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1
Credit Spread Arbitrage in
Emerging Eurobond Markets
Caio Ibsen Rodrigues de Almeida *
Antonio Marcos Duarte, Jr. **
Cristiano Augusto Coelho Fernandes ***
Abstract
Simulating the movements of term structures of interest rates plays an important role when
optimally allocating portfolios in fixed income markets. These movements allow the
generation of scenarios which, on their turn provide the assets’ sensibility to the fluctuation of
interest rates. The problem becomes even more interesting when the portfolio is international.
In this case, there is a need to synchronize the different scenarios for the movements of the
interest rate curves in each country. An important factor to consider, in this context, is credit
risk. For instance, in the corporate Emerging Eurobond fixed income market there are two
main sources of credit risk: sovereign risk and the relative credit among the companies issuers
of the eurobonds. This paper presents a model to estimate, in a one step procedure, both the
term structure of interest rates and the credit spread function of a diversified international
portfolio of eurobonds, with different credit ratings. The estimated term structures can be used
to analyze credit spread arbitrage opportunities in Eurobond markets. Numerical examples
taken from the Argentinean, Brazilian and Mexican Eurobond markets are presented to
illustrate the practical use of the methodology.
Please address all correspondence to:
Cristiano Augusto Coelho Fernandes
Rua Marquês de São Vicente, 225 - Gávea
22453-900, Rio de Janeiro, RJ, Brazil
Electrical Engineering Department
Phones: 55-21-5299415 or 55-21-5375905
E-mail: Cris@ele.puc-rio.br
* Pontifícia Universidade Católica do Rio de Janeiro, Brazil. E-mail: caio@ele.puc-rio.br
** Unibanco S.A., Brazil. E-mail: antonio.duarte@unibanco.com.br
*** Pontifícia Universidade Católica do Rio de Janeiro, Brazil.
2
1. Introduction
The prices of fixed income assets depend on three components (Litterman
and Iben [1988]): the risk free term structure of interest rates, embedded options
values and credit risk. Optimally allocating portfolios in fixed income markets
demands a detailed analysis of each of these components.
Several authors have already considered the risk free term structure
estimation problem. For example, Vasicek and Fong [1982] suggest a statistical model
based on exponential splines. Litterman and Scheinkman [1991] verified that there are
three orthogonal factors which explain the majority of the movements of the US term
structure of interest rates. These three factors form the basis for many fixed income
pricing and hedging applications. For instance, these factors are used in Singh [1997]
to suggest optimal hedges.
Some bonds present embedded options. In general, the price of an embedded
option is a nonlinear function of its underlying bond price on all dates before the
option maturity date. An embedded option depends not only on the actual term
structure of interest rates, but also on the evolution of this term structure during the
life of the option. Several models have been proposed for the evolution of the term
structure of interest rates. These models are classified in two major groups (Duffie
[1992]): equilibrium models (Vasicek [1977], Cox et al. [1985], among others) and
arbitrage free models (Ho and Lee [1986], Black et al. [1990], Heath et al. [1992],
among others). At this point in time, the pricing of embedded options using arbitrage
free models is perceived as the most appropriate because the parameters can be
chosen to be consistent with the actual term structure of interest rates and,
consequently, to the actual prices of bonds (Heath et al. [1992]). The process modeled
can be the short-term interest rate, the whole term structure of interest rates, or the
3
forward rates curve. No matter what the process is, when it is Markovian, it is usually
implemented using binomial trees (Black et al. [1990]) or trinomial trees (Hull and
White [1993]).
Almeida et al. [1998] presented a model to decompose the credit risk of term
structures of interest rates using orthogonal factors (Sansone [1959]), such as
Legendre [1785] polynomials. In this model, the term structure of interest rates is
decomposed in two curves: a benchmark curve and a credit spread function. The last
one is modeled using a linear combination of Legendre polynomials.
In this article we present a model to estimate, in a single step, both the term
structure of interest rate and the credit spread function of an international portfolio of
bonds with different credit ratings. This model extends the approach proposed in
Almeida et al [1998]. It allows the joint estimation of the credit spread function of any
international portfolio with different credit ratings. This extension is crucial when
analyzing credit spread arbitrage opportunities in fixed income markets. For the
purpose of illustration, we concentrate on the Emerging Corporate Eurobond market,
studying the three most important in Latin America: Argentina, Brazil and Mexico.
However, the methodology is quite general, and can be applied to any fixed income
portfolio composed by bonds with different credit ratings.
This article is organized as follows. Section 2 explains the model. Section 3
presents the estimation process for its parameters. Section 4 explains the methodology
used for optimally allocating portfolios using the model. Section 5 presents three
practical examples of detection and exploitation of arbitrage opportunities in the Latin
American Eurobond market. Section 6 presents a summary of the article, and the
conclusions.
4
2. The Model
We want to analyze a portfolio in the Emerging Eurobond market. Assets with
the same cash flow and embedded option structures, but different credit ratings, ought
to have different prices. For this reason, when structuring fixed income portfolios, it is
fundamental to estimate and simulate the movements of different term structures of
interest rates, one for each credit rating in the portfolio. One possibility would be to
estimate a term structure, for each credit rating. There is a statistical problem with the
amount of data available when relying on this approach: in the emerging eurobond
market there are usually very few liquid bonds for each credit rating. A joint
estimation procedure is necessary.
An interesting possibility is to capture the difference in risk between credit
ratings using different credit spread functions. Using this approach, it is possible to
estimate in a single step the term structures for different credit ratings by modifying
the proposal in Almeida et al. [1998].
The equation that describes the term structure of an Emerging Eurobond
market (that is, fixed income instruments of one country, issued in a same currency,
with the same credit rating) can be written as
)1( ].,0[,)1
2
()()( 0
l
l∈∀−+= ∑
≥t
t
PctBtRn
nn
where
t
denotes time, )(tB is a benchmark (for example, the US term structure), n
P is
the Legendre polynomial of degree
n
, n
c is a parameter to be estimated, and l is the
largest maturity of a bond in the Emerging Eurobond market under consideration.
The price of a bond ( A
P) is related to the term structure of interest rates as
5
)2( ))(exp(
1
∑
=−= A
n
iiiiAtRtCP
where i
C denotes the th
i cash flow paid by the bond at time i
t, and A
n denotes the
total number of cash flows paid by the bond.
Setting up the notation, variables ,,...,1,Jjrj=denote different credit ratings.
For instance, a credit rating such as AAA may be associated with 1
r, a credit rating
such as AA1 may be associated with 2
r, and so on.
An extension of )1( is to consider the spread function depending on the
different credit ratings, such as
)3( ].,0[),,...,,()(),...,,(11 l∈∀+= trrtCtBrrtRJJ
The spread function ),...,,(1J
rrtC can be modeled as a linear combination of
orthogonal polynomials in order to exploit the modeling and estimation advantages
illustrated in Almeida et al. [1998].
An application of this equation that captures the difference in risk between
credit ratings using only a translation factor is given by
( )
)4( .,...2,1],,0[,)1
2
()()( 11 Jjt
t
PcStBtRn
nn
j
ii
j=∀∈∀−++= ∑∑ ≥=
l
l
where i
S is a nonnegative spread variable (that is, jiSi,...,2,1 0=∀≥) that measures
the difference in risk between the th
i)1(− and the th
i credit ratings, and
J
represents
the total number of credit ratings.
A limitation of Model )4( is that all
J
estimated term structures are parallel.
Although very limited, Model )4( captures the fact that bonds with higher ratings
ought to have smaller prices (everything else being equal). In other words: the higher
the rating, the higher the interest rates used to price bonds with that particular rating.
6
Exhibit 1 depicts a possible output for Model )4(. It is possible to exhibit more
general models than that given in )4( (that is, a model which allows the term
structures obtained for different credit ratings to differ not only by a translation
factor). Exhibit 2 presents a schematic drawing of possible term structures of interest
rates for different credit ratings, in a more general model.
3. Joint Estimation of Term Structures
Let us consider the simplest case first (that is, Model (4)). The objective is to
estimate the variables JiSi,...,1,=and the coefficients ,...,, 321 ccc . The final results
of this estimation process are J different term structures of interest rates, each related
to a different rating.
Let us define the discount function )(
)( tDjfor rating j
r to be
(
)
)5( ,...,1],,0[,)(exp)( )()( JjtttRtDjj =∈∀−= l
We assume that
m
eurobonds are available to estimate the coefficients in
Model )4(. We assume that j
m eurobonds possess a rating j
r. The residual term k
e
of the statistical fit obtained for the price of the th
k eurobond satisfies
(6) ,...,2,1,)(11 1
)( mketDuooap k
k
f
lkkl
j
kl
c
call
k
p
put
kkk =∀+=−++ ∑
=
where k
p denotes the price of the th
k eurobond, k
a denotes the accrued interest of
the th
k eurobond, put
k
1 and call
k
1 are dummy variables (Draper and Smith [1966])
indicating the existence of embedded put and call options in the eurobond,
o
p and
o
c
are unknown parameters related to the prices of the embedded put and call options, k
f
denotes the number of remaining cash flows of the th
k eurobond, kl
t the time
7
remaining for payment of the
l
th cash flow kl
u of the th
k eurobond, and k
j denotes
the rating of the th
k eurobond (for instance, if the rating of the th
k eurobond is 3
r,
then 3=
k
j).
The estimation process is based in a two step procedure:
1. Identify influential observations (Rousseeuw and Leroy [1987]) using an
extension of Cook’s statistics (Atkinson [1988]). This first step is important
because in the Emerging Eurobond market there are many illiquid or “badly”
priced bonds. If these bonds are not appropriately handled during the estimation
phase, they may distort the term structures estimated (as illustrated in Almeida et.
al. [1998]).
2. Use a duration weighted estimation process after removing all the influential
observations detected in the first step. The estimation should preferably use robust
techniques, such as the Least Sum of Absolute Deviation or the Least Median of
Squares (Rousseeuw and Leroy [1987]). The use of duration weights incorporates
heterocedasticity in the nonlinear regression model by allowing the volatility of
the eurobond prices to be proportional to its duration (as suggested in Vasicek and
Fong [1982]).
A numerical example illustrating the practical use of this methodology is
presented next.
4. A Numerical Example of the Estimation Process
As an example we consider the joint estimation of Brazilian and Mexican
eurobonds term structures. Fifty-two eurobonds are used: twenty-five Brazilian;
8
twenty-seven Mexican. The eurobonds are classified in seven different credit ratings1:
BB1, BB2, BB3, B1, B2, B3 and NR. Exhibit 3 presents the main characteristics of
the fifty-two eurobonds.
Three leverage points were detected in the first step of the estimation
process: one Brazilian (Iochpe); two Mexican (Bufete and Grupo Minero). Exhibit
4 and Exhibit 5 provide the results obtained.
Note that for the Brazilian term structures, the translation factor varies just a
few basis points when different ratings are compared: for instance, the difference
between the B1 and the B3 translation factors is only 34 basis points. On the other
hand there is a difference of 130 basis points between the B1 and B3 Mexican
translation factors. The next sections illustrate how the term structures in Exhibit 5
can be used to exploit arbitrage in the Emerging Eurobond market.
5. Detection and Exploitation of Arbitrage Opportunities
The following five steps are proposed to detect and exploit arbitrage in Latin
American Eurobond markets:
1. Choose a set of eurobonds with a common rating.
2. Estimate the term structures of interest rates for each country.
3. Based on the estimated term structures, consider possible future scenarios for their
relative movement.
4. Analyze the sensibility of different eurobond portfolios to these scenarios
generated.
5. Suggest a portfolio that better adjusts to the scenarios generated.
Three numerical examples are presented:
9
1. Brazil and Mexico: B1 Eurobonds.
2. Brazil and Mexico: B3 Eurobonds.
3. Argentina and Mexico: BB2 Eurobonds.
All the data were collected in June the third of 1998, on J.P. Morgan’s web
site4.
5.1 Brazil and Mexico: B1 Eurobonds
Exhibit 5 depicts the Brazilian and Mexican B1 term structures. The Mexican
term structure lies below the Brazilian term structure, indicating that the Brazilian B1
eurobonds are cheap when compared to Mexican B1 eurobonds. The large difference
between the translation, rotation and torsion factors of the two term structures
suggests as the most probable future scenarios the ones where the curves become
closer. That is, if there are no economic conditions leading these countries to behave
radically different, we could expect a convergence between term structures of assets
of the same rating. Exhibit 6 depicts a scenario representing the convergence of the
term structures. The arrows indicate the direction of the movements that would be
realized by each term structure in this situation. However, in spite of the suggested
convergence, we generate for the analysis of portfolio’s sensibility, unbiased future
scenarios. There are 63 possibilities of generating future scenarios changing a subset
of the term structures factors: Brazilian translation factor, Brazilian rotation factor,
Brazilian torsion factor, Mexican translation factor, Mexican rotation factor and
Mexican torsion factor. In what follows, without loosing generality, we fix as possible
future scenarios the ones where just the Brazilian translation factor and the Mexican
rotation factor change their values. A set of twelve scenarios for each term structure
10
is generated and we calculate the prices of the eurobonds on each of these scenarios.
Exhibit 7 depicts the future scenarios for the Brazilian and the Mexican term
structures. Exhibit 8 presents the prices of the Mexican eurobonds on each future
scenario for the Mexican term structure and Exhibit 9 presents the prices of the
Brazilian eurobonds on each future scenario for the Brazilian term structure.
For instance, suppose the occurrence of the scenario depicted in Exhibit 6, that
is, a diminution in both the Brazilian translation factor and the Mexican rotation
factor, with all the other factors remaining the same. This could mean a decrease in
the external long term lend rate for emerging markets. We note in Exhibit 5 that the 9
years maturity is the largest one in both B1 eurobonds markets. The Legendre
polynomials symmetry suggests an analysis of the term structures based in two
regions: region I, for maturities less than 4.5 years, and region II, for maturities
greater than 4.5 years. In the occurrence of such a scenario both term structures attain
a decrease of interest rates in region II. Exhibit 8 and Exhibit 9 show that in this
situation, all the Brazilian bonds would increase their values, short-term Mexican
bonds would decrease their values and long-term Mexican bonds would increase their
values. A good strategy would be buy Brazilian bonds and Mexican long-term bonds,
and sell Mexican short-term bonds.
Exhibit 10 presents the percent variation of a proposed portfolio long US$ 1.5
million in the Mexican eurobond Azteca (2007), short US$ 1 million in the Mexican
eurobond Vicap (2002), and long US$ 1 million in the Brazilian eurobond Votorantin
(2005). Note that in the worst case scenario the investor of such a portfolio would
loose 9% of its initial wealth. On the other hand, he would profit only 5.6% in the
best-proposed situation, which would occur when the Mexican rotation factor goes
down 94 basis points (sixty percent of its value) and simultaneously the Brazilian
11
translation factor goes down 132 basis points (thirty percent of its value). The
question here is why invest in this portfolio if its profit and loss distribution is
asymmetric with higher extreme loss values than extreme profit values? The answer
depends on the probabilities assigned to each scenario. In the uniform case, where all
the scenarios receive the same probability, this portfolio would not be a good choice
because in average the investor would loose money. However, if the investor
perceives greater chances for occurrence of scenarios favorable to the portfolio, that
is, the ones where the Mexican rotation factor and the Brazilian translation factor fall,
than it would worth investing in such a portfolio. Exhibit 11 presents the portfolio
sensibility to the Brazilian translation factor and the Mexican rotation factor. The
portfolio value is more sensible to changes in the Brazilian translation factor than to
changes in the Mexican rotation factor. For instance, take a variation of 10 percent in
the Brazilian translation factor (44 bps). We observe, in Exhibit 10, that this scenario
would generate around 1.3 percent variation in the portfolio value. Nevertheless, if we
had taken the same percent variation in the Mexican rotation factor (16 bps) it would
generate around 0.6 percent variation in the portfolio value. We also observe that the
portfolio value varies almost linearly with respect to the Brazilian translation factor
but non-linearly with respect to the Mexican rotation factor.
5.2 Brazil and Mexico: B3 Eurobonds
Exhibit 5 also depicts the Brazilian and Mexican B3 term structures of interest
rates. These curves cross each other at the 3.2 years maturity. Due to the curves
disposition and to the Legendre polynomials symmetry, we split the analysis of the
term structures in three regions: region I, for maturities less than 3.2 years, region II,
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for maturities between 3.2 and 4.5 years, and, region III, for maturities greater than
4.5 years. On region I, the Brazilian term structure of interest rates presents values
greater than the Mexican ones, with the difference approaching 150 basis points, for
short maturities. On regions II and III, there is an inversion of the situation: the
Mexican curve presents values greater than the Brazilian curve values, with the
difference approaching 100 basis points, for maturities around 9 years. The major
cause for this difference between the term structures relies in the fact that the Mexican
term structure rotation factor (156 basis points) is much superior to the Brazilian
one (57 basis points).
Just looking at the term structures picture, we could suggest, as a possible
future scenario, an approximation of the curves slopes, that is, the convergence of the
rotation factors.
The B3 eurobonds characteristics are listed in Exhibit 3. Note that the three
eurobonds have maturities less than or equal to two years, meaning that their pricing
is based on region I values of the term structures. According to the supposed future
scenario, the curves approximate each other, on region I, implying a depreciation of
the Mexican eurobond, and an appreciation of the Brazilian eurobonds. In this
context, a good strategy would be buy the Brazilian bonds and sell the Mexican one.
5.3 Argentina and Mexico: BB2 Eurobonds
In this example we consider the joint estimation of Argentinean and Mexican
eurobonds term structures. Exhibit 12 depicts the Argentinean and Mexican BB2 term
structures of interest rates. Exhibit 13 presents the factor values for both curves. We
observe that the Mexican rotation factor is much higher than the Argentinean rotation
13
factor. Suppose a fixed income manager is positioned in these markets on a portfolio
composed by the eurobonds listed in Exhibit 14. The manager is long US$ 1 million
in the Argentinean eurobond Multicanal (2007), long US$ 1 million in the
Argentinean eurobond Perez (2007), long US$ 1 million in the Mexican eurobond
Televisa (2006) and short US$ 2 million in the Mexican eurobond Cemex (2006).
Suppose also the economic committee is expecting a scenario of reduction on long-
term Mexican interest rates combined to a reduction on Argentinean interest rates.
How could the fixed income manager generate scenarios based on the described
expectations to analyze the portfolio exposure? He could begin decreasing the
Argentinean translation factor to get the effect of reducing Argentinean interest rates.
On the other hand, a combination of changes in the Mexican rotation and torsion
factors would provide the desired results for the Mexican term structure. As a matter
of fact, if he reduced the Mexican rotation factor he would decrease long-term interest
rates but also increase short-term interest rates (an undesired effect). Next, increasing
the absolute value of the Mexican torsion factor he would decrease both the short-
term rates and long-term rates, compensating the increase in short-term rates
generated by the rotation factor movement. Exhibit 15 depicts different scenarios
incorporating the economic committee expectations, that is, scenarios of reduction of
the Argentinean translation factor, reduction of the Mexican rotation factor and
reduction of the Mexican torsion factor. We note that the most extreme scenario for
the Mexican term structure really reflects a reduction of long-term Mexican interest
rates. In this scenario it would happen a reduction around a hundred basis points in the
Mexican long-term interest rate, an increase around thirty basis points in the medium-
term interest rate and an increase around ten basis points in the short-term interest
rates. Exhibit 16 presents the prices for the Argentinean eurobonds in the manager’s
14
portfolio for the different scenarios for the Argentinean Term Structure. Exhibit 17
presents the prices for the Mexican eurobonds in the manager’s portfolio for the
different scenarios for the Mexican Term Structure. Exhibit 18 presents, for each
scenario observed in Exhibit 15, the percent variation of the portfolio. We note, in
Exhibit 16 that the reduction of Argentinean interest rates contributes positively to the
portfolio value due to the long position in the BB2 Argentinean market. However,
without the help of Exhibit 17 and Exhibit 18, it would not be a simple task to identify
the exact effects in the portfolio value caused by the expected changes in the Mexican
interest rates. In Exhibit 18, we note that the reduction on Mexican long-term interest
rates decreases the portfolio value (in 1.79%) in the worst case scenario, where the
Argentinean Interest rates do not change. This behavior is attributed to the short
position in the Mexican eurobond Cemex which pursues a very high coupon (12.5%)
responsible for increasing its sensibility to interest rates movements. We also note in
Exhibit 18 that the portfolio would profit in the major portion of the scenarios
proposed. We conclude that translating abstract interest rates expectations to possible
factor movements is a very good analysis tool, because it allows an easy interpretation
of the portfolio sensibility to interest rates movements.
6. Conclusion
This article presents a methodology for jointly estimating term structures of
interest rates for clusters of bonds with different credit ratings. The model is based on
an optimization procedure, which assumes that the term structures movements are
driven by orthogonal factors. The estimated curves are useful for risk analysis,
derivatives pricing and portfolio selection. The methodology is efficient from the
15
computational point of view and is particularly useful when analyzing markets with
few liquid bonds such as Emerging Eurobond markets.
The methodology is completely compatible with scenario analysis models
which have become a very interesting alternative to single point forecasting
methodologies such as the mean-variance model (Markovitz [1959]). The
decomposition of the term structures movements in polynomial orthogonal factors
allows easy generation of interest rates scenarios, even turning it possible to apply the
methodology to dynamic asset-liability models (Cariño et al. [1994]). However, an
important problem involving scenario analysis concerns the choice of the probability
distribution that generates the future scenarios. Although this is not a simple problem,
it could be addressed by applying historical simulation (Jorion [1997]), using the
historical distribution of the term structure factors, or by applying Monte Carlo
simulation (Jorion [1997]) by adjusting a model for the dynamic of the term
structures.
Latin America Eurobond markets were chosen to illustrate the practical use of
the methodology. We explore some simple examples of arbitrage between
international term structures for the same rating, using scenario analysis to select
portfolios. Although the joint estimations realized in the article involve just pairs of
countries (such as Mexico, Brazil and Mexico, Argentina) the joint estimation process
could involve many countries, not necessarily the same number of countries used in
each arbitrage analysis.
16
Endnotes
1 The ratings were made public by Bloomberg Agency. They were created as a
combination of Moody’s Investors Service ratings and Standard and Poors ratings.
The rating “NR” denotes eurobonds not rated by both rating agencies. For more
details see the web page www.bloomberg.com.
2 The eurobonds in Exhibit 3 whose names are marked by a star are step-up bonds,
that is, coupon increasing bonds. For each of these bonds, the coupon shown in
Exhibit 3 is the current coupon on June the third of 1998.
3 We constrain the translation factor for the rating NR to be the greatest among all the
translation factors for the different ratings.
4 www.jpmorgan.com.
5 The prices shown in bold on Exhibit 8 were obtained by discounting the Mexican
eurobonds cash flows using the Mexican B1 estimated term structure.
6 The prices shown in bold on Exhibit 9 were obtained by discounting the Brazilian
eurobonds cash flows using the Brazilian B1 estimated term structure.
7 The prices shown in bold on Exhibit 16 were obtained by discounting the
Argentinean eurobonds cash flows using the Argentinean BB2 estimated term
structure.
8 The prices shown in bold on Exhibit 17 were obtained by discounting the Mexican
eurobonds cash flows using the Mexican BB2 estimated term structure.
9 In this context, we consider as a scenario for the BB2 Mexican term structure, a
combination of simultaneous changes in the Mexican rotation and torsion factors.
17
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18
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19
Exhibit 1. An Example of Term Structures for Different Ratings in
Model (4)
BB3
BB2
AA2
interest rate
AA1
term
20
Exhibit 2. An Example of Term Structures for Different Ratings in a
General Model
BB3
BB2
AA2
interest rate
AA1
term
21
Exhibit 3. Eurobonds Used to Illustrate the Estimation Process
Eurobond
2Rating Country Coupon (%) Maturity
Bco Bradeco
B2
Brazil
8.000
28-Jan-2000
Bco Excel B2 Brazil 10.750 08-Nov-2004
Bco Itau B2 Brazil 7.500 11-Jul-2000
Bco Safra B2 Brazil 8.125 10-Nov-2000
Bco Safra B2 Brazil 8.750 28-Oct-2002
Bco Safra B2 Brazil 10.375 28-Oct-2002
CEMIG NR Brazil 9.125 18-Nov-2004
CESP*NR Brazil 9.125 28-Jun-2007
Copel NR Brazil 9.750 02-May-2005
CSN Iron B2 Brazil 9.125 01-Jun-2007
CVRD NR Brazil 10.000 02-Apr-2004
Ford B2 Brazil 9.250 22-Jan-2007
Ford Ltd B2 Brazil 9.125 08-Nov-2004
Gerdau NR Brazil 11.125 24-May-2004
Iochpe NR Brazil 12.375 08-Nov-2002
Ipiranga
*NR Brazil 10.625 25-Feb-2002
Klabin NR Brazil 10.000 20-Dec-2001
Klabin
*NR Brazil 12.750 28-Dec-2002
Lojas NR Brazil 11.000 04-Jun-2004
Minas X WR-A B3 Brazil 7.875 10-Feb-1999
Minas X WR-B B3 Brazil 8.250 10-Feb-2002
Parmalat
*NR Brazil 9.125 02-Jan-2005
RBS B1 Brazil 11.000 01-Apr-2007
Unibanco B2 Brazil 8.000 06-Mar-2000
Votorantim B1 Brazil 8.500 27-Jun-2005
Altos Hornos B2 Mexico 11.375 30-Apr-2002
Altos Hornos B2 Mexico 11.875 30-Apr-2004
Azteca B1 Mexico 10.125 15-Feb-2004
Azteca B1 Mexico 10.500 15-Feb-2007
Banamex BB2 Mexico 9.125 06-Apr-2000
Bufete B3 Mexico 11.375 15-Jul-1999
Cemex BB2 Mexico 8.500 31-Aug-2000
Cemex BB2 Mexico 9.500 20-Sep-2001
Cemex BB2 Mexico 10.000 05-Nov-1999
Cemex BB2 Mexico 10.750 15-Jul-2000
Cemex BB2 Mexico 12.750 15-Jul-2006
Coke FEMSA BB2 Mexico 8.950 01-Nov-2006
Cydsa NR Mexico 9.375 25-Jun-2002
DESC BB3 Mexico 8.750 15-Oct-2007
ELM NR Mexico 11.375 25-Jan-1999
Empresas ICA B1 Mexico 11.875 30-May-2001
Gruma BB1 Mexico 7.625 15-Oct-2007
Grupo IMSA BB2 Mexico 8.930 30-Sep-2004
Grupo Minero BB1 Mexico 8.250 01-Apr-2008
Hylsa BB3 Mexico 9.250 15-Sep-2007
Pepsi-Gemex BB3 Mexico 9.750 30-Mar-2004
Televisa BB2 Mexico 015-May-2008
Televisa BB2 Mexico 11.375 15-May-2003
Televisa BB2 Mexico 11.875 15-May-2006
Tolmex BB2 Mexico 8.375 01-Nov-2003
Vicap B1 Mexico 10.250 15-May-2002
Vicap B1 Mexico 11.375 15-May-2007
22
Exhibit 4. Values of Factors for the Brazilian and Mexican Term
Structures for Different Ratings
Factor3Value (bps)
Brazilian B1 Translation 441
Brazilian B2 Translation 451
Brazilian B3 Translation 475
Brazilian NR Translation 485
Brazilian Rotation 57
Brazilian Torsion -56
Mexican BB1 Translation 249
Mexican BB2 Translation 322
Mexican BB3 Translation 322
Mexican B1 Translation 379
Mexican B2 Translation 509
Mexican B3 Translation 509
Mexican NR Translation 532
Mexican Rotation 156
Mexican Torsion -114
23
Exhibit 5. A Comparison of Mexican and Brazilian Term Structures of
Interest Rates for Different Credit Ratings
0 1 2 3 4 5 6 7 8 9 10
500
600
700
800
900
1000
1100
1200
Years to Maturity
Interest Rate (bps)
B1 Eurobonds Term Structures
US Strips
Brazil
Mexico
0 1 2 3 4 5 6 7 8 9 10
500
600
700
800
900
1000
1100
1200
1300
Years to Maturity
Interest Rate (bps)
B3 Eurobonds Term Structures
US Strips
Mexico
Brazil
24
Exhibit 6. Possible Convergence Scenario
0 1 2 3 4 5 6 7 8 9 10
500
600
700
800
900
1000
1100
Years to Maturity
Interest Rate (bps)
B1 Eurobonds Term Structures
Brazil
Mexico
US Strips
25
Exhibit 7. Different Scenarios for the B1 Term Structures
0 1 2 3 4 5 6 7 8 9 10
500
600
700
800
900
1000
1100
1200
1300
Years to Maturity
Interest Rate (bps)
Brazilian B1 Term Structure
US Strips
Brazil
0 1 2 3 4 5 6 7 8 9 10
500
600
700
800
900
1000
1100
1200
Years to Maturity
Interest Rate (bps)
Mexican B1 Term Structure
US Strips
Mexico
26
Exhibit 8. Price Variation5 of Mexican B1 Eurobonds for Different
Scenarios for the Mexican Term Structure
Rotation
Factor
(variation in bps)
ICA
2001
(US$)
Vicap
2002
(US$)
Azteca
2004
(US$)
Azteca
2007
(US$)
Vicap
2007
(US$)
94 108.6660 110.7541 102.5180 98.4830 79.0877
78 108.4775 108.6085 102.7050 99.7355 84.5002
62 108.2892 106.8840 102.8769 100.9473 90.3572
47 108.1013 105.5128 103.0322 102.1112 95.9951
31 107.9138 104.4372 103.1698 103.2205 100.9502
16 107.7265 103.6072 103.2897 104.2685 104.9842
0
107.5396
102.9799
103.3919
105.2489
108.0515
-16 107.3530 102.5176 103.4772 106.1557 110.2376
-31 107.1668 102.1876 103.5465 106.9832 111.6975
-47 106.9809 101.9613 103.6011 107.7264 112.6066
-62 106.7953 101.8140 103.6425 108.3804 113.1286
-78 106.6101 101.7247 103.6724 108.9411 113.3996
-94 106.4252 101.6756 103.6925 109.4048 113.5225
27
Exhibit 9. Price Variation6 of Brazilian B1 Eurobonds for Different
Scenarios for the Brazilian Term Structure
Translation
Factor
(variation in bps)
Votorantin
2005
(US$)
RBS
2007
(US$)
132 80.8641 98.4083
110 83.1444 99.6497
88 85.4123 100.9116
66 87.6610 102.1943
44 89.8838 103.4982
22 92.0737 104.8238
094.2236 106.1714
-22 96.3265 107.5414
-44 98.3751 108.9342
-66 100.3624 110.3502
-88 102.2811 111.7899
-110 104.1245 113.2537
-132 105.8856 114.7419
28
Exhibit 10. Percent Variation on the B1 Portfolio Value for Different
Scenarios for the Mexican and Brazilian Term Structures
94 78 62 47 31 16 0 -16 -31 -47 -62 -78 -94
132 -8.96 -7.86 -6.89 -6.03 -5.28 -4.62 -4.05 -3.55 -3.12 -2.76 -2.45 -2.20 -2.00
110 -8.27 -7.17 -6.19 -5.34 -4.59 -3.93 -3.36 -2.86 -2.43 -2.07 -1.76 -1.51 -1.31
88 -7.58 -6.48 -5.51 -4.65 -3.90 -3.25 -2.67 -2.17 -1.75 -1.38 -1.07 -0.82 -0.62
66 -6.90 -5.80 -4.82 -3.97 -3.22 -2.56 -1.99 -1.49 -1.06 -0.70 -0.39 -0.14 0.06
44 -6.23 -5.12 -4.15 -3.30 -2.55 -1.89 -1.32 -0.82 -0.39 -0.02 0.28 0.54 0.74
22 -5.56 -4.46 -3.49 -2.63 -1.88 -1.23 -0.65 -0.15 0.27 0.64 0.95 1.20 1.40
0-4.91 -3.81 -2.83 -1.98 -1.23 -0.57 0.00 0.50 0.93 1.29 1.60 1.85 2.05
-22 -4.27 -3.17 -2.20 -1.34 -0.59 0.06 0.64 1.14 1.56 1.93 2.24 2.49 2.69
-44 -3.65 -2.55 -1.58 -0.72 0.03 0.69 1.26 1.76 2.18 2.55 2.86 3.11 3.31
-66 -3.05 -1.95 -0.97 -0.12 0.63 1.29 1.86 2.36 2.79 3.15 3.46 3.71 3.92
-88 -2.47 -1.36 -0.39 0.46 1.21 1.87 2.44 2.94 3.37 3.73 4.04 4.29 4.50
-110
-1.91 -0.80 0.17 1.02 1.77 2.43 3.00 3.50 3.93 4.29 4.60 4.85 5.06
-132
-1.38 -0.27 0.70 1.56 2.31 2.96 3.54 4.03 4.46 4.83 5.13 5.39 5.59
Horizontal - Changes in the Mexican Rotation Factor in Basis Points
Vertical - Changes in the Brazilian Translation Factor in Basis Points
29
Exhibit 11. B1 Portfolio Sensibility for Different Scenarios
-100 -80 -60 -40 -20 0 20 40 60 80 100
-2
-1.5
-1
-0.5
0
0.5
1x 105Different Scenarios for the Mexican B1 Term Structure
Variation in Mexican Rotation Factor (bps)
Price Variation
-150 -100 -50 0 50 100 150
-1.5
-1
-0.5
0
0.5
1
1.5 x 105
Price Variation
Variation in Brazilian Translation Factor (bps)
Different Scenarios for the Brazilian B1 Term Structure
30
Exhibit 12. Detecting Arbitrage Opportunities in the BB2 Argentinean
and Mexican Eurobond Markets
0 1 2 3 4 5 6 7 8 9 10
500
550
600
650
700
750
800
850
900
950
1000
1050
Years to Maturity
Interest Rate (bps)
BB2 Eurobonds Term Structures
US Strips
Argentina
Mexico
31
Exhibit 13. Values of Factors for the Argentinean and Mexican BB2
Term Structures
Factor Value (bps)
Argentinean Translation 291
Argentinean Rotation 98
Argentinean Torsion -57
Mexican Translation 322
Mexican Rotation 153
Mexican Torsion -74
32
Exhibit 14. BB2 Eurobond Portfolio Used in Example 5.3
Eurobond Country Coupon (%) Maturity
Multicanal Argentina 10.500 01-Feb-2007
Perez Argentina 8.125 15-Jul-2007
Cemex Mexico 12.750 15-Jul-2006
Televisa Mexico 11.875 15-May-2006
33
Exhibit 15. Different Scenarios for the BB2 Term Structures
0 1 2 3 4 5 6 7 8 9 10
500
550
600
650
700
750
800
850
900
950
1000
Years to Maturity
Interest Rate (bps)
Argentinean BB2 Term Structure
Argentina
US Strips
0 1 2 3 4 5 6 7 8 9 10
500
600
700
800
900
1000
1100
Years to Maturity
Interest Rate (bps)
Mexican BB2 Term Structure
US Strips
Mexico
34
Exhibit 16. Price Variation7 of the Argentinean Eurobonds in the BB2
Portfolio, for Different Scenarios for the Argentinean Term Structure
Translation
Factor
(variation in bps)
Multicanal
2007
(US$)
Perez
2007
(US$)
0112.5599 97.9793
-7 112.9957 98.3912
-13 113.4337 98.8054
-20 113.8739 99.2217
-27 114.3163 99.6403
-33 114.7608 100.0612
-40 115.2076 100.4842
-47 115.6566 100.9096
-53 116.1079 101.3372
-60 116.5614 101.7670
35
Exhibit 17. Price Variation8 of the Mexican Eurobonds in the BB2
Portfolio, for Different Scenarios9 for the Mexican Term Structure
Rotation Factor
(variation in bps)
Torsion Factor
(variation in bps)
Televisa
2006
(US$)
Cemex
2006
(US$)
0 0 113.4530 122.8172
-6 -4 113.5656 122.9501
-11 -9 113.6788 123.0836
-17 -13 113.7924 123.2177
-22 -18 113.9065 123.3524
-28 -22 114.0210 123.4877
-33 -27 114.1360 123.6236
-39 -31 114.2515 123.7602
-44 -36 114.3675 123.8974
-50 -40 114.4840 124.0352
36
Exhibit 18. Percent Variation on the BB2 Portfolio Value for Different
Scenarios for the Argentinean and Mexican Term Structures
Rotation
Torsion
0-7 -13 -20 -27 -33 -40 -47 -53 -60
0 0 0.00 1.08 2.17 3.26 4.36 5.47 6.58 7.69 8.81 9.94
-6 -4 -0.20 0.89 1.97 3.07 4.17 5.27 6.38 7.50 8.62 9.75
-11 -9 -0.39 0.69 1.78 2.87 3.97 5.07 6.18 7.30 8.42 9.55
-17 -13 -0.59 0.49 1.58 2.67 3.77 4.88 5.99 7.10 8.22 9.35
-22 -18 -0.79 0.29 1.38 2.48 3.57 4.68 5.79 6.90 8.03 9.15
-28 -22 -0.99 0.10 1.18 2.28 3.37 4.48 5.59 6.71 7.83 8.95
-33 -27 -1.19 -0.10 0.98 2.08 3.17 4.28 5.39 6.51 7.63 8.75
-39 -31 -1.39 -0.31 0.78 1.87 2.97 4.08 5.19 6.30 7.43 8.55
-44 -36 -1.59 -0.51 0.58 1.67 2.77 3.88 4.99 6.10 7.22 8.35
-50 -40 -1.79 -0.71 0.38 1.47 2.57 3.67 4.78 5.90 7.02 8.15
Horizontal - Changes in the Argentinean Translation Factor in Basis Points
Vertical – Changes in the Mexican Rotation and Torsion Factors in Basis Points
