A Term Structure Model for Emerging Economy Bonds

Marco Bonomo

EPGE, Fundação Getulio Vargas and CIREQ.

Alexandre Lowenkron

PUC-Rio and BBM

May 28, 2006

Abstract

We derive and estimate an a¢ ne no-arbitrage model with default risk and macroeconomic state

variable to investigate the determinants of the term structure of emerging market external debt for

Brazil, Colombia and Mexico. In particular we assess the importance of US macroeconomic factors,

country�s solvency ratios and latent variables in determining the risk premium term-structure. Our

results indicate: (i) that the single most important variable is the joint latent variable interpreted

as international liquidity, being more important in longer yields - it accounts for around 35% of

the emerging markets 6 months duration spread movements and around 46% of 10 years duration

spreads; (ii) the contribution of US macro variables ranges from 15% of the movements in short

spread to 10% in the longer spreads; (iii) solvency variables are relatively more important to explain

spreads in Mexico than in Brazil and Colombia; (iv) the idiosyncratic latent factor - interpreted as

political risk - is also relevant accounting for approximately 30% of the movements, but its e¤ect is

larger on shorter yields.

JEL classi�cation: G12, E44, E43, G15, F3

1 Introduction

What makes the risk-premium of emerging market countries external bonds to increase? Is it the increase

in risk aversion from the part of international investors, triggered by US macroeconomic cycle or is it a

deterioration of the emerging country solvency indicators? Or it is explained mainly by other factors,

which can be attributed to political conditions?

To answer these questions, we propose a term structure approach, based on recent contributions to the

�nance literature. The general class of non-arbitrage a¢ ne models (Du¢ e and Kan 1996), which allows

for time-varying risk premia, are known to produce good pricing �t. However, its original implementation

relied on non-observable factors1 , and therefore could not be used to discover the economic driving forces

1Following Litterman and Scheinkman (91), the literature interpreted them as level, slope and curvature.

1

behind price movements. Concurrently, the empirical macro literature2 was attempting to assess the

relative importance of macro factors in determining the yields by using simple regressions and VARs, but

ignoring the restrictions implied by the absence of arbitrage or the empirical failure of the expectations

hypothesis (usually attributed to time-varying risk premia). Ang and Piazzesi (2003) have recently

merged those two branches of the literature by imposing no arbitrage restrictions in a model where the

set of state variables included also macro variables following a VAR dynamic3 . Our paper extends this

approach by allowing for the possibility of default, therefore allowing us to use such models to explain

emerging market spreads.

We present a discrete time model, which is closely related to Du¢ e and Singleton (1999), who derive

an a¢ ne term structure for the default spread. In setting the model, we faced the question of what is the

necessary hypothesis to get an a¢ ne formula for the term structure of default spread in discrete-time,

and what it implies to the possible applications. We found out that the crucial condition is that the

stochastic discount factor should be predetermined with respect to default. In our speci�c application it

should not depend on emerging country variables that a¤ect default contemporaneously (as for example,

solvency ratios). The emerging markets external debt is an environment that �ts well this necessary

assumption, once one �nds plausible the hypothesis that the stochastic discount factor of the relevant

investors (US based, for example) is not a¤ected by the emerging markets risk4 .

Our speci�cation strategy relies on the assumption that the pricing of external bonds of emerging

countries re�ects the preferences of US investors. Then, the price of risk is an a¢ ne function of US

macro and latent factors, but the dynamics of default risk for each emerging economy depends on both

US variables and the country probability of default. The resulting term structure of risk spread for

an emerging economy is an a¢ ne function of the country�s solvency indicators, one idiosyncratic latent

variable, and one extra latent variable common to all emerging economies analyzed. We interpret the

joint latent variable as international liquidity for the set of emerging countries and each idiosyncratic

latent variable as the country�s idiosyncratic political risk.

We estimate the model with base on US and three emerging market countries: Brazil, Colombia

and Mexico, using monthly data5 . The US macro variables are monthly CPI in�ation and monthly

unemployment. In order to capture the probability of default, we use emerging country�s external and

government solvency ratios: external debt over export, and public debt over GDP. Since we work with

four latent variables (one for the USA, 1 that a¤ects all three emerging countries, and one idiosyncratic

2For example Estrella and Mishkin (1997) and Evans and Marshall (1998).3A sequel to this was to model the macro dynamics with a structural model in the place of the VAR (Bekaert, Cho and

Moreno 2005, Hördal, Tristani and Vestin 2005, Rudebush and Wu 2004, Dewatcher and Lyrio 2005).4The framework would not be as suitable to the analysis of the term structure of default spread of �rms in the same

country.5 In order to estimate the model for those emerging countries, we also had to estimate a default free term-structure

model with US data.

2

for each emerging country) the estimation is done by Kalman �lter.

Even though we are interested in the emerging countries spread, we need also to estimate a default-

free a¢ ne term structure model for the US. In order to simplify the estimation, we estimated the US

model separately �rst. Then, we used the US parameters and the US latent variable obtained as an

input for the joint estimation for the three Latin America emerging countries.

Our speci�cation provides sensible interpretation of variables, and to relate them with recent events

that a¤ected the term structure of risk spread for emerging economies. We are able to interpret the joint

latent factor as the international liquidity to Latin-America (or the risk propensity for Latin-America

countries) and each idiosyncratic factor as a "political risk". The model captures well some recent

stylized facts: (i) the recent increase in international liquidity; (ii) some contagion events on emerging

markets as the Russian crisis, the Brazilian real devaluation and the Brazilian electoral crisis; and also

(iii) the decrease in political risk in Brazil after the election of Lula for presidency with a later increase

in this variable (which can be associated with the recent political scandals).

The methodology also allow us to asses the relative importance of each one of the variables analyzed

in explaining movements in the term structure of emerging market spread. The single most important

variable is the joint latent variable, interpreted as international liquidity. Its movements accounts for

about 42% of the variability in emerging markets spread. Its importance varies from 56% in Brazilian

spread to 24% of Mexican spread but it is much more important for bonds with longer duration. Con-

tribution of US macro variables to spread movements ranges from 15% in short spreads to 10% in the

longer spreads.

The solvency variables seems to be more important in Mexico than in Brazil and Colombia. Another

related result is that the idiosyncratic latent variable (political risk) is much more important in Brazil

and Colombia than in Mexico. We conjecture that the cause of these two phenomena is the fact that

Mexico is an investment grade country among the three emerging economies.

The remaining part of the paper is divided in four sections. In the next section we propose a no-

arbitrage framework for pricing defaultable bonds of emerging market economies. In section 3 we present

the data and the estimation method and estimation results. Term structure results are presented and

analyzed in the fourth section. The last section concludes.

2 A Term Structure Model of Defaultable Bonds with Macro-

economic State Variables

In this section we present a no-arbitrage framework for pricing defaultable bonds of emerging market

economies based on US and emerging market state variables. We follow Du¢ e and Singleton (1999) by

specifying a model for the term structure for the default spread, and Ang and Piazzesi (2003) by using

3

macroeconomic and latent variables as driving factors for the US term structure. We further introduce

emerging markets solvency ratios as factors that jointly with US macro variables and latent factors

determine the default spread term-structure.

We proceed as follows. First, we derive a discrete-time recursive equation for the price of the de-

faultable bond, which will depend on dynamics of two processes: the stochastic discount factor for the

US economy, and the recovery intensity. The latter process is de�ned to be one minus the product

between the probability of default and the percentage loss in case of default. Then, we specify a VAR

dynamics for the state variables, which include US latent and macro variables, and emerging market

latent and solvency variables. The price of risk is assumed to be a linear function of US latent and macro

state variables, and the recovery intensity is modeled as a linear function of all state-variables and their

innovation. With those assumptions we are able to derive an a¢ ne term-structure for the default spread

as a function of US macro variables, US and emerging markets latent variables, and emerging markets

solvency variables.

2.1 A No-Arbitrage Framework for the Term Structure of Defaultable Bonds

De�ne Pus(N)t as the time t price of a default-free zero coupon bond in US dollars that makes a $1

payment at time t+N . By this de�nition, Pus(0)t = 1, 8t since there is no default. The yield to maturity

Yus(N)t , is de�ned as Pus(N)t = 1�

Yus(N)t

�N . The absence of arbitrage implies the existence of a positivestochastic discount factor mt. Therefore:

Pus(N)t = Et

�mt+1P

us(N�1)t+1

�: (1)

Given this formula and the absence of default at any given time t bonds of di¤erent maturities can

be priced recursively by Pus(N)t = Et (mt+1mt+2 � � �mt+N ).

Assuming that the variables are lognormally distributed, we have:

pus(N)t = Et

�lnmt+1 + p

us(N�1)t+1

�+1

2vart

�lnmt+1 + p

us(N�1)t+1

�; (2)

where pus(N)t � ln(Pus(N)t ) and yus(N)t = ln(Yus(N)t ).

When a bond is subject to default risk, the pricing equation (1) is no longer valid. Let P (N)t be

the price of a dollar denominated N -period emerging market defaultable bond, and Vt+1 its value next

period. In this case, Vt+1 can be much lower than P(N�1)t+1 , the price in case of no default up to t + 1,

due to the possibility of default in t+ 1. Then, the basic pricing equation gives:

P(N)t = Et

hmt+1V

(N�1)t+1

iLet RNt denote the recovery value of a bond with maturity N in the event of default at time t. We

will assume that once the default occurs the proportional loss is independent of the maturity of the

4

Figure 1: Stochastic structure

bond:

Lt+1 =PNt+1 �RNt+1

PNt+1for every N

Let RNt denote the recovery value of a bond with maturity N in the

event of default at time t. We will assume that the proportional loss, in case of default, is independent

of the maturity of the bond:

Lt+1 =PNt+1 �RNt+1

PNt+1for every N

The other crucial assumption is that the stochastic discount factor mt+1 is conditionally independent

of the occurrence of default in the emerging market bond. Notice, however, that this still allow that

the probability of occurrence of default �(j) and the loss conditional on default L(j) are both a¤ected

by state variables a¤ecting the stochastic discount variable. It is as if the realization of the stochastic

discount factor preceded that of the realization of default or not. This idea is depicted in the tree (�gure

1) below.

Does this crucial assumption rule out our application to emerging markets bonds? We think it does

not. For emerging markets external debt denominated in US dollars, it is reasonable to assume that

the relevant stochastic discount factor is the American one. Therefore, it should not be a¤ected by the

incidence of default in emerging market bonds. On the other hand, US macroeconomic conditions may

trigger the occurrence of emerging bonds default6 .

6This hypothesis could be non-realistic if we wanted to apply the model to bonds of US companies.

5

In order to proceed with our derivation, let Ft+1 be the partition of states which represent all the

possible events in t+1 and let Fmt+1 be a coarser partition generated by the realizations of the stochastic

discount factor. Each element amt+1 2 Fmt+1 contains two other separate eventsnamd;t+1; a

mn;t+1

o, the only

di¤erence between them being that in amd;t+1 the default occurs. Thus, we have

PNt =

ZFt+1

mt+1 (s)VN�1t+1 (s)�t (ds) (3)

We can break this integral in two sets of events: one where default occurs (amd;t+1) and the one where

it does not�amt+1

�. Notice that under condition (2) the distribution of mt+1; �amt+1 ; P

N�1t+1 and Lt+1 are

the same under both partitions. In other words, the only di¤erences between the set of events is that�amt+1

�occurs with probability �amt+1 leaving the price equals to P

N�1t+1

�amt+1

�, while

�adt+1

�occurs with

probability (1��amt+1) and leaves the price equals to RN�1t+1

�amt+1

�= (1�Lt+1

�amt+1

�)PN�1t+1

�amt+1

�. This

last equality follows from condition (1). So we can write:

PNt =

Zamt+12Fm

t+1

mt+1

�amt+1

� �1� �amt+1

�PN�1t+1

�amt+1

��t�damt+1

�+

Zamt+12Fm

t+1

mt+1

�amt+1

��amt+1(1� Lt+1

�amt+1

�)PN�1t+1

�amt+1

��t�damt+1

�: (4)

Putting terms in evidence and summing them up, we have:

PNt =

Zamt+1

2Fmt+1

mt+1

�amt+1

� h�1� �amt+1

�+ �amt+1

�1� Lt+1

�amt+1

��iPN�1t+1

�amt+1

��t�damt+1

�=

Zamt+12Fm

t+1

mt+1

�amt+1

��amt+1P

N�1t+1

�amt+1

��t�damt+1

�= Et

�mt+1�t+1P

(N�1)t+1

�; (5)

where �amt+1 ��1� �amt+1Lt+1

�amt+1

��measures the recovery intensity. Notice that it depends on

the state of the nature since, di¤erently form Du¢ e and Singleton (1999), we do not restrict Lt+1 to

be known at t.7 This allows the recovery intensity �t+1 to depend on the state of the nature and will

enrich our analysis. As before, we have a recursive formula. Imposing lognormality we have:

7Du¢ e and Singleton (1999) propose the following pricing equation for a defaultable bond that has not defaulted up

to time t :

PNt = hte�rtEQt

�RN�1t+1

�+ (1� ht) e�rtEQt

�PN�1t+1

�where it is clear that the probability of default in t+ 1 is predetermined in t:

They also de�ne

Lt =PNt+1 �RNt+1

PNt+1

that is, that the proportional of loss in case of default is predetermined in t. Although they do not comment on the

restrictions necessary to be able to write such an equation, their formulation is clearly more restrictive than ours.

6

p(N)t = Et

�lnmt+1 + ln�t+1 + p

(N�1)t+1

�+1

2V art(lnmt+1 + ln�t+1 + p

(N�1)t+1 ): (6)

2.2 State variable dynamics

We specify a VAR dynamics for the state variables, which include US latent and macro variables, and

emerging market latent and solvency variables.

There are K state variables. Their dynamics are given by:

Xt = �+�0Xt�1 +�"t: (7)

Without loss of generality, we can split the vectors Xt and "t:

Xt =hXus0t Xem0

t

i0:

where Xust refers to US variables that will a¤ect both the US and the emerging spread term structure

and Xemt refers to variables that in�uence only the emerging spread the term structure. We also split

"t accordingly:

"t =h"us0t "em0t

i0:

The vector of US variables Xust will be composed of the US unemployment rate, Y USt , in�ation rate,

�USt , and one latent variable, UUSt :

Xust =

hUUS0t �US0t Y US0t

i0:

The vector of variables for the emerging market economy Xemt will be composed by two latent

variables JEMt and UEM(i)t , and two solvency ratios - net external debt over exports D�Xt and debt

GDP ratio DYt:

Xemt =

hJEM 0t UEM 0

t D�X 0t DY 0t

i0:

The latent variable JEM 0t will be common to all emerging countries, while UEM 0

t will be speci�c to

each emerging country.8

8On our �rst estimate, we didn�t have this joint latent variable JEM ; only one idiosyncratic latent variable for each

emerging country, UEM : However, the results showed us the importance of introducing JEM : when we ploted the series

of UEM for Brazil, Mexico and Colombia we noticed that even though they were estimated totally indepedently, the series

were almost coincidental with a correlation of more than 0,9. We decided then to include this extra latent variable with a

systematic e¤ect on every emerging country.

7

It is assumed that Cov ("t) = I and that � is a lower triangular Cholesky matrix such that

Cov(�"t) = ��0. We impose that most factors have non-correlated contemporaneous shocks, including

the unobservable factors,9 with exception made to US in�ation and output shocks:

X=

26666666666666664

�usUU

0 ���

0 �y� �yy

0 0 0 �emJJ

0 0 0 0 �emUU

0 0 0 0 0 �D�X

0 0 0 0 0 0 �DY

37777777777777775:

We also impose that the US economy is not a¤ected by the emerging economy although the emerging

economy is a¤ected by the US economy:

� =

26666666666666664

�usUU 0 0 0 0 0 0

0 ��� ��y 0 0 0 0

0 �y� �yy 0 0 0 0

�emJUus �emJ� �emJy �emJJ 0 0 0

0 0 0 0 �emUU 0 0

0 0 0 0 0 �emNX 0

0 0 0 0 0 0 �emD

37777777777777775:

The log short rate rt for the US is assumed to be an a¢ ne function of the US state variables, so it

encompasses any form of linear Taylor Rule followed by the Federal Reserve:

rt = �0 + �01X

ust : (8)

2.3 The price of risk

In modeling the US term structure we follow Ang and Piazzesi (2003), the only di¤erences being that

they use 2 latent variables, while we use only one, for parsimony, since we our main interest is the

emerging spread term structure.

We follow the tradition in the literature by specifying the price of risk as an a¢ ne function of state

variables. However, given our assumption that the bond pricing is determined by US investors, we

assume that the price of risk depends only on US state variables:

�t = �0 + �1Xust :

9This a standart practice in the term structure model (see Dai and Singleton (2000) and Ang and Piazzesi (2003) among

others. Since these factors are unobservables, we can do normalizations that give us observationally equivalent systems.

8

where �0 is a Kx1 vector and �1 is a KxK matrix that we assume to be block diagonal:

�1 =

26664�usUU 0 0

0 �us�� �us�y

0 �usy� �usyy

37775 :Then, we can recover the stochastic discount factor through the following relation:

mt+1 =�t+1�te�rt ; (9)

and

�t+1 = �t exp

��12�0t�t � �0t"ust+1

�; (10)

where �t+1 is the Radon-Nikodym �t+1 derivative that converts the US dollars state variables from

probability measure Q into P; and "ust+1 is the vector of unpredictable shocks to the US state variables

Xus.10

Substituting 8 and 10 into 9 we �nd that the stochastic discount factor is driven by:

lnmt+1 = �1

2�0t�t � �0 � �01Xus

t � �0t"ust+1:

As in Dai and Singleton (2002), and di¤erently from a multi-factor Vasicek (1977), our model presents

a time varying risk-premium. Recent empirical work, as Almeida (2003), shows that this is an important

feature to reproduce the term structure dynamics.

2.4 The Recovery Intensity

The log of the recovery intensity �t+1 is a reduced variable measuring the riskiness of the debt by the

interaction of the default probability and the loss of market value processes. We assume that it depends

on the full vector of state variables, from both the US and the emerging economy:

ln�t+1 = ��0 � �01Xt � �0"t+1:

We leave this process totally unrestricted in order to let the data to tell us which variables drive its

dynamics.

2.5 The default free US term structure as a function of the US state variables

The derivation of US term structure is straightforward and familiar from the a¢ ne term structure models

literature. Using pricing equation 1 and the fact that Pus(0)t+1 = 1 we �nd that:

10Note that, consistent with our hypothesis that emerging market variables do not a¤ect US investors risk aversion, we

assumed that the innovation in �t+1 is given only by shocks that a¤ect US state variables.

9

pUS(1)t = lnEt [mt+1] = �rt

= ��0 � �01Xust :

The price of the one-period bond is a linear function pus(1)t = Aus

1 + Bus

1 Xust where Aus1 = ��0 and

Bus1 = ��01. Is it possible to show by induction that this a¢ ne form for the logarithm of the price of

bond also holds for any maturity, that is pNt = AusN +Bus0NXt.

Theorem 1 Under the state variable dynamics (7) the price of an N period default-free bond is given

by

pNt = AusN +Bus

0NXt;

where

Bus0N =

�Bus

0N�1 (�

us � �us�1)� �01�

and

AusN = AusN�1 +Bus0N�1 (�� ��0) +

1

2Bus

0N�1��B

us0N�1 � �0:

Proof. See appendix.

rule0.5em0.5em

De�ning AN = �AN

N and B0N = �B0N

N , we can write the equation for the yields:

yNt = AN +B0NXt:

2.6 The defaultable emerging markets term structure as a function of the

US and emerging market state variables

Using pricing equation 6 and the fact that p(0)t+1 = 0 we �nd that:

p(1)t = Et (mt+1 + �t+1) +

1

2vart(mt+1 + �t+1)

= Et

��12�0t�t � �0 � �01Xus

t � �0t"ust+1 � �o � �01Xt � �0"t+1�+

1

2vart

���0t"ust+1 � �0"t+1

�:

The partition of Xt+1 above induce similar partitions for the vector �1:

�1 =h�us �em

i;

By assuming �(") = I, we imposed that "ust+1 and "emt+1 are uncorrelated. Therefore:

10

p(1)t = �1

2�0t�t � �0 � �01Xus

t � �o � �01Xt +1

2vart

���0t"ust+1 � �us0"ust+1 � �em0"emt+1

�= ��0 � �01Xus

t � �o � �01Xt +1

2�0� + �us0�t

Noticing that pus(1)t = ��0 � �01Xust , we have:

p(1)t = p

us(1)t + (

1

2�0� + �us0�0 � �o) + (�us0�1Xus

t � �01Xt) (11)

Or equivalently,

p(1)t = p

us(1)t +A�1 +B�1Xt (12)

where

�A�1 = (��o +1

2�0� + �us0�0)

and

B�01 =

h(��us01 + �us0�1) ��em01

i= ��em01 +

h�us0�1 0

iIn fact, the property that the di¤erence between emerging market and risk-free bond prices is linear

holds for all maturities, as can be shown by induction.

Theorem 2 Under the state variable dynamics (7) the price of an N period defaultable bond is given

by

pNt = pus(N)t +A�N +B�

0NXt

; where

B�0N = B

�01 +B

�0N�1��

hB�us

0N�1�

us�1 0i

and

A�N = A�1 +A�N�1 +B�0N�1(�+

1

2��0B�N�1)�B�us

0N�1�

us�0

��us0�us0BN�1 � �0�0B�N�1 +B0N�1�

us�us0Bus�N�1

Proof. See appendix

rule0.5em0.5em

De�ning sNt � y(N)t � yus(N)t ; A�N � �

A�N

N and B�0N � �B�0N

N , and we can write an a¢ ne equation for

the spread between the emerging country and the risk-free bond yields:

sNt = A�N +B

�0NXt: (13)

11

3 Estimation

Notice that we have speci�ed the US state variables independently of the emerging market state variables,

and that stochastic discount factor depends only on US state variables. Therefore, we are able to estimate

the model for the US economy independently of the emerging economy information. We use the output

of the US model - the parameter estimates for the dynamics for US state variables, and the series for

the US latent variable - in a joint estimation for the parameters of the three emerging market economies

of our sample.

3.1 Data

We use monthly data for US, Brazil Colombia and Mexico. The yields analyzed are 1; 2; 3; 5; 7 and 10

years. For the US we use data on treasuries provided by the Federal Reserve. As Rudebusch and Wu

(2004), we analyze only the Greenspan period, from Jan/1988 to Oct/2005. For the emerging economies,

we use data on the yield curve for sovereign bonds denominated in US dollars and which is calculated by

Bloomberg. They interpolate the yields of available sovereign bonds at each date, providing their time

series, from Mar/1998 to Oct/2005. We present below the data on yields, where we can notice similar

patterns for those countries US dollar denominated yields, specially among the emerging countries:

Yields Analyzed

0

5

10

15

20

25

30

35

mar/98

jun/98set

/98

dez/98

mar/99

jun/99set

/99

dez/99

mar/00

jun/00set

/00

dez/00

mar/01

jun/01set

/01

dez/01

mar/02

jun/02set

/02

dez/02

mar/03

jun/03set

/03

dez/03

mar/04

jun/04set

/04

dez/04

mar/05

jun/05set

/05

USA_6mUSA_1yUSA_2yUSA_3yUSA_5yUSA_7yUSA_10yBrazil_6mBrazil_1yBrazil_2yBrazil_3yBrazil_5yBrazil_7yBrazil_10yMexico_6mMexico_1yMexico_2yMexico_3yMexico_5yMexico_7yMexico_10yColombia_6mColombia_1yColombia_2yColombia_3yColombia_5yColombia_7yColombia_10y

For the default free US curve we follow most studies in this literature by choosing two variables in

order to account for in�ation pressure and economic activity. More speci�cally, we use are in�ation and

unemployment series from BLS11 .

11Ang and Pizzesi (2003), Rudebusch and Wu (2004) and Hordal, Tristani and Vestin (2004) respectively uses, for

12

For Brazil, Mexico and Colombia, we use monthly data on (total public debt)/GDP and on (net

external public debt)/exports provided by each country�s Central Bank12 . The (total public debt)/GDP

ratio is included to account for the solvency condition of the sovereign government, while the (net external

public debt)/exports is included to account for the capacity of a country to generate dollars to repay its

debts.

3.2 The space-state form, the Kalman �lter and the point estimates

We estimate the model by maximum likelihood, following the recent literature. However, depart from

most term structure papers, which follow Chen and Scott (1993) by inverting the unobservable variables

from some of the yields, and imposing that they are observed without error. In our paper, we use a

Kalman �lter in order to avoid this exogenous asymmetric imposition on pricing errors, treating all yields

equally. The state-space form of the joint estimation is presented in the Appendix.

The estimation results are presented in table (??) below. Most of the coe¢ cients are signi�cant. The

discussion of its signals will be left for the next section, since our main interest is not the coe¢ cients

itself, but the A�s and B�s that are the factor loading of the yields, and these are basically a interaction

of these parameters, given by theorems 1 and 2.

in�ation: (i) the �rst principal component of three in�ation indexes (CPI, PPI and Commodity Price Index), (ii) CPI

in�ation and (iii) CPI in�ation. For economic activity, they use: (i) the �rst principal components of index of Help Wanted

Advertising in Newspapers, unemployment, the growth rate of employment and the growth rate of industrial production,

(ii) de-meaned industrial capacity utilization and (iii) detrended log of industrial production.12All those data are in monthly frequency, except for Colombia�s solvency indicators which are only avalable quarterly.

We then interpolate them to monthly frequency in order for us to introduce Colombia in the joint estimation.

13

Estimates USA

Coefficient St. Dev    phi_us_LL 0.990 (0.0051)

    phi_us_pp 0.978 (0.0275)

    phi_us_py 0.002 (0.0073)

    phi_us_yp 0.000 (0.1974)

    phi_us_yy 0.998 (0.0436)

    mi_p 0.028 (0.0346)

    mi_y 0.005 (0.2410)

    sig_L 0.003 (0.0150)

    sig_p 0.002 (0.0279)

    sig_y 0.001 (0.2029)

    sig_py 0.000 (0.1620)

    delta0 0.011 (0.0150)

    delta1_p 0.032 (0.0358)

    delta1_y ­0.165 (0.0081)

    lambda0_L ­0.073 (0.0014)

    lambda0_p 2.367 (0.0008)

    lambda0_y ­0.348 (0.0016)

    lambda1_LL ­0.984 (0.0024)

    lambda1_pp ­1.764 (0.0001)

    lambda1_py ­5.962 (0.0081)

    lambda1_yy 17.251 (0.0016)

    lambda1_yp ­1.085 (0.0242)

Yield 6 months 0.40%Yield 1 year 0.26%Yield 2 years 0.09%Yield 3 years 0.00%Yield 5 years 0.13%Yield 7 years 0.19%

Log LH ­4259.2 Yield 10 years 0.24%

Pric

ing 

Erro

rs

Estimates emerging countries

Coefficient St.Dev Coefficient St. Dev Coefficient St. Dev

phi_JUus ­0.006 0.0001     phi_UU 0.941 0.0001 0.978 0.0011 0.999 0.1552

phi_Jp ­0.012 0.0055     phi_d 0.929 0.0062 0.941 0.0045 0.979 0.0020

phi_Jy ­0.001 0.0015     phi_x 0.987 0.2610 0.993 0.0898 0.969 0.1400

phi_JJ 0.995 0.0050     mi_U 6.884 0.0000 0.000 0.0000 0.041 0.0007

mi_J 0.017 0.0066     mi_d 0.040 0.0058 0.015 0.0024 0.011 0.0025

sig_J 0.076 0.0016     mi_x 0.010 0.0890 ­0.001 0.0498 0.045 0.0792

    sig_U 12.818 6.610 8.180    sig_d 0.017 0.004 0.004    sig_x 0.096 0.095 0.062    theta1_Uus ­1.62E­02 2.24E­05 ­3.31E­08 1.09E­04 ­8.57E­06 5.73E­05

    theta1_p ­4.34E­03 1.97E­03 8.77E­03 8.38E­03 6.72E­03 3.47E­03

    theta1_y 3.38E­01 4.54E­04 3.13E­02 1.89E­03 6.77E­03 6.60E­04

    theta1_J ­2.50E­02 2.33E­03 ­7.60E­03 7.12E­03 ­6.62E­03 7.56E­03

    theta1_U ­1.14E­04 4.78E­02 1.06E­04 1.56E­01 ­5.67E­05 2.15E­01

    theta1_d 3.72E­02 8.60E­04 1.85E­02 1.55E­03 2.88E­10 1.42E­03

    theta1_x ­3.36E­09 3.59E­03 ­1.17E­02 1.15E­03 ­5.80E­09 1.80E­03

    beta_Uus 8.64E­06 1.45E­04 ­1.94E­08 6.03E­04 ­4.81E­07 6.30E­05

    beta_p ­3.75E­02 2.90E­03 ­8.67E­03 1.04E­02 1.79E­03 9.96E­03

    beta_y ­3.71E­02 5.17E­03 ­1.41E­02 2.03E­02 ­2.46E­03 7.64E­03

    beta_J 1.43E­05 3.36E­04 ­8.00E­03 6.81E­04 ­2.65E­01 1.77E­04

    beta_U 3.82E­01 7.15E­04 ­2.13E­01 1.46E­03 2.26E­08 8.98E­04

    beta_d 3.95E­01 6.17E­04 2.03E­01 1.12E­03 ­1.56E­01 5.90E­05

    beta_x 0.00E+00 3.23E­06 ­1.16E­06 4.74E­04 ­1.48E­01 6.30E­05

Yield 6 months 0.01% 0.38% 0.96%Yield 1 year 0.49% 0.19% 0.75%Yield 2 years 0.67% 0.23% 0.72%Yield 3 years 0.64% 0.26% 0.45%Yield 5 years 0.60% 0.25% 0.24%Yield 7 years 0.58% 0.22% 0.31%Yield 10 years 0.43% 0.31% 0.25%

Log LH 0.49% 0.26% 0.52%

Pric

ing 

Erro

rs

­5779.48

Joint Parameters MexicoBrazil Colombia

Average Pricing Errors

­0.800%

­0.600%

­0.400%

­0.200%

0.000%

0.200%

0.400%

0.600%

0.800%

mar/98

jun/98set

/98

dez/98

mar/99

jun/99set

/99

dez/99

mar/00

jun/00set

/00

dez/00

mar/01

jun/01set

/01

dez/01

mar/02

jun/02set

/02

dez/02

mar/03

jun/03set

/03

dez/03

mar/04

jun/04set

/04

dez/04

mar/05

jun/05set

/05

Brazil Mexico Colombia

The pricing errors are reasonably low. The average in-sample pricing errors are 19 basis points for

the USA, 26 for Mexico, 49 for Brazil and 53 for Colombia.

4

Results

14

First, we brie�y analyze the results for the US default-free term structure. Then, we investigate

the determinants of the term structure of emerging market external debt for Brazil, Colombia and

Mexico, which is our main goal. In particular, we assess the importance of US macroeconomic factors,

country�s solvency ratios and latent variables in determining the risk premium term-structure. After

a brief analysis of the results for the US, we undertake a more detailed scrutiny of the results for the

emerging market risk premiums.

4.1 Results for the USA

We present bellow the model for the USA. Usually latent variables are interpreted as slope, level or

curvature. The reason is that the factor loading of these variables on the yield have this shape. More

recently, Rudebusch and Wu (2004) interpreted the level variable as a proxy for in�ation trend in the

USA. In our model we only use one latent variable, since the macro variables capture important part of

the dynamics. There are two additional reasons: (i) parsimony, since our may concern is the analysis of

the emerging spreads; and (ii) because the �rst principal component of the US yields analyzed accounts

for 96.4% of the variance of all yields13 . It is possible to note in �gure (4.1) a negative trend in this

latent variable for the US from 1988 to 2005.

US State Variables

­0.04

­0.02

0

0.02

0.04

0.06

0.08

0.1

1988

M1

1988

M6

1988

M11

1989

M4

1989

M9

1990

M2

1990

M7

1990

M12

1991

M5

1991

M10

1992

M3

1992

M8

1993

M1

1993

M6

1993

M11

1994

M4

1994

M9

1995

M2

1995

M7

1995

M12

1996

M5

1996

M10

1997

M3

1997

M8

1998

M1

1998

M6

1998

M11

1999

M4

1999

M9

2000

M2

2000

M7

2000

M12

2001

M5

2001

M10

2002

M3

2002

M8

2003

M1

2003

M6

2003

M11

2004

M4

2004

M9

2005

M2

2005

M7

Une

mpl

oym

ent, 

Uno

bs

­0.004

­0.002

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

CPI

Unobservable USA (U_us) Unemployment CPI_SA

sample period also analyzed foremerging countries

US State Variables

In �gure (4.1), in order to better represent the relative intensity of the e¤ect of each state variable

we chose to show the product between the factor loading and the standard deviation Bus0

Nx3

�us;instead of

presenting just the factor loading Bus0

3xN.

13This is due to the fact that we use monthly data. The famous 3 latent variables is usually used for models of daily

data.

15

What drives US Treasury Term Structure?St. Dev * Factor Loading

­0.3%

­0.2%

­0.1%

0.0%

0.1%

0.2%

0.3%

0.4%

6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90 93 96 99 102

105

108

111

114

117

120

123

Yield

Unobs_USCPIUnemp

What drives US Term Structure? (st. dev.*factor loading)

As usual, we can label the US latent variable as level, since its e¤ect is almost the same in all treasury

yields. Notice that CPI and the latent variable a¤ect the yields positively and almost with the same

pattern, i.e. with a slight negative slope. This corroborates Rudebusch and Wu�s interpretation of this

latent variable as trend in�ation. Furthermore, the e¤ect of unemployment is negative, with a much

more important impact on short rates. In other words, an increase in US in�ation or in the latent

(expected US in�ation) provokes an increase in all US interest rates, while an increase in unemployment

provokes a decrease in all US term structure, a¤ecting also its slope.

Con�rming the �nds of Ang and Piazzesi (2003) and Rudebusch and Wu (2004), the inclusion of

observable macroeconomic variables shows its importance. More than 40% of the movements in the US

treasury yields are explained by the movements in these unemployment and in CPI, as can be seen in

table (4.1).

4.2 Results for the Emerging Economies

First, we present the latent variables realizations and their interpretation. Then, we show how important

each of the state variables is for explaining the movements of the spread term structure. Finally, we

present impulse response functions of yield spreads for shocks in each state variable.

4.2.1 Interpreting the latent variables

The estimation for the emerging countries was done jointly in order to recover the joint latent variable,

Jt common to all emerging economies. Besides Jt, each one of the three emerging countries in our sample

16

has its idiosyncratic factor Ut(i) for i = Bra;Mex;Col. As will be shown on the next section, the e¤ect

of Jt on all the yields is negative and the e¤ect of each Ut(i) is positive.

In order to interpret the latent variables, recall that we are controlling for the e¤ect of a set of

observable economic variables: US macroeconomic conditions (US CPI in�ation, US unemployment and

the US latent factor "level") and solvency variables from each emerging country (total debt/GDP and

external debt/exports). So the latent variables must be measuring everything else that is not being

captured by the e¤ect of those variables. Since one of them is common to all emerging countries, we

interpret it as international liquidity or global risk propensity. On the other hand, assuming that our

solvency variables adequately capture the relevance of each country economic environment, the country

speci�c latent variable should be re�ecting predominantly the country political environment.14

The Joint Latent Variable vs. Minus Average Yields (all emerging countries in all maturities)

­1.5

­1.4

­1.3

­1.2

­1.1

­1

­0.9

­0.8

­0.7

­0.6

­0.5

mar/98

jun/98set

/98

dez/98

mar/99

jun/99set

/99

dez/99

mar/00

jun/00set

/00

dez/00

mar/01

jun/01set

/01

dez/01

mar/02

jun/02set

/02

dez/02

mar/03

jun/03set

/03

dez/03

mar/04

jun/04set

/04

dez/04

mar/05

jun/05set

/05

­0.14

­0.12

­0.1

­0.08

­0.06

­0.04

­0.02

0

J (LHS) Minus Average Yields (RHS)

Aug/98:Russian

Crisis

Jan/99:Brazilian

RealDevaluation

Jul/02 ­ Oct/02:Brazil electoral

crisis

The above �gure depicts the resulting dynamic of Jt. Since the e¤ect of Jt on all country spreads

is negative, as we show below, we contrast it with the negative of the total average of the sovereign

spreads.15 Their pattern is extremely similar, which corroborates our interpretation of this variable as

international liquidity to Latin-American countries or the risk propensity for Latin-American countries.16

We can identify the cause of some important movements in Jt. First, the recent increasing trend

in international liquidity, which is pushing down emerging market spreads, can be clearly identi�ed in

14On an earlier version of this paper, we didn�t include the joint latent factor for the emerging economies, only one

idiosyncratic for each emerging. In this formulation, the estimation was done independently for each emerging country.

However, after the output produced a dynamic of the resulting latent variables almost coincidental, their correlation being

higher that 0.9. For this reason we decided to include this joint latent factor in the model.

15At each point in time we averaged all the 7 yields and all countries: = �3P

country=1

7Pduration=1

ycountry;duration(t)=21

16 In this sense, Jt is similar to the negative of an EMBI for Latin America.

17

the graph. We can also notice crisis events that drove all the spreads down: (i) the Russian crisis of

1998; (ii) the Brazilian Real devaluation of Jan/1999 and (iii) The recent Brazilian electoral crisis in

2002, know as Lula e¤ect17 . Even though all of those events were triggered at a speci�c country, there

were undoubtedly contagion to all emerging countries in our sample, since Jt was de�ned to a¤ect those

countries altogether.

Idiosyncratic Latent Variables: Political Risk?

­150

­100

­50

0

50

100

150

mar/98

jun/98set

/98

dez/98

mar/99

jun/99set

/99

dez/99

mar/00

jun/00set

/00

dez/00

mar/01

jun/01set

/01

dez/01

mar/02

jun/02set

/02

dez/02

mar/03

jun/03set

/03

dez/03

mar/04

jun/04set

/04

dez/04

mar/05

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/05

930

940

950

960

970

980

990

1000

1010

1020

1030

U_BraU_MexU_Col

We plot the dynamics of the idiosyncratic latent factors. As it will be shown later, an increase in

these variables leads to an increase in the yields. Since we control for local and US economic conditions,

and for international liquidity (Jt), we interpret them as speci�c political risk.

This "political risk factor" is relatively stable in Mexico and has a random pattern for Colombia. In

Brazil, however, we can clearly identify trends, and relate it to known events. Until 2002, when Cardoso

was in o¢ ce, we can see a slow downward trend in "Brazil�s political risk", until the 2002 election. On

July, there is an increase in this variable - not as much as we know the risk actually increased, because

much of it is being captured by Jt once there was some contagion to other countries. After it became

clear that the approach of the new government would be market friendly, the pace of the downward trend

increased. In the end of 2003, after one year of Lula in charge, the "Brazilian political risk" reached

its lowest levels. However, in 2004, a series of corruption scandals appeared and, as a consequence, the

trend in the "political risk" variable reversed. In 2005, as the deterioration of the political environment

continued, the latent factor continue to increase, reaching a level of 41.1 on October, which is higher

than the Cardoso�s term average (34.2).

17The market feared the victory of the left wing candidate Lula because of the past non-market friendly comitments

of him and his party, including the mention of default on public debt. As the perception that he would have a �scaly

responsible and market friendly approach, the crisis reverted.

18

4.2.2 Accounting for term structure movements

The methodology we use allow us to assess the relative importance of each state variable in explaining

movements in the term structure of emerging market spread. The spreads are given by the formula

presented in theorem 1: sNt = A�N +B

�0NXt, where N refers to the duration of the yield, where the factor

loadings depend on the parameters that determine the dynamics for the state variables.18 . As above,

instead of presenting only the factor loadings, we multiply them by the covariance matrix so that their

values are directly comparable. We plot below the graph of B�0

Nx7

�7x7

for Brazil, Mexico and Colombia as

a function of term structure durations (N = 1 month to 120 months).

What Drives Brazilian Spread?Factor Loading*Sigma

­0.025

­0.02

­0.015

­0.01

­0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109 113 117 121 125

USCPIUnempJointU_BraD_BraX_Bra

What Drives Mexican Spread?Factor Loading*Sigma

­2.50E­02

­2.00E­02

­1.50E­02

­1.00E­02

­5.00E­03

0.00E+00

5.00E­03

1.00E­02

1.50E­02

2.00E­02

2.50E­02

3.00E­02

3.50E­02

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109 113 117 121 125

USCPIUnempJointU_MexD_MexX_Mex

What Drives Colombian Spread?Factor Loading*Sigma

­2.50E­02

­2.00E­02

­1.50E­02

­1.00E­02

­5.00E­03

0.00E+00

5.00E­03

1.00E­02

1.50E­02

2.00E­02

2.50E­02

3.00E­02

3.50E­02

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109 113 117 121 125

USCPIUnempJointU_ColD_ColX_Col

Another analysis of interest is variance decomposition. For each duration of the term structure, we

are able to measure the percentage of its variance explained by each of the state variables. We present

below the graph of the variance decomposition of the spread curve, i.e., the variance explained by each

one of the state variables for each duration.18 In fact, our estimation procedure uses term structure data and this relation between factor loadings and parameter

values as an additional source of information for the parameters that govern the state variables dynamics. So we have the

parameters estimates and the factor loadings as a joint output of our estimation.

19

What Drives Brazilian Spread?% explained by each state variable

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109 113 117 121 125

Duration

What Drives Mexican Spread?% explained by each state variable

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109 113 117 121 125

Duration

What Drives Colombian Spread?% explained by each state variable

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109 113 117 121 125

Duration

To summarize the information contained in the last three graphs, it is helpful to average out the

variance explained by each factor for each country, as shown in the table below.

Brazil Mexico Colombia USAUnobs_USA 1.9% 0.2% 0.3% 59.88%

CPI_USA 3.2% 0.6% 1.9% 9.91%Unemp_USA 17.8% 8.1% 5.0% 30.21%

Joint 56.0% 25.3% 44.7% ­U 15.3% 20.2% 48.1% ­

Total Publ Debt / GDP 5.8% 1.3% 0.0% ­Net Public External Debt / Exports 0.0% 44.2% 0.0% ­

% of variance explained by each state variable (average of all yields)

6 months 3 years 10 years 6 months 3 years 10 years 6 months 3 years 10 years 6 months 3 years 10 years

Unobs_USA 1.1% 1.59% 2.61% 0.0% 0.10% 0.37% 0.0% 0.2% 0.56% 48.60% 55.75% 68.22%CPI_USA 4.6% 3.95% 1.86% 1.6% 0.94% 0.03% 1.8% 1.9% 1.85% 12.78% 10.95% 7.79%

Unemp_USA 19.8% 19.43% 14.90% 10.8% 9.04% 6.29% 7.4% 5.7% 3.42% 38.61% 33.30% 23.99%Joint 38.3% 50.61% 67.28% 21.4% 23.86% 28.18% 47.1% 46.0% 42.09% ­ ­ ­

U 25.6% 17.74% 9.82% 24.9% 22.14% 16.40% 43.8% 46.2% 52.07% ­ ­ ­Total Publ Debt / GDP 10.7% 6.68% 3.53% 2.6% 1.50% 0.74% 0.0% 0.0% 0.00% ­ ­ ­

Net Public External Debt / Exports 0.0% 0.00% 0.00% 38.7% 42.41% 47.99% 0.0% 0.0% 0.00% ­ ­ ­

Colombia USA% of variance explained by each state variable (several yields)

Brazil Mexico

The single most important variable is the joint latent variable, interpreted as international liquidity.

Its movements accounts for around 42% of the emerging markets spread. As can be seen in Figure 5,

the e¤ect of this variable in all countries and in all yields is negative. This means that an increase in

Jt leads to a reduction of all yields in all countries. Jt is more important for Brazil, where it accounts

for 56.6% of the movements in the yields, than for Colombia (46.2%) and Mexico (25.6%). It is also

interesting to note that the relative importance of this variable increases substantially with the duration

for Brazil. It increases slightly with duration for Mexico, and decreases slightly for Colombia.

20

US variables account for approximately 14% of the movements in the spread term structure. Observe

that the e¤ect on emerging market yields is still more important, since US macro variables also a¤ect

US yields, which should be added to the spreads. The single most important US variable a¤ecting the

spread is the unemployment rate, with a positive relation. This means that when the US economy

is doing well, the emerging economy spreads are smaller. The US unemployment rate accounts for

19.2% of the movements in Brazilian spread, 8.6% of the Mexican spread and 5.8% of the Colombian

spread. The US CPI in�ation accounts for 3.9% in Colombia, 1.2% in Brazil and 0.7% in Mexico. It

is somehow surprisingly that, even being closer to the US and having the tightest economic relation

(through NAFTA) among countries in our sample, the e¤ects of US variables in Mexico spreads are

much less important than in Brazil.

The idiosyncratic political factor accounts for 20.1% of the spread movements in Mexico and for

15.6% of the movements in Brazil. Although proportionally this factor is more important for Mexico

than for Brazil, two observations must be made. First, the magnitude of the e¤ect in Brazil is higher

than in Mexico, as can be seen comparing the purple lines in Figure 5. Second, as we argued before,

some events triggered by Brazilian events are being captured by the variable Jt because there were some

contagion, i.e., some joint movements on the yields and thus our model attributed such movements to

the joint unobservable variable19 .

The solvency variables are much more important for Mexico (45%) than for Colombia20 and Brazil

(less than 6%). We believe that a related result is that the idiosyncratic latent variable (political risk) is

much more important for Brazil and Colombia than for Mexico. We conjecture that the cause of these

two phenomena is the fact that Mexico is an investment grade country while Brazil and Colombia are

not.

4.3 Impulse Responses

We present below the impulse response analysis. Each graph depict the response of emerging countries

yields to shocks on each state variable. We chose to present only two yields for each country: one year

19For Colombia the contribution of this idiosyncratic "political risk" is very high, 46,2% on average. But what can be

exacerbating the contribution of this variable in Colombia is the fact that the solvency rations are in fact quarterly data

interpolated to monthly frequency. For this reason we believe that the contribution of the idiosyncratic unobservable is

higher than should be and the solvency ratios are lower than they should be.

20As in the case of the excessive sensibility to the idiosyncratic political risk factor, the fact that in Colombia solvency

ratios are responsible for less than 1% can be understood if we recall that these ratios are actually quarterly and were

interpolated to monthly frequency. We belive the importance of these solvency ratios is totally incorporated by the

idyosincratic unobservable variable.

21

and seven years21 .

Response to 1 st. deviation shock onUS latent factor

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

1.20%

t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10 t+11 t+12 t+13 t+14 t+15 t+16 t+17 t+18 t+19 t+20 t+21 t+22 t+23 t+24 t+25 t+26 t+27 t+28 t+29 t+30 t+31 t+32 t+33 t+34 t+35

Brazil 1 year Brazil 7 years Mexico 1 year Mexico 7 years Colombia 1 year Colombia 7 years

Response to 1 st. deviation shock onUS inflation

­0.20%

­0.15%

­0.10%

­0.05%

0.00%

0.05%

t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10 t+11 t+12 t+13 t+14 t+15 t+16 t+17 t+18 t+19 t+20 t+21 t+22 t+23 t+24 t+25 t+26 t+27 t+28 t+29 t+30 t+31 t+32 t+33 t+34 t+35

Brazil 1 year Brazil 7 years Mexico 1 year Mexico 7 years Colombia 1 year Colombia 7 years

Response to 1 st. deviation shock onUS unemployment

0.00%

0.10%

0.20%

0.30%

0.40%

0.50%

0.60%

0.70%

0.80%

0.90%

1.00%

t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10 t+11 t+12 t+13 t+14 t+15 t+16 t+17 t+18 t+19 t+20 t+21 t+22 t+23 t+24 t+25 t+26 t+27 t+28 t+29 t+30 t+31 t+32 t+33 t+34 t+35

Brazil 1 year Brazil 7 years Mexico 1 year Mexico 7 years Colombia 1 year Colombia 7 years

Response to 1 st. deviation shock on"International Liquidity"

­2.00%

­1.75%

­1.50%

­1.25%

­1.00%

­0.75%

­0.50%

­0.25%

0.00%

0.25%

t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10 t+11 t+12 t+13 t+14 t+15 t+16 t+17 t+18 t+19 t+20 t+21 t+22 t+23 t+24 t+25 t+26 t+27 t+28 t+29 t+30 t+31 t+32 t+33 t+34 t+35

Brazil 1 year Brazil 7 years Mexico 1 year Mexico 7 years Colombia 1 year Colombia 7 years

Response to 1 st. deviation shock onIdiosyncratic "Political Risk"

0.00%

0.10%

0.20%

0.30%

0.40%

0.50%

0.60%

0.70%

0.80%

0.90%

1.00%

1.10%

1.20%

t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10 t+11 t+12 t+13 t+14 t+15 t+16 t+17 t+18 t+19 t+20 t+21 t+22 t+23 t+24 t+25 t+26 t+27 t+28 t+29 t+30 t+31 t+32 t+33 t+34 t+35

Brazil 1 year Brazil 7 years Mexico 1 year Mexico 7 years Colombia 1 year Colombia 7 years

Response to 1 st. deviation shock on a 1% shock onTotal Public Debt/GDP

0.00%

0.05%

0.10%

0.15%

0.20%

0.25%

0.30%

0.35%

t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10 t+11 t+12 t+13 t+14 t+15 t+16 t+17 t+18 t+19 t+20 t+21 t+22 t+23 t+24

Brazil 1 year Brazil 7 years Mexico 1 year Mexico 7 years Colombia 1 year Colombia 7 years

Response to 1 st. deviation shock on a 1% shock onPublic External Debt/Exports

0.00%

0.02%

0.04%

0.06%

0.08%

0.10%

0.12%

0.14%

0.16%

t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+10 t+11 t+12 t+13 t+14 t+15 t+16 t+17 t+18 t+19 t+20 t+21 t+22 t+23 t+24

Brazil 1 year Brazil 7 years Mexico 1 year Mexico 7 years Colombia 1 year Colombia 7 years

5 Conclusions

What drives risk-premium of emerging market countries external bonds? More precisely, what are the

most important economic factors behind the movements on the term-structure of emerging spread? To

answer this question we extended Ang and Piazzesi�s (2003) no-arbitrage term-structure macro model

21Two yields allow us to see movements in the term structure slope. We could have presented movements for the whole

curve, but the �gures would become cumbersome.

22

by allowing for the possibility of default, therefore allowing us to use such models to explain emerging

market spreads. We presented a discrete time model, which is closely related to Du¢ e and Singleton

(1999).

Theoretically, one of the important results we got is that one of the crucial condition for getting a

closed formula is that the stochastic discount factor should be predetermined with respect to default. In

our speci�c application it should not depend on emerging country variables that a¤ect default contempo-

raneously (as for example, solvency ratios). The emerging markets external debt is an environment that

�ts well this necessary assumption, once one �nds plausible the hypothesis that the stochastic discount

factor of the relevant investors (US based, for example) is not a¤ected by the emerging markets risk.

Thus, our speci�cation strategy relies on the assumption that the pricing of external bonds of emerging

countries re�ects the preferences of US investors.

The paper then investigates the determinants of the term structure of emerging market external debt

for Brazil, Colombia and Mexico. In particular our methodology allowed us to assess the importance

of US macroeconomic factors, country�s solvency ratios and latent variables in determining the risk

premium term-structure.

According to a fundamentalist view, the country risk premium should re�ect only the country con-

ditions. However, country solvency ratios and idiosyncratic latent variables account for only 21% of the

variability of the risk premium for Brazil and Mexico. Then, international liquidity and the state of

US macroeconomy are more important than the country condition. One could also object that for big

countries as Brazil and Mexico, the international liquidity is in part determined by the state of their

economies. Even if one take the extreme view to attribute to the emerging market economy the part

explained by their joint latent factor, one is still left with 23% of the variability of Brazil premium

explained by US macroeconomic conditions.

This evidence indicates that international �nancial markets are ine¢ cient, where the country funda-

mentals are not the most important determinant of their bond prices. The methodology of combining

macro variables in a non-arbitrage framework opened a new investigation path for this question, which

should generate more research and results under alternative speci�cations.

6 References

Almeida, C.I. (2003) "Time-Varying Risk Premia in Emerging Markets: Explanation by a Multi-Factor

A¢ ne Term Structure Model", International Journal of Theoretical and Applied Finance , Vol. 7, 7,

(2004) 919-947

Ang, A. and M. Piazzesi (2003) "A No-Arbitrage Vector Autoregression of Term Structure Dynamics

with Macroeconomic and Latent Variables" Journal of Monetary Economics 50, 745-787

23

Bekaert, G., S. Cho, and A. Moreno (2005), New Keynesian Macroeconomics and the Term Structure.

NBER working paper.

Campbell, J.Y., Shiller, R.J., (1991) "Yield spreads and interest rate movements: a bird�s eye view"

Review of

Economic Studies 58, 495�514.

Campbell, J. Y., A. Lo and C. MacKinley (1997) "The Econometrics of Financial Markets" Princeton

University Press, New Jersey

Chen, R.R., Scott, L., (1993) "Maximum likelihood estimation for a multi-factor equilibrium model

of the term structure of interest rates" Journal of Fixed Income 3, 14�31.

Cox, J. C., J. E. Ingersoll, Jr. and S. A. Ross (1985) "A Theory of the Term Structure of the Interest

Rates" Econometrica 53, 385-407

Dewachter, H. and M. Lyrio (2005), A Structural Macro Model of the Yield Curve with Stochastic

Endpoints. Manuscript. Catholic University of Leuven.

Diebold, F., Piazzesi, M. and and Rudebusch, G. (2005) �Modeling Bond Yields in Finance and

Macroeconomics�American Economic Review P&P Volume 95, Issue 2, pp. 415-420.

Du¢ e, D. and R. Kan (1996) "A Yield-Factor Model of Interest Rates" Mathematical Finance 6:

379-406

Du¢ e, D., L. H. Pedersen and K. J. Singleton (2003) "Modeling Sovereign Yield Spreads: A Case

Study of Russian Debt�, Journal of Finance, Vol. LVIII, No. 1, pp. 119-159.

Du¢ e, D. and K. J. Singleton (1999) "Modeling Term Structures of Defaultable Bonds" Review of

Financial Studies 12, 687-720

Estrella, A., F.S. Mishkin (1997) "The predictive power of the term structure of interest rates in

Europe and

the United States: implications for the European central bank" European Economic Review 41:1375�

1401

Evans, C.L., D.A. Marshall (1998) "Monetary policy and the term structure of nominal interest rates:

evidence and theory" Carnegie-Rochester Conference Series on Public Policy 49:53�111

Litterman, R., Scheinkman, J., (1991) "Common factors a¤ectingbond returns" Journal of Fixed

Income 1, 51�61.

Hördal, P., O. Tristani and D. Vestin (2003) A Joint Econometric Model of Macroeconomic and

Term Structure Dynamics. Journal of Econometrics, forthcoming.

Matrumura, M. and Moreira, A. (2005) "Can Macroeconomic Varaibles Account for the Term Struc-

ture of Sovereign Spreads? Studying the Brazilian Case" IPEA TEXTO PARA DISCUSSÃO N� 1106

Meese, R. and Rogo¤, K. (1983) "Empirical Exchange Rate Models of the seventies: Do they �t

out-of-sample?" Journal of International Economics 14: pg. 3-24

24

Rudebusch, G. and T. Wu (2004) "A Macro-Finance Model of the Term Structure, Monetary Policy

and the Economy" Federal Reserve Bank of San Francisco Working Paper 2003-17

Taylor, J.B., (1993) "Discretion versus policy rules in practice" Carnegie-Rochester Conference

Series on Public Policy 39, 195�214.

Vasicek, O.(1977) "An Equilibrium Characterization of the Term Structure" Journal of Financial

Economics 5, 177-188

Appendix A

Proof of Theorem 1

The proof is by induction. We already shown that pNt = AN + B0NXt is valid for N = 1. Suppose

that the log price of a N � 1 period default-free bond is given by pN�1t = AN�1 +B0N�1Xt. We can use

2 and the state variable dynamics of last section to proof that the log price of an N period bond is:

pNt = Et�lnmt+1 + p

N�1t+1

�+1

2vart

�lnmt+1 + p

N�1t+1

�= �1

2�0t�t � �0 � �01Xus

t +AN�1 +Bus0N�1EtX

ust+1 +

1

2vart

h��0t"t+1 +Bus

0N�1X

ust+1

i= �1

2�0t�t � �0 +AusN�1 +Bus0N�1�+

�Bus

0N�1�

us � �01�Xt +

1

2vart

hB0N�1�

us"t+1 � �0t"t+1i

= �12�0t�t � �0 +AN�1 +B

0N�1�+

�B0N�1�

us � �01�Xt

+1

2B0N�1�

us�usB0N�1 +

1

2�0t�t �B

0N�1�

us�t

= ��0 +AN�1 +B0N�1 (�

us � �us�0) +1

2B0N�1�

us�usB0N�1

+�B0N�1 (�

us � �us�1)� �01�Xust

Thus, substituting pNt by AN +B0NXt on the left-hand side:

AN +B0NXt = ��0 +AN�1 +B

0N�1 (�� ��0) +

1

2B0N�1��

0BN�1

+�B0N�1 (� + ��1)� �01

�Xt

By equating the coe¢ cients on the left and right hand side we prove the theorem

Proof of Theorem 2

The proof is by induction. We already shown that pNt = pus(N)t +A�N +B�

0NXt is valid for N = 1.

Suppose that the log price of a N � 1 period defaultable bond is given by pN�1t = pus(N�1)t +A�N�1 +

25

B�0N�1Xt. We can use 6 and the state variable dynamics of last section to proof that the log price of an

N period bond is:

p(N)t = Et

�lnmt+1 + ln�t+1 + p

(N�1)t+1

�+1

2V art(lnmt+1 + ln �t+1 + p

(N�1)t+1 )

= Et

��12�0t�t � �0 � �01Xus

t � �0t"ust+1 � �o � �01Xt � �0"t+1 + pus(N�1)t+1 :::+A�N�1 +B�

0N�1Xt+1

�+

1

2V art(��0t"ust+1 � �0"t+1 +B

0N�1X

ust+1 +B

�0N�1Xt+1)

= �12�0t�t � �0 � �01Xus

t � �o � �01Xt +AN�1 +B0N�1�

us +B0N�1�

usXust +A�N�1 +

B�0N�1�+B

�0N�1�Xt +

1

2V art(��0t"ust+1 � �0"t+1 +B

0N�1�

us"ust+1 +B�0N�1�"t+1) (14)

Let�s extend the 12V ar() term:

1

2V art(::) =

1

2V art(�

0t"ust+1) +

1

2V art(�

0"t+1) +1

2V art(B

0N�1�

us"ust+1) +1

2V art(B�

0N�1�"t+1)

+Covt(�0t"ust+1; �

0"t+1)� Covt(�0t"ust+1; B0N�1�

us"ust+1)� Covt(�0t"ust+1; B�0N�1�"t+1)�

�Covt(�0"t+1; B0N�1�

us"ust+1)� Cov(�0"t+1; B�0N�1�"t+1) + Cov(B

0N�1�

us"ust+1 +B�0N�1�"t+1)

=1

2�0t�t +

1

2�0� +

1

2B0N�1�

us�us0BN�1 +1

2B�

0N�1��

0B�N�1 + Cov(:) (15)

Notice that on the covariance terms, we have a lot of Cov(C 0"ust+1; D0"t+1) terms. The "ust are the

�rst K1 lines corresponding to the errors on the K1 US variables on the K = K1 +K2 line vector "t .

Formally, �!" tKx1

=

2664�!"ustK1x1��!"emtK2x1

3775 where, as before, E(�!"t�!"t 0) = IKxK

. With no loss of generality we can re-write

the terms on D01xK

=

�Dus

1xK1

0 Dem01xK2

�: Thus,

Cov(C 0"ust+1; D0"t+1) = E(C 0"ust+1"

0t+1D)

= E

0B@ C 01xK1

�!"ustK1x1

�!"ust1xK1

0 ��!"emt1xK2

0

264 Dus

K1x1

Dem

K2x1

3751CA

= C 01xK1

�I

K1xK1

0K1xK2

�264 Dus

K1x1

Dem

K2x1

375= C 0

1xK1

Dus

K1x1

So, in solving the Cov we will assign the Dus to the �rst K1 elements of a vector D, the ones

26

multiplying the US state variables . Having said that, the Cov(::) term on 15 can be substituted by:

Cov(::) = �0t�us � �0t�us0BN�1 � �0t�us0Bus�N�1 �

��us0�us0BN�1 � �us0�0B�N�1 +B0N�1�

us�us0Bus�N�1

Substituting Cov(:) in 15 and then all that in 14 we have:

p(N)t = ��0 � �01Xus

t � �o � �01Xt +AN�1 +B0N�1�

us +B0N�1�

usXust +A�N�1 +B�

0N�1�+B

�0N�1�Xt +

1

2�0� +

1

2B0N�1�

us�us0BN�1 +1

2B�

0N�1��

0B�N�1 + �0t�us � �0t�us0BN�1 � �0t�us0Bus�N�1 �

��us0�us0BN�1 � �0�0B�N�1 +B0N�1�

us�us0Bus�N�1

Recalling that �t = �0 + �01X

ust :

p(N)t =

��AN�1 +B

0N�1(�

us � �us�0) +1

2B0N�1�

us�us0BN�1 � �0�+hB0N�1(�

us � �us�01)� �01)iXust

���o � �01Xt +A�N�1 +B�

0N�1�+B

�0N�1�Xt +

1

2�0� +

1

2B�

0N�1��

0B�N�1 +

�us0�0 + �us0�1X

ust �B�us0N�1�us�0 �B�us

0N�1�

us�1Xust � �us0�us0BN�1 � �0�0B�N�1 +B

0N�1�

us�us0Bus�N�1

Using Theorem 1, f:::g = AN +BNXust = p

us(N)t

p(N)t = p

us(N)t +

A�1z }| {

(1

2�0� + �us0�0 � �o) +

B�01Xtz }| {

(�us0�1Xust � �01Xt) +A�N�1 +B�

0N�1�+B

�0N�1�Xt +

1

2B�

0N�1��

0B�N�1 �B�us0N�1�

us�0 �B�us0N�1�

us�1Xust � �us0�us0BN�1 � �0�0B�N�1 +B

0N�1�

us�us0Bus�N�1

p(N)t = p

us(N)t +A�1 +A�N�1 +B�

0N�1�+

1

2B�

0N�1��

0B�N�1 �B�us0N�1�

us�0 � �us0�us0BN�1 � �0�0B�N�1 +B0N�1�

us�us0Bus�N�1 +

+B�01Xt +B

�0N�1�Xt �B�us

0N�1�

us�1Xust

= pus(N)t +

�A�1 +A�N�1 +B�

0N�1(�+

1

2��0B�N�1)�B�us

0N�1�

us�0 � �us0�us0BN�1 � �0�0B�N�1 +B0N�1�

us�us0Bus�N�1

�+

+

("Bus�

01

1xK1

+�B�

0N�1�

�us1xK1

�B�us0N�1�us�11xK1

Bem�01

1xK2

+�B�

0N�1�

�em1xK2

#XtKx1

)

Thus, substituting pNt by pus(N)t +A�N +B�

0NXt on the left-hand side and equating the coe¢ cients:

B�0N

1xK

��Bus�

0N

1xK1

Bem�0N

1xK2

�0=

"Bus�

01

1xK1

+�B�

0N�1�

�us1xK1

�B�us0N�1�us�11xK1

Bem�01

1xK2

+�B�

0N�1�

�em1xK2

#0= B�

01

1xK

+B�0N�1�1xK

��B�us

0N�1�

us�11xKus

01xKem

�(16)

27

and

A�N = A�1+A�N�1+B�0N�1(�+

1

2��0B�N�1)�B�us

0N�1�

us�0��us0�us0BN�1��0�0B�N�1+B0N�1�

us�us0Bus�N�1

(17)

Appendix B

The space-state representation.

The dynamics of the state variables are given by equation (7): Yt = � + �0Yt�1 + �"t; where the

state variables are:

Yt =

26666666666666666666666666666666664

UUSt

�t

yt

JEMt

UBrat

D=Y Brat

Dx=ExBrat

UMext

D=YMext

Dx=ExMext

UColt

D=Y Colt

Dx=ExColt

37777777777777777777777777777777775The observation equation is Xt = A� +HYt +Nut where Xt are the observable variables,

Xt(29x1)

=

26666666666666666666666666666664

�t

yt

D=Y Brat

Dx=ExBrat

D=YMext

Dx=ExMext

D=Y Colt

Dx=ExColt

spreadBrat(7x1)

spreadBrat(7x1)

spreadBrat(7x1)

37777777777777777777777777777775

where spreadit(7x1)

=

26666666666666664

spreadi6months(t)

spreadi1year(t)

spreadi2years(t)

spreadi3years(t)

spreadi5years(t)

spreadi7years(t)

spreadi10years(t)

37777777777777775.

Nut are the observation errors. The constants are de�ned as follows,

28

A�(30x1)

=

26666666664

0(9x1)

ABra(7x1)

AMex

(7x1)

ACol(7x1)

37777777775where, Ai

(7x1)=

26666666666666664

Ai6months

Ai1year

Ai2years

Ai3years

Ai5years

Ai7years

Ai10years

37777777777777775for i = Bra;Mex;Col

And,

H(30x13)

=

2666666666666666666666666666666664

1 0 0 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 0 0 0 0 0

0 0 1 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 0 0 0 1

BBra(7x13)

BMex

(7x13)

BCol(7x13)

3777777777777777777777777777777775

29