 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D AAA 8 Y −2, 118 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D AAA 9 Y −2, 205 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D AAA 10Y −2, 333 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D AAA 15Y −3, 317 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D AAA 20Y −3, 4 24 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
T ab ela C.3: T estes de Raız U nitaria - IN D AAA.
IN D B −
S eries t ob s t(1% ) t(5% ) t(10% ) Confi g . V ar. E x og enas
IN D B − 3M −0, 54 1 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D B − 6M −0, 205 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D B − 1Y 0, 024 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D B − 2Y 0, 069 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D B − 3Y 0, 327 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D B − 4 Y 0, 327 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D B − 5Y 0, 27 0 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D B − 7 Y −0, 201 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D B − 8 Y 0, 08 6 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D B − 9 Y 0, 030 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D B − 10Y −0, 002 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D B − 15Y −0, 029 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D B − 20Y −0, 138 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
IN D B − 30Y −0, 257 −3, 9 7 5 −3, 4 18 −3, 131 constante e tend. linear
T ab ela C.4 : T estes de Raız U nitaria - IN D B -.
D
Ap end ice - Constru cao d e Dad os
D.1
Constru cao d e Dad os: S overeign Bond s
.00
.02
.04
.06
9 8 9 9 00 01 02 03 04 05 06 07 08
E U A 3 M
E U A 6 M
E U A 1 A
E U A 2 A
E U A 3 A
E U A 4 A
E U A 5 A
E U A 7 A
E U A 8 A
E U A 9 A
E U A 1 0A
E U A 1 5 A
E U A 2 0A
E U A 2 5 A
E U A 3 0A
F ig ura D .1: Y ields dos E U A. Ab cissa y rep resenta as tax as e x o temp o.
A p end ice D . A p end ice - C onstru cao d e D ad os 101
.01
.02
.03
.04
.05
.06
.07
9 8 9 9 00 01 02 03 04 05 06 07 08
A L M 3 M
A L M 6 M
A L M 1A
A L M 2 A
A L M 3 A
A L M 4 A
A L M 5 A
A L M 7 A
A L M 8 A
A L M 9 A
A L M 10A
A L M 15 A
A L M 2 0A
A L M 2 5 A
A L M 3 0A
F ig ura D .2: Y ields da Alemanh a. Ab cissa y rep resenta as tax as e x o temp o.
.0
.1
.2
.3
9 8 9 9 00 01 02 03 04 05 06 07 08
B R A 3 M
B R A 6 M
B R A 1A
B R A 2 A
B R A 3 A
B R A 4 A
B R A 5 A
B R A 7 A
B R A 8 A
B R A 9 A
B R A 10A
B R A 15 A
B R A 2 0A
B R A 2 5 A
B R A 3 0A
F ig ura D .3: Y ields do B rasil. Ab cissa y rep resenta as tax as e x o temp o.
A p end ice D . A p end ice - C onstru cao d e D ad os 102
.00
.05
.1 0
.1 5
9 8 9 9 00 01 02 03 04 05 06 07 08
M E X 3 M
M E X 6 M
M E X 1 A
M E X 2 A
M E X 3 A
M E X 4 A
M E X 5 A
M E X 7 A
M E X 8 A
M E X 9 A
M E X 1 0A
M E X 1 5 A
M E X 2 0A
M E X 2 5 A
M E X 3 0A
F ig ura D .4 : Y ields do M ex ico. Ab cissa y rep resenta as tax as e x o temp o.
.00
.05
.1 0
.1 5
9 8 9 9 00 01 02 03 04 05 06 07 08
C O L 3 M
C O L 6 M
C O L 1 A
C O L 2 A
C O L 3 A
C O L 4 A
C O L 5 A
C O L 7 A
C O L 8 A
C O L 9 A
C O L 1 0A
C O L 1 5 A
C O L 2 0A
C O L 2 5 A
C O L 3 0A
F ig ura D .5: Y ields da Colomb ia. Ab cissa y rep resenta as tax as e x o temp o.
A p end ice D . A p end ice - C onstru cao d e D ad os 103
E stados U nidos
M at (meses) M E D D P M IN M AX ρ(0, 2) ρ(1) ρ(3) ρ(6) ρ(12)
3 3,29 1 1,7 06 0,09 3 6,000 0,9 8 8 0,9 39 0,8 56 0,7 27 0,505
6 3,39 5 1,7 23 0,207 6,08 7 0,9 8 8 0,9 4 7 0,8 67 0,7 39 0,508
12 3,521 1,64 7 0,4 16 6,354 0,9 8 8 0,9 4 5 0,8 65 0,7 38 0,525
24 3,7 36 1,4 61 0,67 4 6,4 8 7 0,9 8 5 0,9 29 0,8 32 0,69 4 0,4 9 8
36 3,9 4 0 1,302 0,9 64 6,553 0,9 8 2 0,9 13 0,8 03 0,651 0,4 68
4 8 4 ,113 1,161 1,120 6,58 4 0,9 7 7 0,9 00 0,7 8 7 0,638 0,4 58
60 4 ,253 1,058 1,361 6,613 0,9 7 5 0,8 9 6 0,7 7 6 0,614 0,4 32
8 4 4 ,526 0,8 8 1 2,365 6,609 0,9 7 7 0,9 00 0,7 7 2 0,59 8 0,4 16
9 6 4 ,632 0,8 14 2,67 5 6,616 0,9 7 7 0,9 02 0,7 7 2 0,59 5 0,4 02
108 4 ,7 08 0,7 7 9 2,7 21 6,652 0,9 7 5 0,9 00 0,7 7 4 0,603 0,4 15
120 4 ,8 36 0,7 20 2,8 66 6,68 9 0,9 7 1 0,8 8 8 0,7 62 0,6 0,4 02
18 0 5,112 0,620 3,19 2 6,7 19 0,9 65 0,8 7 0 0,7 4 1 0,58 4 0,39 5
24 0 5,17 9 0,59 6 3,059 6,7 04 0,9 58 0,8 55 0,7 28 0,58 1 0,4 02
300 5,14 6 0,59 0 2,9 7 3 6,626 0,9 55 0,8 50 0,7 22 0,57 8 0,4 09
360 5,04 8 0,610 2,7 13 6,57 5 0,9 53 0,8 4 1 0,7 16 0,57 6 0,4 14
T ab ela D .1: E statısticas das series de tax as dos E U A, p ara maturidades e correlacoesmedidas em meses.
A p end ice D . A p end ice - C onstru cao d e D ad os 104
Alemanh a
M at (meses) M E D D P M IN M AX ρ(0, 2) ρ(1) ρ(3) ρ(6) ρ(12)
3 3,124 0,8 63 1,59 1 4 ,9 30 0,9 8 9 0,9 38 0,8 7 2 0,7 11 0,333
6 3,17 7 0,8 7 0 1,7 58 4 ,9 9 9 0,9 8 9 0,9 39 0,8 66 0,7 04 0,34 0
12 3,263 0,8 59 1,8 32 5,067 0,9 9 0,9 38 0,8 4 9 0,69 0 0,34 9
24 3,39 3 0,7 9 2 1,9 29 5,14 9 0,9 8 6 0,9 21 0,8 03 0,639 0,333
36 3,57 2 0,7 4 5 2,162 5,17 2 0,9 8 5 0,9 15 0,7 9 1 0,619 0,332
4 8 3,7 29 0,69 6 2,360 5,19 3 0,9 8 4 0,9 28 0,7 7 9 0,602 0,325
60 3,8 23 0,657 2,511 5,18 3 0,9 8 2 0,9 00 0,7 62 0,57 7 0,313
8 4 4 ,060 0,611 2,7 68 5,37 5 0,9 8 1 0,9 05 0,7 8 1 0,610 0,37 0
9 6 4 ,14 7 0,59 8 2,8 67 5,4 05 0,9 8 2 0,9 09 0,7 9 2 0,631 0,4 10
108 4 ,19 0 0,57 4 2,9 67 5,4 00 0,9 8 0 0,9 05 0,7 8 6 0,625 0,4 02
120 4 ,218 0,558 3,035 5,4 4 9 0,9 8 0 0,9 03 0,7 7 8 0,607 0,369
18 0 4 ,4 9 8 0,522 3,336 5,58 9 0,9 8 4 0,9 21 0,8 16 0,665 0,4 69
24 0 4 ,68 9 0,57 9 3,4 4 7 5,8 9 5 0,9 8 7 0,9 39 0,8 65 0,7 54 0,58 8
300 4 ,7 52 0,59 6 3,505 6,059 0,9 8 6 0,9 34 0,8 62 0,7 58 0,59 4
360 4 ,69 8 0,57 7 3,361 5,9 68 0,9 8 1 0,9 20 0,8 4 3 0,7 39 0,58 2
T ab ela D .2: E statısticas das series de tax as da Alemanh a, p ara maturidades ecorrelacoes medidas em meses.
B rasil
M at (meses) M E D D P M IN M AX ρ(0, 2) ρ(1) ρ(3) ρ(6) ρ(12)
3 6,24 1 3,7 7 2 1,015 28 ,4 4 0 0,9 7 0 0,8 4 0 0,64 0 0,34 0 0,08 0
6 6,4 4 6 3,8 18 1,09 7 28 ,7 22 0,9 7 0 0,8 50 0,650 0,360 0,08 0
12 6,7 56 3,8 56 1,8 13 29 ,528 0,9 8 0 0,8 50 0,660 0,360 0,120
24 7 ,531 3,7 57 3,166 29 ,64 3 0,9 8 0 0,8 50 0,650 0,37 0 0,19 0
36 8 ,4 50 3,9 23 3,68 6 27 ,8 37 0,9 8 0 0,8 8 0 0,7 00 0,4 7 0 0,28 0
4 8 9 ,114 4 ,051 4 ,08 3 25,8 11 0,9 9 0 0,9 00 0,7 4 0 0,500 0,29 0
60 9 ,4 9 6 4 ,016 4 ,38 5 26,14 9 0,9 9 0 0,9 10 0,7 50 0,520 0,310
8 4 9 ,8 56 3,9 19 4 ,8 36 25,319 0,9 9 0 0,9 20 0,7 7 0 0,550 0,330
9 6 10,08 7 3,9 05 5,08 0 25,4 58 0,9 9 0 0,9 30 0,7 8 0 0,560 0,360
108 10,258 3,8 7 2 5,24 5 24 ,604 0,9 9 0 0,9 4 0 0,7 9 0 0,58 0 0,4 00
120 10,332 3,8 55 5,363 24 ,9 7 6 0,9 9 0 0,9 30 0,7 9 0 0,600 0,4 10
18 0 10,7 9 8 3,8 02 5,67 4 25,202 0,9 9 0 0,9 4 0 0,8 10 0,610 0,4 20
24 0 10,59 0 3,527 5,8 00 22,4 8 9 0,9 9 0 0,9 4 0 0,8 10 0,630 0,4 4 0
300 10,68 5 3,4 20 5,8 34 22,168 0,9 9 0 0,9 4 0 0,8 10 0,620 0,4 10
360 10,667 3,7 12 5,67 3 25,18 7 0,9 9 0 0,9 4 0 0,8 10 0,620 0,4 30
T ab ela D .3: E statısticas das series de tax as do B rasil, p ara maturidades e correlacoesmedidas em meses.
A p end ice D . A p end ice - C onstru cao d e D ad os 105
M ex ico
M at(meses) M E D D P M IN M AX ρ(0, 2) ρ(1) ρ(3) ρ(6) ρ(12)
3 4 ,14 3 1,9 56 1,108 13,122 0,9 8 9 0,9 11 0,8 21 0,7 04 0,505
6 4 ,29 7 1,9 7 9 1,14 7 13,09 2 0,9 9 0,9 17 0,8 37 0,7 14 0,518
12 4 ,538 1,9 58 1,169 13,058 0,9 9 1 0,9 25 0,8 60 0,7 32 0,54
24 5,015 1,9 01 1,18 1 13,020 0,9 9 1 0,9 28 0,8 7 2 0,7 4 6 0,566
36 5,522 1,7 9 8 2,24 0 12,9 67 0,9 9 1 0,9 31 0,8 7 2 0,7 51 0,57 3
4 8 5,9 32 1,7 58 3,114 12,8 35 0,9 9 2 0,9 38 0,8 8 8 0,7 8 6 0,62
60 6,27 6 1,7 53 3,539 12,59 4 0,9 9 3 0,9 4 4 0,8 9 1 0,7 8 6 0,623
8 4 6,7 10 1,68 2 4 ,54 9 12,08 5 0,9 9 3 0,9 4 9 0,8 9 6 0,7 9 8 0,635
9 6 6,8 10 1,67 4 4 ,68 5 11,9 7 3 0,9 9 3 0,9 51 0,9 02 0,8 08 0,637
108 6,8 7 6 1,64 9 4 ,7 69 11,9 7 3 0,9 9 3 0,9 50 0,9 00 0,8 05 0,635
120 6,9 63 1,64 9 4 ,7 8 4 12,062 0,9 9 3 0,9 51 0,8 9 7 0,7 9 9 0,635
18 0 7 ,4 7 5 1,67 4 5,153 12,8 7 4 0,9 9 3 0,9 53 0,8 9 8 0,7 9 5 0,611
24 0 7 ,635 1,519 5,622 12,9 53 0,9 9 2 0,9 4 8 0,8 9 2 0,7 8 2 0,58
300 7 ,7 33 1,4 9 5 5,58 3 12,4 8 5 0,9 9 2 0,9 4 9 0,8 8 8 0,7 7 6 0,565
360 7 ,58 0 1,4 65 5,606 12,27 2 0,9 9 2 0,9 4 8 0,8 9 4 0,7 8 8 0,58 7
T ab ela D .4 : E statısticas das series de tax as do M ex ico, p ara maturidades e cor-relacoes medidas em meses.
Colomb ia
M at(meses) M E D D P M IN M AX ρ(0, 2) ρ(1) ρ(3) ρ(6) ρ(12)
3 4 ,9 8 0 1,9 63 1,238 12,8 21 0,9 7 7 0,8 52 0,7 17 0,64 2 0,4 7 4
6 5,14 5 1,9 66 1,366 12,9 01 0,9 7 9 0,8 62 0,7 27 0,627 0,4 58
12 5,39 3 2,037 1,601 12,9 9 7 0,9 8 6 0,8 9 0 0,7 54 0,608 0,4 4 0
24 6,154 2,210 2,54 1 13,121 0,9 9 0 0,9 09 0,7 68 0,616 0,4 14
36 7 ,126 2,38 2 3,7 12 13,7 59 0,9 9 0 0,9 20 0,7 9 4 0,67 3 0,4 62
4 8 7 ,69 6 2,4 03 4 ,4 09 14 ,34 4 0,9 9 1 0,9 30 0,8 08 0,69 5 0,4 8 9
60 8 ,09 2 2,338 4 ,67 1 14 ,19 0 0,9 9 2 0,9 35 0,8 17 0,68 9 0,4 65
8 4 8 ,59 9 2,29 4 5,051 14 ,231 0,9 9 2 0,9 34 0,8 19 0,68 7 0,4 7 1
9 6 8 ,7 4 8 2,307 5,24 2 14 ,223 0,9 9 2 0,9 38 0,8 30 0,7 09 0,501
108 8 ,8 7 2 2,28 5 5,368 14 ,4 7 5 0,9 9 2 0,9 38 0,8 32 0,7 11 0,517
120 8 ,9 65 2,233 5,4 37 14 ,654 0,9 9 2 0,9 39 0,8 36 0,7 12 0,508
18 0 9 ,4 8 1 2,34 9 5,9 4 3 14 ,622 0,9 9 4 0,9 4 9 0,8 55 0,7 4 2 0,54 2
24 0 9 ,4 8 8 2,320 6,08 7 14 ,602 0,9 9 4 0,9 35 0,8 51 0,7 4 5 0,561
300 9 ,4 52 2,14 8 6,14 6 14 ,09 8 0,9 9 3 0,9 4 5 0,8 53 0,7 4 0 0,531
360 9 ,4 19 2,050 6,14 4 13,8 4 7 0,9 9 2 0,9 4 2 0,8 4 7 0,7 39 0,527
T ab ela D .5: E statısticas das series de tax as da Colomb ia, p ara maturidades ecorrelacoes medidas em meses.
A p end ice D . A p end ice - C onstru cao d e D ad os 106
D.2
Constru cao d e Dad os: Corp orate Bond s
.00
.02
.04
.06
.08
.1 0
9 8 9 9 00 01 02 03 04 05 06 07 08
IN D A A A 3 M
IN D A A A 6M
IN D A A A 1 A
IN D A A A 2 A
IN D A A A 3 A
IN D A A A 4 A
IN D A A A 5 A
IN D A A A 7 A
IN D A A A 8 A
IN D A A A 9 A
IN D A A A 1 0A
IN D A A A 1 5 A
IN D A A A 2 0A
Figura D.6: Yields Industrial AAA. Abcissa y representa as taxas e x o tempo.
Apendice D. Apendice - Construcao de Dados 107
.00
.02
.04
.06
.08
.1 0
9 8 9 9 00 01 02 03 04 05 06 07 08
IN D A A 3 M
IN D A A 6 M
IN D A A 1 A
IN D A A 2 A
IN D A A 3 A
IN D A A 4 A
IN D A A 5 A
IN D A A 7 A
IN D A A 8 A
IN D A A 9 A
IN D A A 1 0A
IN D A A 1 5 A
IN D A A 2 0A
IN D A A 3 0A
Figura D.7 : Yields Industrial AA. Abcissa y representa as taxas e x o tempo.
.00
.02
.04
.06
.08
.1 0
9 8 9 9 00 01 02 03 04 05 06 07 08
IN D A + 3 M
IN D A + 6 M
IN D A + 1 A
IN D A + 2 A
IN D A + 3 A
IN D A + 4 A
IN D A + 5 A
IN D A + 7 A
IN D A + 8 A
IN D A + 9 A
IN D A + 1 0A
IN D A + 1 5 A
IN D A + 2 0A
IN D A + 3 0A
Figura D.8 : Yields Industrial A+ . Abcissa y representa as taxas e x o tempo.
Apendice D. Apendice - Construcao de Dados 108
.00
.02
.04
.06
.08
.1 0
9 8 9 9 00 01 02 03 04 05 06 07 08
IN D A 3 M
IN D A 6 M
IN D A 1 A
IN D A 2 A
IN D A 3 A
IN D A 4 A
IN D A 5 A
IN D A 7 A
IN D A 8 A
IN D A 9 A
IN D A 1 0A
IN D A 1 5 A
IN D A 2 0A
IN D A 3 0A
Figura D.9 : Yields Industrial A. Abcissa y representa as taxas e x o tempo.
.00
.02
.04
.06
.08
.1 0
9 8 9 9 00 01 02 03 04 05 06 07 08
IN D A - 3 M
IN D A - 6 M
IN D A - 1 A
IN D A - 2 A
IN D A - 3 A
IN D A - 4 A
IN D A - 5 A
IN D A - 7 A
IN D A - 8 A
IN D A - 9 A
IN D A - 1 0A
IN D A - 1 5 A
IN D A - 2 0A
IN D A - 3 0A
Figura D.1 0 : Yields Industrial A−. Abcissa y representa as taxas e x o tempo.
Apendice D. Apendice - Construcao de Dados 109
.00
.02
.04
.06
.08
.1 0
9 8 9 9 00 01 02 03 04 05 06 07 08
IN D B B B + 3 M
IN D B B B + 6 M
IN D B B B + 1 A
IN D B B B + 2 A
IN D B B B + 3 A
IN D B B B + 4 A
IN D B B B + 5 A
IN D B B B + 7 A
IN D B B B + 8 A
IN D B B B + 9 A
IN D B B B + 1 0A
IN D B B B + 1 5 A
IN D B B B + 2 0A
IN D B B B + 3 0A
Figura D.1 1 : Yields Industrial B B B + . Abcissa y representa as taxas e x o tempo.
Apendice D. Apendice - Construcao de Dados 110
.00
.02
.04
.06
.08
.1 0
9 8 9 9 00 01 02 03 04 05 06 07 08
IN D B B B 3 M
IN D B B B 6 M
IN D B B B 1 A
IN D B B B 2 A
IN D B B B 3 A
IN D B B B 4 A
IN D B B B 5 A
IN D B B B 7 A
IN D B B B 8 A
IN D B B B 9 A
IN D B B B 1 0A
IN D B B B 1 5 A
IN D B B B 2 0A
IN D B B B 3 0A
Figura D.1 2 : Yields Industrial B B B . Abcissa y representa as taxas e x o tempo.
.00
.02
.04
.06
.08
.1 0
9 8 9 9 00 01 02 03 04 05 06 07 08
IN D B B B - 3 M
IN D B B B - 6 M
IN D B B B - 1 A
IN D B B B - 2 A
IN D B B B - 3 A
IN D B B B - 4 A
IN D B B B - 5 A
IN D B B B - 7 A
IN D B B B - 8 A
IN D B B B - 9 A
IN D B B B - 1 0A
IN D B B B - 1 5 A
IN D B B B - 2 0A
IN D B B B - 3 0A
Figura D.1 3 : Yields Industrial B B B −. Abcissa y representa as taxas e x o tempo.
Apendice D. Apendice - Construcao de Dados 111
.00
.04
.08
.1 2
9 8 9 9 00 01 02 03 04 05 06 07 08
IN D B B + 3 M
IN D B B + 6 M
IN D B B + 1 A
IN D B B + 2 A
IN D B B + 3 A
IN D B B + 4 A
IN D B B + 5 A
IN D B B + 7 A
IN D B B + 8 A
IN D B B + 9 A
IN D B B + 1 0A
IN D B B + 1 5 A
IN D B B + 2 0A
IN D B B + 3 0A
Figura D.1 4 : Yields Industrial B B + . Abcissa y representa as taxas e x o tempo.
.00
.04
.08
.1 2
9 8 9 9 00 01 02 03 04 05 06 07 08
IN D B B 3 M
IN D B B 6 M
IN D B B 1 A
IN D B B 2 A
IN D B B 3 A
IN D B B 4 A
IN D B B 5 A
IN D B B 7 A
IN D B B 8 A
IN D B B 9 A
IN D B B 1 0A
IN D B B 1 5 A
IN D B B 2 0A
IN D B B 3 0A
Figura D.1 5 : Yields Industrial B B . Abcissa y representa as taxas e x o tempo.
Apendice D. Apendice - Construcao de Dados 112
.00
.05
.1 0
.1 5
9 8 9 9 00 01 02 03 04 05 06 07 08
IN D B B - 3 M
IN D B B - 6 M
IN D B B - 1 A
IN D B B - 2 A
IN D B B - 3 A
IN D B B - 4 A
IN D B B - 5 A
IN D B B - 7 A
IN D B B - 8 A
IN D B B - 9 A
IN D B B - 1 0A
IN D B B - 1 5 A
IN D B B - 2 0A
Figura D.1 6: Yields Industrial B B −. Abcissa y representa as taxas e x o tempo.
.00
.05
.1 0
.1 5
9 8 9 9 00 01 02 03 04 05 06 07 08
IN D B + 3 M
IN D B + 6 M
IN D B + 1 A
IN D B + 2 A
IN D B + 3 A
IN D B + 4 A
IN D B + 5 A
IN D B + 7 A
IN D B + 8 A
IN D B + 9 A
IN D B + 1 0A
IN D B + 1 5 A
IN D B + 2 0A
IN D B + 3 0A
Figura D.1 7 : Yields Industrial B + . Abcissa y representa as taxas e x o tempo.
Apendice D. Apendice - Construcao de Dados 113
.00
.05
.1 0
.1 5
9 8 9 9 00 01 02 03 04 05 06 07 08
IN D B 3 M
IN D B 6 M
IN D B 1 A
IN D B 2 A
IN D B 3 A
IN D B 4 A
IN D B 5 A
IN D B 7 A
IN D B 8 A
IN D B 9 A
IN D B 1 0A
IN D B 1 5 A
IN D B 2 0A
IN D B 3 0A
Figura D.1 8 : Yields Industrial B . Abcissa y representa as taxas e x o tempo.
.00
.05
.1 0
.1 5
9 8 9 9 00 01 02 03 04 05 06 07 08
IN D B - 3 M
IN D B - 6 M
IN D B - 1 A
IN D B - 2 A
IN D B - 3 A
IN D B - 4 A
IN D B - 5 A
IN D B - 7 A
IN D B - 8 A
IN D B - 9 A
IN D B - 1 0A
IN D B - 1 5 A
IN D B - 2 0A
IN D B - 3 0A
Figura D.1 9 : Yields Industrial B −. Abcissa y representa as taxas e x o tempo.
Apendice D. Apendice - Construcao de Dados 114
.00
.02
.04
.06
.08
.1 0
9 8 9 9 00 01 02 03 04 05 06 07 08
B A N K A 3 M
BANK A 6M
BANK A 1 A
BANK A 2 A
BANK A 3 A
BANK A 4 A
BANK A 5 A
BANK A 7 A
BANK A 8 A
BANK A 9 A
BANK A 1 0 A
BANK A 1 5 A
BANK A 2 0 A
Figura D.20: Yields Bank A. Abcissa y representa as taxas e x o tempo.
.00
.02
.04
.06
.08
.1 0
9 8 9 9 00 01 02 03 04 05 06 07 08
B A N K B B B 3 M
B A N K B B B 6 M
B A N K B B B 1 A
B A N K B B B 2 A
B A N K B B B 3 A
B A N K B B B 4 A
B A N K B B B 5 A
B A N K B B B 7 A
B A N K B B B 8 A
B A N K B B B 9 A
B A N K B B B 1 0A
B A N K B B B 1 5 A
Figura D.21: Yields Bank B B B . Abcissa y representa as taxas e x o tempo.
Apendice D. Apendice - Construcao de Dados 115
.00
.02
.04
.06
.08
.1 0
9 8 9 9 00 01 02 03 04 05 06 07 08
R E T A A 3 M
R E T A A 6 M
R E T A A 1 A
R E T A A 2 A
R E T A A 3 A
R E T A A 4 A
R E T A A 5 A
R E T A A 7 A
R E T A A 8 A
R E T A A 9 A
R E T A A 1 0A
R E T A A 1 5 A
R E T A A 2 0A
Figura D.22: Yields R etail AA. Abcissa y representa as taxas e x o tempo.
.00
.02
.04
.06
.08
.1 0
9 8 9 9 00 01 02 03 04 05 06 07 08
R E T A 3 M
R E T A 6 M
R E T A 1 A
R E T A 2 A
R E T A 3 A
R E T A 4 A
R E T A 5 A
R E T A 7 A
R E T A 8 A
R E T A 9 A
R E T A 1 0A
R E T A 1 5 A
R E T A 2 0A
R E T A 3 0A
Figura D.23: Yields R etail A. Abcissa y representa as taxas e x o tempo.
Apendice D. Apendice - Construcao de Dados 116
.00
.02
.04
.06
.08
.1 0
9 8 9 9 00 01 02 03 04 05 06 07 08
R E T B B B 3 M
R E T B B B 6 M
R E T B B B 1 A
R E T B B B 2 A
R E T B B B 3 A
R E T B B B 4 A
R E T B B B 5 A
R E T B B B 7 A
R E T B B B 8 A
R E T B B B 9 A
R E T B B B 1 0A
R E T B B B 1 5 A
R E T B B B 2 0A
R E T B B B 3 0A
Figura D.24: Yields R etail B B B . Abcissa y representa as taxas e x o tempo.
Apendice D. Apendice - Construcao de Dados 117
Ind ustrial AAA
M at(meses) M E D DP M IN M AX ρ(3) ρ(12) ρ(18)
3 3, 763 1, 713 0, 979 6, 598 0, 915 0, 552 0, 241
6 3, 853 1, 701 1, 015 6, 807 0, 981 0, 566 0, 250
12 3, 957 1, 618 1, 009 7, 055 0, 913 0, 565 0, 258
24 4, 180 1, 448 1, 268 7, 152 0, 901 0, 562 0, 269
36 4, 436 1, 284 1, 632 7, 195 0, 884 0, 561 0, 284
48 4, 667 1, 126 2, 090 7, 232 0, 861 0, 534 0, 295
60 4, 808 1, 038 2, 400 7, 243 0, 852 0, 526 0, 302
84 5, 087 0, 882 2, 975 7, 310 0, 844 0, 519 0, 326
96 5, 214 0, 818 3, 314 7, 320 0, 845 0, 507 0, 317
108 5, 293 0, 780 3, 499 7, 329 0, 845 0, 494 0, 308
120 5, 344 0, 747 3, 628 7, 325 0, 839 0, 481 0, 299
180 5, 670 0, 636 4, 300 7, 329 0, 828 0, 491 0, 344
240 5, 826 0, 592 4, 626 7, 333 0, 840 0, 507 0, 365
Ind ustrial AA
M at(meses) M E D DP M IN M AX ρ(3) ρ(12) ρ(18)
3 3, 842 1, 696 1, 043 6, 691 0, 924 0, 556 0, 242
6 3, 926 1, 685 1, 132 6, 857 0, 927 0, 570 0, 251
12 4, 033 1, 596 1, 193 7, 079 0, 920 0, 569 0, 261
24 4, 257 1, 425 1, 425 7, 173 0, 906 0, 565 0, 275
36 4, 520 1, 257 1, 811 7, 245 0, 895 0, 568 0, 239
48 4, 744 1, 111 2, 240 7, 279 0, 874 0, 544 0, 302
60 4, 896 1, 024 2, 474 7, 314 0, 870 0, 534 0, 306
84 5, 186 0, 873 3, 223 7, 372 0, 858 0, 520 0, 326
96 5, 307 0, 819 3, 470 7, 392 0, 857 0, 514 0, 319
108 5, 382 0, 786 3, 633 7, 394 0, 860 0, 505 0, 311
120 5, 430 0, 758 3, 818 7, 420 0, 852 0, 491 0, 302
180 5, 766 0, 650 4, 513 7, 455 0, 832 0, 506 0, 345
240 5, 933 0, 607 4, 800 7, 500 0, 855 0, 528 0, 377
360 5, 935 0, 634 4, 852 7, 461 0, 870 0, 576 0, 427
Apendice D. Apendice - Construcao de Dados 118
Ind ustrial A+
M at(meses) M E D DP M IN M AX ρ(3) ρ(12) ρ(18)
3 3, 921 1, 744 0, 977 6, 952 0, 932 0, 578 0, 263
6 4, 006 1, 675 1, 149 7, 001 0, 933 0, 582 0, 268
12 4, 165 1, 550 1, 393 7, 090 0, 933 0, 588 0, 278
24 4, 445 1, 353 1, 820 7, 236 0, 928 0, 592 0, 294
36 4, 682 1, 207 2, 182 7, 350 0, 918 0, 585 0, 307
48 4, 881 1, 099 2, 509 7, 438 0, 905 0, 573 0, 316
60 5, 051 1, 017 2, 802 7, 505 0, 893 0, 559 0, 324
84 5, 321 0, 905 3, 304 7, 598 0, 873 0, 536 0, 338
96 5, 428 0, 865 3, 518 7, 629 0, 866 0, 530 0, 344
108 5, 521 0, 831 3, 710 7, 653 0, 861 0, 526 0, 351
120 5, 602 0, 803 3, 883 7, 672 0, 859 0, 525 0, 341
180 5, 881 0, 712 4, 524 7, 717 0, 857 0, 541 0, 390
240 6, 039 0, 663 4, 866 7, 729 0, 858 0, 565 0, 426
360 6, 204 0, 620 5, 004 7, 732 0, 852 0, 616 0, 482
Ind ustrial A
M at(meses) M E D DP M IN M AX ρ(3) ρ(12) ρ(18)
3 4, 045 1, 658 1, 168 6, 854 0, 932 0, 565 0, 255
6 4, 126 1, 659 1, 207 7, 124 0, 936 0, 579 0, 265
12 4, 236 1, 575 1, 344 7, 297 0, 928 0, 578 0, 278
24 4, 472 1, 406 1, 751 7, 455 0, 916 0, 580 0, 294
36 4, 756 1, 240 2, 192 7, 540 0, 910 0, 591 0, 321
48 4, 982 1, 105 2, 575 7, 589 0, 902 0, 585 0, 338
60 5, 137 1, 041 2, 808 7, 613 0, 891 0, 578 0, 350
84 5, 434 0, 912 3, 517 7, 685 0, 878 0, 554 0, 373
96 5, 627 0, 829 3, 934 7, 770 0, 875 0, 548 0, 365
108 5, 552 0, 866 3, 834 7, 729 0, 873 0, 544 0, 356
120 5, 673 0, 805 4, 085 7, 759 0, 866 0, 543 0, 345
180 6, 059 0, 711 4, 840 7, 811 0, 856 0, 560 0, 395
240 6, 223 0, 692 4, 992 7, 909 0, 877 0, 583 0, 431
360 6, 219 0, 706 4, 972 7, 922 0, 855 0, 637 0, 485
Ind ustrial A−
M at(meses) M E D DP M IN M AX ρ(3) ρ(12) ρ(18)
3 4, 171 1, 629 1, 210 6, 969 0, 937 0, 568 0, 259
6 4, 260 1, 628 1, 296 7, 158 0, 941 0, 584 0, 271
12 4, 378 1, 533 1, 478 7, 358 0, 933 0, 584 0, 284
24 4, 622 1, 367 1, 956 7, 509 0, 922 0, 588 0, 303
36 4, 902 1, 221 2, 366 7, 646 0, 909 0, 593 0, 329
48 5, 125 1, 100 2, 755 7, 722 0, 904 0, 586 0, 348
60 5, 291 1, 028 3, 082 7, 728 0, 892 0, 583 0, 361
84 5, 592 0, 918 3, 683 7, 800 0, 881 0, 584 0, 394
96 5, 706 0, 879 3, 941 7, 857 0, 873 0, 580 0, 390
108 5, 782 0, 850 4, 054 7, 890 0, 869 0, 567 0, 383
120 5, 830 0, 821 4, 281 7, 900 0, 863 0, 559 0, 381
180 6, 212 0, 736 4, 930 7, 940 0, 854 0, 599 0, 414
240 6, 382 0, 718 5, 053 8, 042 0, 875 0, 623 0, 436
360 6, 383 0, 709 5, 089 8, 079 0, 884 0, 633 0, 461
Apendice D. Apendice - Construcao de Dados 119
Ind ustrial B B B +
M at(meses) M E D DP M IN M AX ρ(3) ρ(12) ρ(18)
3 4, 293 1, 613 1, 356 7, 141 0, 937 0, 572 0, 266
6 4, 378 1, 611 1, 408 7, 262 0, 941 0, 588 0, 277
12 4, 501 1, 519 1, 588 7, 559 0, 934 0, 587 0, 289
24 4, 763 1, 354 2, 060 7, 668 0, 924 0, 593 0, 309
36 5, 034 1, 220 2, 464 7, 820 0, 909 0, 598 0, 333
48 5, 262 1, 101 2, 861 7, 890 0, 905 0, 594 0, 353
60 5, 430 1, 034 3, 171 7, 920 0, 894 0, 588 0, 363
84 5, 737 0, 922 3, 771 8, 003 0, 882 0, 590 0, 396
96 5, 841 0, 884 3, 990 8, 062 0, 872 0, 586 0, 392
108 5, 922 0, 848 4, 122 8, 095 0, 866 0, 573 0, 385
120 5, 985 0, 810 4, 435 8, 106 0, 865 0, 565 0, 383
180 6, 361 0, 712 5, 216 8, 235 0, 836 0, 605 0, 416
240 6, 532 0, 688 5, 274 8, 195 0, 853 0, 630 0, 438
360 6, 552 0, 690 5, 255 8, 188 0, 871 0, 640 0, 464
Ind ustrial B B B
M at(meses) M E D DP M IN M AX ρ(3) ρ(12) ρ(18)
3 4, 413 1, 568 1, 516 7, 240 0, 937 0, 568 0, 265
6 4, 505 1, 569 1, 614 7, 334 0, 941 0, 584 0, 276
12 4, 633 1, 481 1, 773 7, 602 0, 932 0, 583 0, 289
24 4, 893 1, 322 2, 311 7, 754 0, 922 0, 591 0, 312
36 5, 164 1, 188 2, 644 7, 901 0, 904 0, 596 0, 337
48 5, 393 1, 072 3, 090 7, 999 0, 897 0, 592 0, 358
60 5, 569 1, 008 3, 378 8, 057 0, 884 0, 579 0, 367
84 5, 873 0, 904 3, 977 8, 127 0, 870 0, 580 0, 400
96 5, 986 0, 866 4, 217 8, 143 0, 856 0, 576 0, 397
108 6, 077 0, 829 4, 351 8, 188 0, 849 0, 561 0, 389
120 6, 144 0, 794 4, 589 8, 193 0, 841 0, 537 0, 387
180 6, 539 0, 714 5, 318 8, 497 0, 809 0, 575 0, 421
240 6, 704 0, 692 5, 397 8, 472 0, 826 0, 582 0, 443
360 6, 720 0, 681 5, 339 8, 304 0, 851 0, 617 0, 469
Ind ustrial B B B −
M at(meses) M E D DP M IN M AX ρ(3) ρ(12) ρ(18)
3 4, 613 1, 531 1, 726 7, 555 0, 937 0, 580 0, 275
6 4, 716 1, 530 1, 821 7, 529 0, 940 0, 593 0, 287
12 4, 846 1, 452 1, 938 7, 754 0, 931 0, 585 0, 295
24 5, 101 1, 315 2, 504 7, 994 0, 917 0, 591 0, 314
36 5, 376 1, 193 2, 917 8, 134 0, 902 0, 591 0, 337
48 5, 595 1, 096 3, 371 8, 228 0, 900 0, 598 0, 359
60 5, 771 1, 035 3, 631 8, 259 0, 887 0, 588 0, 362
84 6, 087 0, 923 4, 213 8, 377 0, 872 0, 585 0, 395
96 6, 200 0, 888 4, 395 8, 427 0, 860 0, 580 0, 391
108 6, 289 0, 848 4, 530 8, 447 0, 848 0, 572 0, 378
120 6, 366 0, 820 4, 760 8, 469 0, 844 0, 563 0, 375
180 6, 726 0, 747 5, 497 8, 772 0, 799 0, 567 0, 385
240 6, 892 0, 712 5, 552 8, 723 0, 812 0, 586 0, 413
360 6, 918 0, 697 5, 570 8, 577 0, 835 0, 621 0, 420
Apendice D. Apendice - Construcao de Dados 12 0
Ind ustrial B B +
M at(meses) M E D DP M IN M AX ρ(3) ρ(12) ρ(18)
3 5, 472 1, 497 2, 207 8, 750 0, 889 0, 410 0, 176
6 5, 551 1, 479 2, 277 8, 851 0, 897 0, 437 0, 200
12 5, 706 1, 414 2, 609 8, 900 0, 892 0, 463 0, 232
24 5, 982 1, 301 3, 238 8, 937 0, 894 0, 532 0, 307
36 6, 264 1, 199 3, 739 9, 030 0, 880 0, 550 0, 330
48 6, 490 1, 137 4, 120 9, 075 0, 880 0, 554 0, 339
60 6, 700 1, 110 4, 410 9, 482 0, 842 0, 541 0, 339
84 6, 977 1, 061 4, 885 10, 021 0, 797 0, 521 0, 332
96 7, 094 1, 048 5, 126 10, 310 0, 780 0, 516 0, 333
108 7, 204 1, 029 5, 316 10, 377 0, 772 0, 507 0, 328
120 7, 315 1, 007 5, 493 10, 373 0, 771 0, 500 0, 320
180 7, 636 1, 007 5, 853 10, 899 0, 727 0, 479 0, 298
240 7, 767 1, 010 5, 904 10, 950 0, 722 0, 481 0, 293
360 7, 747 1, 046 5, 796 10, 837 0, 755 0, 517 0, 328
Ind ustrial B B
M at(meses) M E D DP M IN M AX ρ(3) ρ(12) ρ(18)
3 5, 787 1, 503 2, 534 9, 898 0, 846 0, 415 0, 188
6 5, 872 1, 472 2, 603 9, 562 0, 854 0, 444 0, 216
12 6, 040 1, 415 2, 931 10, 049 0, 837 0, 465 0, 241
24 6, 343 1, 294 3, 974 10, 407 0, 835 0, 511 0, 298
36 6, 636 1, 213 4, 465 10, 849 0, 811 0, 517 0, 314
48 6, 889 1, 144 4, 907 10, 624 0, 814 0, 520 0, 324
60 7, 094 1, 129 5, 204 11, 077 0, 777 0, 516 0, 329
84 7, 379 1, 098 5, 534 11, 350 0, 736 0, 505 0, 333
96 7, 509 1, 099 5, 670 11, 787 0, 706 0, 484 0, 323
108 7, 617 1, 077 5, 802 11, 916 0, 702 0, 478 0, 315
120 7, 732 1, 059 5, 907 11, 950 0, 699 0, 468 0, 307
180 8, 079 1, 037 6, 275 12, 553 0, 643 0, 417 0, 263
240 8, 220 1, 041 6, 289 12, 617 0, 643 0, 420 0, 261
360 8, 236 1, 029 6, 251 12, 345 0, 668 0, 443 0, 271
Ind ustrial B B −
M at(meses) M E D DP M IN M AX ρ(3) ρ(12) ρ(18)
3 6, 059 1, 608 2, 689 10, 302 0, 843 0, 434 0, 202
6 6, 144 1, 574 2, 758 10, 151 0, 849 0, 456 0, 223
12 6, 317 1, 518 3, 088 10, 654 0, 838 0, 478 0, 249
24 6, 646 1, 404 4, 107 11, 119 0, 837 0, 510 0, 285
36 6, 937 1, 331 4, 542 11, 595 0, 818 0, 516 0, 298
48 7, 208 1, 275 4, 979 11, 415 0, 826 0, 529 0, 314
60 7, 413 1, 256 5, 297 11, 920 0, 794 0, 529 0, 319
84 7, 696 1, 223 5, 628 12, 298 0, 754 0, 521 0, 326
96 7, 822 1, 217 5, 801 12, 740 0, 728 0, 513 0, 326
108 7, 918 1, 189 5, 927 12, 868 0, 725 0, 515 0, 329
120 8, 018 1, 167 6, 015 12, 878 0, 721 0, 512 0, 326
180 8, 391 1, 163 6, 362 13, 432 0, 687 0, 480 0, 307
240 8, 554 1, 183 6, 458 13, 471 0, 705 0, 500 0, 321
Apendice D. Apendice - Construcao de Dados 12 1
Ind ustrial B +
M at(meses) M E D DP M IN M AX ρ(3) ρ(12) ρ(18)
3 6, 371 1, 574 3, 294 11, 213 0, 817 0, 446 0, 221
6 6, 459 1, 570 3, 362 11, 489 0, 805 0, 456 0, 237
12 6, 645 1, 492 3, 691 11, 599 0, 806 0, 486 0, 266
24 6, 999 1, 349 4, 454 11, 953 0, 802 0, 505 0, 296
36 7, 317 1, 267 5, 151 12, 372 0, 779 0, 506 0, 300
48 7, 578 1, 223 5, 491 12, 279 0, 777 0, 519 0, 315
60 7, 777 1, 224 5, 863 12, 777 0, 743 0, 512 0, 313
84 8, 045 1, 213 6, 117 13, 016 0, 720 0, 517 0, 326
96 8, 160 1, 226 6, 220 13, 488 0, 697 0, 513 0, 331
108 8, 240 1, 221 6, 237 13, 641 0, 697 0, 514 0, 333
120 8, 326 1, 205 6, 324 13, 624 0, 694 0, 514 0, 330
180 8, 696 1, 209 6, 785 14, 129 0, 669 0, 484 0, 312
240 8, 848 1, 231 6, 805 14, 165 0, 686 0, 510 0, 331
360 8, 882 1, 250 6, 783 13, 975 0, 714 0, 547 0, 357
Ind ustrial B
M at(meses) M E D DP M IN M AX ρ(3) ρ(12) ρ(18)
3 6, 786 1, 726 3, 484 11, 445 0, 814 0, 424 0, 219
6 6, 900 1, 717 3, 548 11, 755 0, 804 0, 437 0, 235
12 7, 103 1, 634 3, 893 11, 785 0, 809 0, 469 0, 266
24 7, 480 1, 458 5, 038 12, 214 0, 812 0, 504 0, 312
36 7, 810 1, 383 5, 627 12, 661 0, 798 0, 501 0, 308
48 8, 103 1, 353 5, 990 12, 588 0, 802 0, 520 0, 328
60 8, 297 1, 368 6, 198 13, 087 0, 791 0, 540 0, 339
84 8, 567 1, 381 6, 405 13, 320 0, 780 0, 548 0, 352
96 8, 671 1, 399 6, 445 13, 801 0, 764 0, 550 0, 360
108 8, 751 1, 405 6, 464 13, 950 0, 765 0, 565 0, 375
120 8, 810 1, 399 6, 465 13, 928 0, 762 0, 577 0, 378
180 9, 173 1, 410 6, 846 14, 427 0, 747 0, 548 0, 362
240 9, 323 1, 463 6, 860 14, 476 0, 762 0, 567 0, 378
360 9, 372 1, 507 6, 845 14, 269 0, 785 0, 581 0, 380
Apendice D. Apendice - Construcao de Dados 12 2
Ind ustrial B −
M at(meses) M E D DP M IN M AX ρ(3) ρ(12) ρ(18)
3 7, 417 2, 013 3, 931 13, 115 0, 798 0, 443 0, 255
6 7, 546 1, 996 4, 249 13, 482 0, 783 0, 457 0, 273
12 7, 751 1, 933 4, 602 13, 494 0, 789 0, 492 0, 297
24 8, 207 1, 744 5, 718 13, 905 0, 788 0, 523 0, 336
36 8, 633 1, 630 6, 329 14, 355 0, 766 0, 516 0, 322
48 8, 941 1, 585 6, 715 14, 398 0, 765 0, 537 0, 337
60 9, 177 1, 632 6, 833 14, 738 0, 761 0, 548 0, 344
84 9, 448 1, 669 6, 822 14, 736 0, 761 0, 565 0, 362
96 9, 535 1, 717 6, 724 15, 154 0, 759 0, 574 0, 376
108 9, 620 1, 745 6, 675 15, 269 0, 763 0, 579 0, 380
120 9, 674 1, 767 6, 728 15, 280 0, 770 0, 587 0, 380
180 9, 946 1, 795 7, 020 15, 833 0, 748 0, 570 0, 373
240 10, 049 1, 842 6, 977 15, 876 0, 751 0, 574 0, 372
360 10, 071 1, 831 6, 993 15, 645 0, 760 0, 579 0, 374
T abela D.6: E statısticas d as series d o ramo ind ustrial para d iferentes ratings, paramaturid ad es e correlacoes med id as em meses.
R etail AA
M at(meses) M E D DP M IN M AX ρ(3) ρ(12) ρ(18)
3 3, 820 1, 747 1, 009 6, 923 0, 929 0, 562 0, 247
6 3, 880 1, 734 1, 023 6, 955 0, 928 0, 574 0, 257
12 3, 989 1, 648 1, 120 7, 189 0, 919 0, 573 0, 264
24 4, 223 1, 476 1, 236 7, 189 0, 900 0, 561 0, 278
36 4, 482 1, 275 1, 726 7, 254 0, 899 0, 565 0, 291
48 4, 687 1, 132 2, 116 7, 301 0, 876 0, 542 0, 294
60 4, 868 1, 032 2, 452 7, 360 0, 871 0, 521 0, 296
84 5, 187 0, 856 3, 301 7, 444 0, 845 0, 495 0, 315
96 5, 286 0, 814 3, 542 7, 464 0, 848 0, 506 0, 329
108 5, 377 0, 770 3, 677 7, 505 0, 846 0, 499 0, 325
120 5, 453 0, 736 3, 814 7, 511 0, 833 0, 481 0, 314
180 5, 747 0, 664 4, 184 7, 527 0, 813 0, 465 0, 342
240 5, 977 0, 586 4, 783 7, 520 0, 823 0, 498 0, 356
Apendice D. Apendice - Construcao de Dados 12 3
R etail A
M at(meses) M E D DP M IN M AX ρ(3) ρ(12) ρ(18)
3 4, 033 1, 744 1, 066 7, 321 0, 924 0, 549 0, 246
6 4, 093 1, 714 1, 152 7, 280 0, 928 0, 558 0, 254
12 4, 207 1, 626 1, 312 7, 440 0, 928 0, 571 0, 270
24 4, 468 1, 432 1, 720 7, 466 0, 919 0, 584 0, 301
36 4, 694 1, 287 1, 955 7, 513 0, 909 0, 578 0, 319
48 4, 918 1, 136 2, 479 7, 535 0, 899 0, 576 0, 333
60 5, 109 1, 045 2, 655 7, 561 0, 886 0, 566 0, 345
84 5, 438 0, 896 3, 613 7, 620 0, 869 0, 572 0, 367
96 5, 548 0, 859 3, 858 7, 676 0, 861 0, 585 0, 383
108 5, 630 0, 830 3, 972 7, 718 0, 860 0, 573 0, 401
120 5, 705 0, 803 4, 088 7, 763 0, 854 0, 566 0, 397
180 6, 126 0, 689 4, 864 7, 855 0, 792 0, 513 0, 432
240 6, 329 0, 675 5, 015 7, 933 0, 829 0, 577 0, 384
360 6, 285 0, 705 4, 996 7, 988 0, 845 0, 583 0, 386
R etail B B B
M at(meses) M E D DP M IN M AX ρ(3) ρ(12) ρ(18)
3 4, 479 1, 689 1, 279 8, 210 0, 923 0, 535 0, 234
6 4, 571 1, 663 1, 311 8, 337 0, 927 0, 554 0, 248
12 4, 737 1, 557 1, 785 8, 390 0, 926 0, 564 0, 267
24 4, 980 1, 415 2, 236 8, 493 0, 916 0, 564 0, 290
36 5, 236 1, 266 2, 698 8, 678 0, 901 0, 557 0, 306
48 5, 493 1, 152 3, 214 8, 794 0, 897 0, 553 0, 318
60 5, 696 1, 119 3, 372 8, 851 0, 887 0, 541 0, 318
84 6, 084 0, 995 4, 110 9, 028 0, 862 0, 500 0, 286
96 6, 218 0, 975 4, 421 9, 083 0, 844 0, 486 0, 280
108 6, 313 0, 963 4, 447 9, 139 0, 837 0, 470 0, 267
120 6, 384 0, 949 4, 480 9, 154 0, 840 0, 472 0, 272
180 6, 717 0, 851 4, 991 9, 107 0, 811 0, 442 0, 247
240 6, 932 0, 794 5, 686 9, 090 0, 811 0, 483 0, 276
360 6, 973 0, 817 5, 684 9, 194 0, 814 0, 468 0, 271
T abela D.7: E statısticas d as series d o ramo retail para d iferentes ratings, paramaturid ad es e correlacoes med id as em meses.
Apendice D. Apendice - Construcao de Dados 12 4
Bank A
M at(meses) M E D DP M IN M AX ρ(3) ρ(12) ρ(18)
3 4, 054 1, 725 1, 094 6, 958 0, 942 0, 579 0, 276
6 4, 173 1, 734 1, 089 7, 277 0, 947 0, 587 0, 281
12 4, 322 1, 608 1, 237 7, 392 0, 941 0, 597 0, 300
24 4, 627 1, 400 1, 720 7, 539 0, 930 0, 611 0, 332
36 4, 919 1, 220 2, 354 7, 585 0, 917 0, 609 0, 353
48 5, 160 1, 092 2, 646 7, 624 0, 904 0, 604 0, 379
60 5, 296 1, 024 3, 055 7, 720 0, 898 0, 606 0, 385
84 5, 667 0, 890 3, 838 7, 839 0, 891 0, 607 0, 419
96 5, 771 0, 852 3, 896 7, 900 0, 877 0, 569 0, 399
108 5, 810 0, 833 3, 985 7, 913 0, 869 0, 569 0, 395
120 5, 881 0, 825 4, 040 8, 009 0, 857 0, 569 0, 390
180 6, 200 0, 835 4, 526 8, 066 0, 861 0, 632 0, 428
240 6, 460 0, 742 5, 062 8, 149 0, 851 0, 587 0, 403
Bank B B B
M at(meses) M E D DP M IN M AX ρ(3) ρ(12) ρ(18)
3 4, 217 1, 697 1, 228 7, 279 0, 941 0, 589 0, 277
6 4, 341 1, 704 1, 236 7, 509 0, 941 0, 595 0, 280
12 4, 505 1, 582 1, 562 7, 605 0, 931 0, 593 0, 288
24 4, 840 1, 359 2, 135 7, 685 0, 911 0, 599 0, 318
36 5, 114 1, 228 2, 536 7, 905 0, 903 0, 609 0, 338
48 5, 400 1, 082 3, 013 7, 968 0, 871 0, 565 0, 340
60 5, 556 1, 062 3, 363 8, 038 0, 849 0, 558 0, 340
84 5, 928 0, 946 4, 086 8, 134 0, 809 0, 550 0, 358
96 6, 048 0, 933 4, 196 8, 648 0, 770 0, 521 0, 345
108 6, 122 0, 922 4, 501 8, 737 0, 772 0, 532 0, 350
120 6, 136 0, 935 4, 595 8, 884 0, 757 0, 518 0, 344
180 6, 512 0, 970 4, 958 9, 706 0, 718 0, 512 0, 359
T abela D.8: E statısticas d as series d o ramo bank para d iferentes ratings, paramaturid ad es e correlacoes med id as em meses.
E
Apendice - Resultados
E.1
Resultados: Sovereign Bonds
E stad os U nid os
S erie M E D DP M IN M AX ρ(0, 2) ρ(1) ρ(3) ρ(6) ρ(12)
L E U A 5, 431 0, 501 3, 410 6, 430 0, 946 0, 840 0, 734 0, 624 0, 454
S E U A −2, 246 1, 854 −5, 540 0, 270 0, 996 0, 973 0, 897 0, 775 0, 514
Alemanh a
S erie M E D DP M IN M AX ρ(0, 2) ρ(1) ρ(3) ρ(6) ρ(12)
L G E R 5,091 0,622 3,630 6,370 0,987 0,944 0,888 0,809 0,639
S G E R -2,033 0,996 -3,720 -0,290 0,994 0,955 0,865 0,679 0,536
B rasil
S erie M E D DP M IN M AX ρ(0, 2) ρ(1) ρ(3) ρ(6) ρ(12)
L B R A 10, 662 3, 138 6, 160 22, 500 0, 987 0, 942 0, 816 0, 635 0, 435
S B R A −4, 886 2, 528 −10, 770 7, 180 0, 962 0, 775 0, 619 0, 405 0, 027
M exico
S erie M E D DP M IN M AX ρ(0, 2) ρ(1) ρ(3) ρ(6) ρ(12)
L M E X 8, 036 1, 323 6, 030 12, 89 0, 990 0, 933 0, 856 0, 728 0, 481
S M E X −4, 136 2, 021 −8, 290 0, 930 0, 993 0, 949 0, 893 0, 798 0, 528
Apendice E . Apendice - R esultados 12 6
C olombia
S erie M E D DP M IN M AX ρ(0, 2) ρ(1) ρ(3) ρ(6) ρ(12)
L C O L 9, 580 1, 855 6, 450 14, 330 0, 990 0, 931 0, 818 0, 716 0, 516
S C O L −5, 085 2, 242 −9, 330 −1, 480 0, 989 0, 930 0, 818 0, 727 0, 443
T abela E .1: E statısticas d as series d e fatores d os so vereign bo nds, para maturid ad ese correlacoes med id as em meses.
Apendice E . Apendice - R esultados 12 7
E.2
Resultados: C orporate Bonds
Ind ustrial
S erie M E D DP M IN M AX ρ(0, 2) ρ(6) ρ(12)
L AAA 6, 337 0, 545 4, 960 7, 820 0, 977 0, 822 0,597
L AA 6, 348 0, 541 5, 180 7, 570 0, 984 0, 706 0, 513
L A+ 6, 538 0, 578 5, 290 7, 870 0, 985 0, 691 0,502
L A 6, 658 0, 626 5, 360 8, 170 0, 988 0,693 0,504
L A- 6, 817 0, 637 5, 430 8, 560 0, 984 0, 74 0, 561
L B B B + 6, 985 0, 597 5, 680 8, 890 0, 982 0,740 0,560
L B B B 7, 180 0, 615 5, 730 9, 180 0, 982 0, 629 0,477
L B B B − 7, 360 0, 625 5, 930 9, 460 0, 98 0,628 0,476
L B B + 8, 167 1, 095 5, 960 11, 450 0, 974 0, 532 0, 416
L B B 8, 666 1, 087 6, 470 13, 100 0, 946 0, 49 0, 342
L B B − 9, 107 1, 205 6, 830 14, 340 0, 943 0, 509 0, 404
L B + 9, 234 1, 354 6, 620 14, 570 0, 951 0, 586 0, 493
L B 9, 660 1, 689 6, 500 14, 870 0, 97 0, 653 0, 54
L B − 10, 200 2, 179 6, 290 16, 140 0, 974 0, 648 0, 525
S AAA −2, 650 1, 929 −6, 210 −0, 310 0, 995 0, 805 0, 544
S AA −2, 627 1, 771 −5, 970 −0, 370 0, 996 0, 815 0, 559
S A+ −2, 707 1, 723 −6, 020 −0, 500 0, 996 0, 801 0, 55
S A −2, 739 1, 686 −5, 990 −0, 570 0, 996 0, 801 0, 551
S A− −2, 767 1, 656 −6, 000 −0, 650 0, 996 0, 802 0, 541
S B B B + −2, 814 1, 635 −5, 990 −0, 660 0, 996 0, 798 0, 539
S B B B −2, 885 1, 579 −6, 010 −0, 670 0, 996 0, 776 0, 520
S B B B − −2, 861 1, 482 −5, 950 −0, 640 0, 995 0, 762 0, 500
S B B + −2, 840 1, 378 −5, 620 −0, 440 0, 992 0, 638 0, 326
S B B −3, 023 1, 243 −5, 940 −0, 440 0, 99 0, 59 0, 274
S B B − −3, 159 1, 255 −5, 820 −0, 590 0, 988 0, 553 0, 192
S B + −3, 001 0, 995 −5, 290 −0, 570 0, 986 0, 493 0, 102
S B −3, 004 0, 956 −5, 150 −0, 790 0, 985 0, 466 0, 033
S B − −2, 972 1, 121 −5, 170 −0, 380 0, 986 0, 524 0, 065
T abela E .2: E statısticas d as series d e fatores d os co rpo rate bo nds d o ramo ind ustrial,para maturid ad es e correlacoes med id as em meses.
Apendice E . Apendice - R esultados 12 8
Bank
S erie M E D DP M IN M AX ρ(0, 2) ρ(6) ρ(12)
L A 6, 923 0, 742 5, 290 8, 700 0, 977 0, 669 0, 504
L B B B 7, 181 1, 152 5, 100 12, 080 0, 961 0, 464 0, 327
S A −2, 955 1, 870 −6, 070 −0, 550 0, 994 0, 799 0, 529
S B B B −3, 073 1, 966 −7, 190 −0, 420 0, 988 0, 725 0, 475
T abela E .3: E statısticas d as series d e fatores d os co rpo rate bo nds d o ramo bank, paramaturid ad es e correlacoes med id as em meses.
R etail
S erie M E D DP M IN M AX ρ(0, 2) ρ(6) ρ(12)
L AA 6, 515 0, 606 5, 000 8, 600 0, 984 0,640 0,421
L A 6, 828 0, 688 5, 360 9, 010 0, 98 0, 638 0, 419
L B B B 7, 460 0, 758 6, 240 9, 540 0, 977 0, 54 0, 364
S AA −2, 783 1, 943 −6, 260 −0, 350 0, 995 0, 779 0, 526
S A −2, 928 1, 821 −6, 480 −0, 520 0, 996 0, 774 0, 522
S B B B −3, 120 1, 563 −6, 040 −0, 830 0, 995 0, 74 0, 503
T abela E .4: E statısticas d as series d e fatores d os co rpo rate bo nds d o ramo retail,para maturid ad es e correlacoes med id as em meses.
Apen
dice
E.
Apen
dice
-Resu
ltados
129
Correlacao entre series de level
LINDA LINDA+ LINDA- LINDAA LINDAAA LINDB LINDB + LINDB - LINDB B LINDB B +
L IN D A 1, 000 0, 9 9 0 0, 9 8 0 0, 9 6 5 0, 8 7 9 0, 8 07 0, 7 9 7 0, 7 5 2 0, 7 13 0, 7 6 5
L IN D A + 0, 9 9 0 1, 000 0, 9 6 7 0, 9 6 7 0, 8 9 2 0, 7 7 9 0, 7 6 9 0, 7 16 0, 6 9 6 0, 7 5 3
L IN D A − 0, 9 8 0 0, 9 6 7 1, 000 0, 9 3 1 0, 8 6 3 0, 8 5 6 0, 8 5 4 0, 7 9 8 0, 7 8 6 0, 8 2 1
L IN D A A 0, 9 6 5 0, 9 6 7 0, 9 3 1 1, 000 0, 9 2 8 0, 7 2 3 0, 7 03 0, 6 8 6 0, 6 2 7 0, 6 9 2
L IN D A A A 0, 8 7 9 0, 8 9 2 0, 8 6 3 0, 9 2 8 1, 000 0, 6 9 1 0, 6 8 3 0, 6 6 1 0, 6 7 8 0, 7 3 5
L IN D B 0, 8 07 0, 7 7 9 0, 8 5 6 0, 7 2 3 0, 6 9 1 1, 000 0, 9 7 8 0, 9 7 0 0, 8 9 7 0, 8 9 5
L IN D B + 0, 7 9 7 0, 7 6 9 0, 8 5 4 0, 7 03 0, 6 8 3 0, 9 7 8 1, 000 0, 9 4 2 0, 9 3 1 0, 9 14
L IN D B − 0, 7 5 2 0, 7 16 0, 7 9 8 0, 6 8 6 0, 6 6 1 0, 9 7 0 0, 9 4 2 1, 000 0, 8 4 5 0, 8 5 7
L IN D B B 0, 7 13 0, 6 9 6 0, 7 8 6 0, 6 2 7 0, 6 7 8 0, 8 9 7 0, 9 3 1 0, 8 4 5 1, 000 0, 9 5 4
L IN D B B + 0, 7 6 5 0, 7 5 3 0, 8 2 1 0, 6 9 2 0, 7 3 5 0, 8 9 5 0, 9 14 0, 8 5 7 0, 9 5 4 1, 000
L IN D B B − 0, 7 6 4 0, 7 4 1 0, 8 2 8 0, 6 7 3 0, 7 07 0, 9 3 0 0, 9 6 8 0, 8 9 1 0, 9 6 8 0, 9 4 0
L IN D B B B 0, 9 2 9 0, 9 18 0, 9 6 3 0, 8 5 4 0, 7 9 9 0, 8 6 3 0, 8 7 3 0, 8 00 0, 8 4 3 0, 8 5 8
L IN D B B B + 0, 9 6 9 0, 9 5 8 0, 9 8 8 0, 9 16 0, 8 5 2 0, 8 5 6 0, 8 6 0 0, 7 9 9 0, 8 06 0, 8 4 4
L IN D B B B − 0, 9 17 0, 8 9 9 0, 9 5 6 0, 8 3 6 0, 7 6 8 0, 8 7 1 0, 8 8 3 0, 8 15 0, 8 4 1 0, 8 5 7
L B A N K A 0, 7 4 6 0, 7 2 1 0, 8 11 0, 6 7 6 0, 6 8 9 0, 7 9 2 0, 7 9 5 0, 7 5 4 0, 7 5 3 0, 7 7 0
L B A N K B B B 0, 7 2 1 0, 6 9 5 0, 8 03 0, 6 02 0, 6 3 2 0, 8 3 8 0, 8 8 1 0, 7 7 6 0, 8 9 8 0, 8 5 7
L R E T A 0, 9 2 6 0, 9 18 0, 9 4 0 0, 8 6 4 0, 8 2 2 0, 8 15 0, 8 2 4 0, 7 5 3 0, 8 14 0, 8 3 2
L R E T B B B 0, 8 2 8 0, 8 2 1 0, 8 5 3 0, 7 2 5 0, 6 7 4 0, 7 9 9 0, 8 2 9 0, 7 17 0, 8 2 9 0, 8 3 7
L R E T A A 0, 8 4 6 0, 8 5 5 0, 8 7 3 0, 8 07 0, 8 5 9 0, 7 9 5 0, 8 01 0, 7 3 7 0, 8 5 7 0, 8 7 2
Correlacao entre series de level
LINDB B - LINDB B B LINDB B B + LINDB B B - LB ANK A LB ANK B B B LR E T A LR E T B B B LR E T AILAA
L IN D A 0, 7 6 4 0, 9 2 9 0, 9 6 9 0, 9 17 0, 7 4 6 0, 7 2 1 0, 9 2 6 0, 8 2 8 0, 8 4 6
L IN D A + 0, 7 4 1 0, 9 18 0, 9 5 8 0, 8 9 9 0, 7 2 1 0, 6 9 5 0, 9 18 0, 8 2 1 0, 8 5 5
L IN D A − 0, 8 2 8 0, 9 6 3 0, 9 8 8 0, 9 5 6 0, 8 11 0, 8 03 0, 9 4 0 0, 8 5 3 0, 8 7 3
L IN D A A 0, 6 7 3 0, 8 5 4 0, 9 16 0, 8 3 6 0, 6 7 6 0, 6 02 0, 8 6 4 0, 7 2 5 0, 8 07
L IN D A A A 0, 7 07 0, 7 9 9 0, 8 5 2 0, 7 6 8 0, 6 8 9 0, 6 3 2 0, 8 2 2 0, 6 7 4 0, 8 5 9
L IN D B 0, 9 3 0 0, 8 6 3 0, 8 5 6 0, 8 7 1 0, 7 9 2 0, 8 3 8 0, 8 15 0, 7 9 9 0, 7 9 5
L IN D B + 0, 9 6 8 0, 8 7 3 0, 8 6 0 0, 8 8 3 0, 7 9 5 0, 8 8 1 0, 8 2 4 0, 8 2 9 0, 8 01
L IN D B − 0, 8 9 1 0, 8 00 0, 7 9 9 0, 8 15 0, 7 5 4 0, 7 7 6 0, 7 5 3 0, 7 17 0, 7 3 7
L IN D B B 0, 9 6 8 0, 8 4 3 0, 8 06 0, 8 4 1 0, 7 5 3 0, 8 9 8 0, 8 14 0, 8 2 9 0, 8 5 7
L IN D B B + 0, 9 4 0 0, 8 5 8 0, 8 4 4 0, 8 5 7 0, 7 7 0 0, 8 5 7 0, 8 3 2 0, 8 3 7 0, 8 7 2
L IN D B B − 1, 000 0, 8 6 3 0, 8 4 5 0, 8 6 9 0, 7 8 7 0, 9 17 0, 8 3 3 0, 8 3 6 0, 8 4 6
L IN D B B B 0, 8 6 3 1, 000 0, 9 7 5 0, 9 8 4 0, 8 2 4 0, 8 6 3 0, 9 5 7 0, 9 05 0, 8 9 7
L IN D B B B + 0, 8 4 5 0, 9 7 5 1, 000 0, 9 6 7 0, 8 07 0, 8 16 0, 9 5 2 0, 8 6 5 0, 8 8 4
L IN D B B B − 0, 8 6 9 0, 9 8 4 0, 9 6 7 1, 000 0, 8 3 3 0, 8 7 6 0, 9 3 9 0, 9 00 0, 8 6 6
L B A N K A 0, 7 8 7 0, 8 2 4 0, 8 07 0, 8 3 3 1, 000 0, 8 2 5 0, 7 8 3 0, 7 7 8 0, 7 5 0
L B A N K B B B 0, 9 17 0, 8 6 3 0, 8 16 0, 8 7 6 0, 8 2 5 1, 000 0, 8 3 6 0, 8 3 2 0, 8 2 9
L R E T A 0, 8 3 3 0, 9 5 7 0, 9 5 2 0, 9 3 9 0, 7 8 3 0, 8 3 6 1, 000 0, 8 8 5 0, 9 2 0
L R E T B B B 0, 8 3 6 0, 9 05 0, 8 6 5 0, 9 00 0, 7 7 8 0, 8 3 2 0, 8 8 5 1, 000 0, 8 2 9
L R E T A A 0, 8 4 6 0, 8 9 7 0, 8 8 4 0, 8 6 6 0, 7 5 0 0, 8 2 9 0, 9 2 0 0, 8 2 9 1, 000
T abela E .5: C orrelacao entre as series d e level d e co rpo rate bo nds e primeira componente comum.
Apen
dice
E.
Apen
dice
-Resu
ltados
130
Correlacao entre series de slo pe
S INDA S INDA+ S INDA- S INDAA S INDAAA S INDB S INDB + S INDB - S INDB B S INDB B +
S IN D A 1, 000 0, 9 9 9 0, 9 9 6 0, 9 9 6 0, 9 9 0 0, 7 2 1 0, 7 8 9 0, 6 2 4 0, 8 4 2 0, 9 02
S IN D A + 0, 9 9 9 1, 000 0, 9 9 5 0, 9 9 7 0, 9 9 3 0, 7 2 2 0, 7 9 3 0, 6 3 1 0, 8 4 8 0, 9 04
S IN D A − 0, 9 9 6 0, 9 9 5 1, 000 0, 9 9 3 0, 9 8 9 0, 7 3 6 0, 8 01 0, 6 3 2 0, 8 5 1 0, 9 14
S IN D A A 0, 9 9 6 0, 9 9 7 0, 9 9 3 1, 000 0, 9 9 7 0, 7 11 0, 7 8 2 0, 6 2 7 0, 8 3 6 0, 8 9 5
S IN D A A A 0, 9 9 0 0, 9 9 3 0, 9 8 9 0, 9 9 7 1, 000 0, 7 18 0, 7 9 1 0, 6 3 4 0, 8 4 4 0, 8 9 7
S IN D B 0, 7 2 1 0, 7 2 2 0, 7 3 6 0, 7 11 0, 7 18 1, 000 0, 9 3 6 0, 8 7 8 0, 8 3 5 0, 8 2 3
S IN D B + 0, 7 8 9 0, 7 9 3 0, 8 01 0, 7 8 2 0, 7 9 1 0, 9 3 6 1, 000 0, 7 8 7 0, 9 3 3 0, 9 13
S IN D B − 0, 6 2 4 0, 6 3 1 0, 6 3 2 0, 6 2 7 0, 6 3 4 0, 8 7 8 0, 7 8 7 1, 000 0, 6 5 5 0, 6 6 5
S IN D B B 0, 8 4 2 0, 8 4 8 0, 8 5 1 0, 8 3 6 0, 8 4 4 0, 8 3 5 0, 9 3 3 0, 6 5 5 1, 000 0, 9 7 0
S IN D B B + 0, 9 02 0, 9 04 0, 9 14 0, 8 9 5 0, 8 9 7 0, 8 2 3 0, 9 13 0, 6 6 5 0, 9 7 0 1, 000
S IN D B B − 0, 8 3 3 0, 8 3 7 0, 8 4 2 0, 8 2 7 0, 8 3 8 0, 8 5 6 0, 9 5 8 0, 6 8 1 0, 9 7 6 0, 9 5 3
S IN D B B B 0, 9 9 2 0, 9 9 2 0, 9 9 3 0, 9 8 7 0, 9 8 3 0, 7 4 2 0, 8 2 5 0, 6 3 2 0, 8 8 5 0, 9 3 5
S IN D B B B + 0, 9 9 4 0, 9 9 4 0, 9 9 7 0, 9 9 2 0, 9 8 6 0, 7 3 1 0, 8 08 0, 6 2 5 0, 8 6 7 0, 9 2 5
S IN D B B B − 0, 9 7 9 0, 9 8 0 0, 9 7 9 0, 9 7 4 0, 9 6 8 0, 7 4 5 0, 8 3 8 0, 6 3 4 0, 9 08 0, 9 4 9
S B A N K A 0, 9 4 6 0, 9 5 0 0, 9 4 2 0, 9 5 9 0, 9 6 4 0, 6 3 5 0, 7 3 5 0, 5 4 8 0, 7 9 9 0, 8 4 4
S B A N K B B B 0, 9 6 5 0, 9 6 4 0, 9 6 6 0, 9 6 0 0, 9 6 4 0, 7 7 9 0, 8 2 8 0, 6 7 2 0, 8 4 6 0, 9 02
S R E T A 0, 9 9 0 0, 9 9 2 0, 9 8 6 0, 9 8 8 0, 9 8 5 0, 7 4 8 0, 8 19 0, 6 5 6 0, 8 7 6 0, 9 2 1
S R E T B B B 0, 9 7 4 0, 9 7 5 0, 9 7 2 0, 9 6 8 0, 9 6 6 0, 7 3 8 0, 8 4 1 0, 6 2 4 0, 9 05 0, 9 4 2
S R E T A IL A A 0, 9 8 3 0, 9 8 8 0, 9 8 0 0, 9 8 6 0, 9 8 9 0, 7 4 4 0, 8 15 0, 6 6 6 0, 8 7 1 0, 9 15
Correlacao entre series de slo pe
S IN D B B − S IN D B B B S IN D B B B + S IN D B B B − S B A N K A S B A N K B B B S R E T A S R E T B B B S R E T A IL A A
S IN D A 0, 8 3 3 0, 9 9 2 0, 9 9 4 0, 9 7 9 0, 9 4 6 0, 9 6 5 0, 9 9 0 0, 9 7 4 0, 9 8 3
S IN D A + 0, 8 3 7 0, 9 9 2 0, 9 9 4 0, 9 8 0 0, 9 5 0 0, 9 6 4 0, 9 9 2 0, 9 7 5 0, 9 8 8
S IN D A A 0, 8 2 7 0, 9 8 7 0, 9 9 2 0, 9 7 4 0, 9 5 9 0, 9 6 0 0, 9 8 8 0, 9 6 8 0, 9 8 6
S IN D A A A 0, 8 3 8 0, 9 8 3 0, 9 8 6 0, 9 6 8 0, 9 6 4 0, 9 6 4 0, 9 8 5 0, 9 6 6 0, 9 8 9
S IN D B 0, 8 5 6 0, 7 4 2 0, 7 3 1 0, 7 4 5 0, 6 3 5 0, 7 7 9 0, 7 4 8 0, 7 3 8 0, 7 4 4
S IN D B + 0, 9 5 8 0, 8 2 5 0, 8 08 0, 8 3 8 0, 7 3 5 0, 8 2 8 0, 8 19 0, 8 4 1 0, 8 15
S IN D B − 0, 6 8 1 0, 6 3 2 0, 6 2 5 0, 6 3 4 0, 5 4 8 0, 6 7 2 0, 6 5 6 0, 6 2 4 0, 6 6 6
S IN D B B 0, 9 7 6 0, 8 8 5 0, 8 6 7 0, 9 08 0, 7 9 9 0, 8 4 6 0, 8 7 6 0, 9 05 0, 8 7 1
S IN D B B + 0, 9 5 3 0, 9 3 5 0, 9 2 5 0, 9 4 9 0, 8 4 4 0, 9 02 0, 9 2 1 0, 9 4 2 0, 9 15
S IN D B B − 1, 000 0, 8 7 1 0, 8 5 5 0, 8 9 3 0, 7 9 9 0, 8 4 4 0, 8 6 2 0, 8 8 5 0, 8 5 6
S IN D B B B 0, 8 7 1 1, 000 0, 9 9 6 0, 9 9 3 0, 9 3 8 0, 9 5 7 0, 9 9 0 0, 9 8 6 0, 9 8 2
S IN D B B B + 0, 8 5 5 0, 9 9 6 1, 000 0, 9 8 8 0, 9 4 1 0, 9 5 5 0, 9 8 7 0, 9 7 7 0, 9 8 0
S IN D B B B − 0, 8 9 3 0, 9 9 3 0, 9 8 8 1, 000 0, 9 2 7 0, 9 4 3 0, 9 8 6 0, 9 8 7 0, 9 7 5 4
S B A N K A 0, 7 9 9 0, 9 3 8 0, 9 4 1 0, 9 2 7 1, 000 0, 9 07 0, 9 4 3 0, 9 2 9 0, 9 5 0
S B A N K B B B 0, 8 4 4 0, 9 5 7 0, 9 5 5 0, 9 4 3 0, 9 07 1, 000 0, 9 6 8 0, 9 5 0 0, 9 6 8
S R E T A 0, 8 6 2 0, 9 9 0 0, 9 8 7 0, 9 8 6 0, 9 4 3 0, 9 6 8 1, 000 0, 9 8 3 0, 9 9 2
S R E T B B B 0, 8 8 5 0, 9 8 6 0, 9 7 7 0, 9 8 7 0, 9 2 9 0, 9 5 0 0, 9 8 3 1, 000 0, 9 7 8
S R E T A IL A A 0, 8 5 6 0, 9 8 2 0, 9 8 0 0, 9 7 5 0, 9 5 0 0, 9 6 8 0, 9 9 2 0, 9 7 8 1, 000
T abela E .6: C orrelacao entre as series d e slo pe d e co rpo rate bo nds e primeira componente comum.
F
Apendice - Resultados Filtro de K alm an
F.1
Filtro de K alm an: Sovereign Bonds - L evel
L1,t = 0, 9 9 7 4L1,t−1 + U l1,t
L2,t = 0, 9 7 50L2,t−1 + U l2,t
LEUA − µ(LEUA) = 0, 0004 9 0L1,t + 0, 0002 9 7L2,t + εlEUA,t
εlEUA,t = 0, 9 8 6 9 εl
EUA,t−1+ [var = 2 , 9 8 4 ∗ 10−7]
LALM − µ(LALM ) = 0, 0004 2 9L1,t + 0, 0003 6 1L2,t + εlALM,t
εlALM,t = 0, 9 7 54 εl
ALM,t−1+ [var = 2 , 4 6 5 ∗ 10−7]
LBRA − µ(LBRA) = 0, 0017 52L1,t − 0, 0018 10L2,t + εlBRA,t
εlBRA,t = 0, 9 7 3 6 εl
BRA,t−1+ [var = 1, 18 2 ∗ 10−5]
LMEX − µ(LMEX) = 0, 00102 3L1,t − 0, 0007 9 9L2,t + εlMEX,t
εlMEX,t = 0, 9 8 6 7 εl
MEX,t−1+ [var = 1, 2 3 1 ∗ 10−6]
LCOL − µ(LCOL) = 0, 00114 7L1,t − 0, 00107 0L2,t + εlCOL,t
εlCOL,t = 0, 9 7 18 εl
COL,t−1+ [var = 3 , 19 1 ∗ 10−6]
F.2
Filtro de K alm an: Sovereign Bonds - Slope
S1,t = 0, 9 9 7 6S1,t−1 + US1,t
S2,t = 0, 9 6 4 2S2,t−1 + US2,t
SEUA − µ(SEUA) = 0, 001016S1,t + 0, 0002 53S2,t + εsEUA,t
εsEUA,t = 0, 9 9 8 8 εs
EUA,t−1+ [var = 2 , 16 8 ∗ 10−7]
Apendice F . Apendice - R esultados F iltro de K alm an 13 2
SALM − µ(SALM ) = 0, 00053 4S1,t + 0, 00017 6S2,t + εsALM,t
εsALM,t = 0, 9 9 2 7 εs
ALM,t−1+ [var = 6 , 14 1 ∗ 10−7]
SBRA − µ(SBRA) = 0, 0008 2 1S1,t − 0, 004 7 19S2,t + εsBRA,t
εsBRA,t = 0, 9 2 6 7 εs
BRA,t−1+ [var = 2 , 14 0 ∗ 10−5]
SMEX − µ(SMEX) = 0, 00102 6S1,t − 0, 00059 7S2,t + εsMEX,t
εsMEX,t = 0, 9 158 εs
MEX,t−1+ [var = 4 , 07 1 ∗ 10−6]
LCOL − µ(SCOL) = 0, 0009 9 9S1,t − 0, 00153 4S2,t + εsCOL,t
εsCOL,t = 0, 9 56 4 εs
COL,t−1+ [var = 6 , 12 2 ∗ 10−6]
F.3
Filtro de K alm an: C orporate Bonds - L evel
L1,t = 0, 9 8 2L1,t−1 + U l1,t
L2,t = 0, 9 9 9L2,t−1 + U l2,t
LI N D AAA − µ(LI N D AAA) = 0, 0009 52L1,t + 0, 000055L2,t + εlI N D AAA,t
εlI N D AAA,t = 0, 9 6 6 7 εl
I N D AAA,t−1+ [var = 4 , 06 4 ∗ 10−7]
LI N D A −−µ(LI N D A−) = 0, 0007 7 2L1,t − 0, 00018 0L2,t + εlI N D A−,t
εlI N D A−,t = 0, 9 7 4 6 εl
I N D A−,t−1+ [var = 2 , 52 5 ∗ 10−7]
LI N D BB − µ(LI N D BB) = 0, 0007 53L1,t − 0, 0008 7 0L2,t + εlI N D BB,t
εlI N D BB,t = 0, 9 3 8 8 εl
I N D BB,t−1+ [var = 8 , 8 8 7 ∗ 10−7]
LI N D B − µ(LI N D B) = 0, 0006 4 2L1,t − 0, 0012 2 7L2,t + εlI N D B,t
εlI N D B,t = 0, 9 8 6 9 εl
I N D B,t−1+ [var = 1, 6 3 8 ∗ 10−6]
F.4
Filtro de K alm an: C orporate Bonds - Slope
S1,t = 0, 9 9 8 0S1,t−1 + U s1,t
S2,t = 0, 9 7 9 6S2,t−1 + U s2,t
SI N D AAA − µ(SI N D AAA) = 0, 00104 3S1,t − 0, 0006 7 8S2,t + εsI N D AAA,t
εlI N D AAA,t = 0, 9 7 55εl
I N D AAA,t−1+ [var = 4 , 19 6 ∗ 10−7]
Apendice F . Apendice - R esultados F iltro de K alm an 13 3
SI N D A −−µ(SI N D A−) = 0, 0009 3 8S1,t − 0, 0006 9 0S2,t + εsI N D A−,t
εsI N D A−,t = 0, 9 6 04 εs
I N D A−,t−1+ [var = 2 , 17 5 ∗ 10−7]
SI N D BB − µ(SI N D BB) = 0, 0006 7 5S1,t − 0, 00107 4S2,t + εsI N D BB,t
εlI N D BB,t = 0, 9 8 3 6 εl
I N D BB,t−1+ [var = 9 , 6 59 ∗ 10−7]
SI N D B − µ(SI N D B) = 0, 0002 9 6S1,t − 0, 001510S2,t + εsI N D B,t
εsI N D B,t = 0, 9 12 3 εs
I N D B,t−1+ [var = 3 , 03 1 ∗ 10−7]
F.5
Filtro de K alm an: C orporate e Sovereign Bonds - L evel
L1,t = 0, 9 8 7 5L1,t−1 + U l1,t
L2,t = 0, 9 8 52L2,t−1 + U l2,t
LEUA − µ(LEUA) = 0, 0003 6 7L1,t + 0, 0004 19L2,t + εlEUA,t
εlEUA,t = 0, 9 9 59 εl
EUA,t−1+ [var = 2 , 6 7 2 ∗ 10−7]
LALM − µ(LALM ) = 0, 00019 5L1,t + 0, 000152L2,t + εlALM,t
εlALM,t = 0, 9 9 9 0εl
ALM,t−1+ [var = 4 , 6 6 5 ∗ 10−7]
LBRA − µ(LBRA) = −0, 0008 4 9L1,t + 0, 002 6 4 6L2,t + εlBRA,t
εlBRA,t = 0, 9 9 8 0εl
BRA,t−1+ [var = 2 , 7 03 ∗ 10−5]
LMEX − µ(LMEX) = −0, 0003 7 9L1,t + 0, 00104 6L2,t + εlMEX,t
εlMEX,t = 0, 9 8 57 εl
MEX,t−1+ [var = 2 , 54 5 ∗ 10−6]
LCOL − µ(LCOL) = −0, 0013 6 6L1,t − 0, 0013 15L2,t + εlCOL,t
εlCOL,t = 0, 9 9 52 εl
COL,t−1+ [var = 4 , 6 2 6 ∗ 10−6]
LI N D AAA − µ(LI N D AAA) = 0, 0004 9 4L1,t + 0, 0008 2 4L2,t + εlI N D AAA,t
εlI N D AAA,t = −0, 18 6 3 εl
I N D AAA,t−1+ [var = 1, 3 4 7 ∗ 10−7]
LI N D A −−µ(LI N D A−) = 0, 000505L1,t + 0, 0006 3 5L2,t + εlI N D A−,t
εlI N D A−,t = 0, 019 2 εl
I N D A−,t−1+ [var = 4 , 7 2 4 ∗ 10−6]
LI N D BB − µ(LI N D BB) = 0, 0012 15L1,t + 0, 0006 8 7L2,t + εlI N D BB,t
εlI N D BB,t = −0, 2 9 17 εl
I N D BB,t−1+ [var = 8 , 04 4 ∗ 10−6]
Apendice F . Apendice - R esultados F iltro de K alm an 13 4
LI N D B − µ(LI N D B) = 0, 0009 9 1L1,t + 0, 000507L2,t + εlI N D B,t
εlI N D B,t = 0, 4 6 7 0εl
I N D B,t−1+ [var = 1, 8 00 ∗ 10−6]
F.6
Filtro de K alm an: C orporate e Sovereign Bonds - Slope
S1,t = 0, 9 9 15S1,t−1 + US1,t
S2,t = 0, 9 8 8 4S2,t−1 + US2,t
SEUA − µ(SEUA) = 0, 0014 18S1,t + 0, 0003 7 2S2,t + εsEUA,t
εsEUA,t = 0, 9 8 6 2 εs
EUA,t−1+ [var = 3 , 512 ∗ 10−7]
SALM − µ(SALM ) = 0, 0007 6 5S1,t + 0, 0003 7 6S2,t + εsALM,t
εsALM,t = 0, 9 8 8 9 εs
ALM,t−1+ [var = 8 , 3 12 ∗ 10−7]
SBRA − µ(SBRA) = −0, 0004 2 3S1,t − 0, 0057 54S2,t + εsBRA,t
εsBRA,t = 0, 9 8 9 5εs
BRA,t−1+ [var = 7 , 052 ∗ 10−5]
SMEX − µ(SMEX) = 0, 00116 8S1,t − 0, 0008 4 3S2,t + εsMEX,t
εsMEX,t = 0, 9 6 04 εs
MEX,t−1+ [var = 1, 019 ∗ 10−5]
LCOL − µ(SCOL) = 0, 00057 8S1,t − 0, 002 7 3 7S2,t + εsCOL,t
εsCOL,t = 0, 9 8 6 5εs
COL,t−1+ [var = 1, 3 14 ∗ 10−5]
SI N D AAA − µ(SI N D AAA) = 0, 002 02 8S1,t + 0, 0002 3 1S2,t + εsI N D AAA,t
εlI N D AAA,t = −0, 09 8 0εl
I N D AAA,t−1+ [var = 2 , 8 9 8 ∗ 10−7]
SI N D B − µ(SI N D B) = 0, 001513S1,t + 0, 0006 8 1S2,t + εsI N D B,t
εsI N D B,t = 0, 2 4 3 2 εs
I N D B,t−1+ [var = 2 , 02 8 ∗ 10−6]
SI N D BB − µ(SI N D BB) = 0, 0014 3 5S1,t + 0, 0006 19S2,t + εsI N D BB,t
εlI N D BB,t = −0, 3 001εl
I N D BB,t−1+ [var = 2 , 4 8 2 ∗ 10−5]
SI N D A −−µ(SI N D A−) = 0, 0017 17S1,t + 0, 0006 19S2,t + εsI N D A−,t
εsI N D A−,t = 0, 0503 εs
I N D A−,t−1+ [var = 5, 2 8 7 ∗ 10−6]
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