Capa 85 ING.indd - Serasa Experian

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06
Homogeneous Risk Groups:
A Proposal Using Cluster Analysis
Fabio Augusto Scalet Medina
Edson Luiz de Carvalho Barbosa
The article investigates the applicability of Cluster
Analysis to segregating a portfolio of retail exposures
into homogeneous risk groups, according to the rules
set forth in Central Bank of Brazil Circular Letter No.
3.648/2013. The study concludes that Cluster Analysis
is a viable option.
21
Survival Analysis in Credit Models:
a View of Covariates Treatment
Melissa Sousa
Tiago Lima
Wanderson Rocha
The study proposes adjusting a credit model based on
survival analysis, with a main focus on the treatment of
predictive variables and the creation of homogeneous
groups. The method’s advantage over today’s logit regression lies in its ability to predict defaulters over different horizons.
31
Spatial Correlation of
Corporate Defaults
Guilherme B. Fernandes
Rinaldo Artes
Local economic effects may provide information on
the default rate of individuals or business firms that live
or operate in the relevant regions, and spatial analysis
techniques enable measurement. The study uses the
Moran’s I to evaluate the spatial correlation of defaults
among São Paulo State business firms.
39
Infrastructure Credit and
Financing in Brazil
Frederico A. Turolla
Márcio F. Gabrielli
Igor J. C. Gondim
The financial and capital markets fund infrastructure
projects in many ways, with both debt and equity. Financing environments include corporate finance, which creates liabilities directly on the service operators’
balance sheets, and project finance, which is associated with Special Purpose Societies (“Sociedades de
Propósito Específico” – SPE).
4
From the Editors
The articles “Homogeneous
Risk Groups: A proposal using Cluster Analysis” and “Survival Analysis
in Credito Models: a View of Covariates Treatment”, selected for this issue of Tecnologia de Crédito review,
address a methodology capable of
predicting default among homogeneous groups. That is, risk groups
in which a set of exposures prevails
with shared characteristics for the
purposes of credit risk evaluation and
quantification.
In the study “Homogeneus
Risk Groups” by Statistics experts Fabio Augusto Scalet Medina and Edson Luiz de Carvalho Barbosa, the
groups formed are well distributed
across the number of contracts. They
were shown to be consistent through
analysis of characteristics vectors and
quite distinctive in terms of percentage of default, one of the most important points to support the hypothesis
of using cluster analysis to place retail exposures into homogeneous risk
groups. According to the authors, a
subject for future studies lies in developing a methodology to allocate
exposures with observation vectors
not present in the development sample, or classes to be created over time
within one of the resulting homogeneous groups.
In their turn, statisticians
Melissa Sousa, Tiago Lima and Wanderson Rocha, who specialize in
credit risk modeling, present a study
- Survival Analysis in Credit Models
- Analysis in Credito Mdels that proposes using survival analysis to adjust
a credit model, with a main focus on
the treatment of predictive variables
and particular attention to the creation of homogeneous groups. The
study’s highlight is a concern with
the relationship between output and
predictive variables, and the authors
point out the presence of two main
lines of thinking: occurrence of default and time to default. They use the
Cox non-parametric model to perform
the adjustment in such a manner as
to align time to default and rate of default. The Logrank test was used at two
stages in the study: treatment of the
predictive variables to ensure classes
with distinctive survival curves, and
the creation of homogeneous groups
that, in addition to sporting different
rates of default over time, also show
distinctive survival curves.
This issue also contains an important article on modeling – “Spatial
Correlation of Corporate Defaults”. Its
authors, statisticians Guilherme Fernandes and Prof. Rinaldo Artes, note
that, during development of a credit
model, a spatial correlation may occur
among small and medium-sized business firms due to the non-observation
of local economic activity factors. The
level of the correlation depends on
the definition of the regions to be an-
5
alyzed, and this study finds that spatial correlat Analysis in Credito Mdels
ion as measured by Moran’s I is weak
when only 19 São Paulo State regions
(as defined by the first two Postal
Code numerals) are analyzed. However, when the area is defined based on
sector (first four Postal Code numerals), Moran’s I shows the presence of
a reasonably high spatial correlation.
If development of a credit risk model
fails to take this information into consideration, the model’s parameters
may be biased as a result of the endogeneity created by omitted variables.
Professors Frederico Araujo Turolla and Márcio Fernandes Gabrielli, and consultant Igor J. C. Gondim are the authors of “Infrastructure
Credit and Financing in Brazil”. They
discuss certain relevant challenges
to infrastructure financing. That is,
they point out the importance of costto-benefit analysis in taking large fiscal risks and of whether public and
private financing modes are substitute or complementary goods. They
also inquire whether a higher share of
credit can be achieved relative to equity in infrastructure projects. They
emphasize the need to re-discuss the
institutional environment where industry risks are more relevant, particularly as concerns stability and the introduction of competition. The challenges are complex and inter-related, but offer fundamental answers for
Brazil’s development.
CREDIT TECHNOLOGY
YEAR XIII
Trimonthly published by Serasa Experian
Nº 85
ISSN 2177-6032
President - Brazil
Desktop Publishing
Ricardo Loureiro
Eric Miranda e Gerson Lezak
Business Units Presidents/Superintendents
Illustration
Igor Ramos Rocha, Juliana Azuma, Marcelo Kekligian, Maria
Zanforlin and Steven Wagner
Translation
Directors
Allan Hastings
Amador Rodriguez, Guilherme Cavalieri, Laércio Oliveira Pinto,
Correspondência
Lisias Lauretti, Paulo Melo, Silvânio Covas and Valdemir Bertolo
Serasa Experian - Comunicação & Branding
Responsible Editor
Al. dos Quinimuras, 187 - CEP 04068-900 - São Paulo - SP
Rosina I. M. D’Angina (MTb 8251)
www.serasaexperian.com.br
Assistant Editor
[email protected]
Nancy Galvão
The concepts issued in the signed articles are the responsibility
Graphic Design
of the authors, which do not necessarily express the point of view
Luis Barbuda
of Serasa Experian and the Editorial Council.
Cover
Total or partial reproduction of the articles hereby published
is strictly forbidden.
6
Homogeneous
Risk Groups:
A Proposal Using
Cluster Analysis
7
Introdução
Abstract
The purpose
Nas
últimas décadas,
of this paper
a evolução
was to determine
das tecnologias
the applicade informação
bility
of Cluster
e de transmissão
Analysis to segregate
de dadosaeportfolio
a criação
of da
retail
internet
expomarcaram
sures
into homogeneous
uma nova fase risk
do processo
groups according
de globalização
to the rules
da ecoof
nomia. Nesse
Central
Bank ofnovo
Brazil
cenário
Circular
surge,
Lettercomo
No. 3.648/2013,
grande inovação
which sets
no
mundo econômico,
minimum
requirements
o comércio
for the calculation
eletrônico,ofpossibilitando
the element assoa realização
ciated
with
de credit
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risk exposures
comerciais
subject
sem ato
defi
required
nição exata
capital
docallocal de origem
culation
undereinternal
destino.credit risk rating systems (IRB approaches) (RWACIRB ). The study’s main goal was achieved, proving
that Cluster
Analysis is aComércio
viable option
to segregate
a retail
porPalavras-chave:
Eletrônico,
Gestão
da Frautfolio
into homogeneous
risk groups
de,
Informações
de Bureau.
Keywords: Basle II, Retail, Homogeneous risk
groups, Cluster Analysis.
Introduction
In order to standardize supervision and discuss ways to strengthen
the international banking system’s security, G-10 banking supervisors (Central Banks) established in 1974 the Basel Committee on Banking Supervision, headquartered in the Bank for
International Settlements, in Basel,
Switzerland.
As a means to manage the risk
of third-party funds leveraging on the
part of Financial Institutions, in June
1988 the Basel Committee issued the
International Convergence of Capital Measurement and Capital Standards, also known as Basel Agreement, or
Basel I, whose main purpose was to require financial institutions to maintain
sufficient capital to cover potential asset value losses and thereby ensure
solvency.
Several changes occurred in the
financial market since Basel I. Among
them, Jorion (2010) points out the inter-
ruption of the economic and monetary
unification path in Europe as a result of
the European Monetary System’s crisis
in September 1992; in the aftermath of
the securities crisis of 1994, the Federal
Reserve Bank (FED), after keeping interest rates low for three years, began
a series of six consecutive hikes, causing $1.5 trillion in global capital to disappear; the Asian crisis of 1997 and
the Russian default of 1998, which is
regarded as the trigger of a global financial crisis.
These changes led the Basel Committee to review the 1988 framework and release the New Capital
Accord, or Basel II, in June 2004.
According to Carneiro, Vivan
and Krause (2005), Basel II proposes
a new capital requirements framework
based on three pillars: pillar I addresses capital requirements based on operational, market and credit risks; pillar
II reinforces the ability of banking su-
8
pervisors to evaluate and adapt capital
requirements to the individual circumstances of financial institutions; and the
third pillar casts transparency and disclosure in an important and relevant role
for the development of market discipline.
Pillars I and II contain the calculation of Reference Equity (RE), which
represents the capital a financial institution must have to face the risk of extreme
losses in their exposures portfolios.
Resolution No. 4.193, dated
March 1st, 2013, governs the determination of minimum requirements for
Reference Equity (RE), Level I Capital, and Core Capital, and institutes
Additional Core Capital. According to
the Resolution, for the purposes of minimum requirements and Additional
Core Capital, the amount of Risk-Weighted Assets (RWA) must be determined as the sum total of the following
(Equation 1), where RWACPAD and RWAconcern credit risk.
CIRB
According to Assaf Neto (2011,
p. 136), credit risk “is the possibility of
a financial institution not collecting on
the amounts (principal and interest)
promised by the securities it has in its
receivables portfolio.”
Jorion (2010, p.15), in his turn,
reports that “credit risk arises when
the counterparts will not or cannot honor their contractual obligations.”
Basel II admits two alternative
approaches to measuring asset risk for
credit-risk purposes: the standard approach, represented by RWACPAD and
the internal risk ratings-based approach (IRB), represented by RWACIRB.
According to the standard approach, which is governed in Brazil by
Circular Letter No. 3.644, dated March
4th, 2013, RWACPAD must equal the sum
of the products of the exposures multiplied by the respective Risk-Weighting
Factors (RWF), where RWF varies according to the risk assigned to exposure types.
IRB approaches, in their turn,
are based on estimates of the following
risk elements:
• Expected Losses - EL;
• Unexpected Losses - UL;
• Probability of Default - PD;
• Loss Given Default - LGD;
• Exposure at Default - EAD;
• Maturity - M.
Central Bank of Brazil (BACEN)
Circular Letter No. 3.648, dated March
4th, 2013, establishes the minimum requirements for calculating credit risk
exposures subject to required capital calculation based on internal credit
risk rating systems (IRB approaches)
(RWACIRB)
According to Circular Letter
No. 3.648/2013, exposures subject to
the IRB approach for the purposes of
regulatory capital determination must
be segmented as follows:
• Sovereign Entities;
• Financial Institutions;
• Retail;
• Stockholdings;
• Wholesale.
RWA = RWACPAD + RWACIRB + RWAMPAD + RWACINT + RWAOPAD + RWAOAMA
Credit Risk
Market Risk
Operational Risk
(1)
9
The retail category includes:
a) exposures to individuals and
legal entities with gross annual sales
under R$3.6 million, managed non-individually by means of homogeneous
risk groups, and in the shape of typically retail-oriented financial instruments; and
b) exposures from loans and
financings to individuals with home
equity for collateral;
Chapter VI of the Circular letter
in question addresses the retail category and provides the following definition in Section One, Article 44: “For exposures in the “Retail” category, credit risk-based exposure rating systems
must enable associating each exposure to a certain homogeneous risk group
(...).” Paragraph 1 of the same section
reads: “A homogeneous risk group is
defined as the group of retail exposures with common characteristics for
the purposes of credit risk evaluation
and quantification (...).”
Still according to Article 44, the
association of exposures to a certain
homogeneous risk group must be based on the following criteria:
• Risk characteristics of the
obligor or counterpart;
• Risk characteristics of the exposure, including product type and
collateral, among others; and
• Lateness in the operations associated with the exposures.
Among the appropriate statistical techniques for the classifying a
group of exposures according to homogeneous groups, the option of cluster analysis stands out. The technique
can be found in several practical expe-
riments in various domains.
One example of the application of cluster analysis in the medical
area can be found in Rapeli e Botega (2005), where cluster analysis is applied to identify the existence of different groups among individuals who attempted suicide with more severe clinical or surgical impact and who needed
to be admitted to the UNICAMP Hospital das Clínicas. The study identified
three groups of patients with different
profiles in terms of the method used in
their attempts.
In the financial arena, Sanvicente and Minardi (1999) developed a risk
rating system for Brazilian listed corporations using cluster analysis. The
rating system was built using only accounting data from 301 publicly listed
companies. After they were grouped,
each cluster was assigned a rating.
Given the recent publication of
Circular Letter No. 3.648, there is little literature on the segregation of retail exposures into homogeneous risk
groups. No application using cluster
analysis was found in the Brazilian literature.
Therefore, this paper will introduce a proposal for categorizing retail
exposures according to homogeneous
risk groups based on cluster analysis.
By the end of the study, we expect to
demonstrate that cluster analysis is applicable to the purpose.
2. Literature Review
2.1 Cluster Analysis
According to Barroso and Artes (2003), cluster analysis is the name
10
of a series of techniques used to identify behavior patterns in data bans by
means of the formation of homogeneous groups.
Johnson and Wichern (2007)
address cluster analysis as an important exploratory technique, as, by studying a natural group structure, it enables evaluating data dimensionality,
identifying outliers and raising hypotheses relative to the objects’ structure (associations).
Mingoti (2005) reports that
cluster analysis aims to segregate the
sample’s or population’s elements into
groups so that elements belonging to
the same group are similar to one another and different from the measured variables (characteristics) and elements in other groups.
2.1.1 Resemblance metrics
Resemblance metrics play a
very important role in clustering algorithms. They define the criteria to determine whether two points are close and,
therefore, may or may not belong in the
same group. There are two kinds of resemblance metrics:
• Similarity metrics (the bigger
the value, the greater the similarity between objects);
• Dissimilarity metrics (the bigger the value, the greater the difference between objects).
According to Landim (2000), if
the data to be analyzed are a mixture of
continuous values and binary measurements, the Gower general similarity coefficient can be applied, as it is a metric coefficient.
According to the Help function of the SAS statistics package, version 9.3, the Gower similarity coefficient accepts all kinds of variables, including interval, ratio, ordinal, nominal,
and asymmetric nominal. SAS calculates the similarity by means of the Procedure Distance. The equation, also provided in the Help section, is:
v
Ʃw • δ
j
s1 (x, y) =
j
x,y
d
•
j=1
j
x,y
v
Ʃw • δ
j
j
x,y
j=1
Where:
v is the number of variables, or
dimensionality
wj is the weight of the jth variable where specified in the Procedure Distance, where wj = 0 when xj or yj
is missing.
s1(x,y) is the similarity between
records x and y.
For nominal, ordinal, interval or
j
ratio variables, we assume δ x,y = 1;
For asymmetric nominal variables:
j
δ x,y = 1, if xj or yj are present;
j
δ x,y = 0, if xj and yj are missing.
For nominal or asymmetric nominal variables:
j
dx,y = 1, if xj = yj
j
dx,y = 0, if xj ≠ yj
For ordinal (where the corresponding rankings are used), interval or
ratio variables:
j
dx,y = 1 - | xj - yj |
The equation of the Gower general dissimilarity coefficient is given
11
as:
d1 (x, y) = 1 ̶ s1 (x, y)
2.1.2 Clustering Algorithms
According to Barroso and Artes (2003), most of the algorithms used
for clustering purposes can be grouped into two main families of methods:
hierarchical and non-hierarchical, also
known as partition methods
2.1.2.1 Hierarchical methods
In the application of hierarchical methods, clusters are formed based on a resemblance matrix (distances matrix). The first step in the algorithm is to identify the closest pair of
observations. This pair is then grouped together to form the first cluster,
and is regarded as a single record. The
next step involves recalculating the
distance matrix, given the change arising from the union of the pair of records in the preceding step. After recalculating, the closest pair is again identified and grouped, and so on successively until all the records have been
grouped.
What distinguishes between different hierarchic methods is the rule
for redefining the resemblance matrix
at each grouping of pairs. Some illus-
trative methods follow:
Single linkage method:
The distance to be considered
is the smallest distance between one
element of groups G1 and G2, that is
(equation 2).
Complete linkage method:
The distance to consider is
the greatest distance between one
element of groups G1 and G2, that is
(equation 3).
Ward method:
Barroso and Artes (2003) report
that, at each step, the Ward method attempts to link exposures to make the
clusters formed as homogeneous as
possible, using the total sum of squares partition from a variance analysis
as a homogeneity metric. The Equation
is (Equation 4):
where SQT(X1) denotes the total
sum of squares of the first information
vector variable, SQE(X1) is the sum of
squares between the groups (measuring the level of heterogeneity between groups) and SQD(X1) is the sum of
squares within the groups (measuring
the level of internal group homogeneity), Gj is the set of elements in group j,
nj is the number of elements in group
X
X
j, 1 is the measure of variable 1 and
d (G1,G2)=min{d(i,k)}, where iЄG1e kЄG2
(2)
d (G1,G2)=max{d(i,k)}, where iЄG1e kЄG2
(3)
12
SQT( X 1 ) = SQ E( X 1 )+SQ D( X 1 ) or
k
ƩƩ ( X
j=1 1ЄGj
k
i1
-X 1 ) 2 =
Ʃ n (X
j=1
j
X
is the measure of the variable X1 in
group j; therefore, the best initial partition for X1 is the one that minimizes
SQD(X1) and, consequently, maximizes
SQE(X1).
The method calculates the sum
of squares for every variable in the information vector and then calculates
the partition’s sum of squares. The Formula is:
j1
P
SQDP=
Ʃ SQD(i)
i=1
where P is the total number of
variables in the information vector
The first step in the method’s algorithm involves forming (n-1) groups,
with n as the total number of observations, and calculating SQDP for every
possible cluster, choosing the one with
the lowest SQDP.
The next steps are forming
(n-2), (n-3) to (n-k) groups, always
taking the lowest SQPD as a selection
criterion.
Barroso and Artes (2003) note
that, out of all hierarchical methods,
Ward is the most attractive because it
is based on a metric with strong statistical appeal and because it generates
groups with high internal homogeneity.
k
j1
-X 1 ) 2 +
ƩƩ ( X
j=1 1ЄGj
i1
-X j1 ) 2 ,
(4)
2.1.2.2 Non-hierarchical
methods: k-means
Partition methods attempt to
find the partition whose groups show
high internal homogeneity and are different from one another. The criterion used by the k-means method is
based on the partition of the total sum
of squares of a variance analysis, like
the Ward method (Barroso and Artes,
2003).
Mingoti (2005) summarizes that,
in the k-means method, each element
in the sample is allocated to the cluster whose centroid (sample means vector) is the closest to the observed values
vector for the respective observation.
The grouping algorithm begins
with the a-priori definition of the desired number of groups and, based on
this number, the same number of initial centroids, also known as seeds, is
selected. The initial clustering is done
based on the smallest distance between each exposure and the selected seeds, and the group’s centroid is recalculated after the union. The next step
requires calculating the distance between each new record and the new
centroids, attempting to determine
whether the observations already allocated to one group are closer to other
groups if affirmative, the observations
are reallocated.
13
2.1.3 Comparison of Methods
The main benefit of the k-means method is that it checks, with every
step, whether the observations are allocated in the best way possible and allows reallocation when they are not. Under the Ward method, once two observations are grouped together, they will
remain in the same group until the end
of the procedure; in other words, the
method does not take account of the
fact that the inclusion of new observations in the groups may cause a certain
observation to be closer to a neighboring cluster.
Hierarchical methods, in turn,
do not require aprioristic knowledge
of the number of groups to be formed
and, as a consequence, do not require
setting the initial seeds.
2.1.4 Selection of the Number
of Groups
One of the main challenges in
cluster analysis is defining the optimal number of groups to form. Several statistics exist to assist in this selection, such as the R 2 coefficient and
the Pseudo-F statistic.
According to Mingoti (2005), the
Pseudo-F statistics runs an F test on
variance analysis at every step to compare the mean vectors of the groups
formed in the respective step.
R2, in its turn, means the percentage of the total variability of the
data that the clusters formed explain,
as variability drops with the reduction
of the dimension of the data.
A higher Pseudo-F is desired,
associated with a lower p-value for the
test and, consequently, rejection of
equality of the most significant mean
vectors. For R 2 we would like values
closer to one, so that little variability is
lost by grouping observations.
3. Methodology
For this application, we selected 20,000 overdraft limit contracts that
were not in default, that is, less than 90
days late in June 2011. These contracts
are part of the retail portfolio of a domestic financial institution.
The exposures were tracked for
the 12 following months, that is, until
June 2012, and checked for lateness in
excess of 90 days. Where such lateness
occurred, the exposures were marked
as in default.
Application of the methodology used the software packages SAS 9.3
and SAS Enterprise Miner Workstation 7.1.
3.1 Variables Selection
To obtain mutually heterogeneous groups in terms of risk of default,
the variables that are most predictive of
credit risk must be selected from those available. To this end, we used the
SAS Enterprise Miner Workstation 7.1 software, Decision Tree node, to determine
the most predictive variables for default
based on the–log(p-value) statistic; the
greater the statistic’s value, the lower
its p-value and, therefore, the most predictive the variable. It is worth noting
that the equation’s p-value is the p-value of the Chi-Squared test.
3.2 Variables Categorization
Categorizing the selected variables is very important, as this will enable characterizing the groups formed
14
and subsequently allocating new exposures to those groups.
Shiraiwa and Siqueira (2012) report that two different processes can
be called variables categorization: the
discretization of quantitative variables
and the consolidation of qualitative variables.
Discretization of quantitative
variables consists of creating intervals
so that each interval corresponds to
one category.
Qualitative variables are already
presented as categories, although these categories may not meet the needs
of the modeling process. For example,
a variable may display too many categories, or some categories may display
too small a number of observations.
For the purposes of this study,
the variables were categorized using
the Chi-squared Automatic Interaction
Detector, method, or CHAID, based on
the SAS Enterprise Miner Workstation
7.1 statistical software. According to
Kass apud Shiraiwa and Siqueira (2012,
p.6) the method performs the following
steps:
1. For each explanatory variable,
draw a contingency table with the dimensions (c x d), where c is the number
of categories for the independent variable and d is the number of categories
for the dependent variable.
2. Find the pair of categories for
the independent variable whose sub-table (2 x d) is significantly different. If the
significance does not achieve the critical value, normally 5%, merge the two
categories, regarding the merger as a
single category, and repeat the step.
3. For each category made up of
three or more original categories, find
the most significant binary division. If
significance is above a critical value,
perform the division and return to step 2.
4. Calculate the significance of
each consolidated independent variable and isolate the most significant. If
the significance exceeds a critical value, sub-divide the data according to
the (consolidated) categories of the selected independent variable
5. For each data partition that
has not yet been analyzed, return to
step 1.
3.3 Application of Cluster
Analysis
This study applied the following:
• Gower’s General Dissimilarity Coefficient as a resemblance metric;
• Ward’s hierarchical method as
clustering method;
• Pseudo-F and R2 statistics to
define the ideal number of groups to
form.
4. Results
4.1 Selected Variables
Variables were selected by means of the application of a Decision
Tree using the CHAID method, through
the Decision Tree node of SAS Enterprise Miner Workstation 7.1.
Every variable in table 1 was
tested, but we decided to use a single
variable for each of the dimensions required by the regulator, in order to ensure forming homogeneous groups based on the principle of parsimony. The
results were as follows in Table 1.
15
■ Table 1: Selected variables and value of the–log(p) statistic.
Variable
Description
Dimension - log(p)
perc_vr_utilizado
Amount used / Contracted amount
Operation
812,97
escore
Behavior Score
Obligor
739,41
atraso
Days late
Lateness
567,06
perc_crot_excesso Excess over limit / Contracted amount
Operation
538,3
vr_excesso
Excess amount t over limit
Operation
527,17
qt_md_excesos
Number of excesses over limit / Age of the checking account Operation
458,58
qtd_excessos
Number of excesses over limit
Operation
444,67
vr_utilizado
Amount used
Operation
308,08
tx_juros
Interest rate
Operation
78,1
vr_contratado
Contracted amount
Operation
42,24
Therefore, based on the–log(p) statistic, the following variables were selected:
• Obligor Dimension:
• Behavior Score (escore)
• Lateness Dimension:
• Number of days late on the
month of reference (atraso);
• Operation Dimension:
• Percentage Amount Used
(perc.vr.utilizado);
The selected variables were also
categorized using the CHAID method,
Decision Tree node of the SAS Enterprise
Miner Workstation 7.1 statistical package.
The days late variable was categorized in
a specialist manner, with a 30-day interval for each class. It is important to point
out that the classes were arranged according to their percentage of default, so that
class #1 corresponds to the one with the
least percentage of defaults and so forth.
The results were as follows (Table 2)
4.2 Categorization of the
Selected Variables
■ Table 2: Categories for the selected variables.
Behavior Score
Days Late
Pct Amount Used
Class
Intervals
Class
Intervals
Class
Intervals
1
>= 89,5
1
0
1
< 6,876
2
[70,5;89,5]
2
[1;30]
2
[6,876;21,08]
3
[55,5;70,5]
3
[31;60]
3
[21,08;54,665]
4
[43,5;55,5]
4
[61;89]
4
[54,665;72,013]
5
[14,5;43,5]
5
[72,013;100,002]
6
[2,5;14,5]
6
> = 100,002
7
< 2,5
16
4.3 Number of groups formed
The results indicate the formation of seven groups, where the Pseudo-F value was 319,784.07 and R2 was
99.556%, as the Table 3 next shows
■ Table 3: Decision criterion for the
optimal number of groups.
■ Table 4: Number of contracts per group.
Group
Number of
Contracts
Percentage
of Total
1
5.756
28,78%
2
6.342
31,71%
3
2.272
11,36%
4
2.441
12,21%
Number of
Groups
5
1.568
7,84%
R2
Pseudo F
6
471
2,36%
15
0,99481
294.487,46
7
1.150
5,75%
14
0,99313
262.780,86
13
0,99402
276.831,93
12
0,99098
243.921,66
11
0,98941
233.443,04
10
0,98669
211.781,58
9
0,99217
253.418,31
8
0,96326
104.846,90
7
0,99556
319.784,07
6
0,97514
130.693,86
5
0,93963
77.809,93
4
0,86544
42.869,59
3
0,78477
36.457,50
2
0,6565
38.220,22
1
0
.
4.5 Default rate by group
The technique used to segregate the retail exposures portfolio into
homogeneous risk groups is expected
to form groups that are heterogeneous
one in relation to another as concerns
Probability of Default (PD).
Since we have not yet provided
a PD model to ascertain this difference, we calculated the Percentage Default (number of contracts in default divided by total contracts) for each group
formed and observed the following:
■ Table 5: Percentage Default by Groups.
4.4 Number of contracts
per group
As for the distribution of contracts across the groups formed, Table
4 shows that the were well distributed,
an no single groups shows too great a
concentration.
Group
Percentage
in Default
2
0,32%
7
1,57%
1
2,57%
3
6,07%
5
12,12%
4
22,33%
6
63,69%
17
As seen, the groups formed are
significantly different in terms of Percentage of Default, supporting the hypothesis that the groups thus formed
are different in terms of risk of default.
The smallest difference (1%) was found
between groups 1 and 7.
4.6 Specification of the
Groups Formed
To specify the groups formed for
later classification of new exposures into
one of the um dos homogeneous groups,
we must find the frequency of the class
vector of the variables that constitute each
group. This class vector has been termed
characteristics vector and is made up of
the concatenation of the Behavior Score,
Days Late and Percentage Amount Used
variables, respectively. Cluster Analysis ensures that exposures with the same
characteristics vector will always be in
the same group, as they are the first to
be grouped together by the clustering algorithm, given that the distance between
them is zero. The results were:
■ Table 6: Characteristics vectors
by group.
Group
Characteristics Vectors
1
211, 311, 411, 511, 611, 711
2
111
3
212, 213, 214, 215
4
315, 415, 515, 615, 715
5
312, 313, 314, 412, 413, 414, 512, 513,
514, 612, 613, 614, 712, 713, 714
6
126, 226, 241, 326, 436, 525,
526, 536, 546, 626, 636,
646, 726, 736, 741, 746
7
112, 113, 114, 115
4.7 Interpretation of the
groups formed
Table 6 contains the characteristics vectors and allow interpreting the
groups formed.
Generally speaking, the lateness
variable is a strong characteristic for the
identification of risk of default in a credit portfolio, and so is the percentage
amount used variable, given that as the
credit limit is used up, the risk increases
of a customer not honoring repayment
and becoming late.
However, it is interesting to point
out that the obligor risk characteristic, represented by the Behavior Score, was
also significant for the definition of homogeneous risk groups. This can be seen
in group 1, which is formed by exposures
that display class 1 for the lateness and
operation dimensions, that is, contracts
without late payments and whose usage
is up to 6.876%, and with BS scores below 89.5, on a 0-100 scale. Group 2, in its
turn, is made up only of exposures that
are class 1 for all dimensions, representing the lowest risk group, comprehending contracts without late payments,
whose usage is of up to 6.876%, and whose Behavior Score is over 89.5 and under
100. Table 5 shows that this is the group
with the smallest percentage of defaults,
at 0.32%.
Group 3 is made up of exposures
with Behavior Scores between 70.5 and
89.5 (class 2) on the obligor dimension,
zero days late (class 1), and with operation dimension classes ranging between
2 and 5, that is 6.876% to 100.002% credit limit usage. Note that the obligor and
lateness dimension classes, respectively 2 and 1, are low-risk classes, which re-
18
Authors
flects on the group’s default percentage
of 6.07%
In group 4, the obligor dimension
classes range from 3 to 7 (Behavior Score
below 70.5), while the lateness dimension
class is 1 (zero days late) and the operation dimension’s is 5 (72.013% to 100.002%
usage). The group’s classes for the obligor and operation dimensions are riskier,
impacting the group’s percentage default
of 22.33% (Table 5).
In group 5, the obligor dimension also ranges from 3 to 7 (BS under 70.5), while the lateness dimension
class is 1 (zero days late) and the operation dimension’s classes go from 2 to 4
(6.876% to 72.013% limit usage). As the
data show, the class variations are rather
similar to group 4, but group 5’s obligor dimension classes are less risky and this leads to a percentage of default of 12.12%,
below group 4’s.
In group 6, the obligor dimension’s
classes vary between 1 and 6 (89.5 to 14.5),
while the lateness dimension’s classes
range from 2 to 4 (1-89 days late) and the
operation dimension’s classes are between 2 and 4 (6.876% to 72.013% limit usage). This group showed the most variation
in terms of the dimension’s classes, which may have reflected on its 63.69% defaults percentage.
In group 7, exposures were class
1 (the best class) for the obligor and lateness dimensions (BS 89.5 or higher
and zero days late) and the operation
dimension’s classes varied between 2 and
5 (6.876% to 100.002% limit usage), indicating that the obligor and lateness dimensions contribute the most to the allocation
of exposures to the group. As Table 5 shows, this is the group with the second lowest percentage of defaults, at 1.57%.
5. Final Comments
The clusters formed showed
good distribution in terms of the number of contracts, were consistent based
on characteristics vectors analysis, and
quite distinctive in terms of percentage
of default, which is one of the most important traits to support the hypothesis
of using cluster analysis to categorize retail exposures according to homogeneous
risk groups.
Therefore, the study’s main objective was reached and it has been proven that Cluster Analysis is a viable option to segregate a retail exposures portfolio into homogeneous risk groups.
One topic future studies may
address involves developing a methodology to allocate exposures with observation
vectors not found in the development sample, or to classes that may be created over
time in one of the homogeneous groups
formed. A conservative way of dealing
with this problem is to allocate such exposures to the worst group, that is, the one
with the highest percentage of defaults.
Bachelor of Statistics and Specialist in Applied Statistics, currently Senior Executive Assistant at the Credit Risk
and Collection Modeling Area of a domestic retail bank.
Contact: [email protected]
Authors
19
Master of Production engineering with emphasis on Operational Research from COPPE/UFRJ and Bachelor of
Statistics from UERJ. Has an MBA in Risk Management from FIPECAFI. Currently National Credit Risk and Collection Modeling manager in a domestic retail bank.
Bibliography
Contact: [email protected]
ASSAF NETO, A. Mercado Financeiro. 10ª ed. São Paulo: Atlas, 2011. 339 p.
BARROSO, L. P.; ARTES, R. 10º Simpósio de Estatística Aplicada à Experimentação Agronômica (SEAGRO),
2003, Lavras. Análise Multivariada: Minicurso. Lavras: UFLA, 2003.151 p.
BIS - Bank for International Settlements. Disponível em: <http://www.bis.org/bcbs/history.htm>. Acessado em
30/01/2013.
CARNEIRO, F. F. L.; VIVAN, G. F. A.; KRAUSE, K. Novo Acordo da Basileia: estudo de caso para o contexto brasileiro. Resenha BM& F, São Paulo, n.163, 2005. Disponível em < http://www4.bcb.gov.br/pre/inscricaoContaB/trabalhos/O%20Novo%20Acordo%20de%20Basil%C3%A9ia_um%20estudo%20de%20caso%20para%20
o%20contexto%20brasileiro.pdf>. Acessado em 05/02/2013.
Circular BACEN nº. 3.360 de 12 de setembro de 2007. Disponível em <http://www.bcb.gov.br/pre/normativos/busca/normativo.asp?tipo=circ&ano=2007&numero=3360>. Acessado em 05/02/2013.
Circular BACEN nº. 3.581 de 8 de março de 2012. Disponível em <http://www.bcb.gov.br/pre/normativos/busca/
normativo.asp?tipo=circ&ano=2012&numero=3581>. Acessado em 05/02/2013.
JOHNSON, R.A.; WICHERN, D.W. Applied Multivariate Statistical Analysis. 4th ed. Upper Saddle River: Ed.
Prentice Hall, 1998. 816 p.
JORION, P. Value at Risk: a nova fonte de referência para a gestão do risco financeiro. São Paulo:
BM&FBOVESPA: Bolsa de Valores, Mercadorias e Futuros, 2010. 487 p.
LANDIM, P.M.B. Análise estatística de dados geológicos multivariados. Lab. Geomatemática, DGA, IGCE,
UNESP/Rio Claro, Texto Didático 03, 128 p. 2000. Disponível em <http://www.rc.unesp.br/igce/aplicada/DIDATICOS/LANDIM/multivariados.pdf>. Acessado em 30/01/2013.
MENDONÇA, A. R. R. de. O Acordo da Basiléia de 2004: uma revisão em direção às práticas de mercado.
Economia Política Internacional: Análise Estratégica, Campinas, Instituto de Economia, Unicamp, n. 2, jul./set.
2004. Disponível em: <http://www.eco.unicamp.br/ceri/boletim2.htm>. Acessado em 02/02/2013.
MINGOTI, S.A. Análise de dados através de métodos de estatística multivariada: Uma abordagem aplicada.
Belo Horizonte: Ed. UFMG, 2005. 297 p.
RAPELI, C. B.; BOTEGA, N. J. Clinical profiles of serious suicide attempters consecutively admitted to a university-based hospital: a cluster analysis study. Revista Brasileira de Psiquiatria, nº 27, 285-289, 2005. Disponível em
<http://www.scielo.br/scielo.php?pid=S1516-44462005000400006&script=sci_arttext>. Acessado em 02/02/2013.
Bibliography
20
Resolução CMN nº. 3.490, de 29 de agosto de 2007. Disponível em <http://www.bcb.gov.br/pre/normativos/busca/
normativo.asp?tipo=res&ano=2007&numero=3490> Acessado em 02/02/2013.
SANVICENTE, A. Z.; MINARDI, A. M. A. F. Migração de risco de crédito de empresas brasileiras: uma aplicação
de análise de clusters na área de crédito. Instituto Brasileiro de Mercado de Capitais, Working Paper, março de
1999. Disponível em <http://www.risktech.com.br/PDFs/migra%C3%A7%C3%A3o.pdf>. Acessado em 02/02/2013.
SAS Help. Coeficiente de Similaridade e Dissimilaridade geral de Gower. Disponível em <http://support.
sas.com/documentation/cdl/en/statug/63962/HTML/default/viewer.htm#statug_distance_sect008.htm>. Acessado em 02/02/2013.
SAS Help. Fórmulas do Coeficiente de Similaridade e Dissimilaridade geral de Gower. Disponível em <http://
support.sas.com/documentation/cdl/en/statug/63962/HTML/default/viewer.htm#statug_distance_sect016.
htm>. Acessado em 02/02/2013.
SHIRAIWA, C. S.; SIQUEIRA, J.O. Categorização de Variáveis Em Modelos de Risco De Crédito, Artigo referente à conclusão de MBA em Gestão de Riscos da Fundação Instituto de Pesquisas Contábeis, Atuariais e Financeiras – FIPECAFI, 2012, 13p.
21
Survival Analysis
in Credit Models:
a View of Covariates
Treatment
Melissa Sousa
Tiago Lima
Wanderson Rocha
22
Abstract
The study proposes using survival analysis to adjust a credit model, with particular focus on the treatment of its predictive variables, as well as on the creation of homogeneous clusters. Unlike other studies that
use survival analysis in connection with credit data, this
study’s highlight is a concern with the relationship between output and predictive variables. We refer to output variables in the plural because we understand that
two main aspects exist in the credit arena: the default
event and time to default; the former captures the core
concern of credit models – default -, while the latter is
concerned with when an individual will default. We use
the nonparametric Cox model to adjust the model so that
time to default and default rate are aligned. The logrank
test was used at two stages in the study: treatment of
the predictive variables, to ensure categories with distinct survival curves, and the creation of de homogeneous clusters that, in addition to different default rates
over time, also show different survival curves. The study has been divided into four sections, with an introduction of the problem at hand, a view of the variable-treatment process, the adjustment of the model via Cox and,
finally, the method for creating homogeneous clusters.
KEYWORDS: Survival analysis, Cox Model, Logrank
Test, Variables Treatment.
1. Introduction
Several studies exist on the
use of the survival analysis technique
in credit applications. The output variables that regulatory authorities defend are mostly concerned with the observation of an event over a certain period of time, which makes for binary
outputs. However, if an institution knows, in addition to the rate at which an
event will occur in the coming months,
the form of the distribution over this
period, such an institution will be able
to improve its strategy and increase financial returns.
One of the solutions frequently suggested in such cases is survival analysis. In the majority of the discussions about the topic, the main fo-
23
cus lies on the selected technique and
the evaluation of its performance. Variables treatment ends up in a secondary role and, often, the same treatments used for logit regression models
are used, based on a binary output variable.
In practical application however, the treatment of variables requires
plenty of attention, particularly where one wants a single model to provide the regulatory probability of default
and the timing of its distribution. It is
important to make sure that the independent variable identifies the behavior of the two elements of the output.
This study proposes a joint treatment of three variables: the relevant predictive variable, the regulatory default
rate, and the time to default. Treatment
is important because there may be variables with distinct behaviors for each of
the outputs. For example, a certain age
group may show a higher rate of default,
but with a longer time-to-default than
another group with a lower default rate.
■ Table 1: Variable categorization example
Age
Time to
default
(days)
Default rate
(12 months)
Up to 30
250
5.0%
30 - 40
230
4.0%
40 - 50
200
3.0%
50 - 60
180
2.0%
60 - 70
140
1.0%
Over 70
110
0.5%
If the categorization only takes
account of default at a certain point
in time, the variable will not make the
best contribution possible to the model
when it comes to estimating the event
over different spans of time.
2. Modeling Process
The modeling process we propose in this study assumes that the
population sampling and segmentation stage has been completed. In a
three-stage process, we begin with
the analysis of predictive variables and
proceed to the construction of homogeneous clusters, as proposed by the
regulators. The stages are:
• Variables treatment;
• Model adjustment and performance analysis;
• Construction of homogeneous clusters.
2.1 Variables Treatment
The first stage in the process
attempts to fully understand the predictive variables in connection with the
default event and time to default. To
adjust the credit risk model, we must
make sure that its predictive variables
are consistent. This evaluation is done
based on the predictive variable and
its relationship with defaults. All covariates are evaluated, regardless of
type (numeric or categorical); the difference lies in the kind of summarization
used: mean and median are considered for numeric variables, while categorical ones rely on frequency. The treatment of the covariates for the purposes of risk model adjustment abides by
a pre-selection analysis flow. As each
24
covariate meets a criterion, it is brought to the following phase.
2.1.1 Variability and Stability
Assessment
The first pre-selection criterion
measures whether the covariates have
many missing values or concentrate on a
certain value, in addition to checking the
temporal behavior of the relationship between each covariate and defaulting.
2.1.2 Categorization Analysis
The bivariate analysis method is
widespread among Analytics teams; generally speaking, it involves categorizing
the continuous covariate so that each category makes sense when it comes to evaluating defaults. Adjusting a survival model does not greatly depart from this, but
the analysis of the covariate’s meaning
must be performed for both default and
time to default.
We propose to divide the ordinal
continuous covariates into deciles, whe-
re each decile is regarded as a stratum
for the survival curve’s adjustment. The
goal, here, is to check whether each of
the variable’s strata (categories) produces
distinct survival curves where each curve is monotone in meaning relative to default and time to default.
We used the Logrank test to
compare the consecutive categories;
categories were reclustered where statistically equal. The test was repeated
until every category showed a statistically different survival curve.
After the pre-definition of categories, we simultaneously compared
the default rates by category and the
median time to default.
For the model to correctly provide the rate of default for each observation period, the two indicators had to
be aligned and with opposite trends.
Graphic 1 illustrates the analysis.
Graphic 1 (A) shows the behavior of the default rate and median time
to default observed in the pre-catego-
■ Graphic 1: Default rate and median time to default by category.
25
rization. As seen, we were unable to
obtain monotone effect with 10 categories. We achieved the effect by reclustering categories [2 and 3], [5 and
6] and [8 and 9], as Graphic 1 (B) shows. After defining the categories, a Kaplan-Meier model and a Logrank test
were again run using the new categories.
2.1.3 Category Stability Analysis
Once the categories were defined for each covariate, we investigated whether they were stable over time.
This stage concerns itself with default
and each category’s share. The main
point at this stage is to check for variables with a volume of individuals per
category such that the default rate is
not time-dependent, that is, stationary. Visual analysis is recommended for
this stage, and Graphic 2 illustrates the
■ Graphic 2: Default
kind of graph proposed for visualization, considering a covariate with 4 final categories.
2.2 Model Adjustment and
Performance Analysis
Different survival analysis methodologies exist. This study focuses
on nonparametric adjustment, using
the Cox model. Performance analysis
was an innovation on the part of the
study, as this chapter will show.
2.2.1 The Cox Nonparametric
Model
The Cox regression model allows analyzing data from lifetime studies
where the output is the time until the
occurrence of a relevant event, with adjustment via covariates.
Generically, considering p covariates, so that x is a vector with the
rate and volume stability by category.
26
components x=(x1, x2,...,xp), the general
expression of the Cox Model is:
se the ratio between the failure rates of two
different individuals is constant over time.
The ratio of the failure rate functions for
individuals i and j is given by (Equation 2)
and is not time-dependent.
λ(t ) =λ 0 (t )g (x´β)
where g is a non-negative function that must be specified so that
g(0)=1. This model is made up of the product of two components, of which one
is nonparametric and the other is parametric. The nonparametric component
λ0( t ) is not specified and is a non-negative function of time. It is usually referred to as baseline, sinceλ( t )=λ0 when
x=0. The parametric component is often
used in the following multiplicative form
(Equation 1):
where β is the parameters vector associated with the covariates. This
ensures that λ( t ) is always non-negative. The constant β0 is not shown in the
Equation above because of the presence of the model’s nonparametric component, which absorbs the constant term.
The Cox model is also referred to
as the proportional hazards model becau-
2.2.2 Cox Model Adjustment
The Cox regression model is
characterized by the β´s coefficients,
which measure the effects of the covariates on the failure rate function. An estimation method is needed to allow inferences about the model’s parameters.
The most frequently used method is the
Cox partial maximum likelihood model,
which consists of conditioning the construction of the likelihood function on
awareness of the past history of failures
and censures.
In a sample of n individuals with k = ≤ distinct failures at times
t1 < t2 ... < tn , the conditional probability
of the i th observation failing at time ti is
given by (Equation 3):
where R ( ti ) is the set of the indices of observations at risk at time ti .
g(x´β) = exp{x´β}= exp{β1 x1+...+βp xp }
λ i (t )
λ j (t )
=
λ 0 (t )exp{x i ´β}
λ 0 (t )exp{x´ j β}
= exp{x´i β –x´ j β},
(1)
(2)
P [ individual failure at ti | One failure at ti and history until ti ] =
λ 0 (t )exp{x i´ β}
=
exp{x i´ β}
Ʃj Є R (t ) λ 0 (t )exp{x j´ β} Ʃj Є R (t ) exp{x j´ β}
i
i
(3)
27
The likelihood function to be
used for the purposes of inferring the
model’s parameters is therefore given
by the product of all of the terms presented, associated with their distinct
failure times, where δi is the failure indicator (Equation 4).
k
L (β) =
Π
i=1 Ʃ
λ (t )exp{x j´ β}
j Є R (t ) 0
i
2.2.3 Model Performance
The literature discusses several
methods to evaluate the fit and quality
of the Cox Model. These methods are
essentially based on the residuals of
Cox-Snell, Schoenfeld, Martingal and
Deviance. The firmer two evaluate the
fit of the assumption of proportional
hazards and the latter two evaluate atypical points and the covariates’ functional form. Proportional hazards assumption is often not applicable to the
variables credit models study. Given
this, validations are required in terms
of the model’s estimated values. Evaluation of the performance of a model
with a given portfolio, with the purpose
of direct application to credit management, is given by the metrics practitioners generally use: Kolmogorov Smirnov (KS), Gini Coefficient, and AUROC (Area under Receiver Operating
Characteristic). A new proposition that
may be adopted based on the construction of survival models is measuring these statistics over time, that is,
over different evaluation periods, such
as 3, 6, 12 and 24 months, for example.
One important aspect in the evaluation
of the estimated model is the comparison of estimated and observed rates of
default. The estimated rates must not
underestimate the portfolio’s actual rates, which also applies to the different
n
=
Π
i=1
(Ʃ
j Є R (t i )
δi
)
λ 0 (t )exp{x j´ β}
(4)
evaluation periods. Therefore, a graphic method to evaluate the observed
and estimated default curves for different observation periods can be used
to validate the final model. The estimated rate of default for the observation
of the model over time us given by the
following relationship according to the
Cox model:
estimed rate = 1 – S0(t),
Where S0(t) is given by:
S (t) = λ 0 (t)*e x´β
Therefore, in addition to the estimated βj parameters, we must obtain
the baseline λ0 (t) for every t .
For example, the estimated rate of
default for 365 days would be given by:
estimed rate (365)= λ 0 (365)* ex´β
Below, we provide an illustration
of the estimated and observed rates over
the previously defined times (Graphic 3):
28
■ Graphic 3: Observed and expected rates.
2.3 Construction of
Homogeneous Clusters
According to Public Hearing
Notice No. 37, published in 2011 by the
Central Bank of Brazil, a homogeneous
cluster may be defined as a “set of exposures or obligors with shared characteristics for the purposes of credit risk
evaluation and quantification”. Homogeneous clusters act as facilitators for the
management of the institution’s credit
portfolio.
The constitution of these clusters must take into consideration certain
specific criteria:
• A sufficient number of observations per cluster. The
observed rate of default must
be an efficient PD estimator
(non-biased and with minimum variance);
• The rate of default must be
monotone rising or falling as
a function of the direction of
each cluster’s score;
• The rates of default obtained
for each cluster must be statistically different;
• There can be no concentration of observations in a specific cluster.
• Each cluster’s rates of default must show distinct levels
across the analyzed vintages
and must also be stable.
The means practitioners use
most frequently to build these clusters relies on breaking the development
sample into percentiles so that the rates of default are ordered. These breaks are then reclustered. The most frequently used tests to measure differences between the clusters’ default rate
levels are the Duncan, Tukey and Scheffé tests. To check for the rate’s stability
across vintages, they use the Population
Stability Index (PSI), so that distribution
shifts can be measured. The Herfindahl
test can be applied to measure the concentration of observations in the clusters formed.
After the homogeneous clus-
29
ters are defined, each cluster’s empirical survival curve can be studied. These curves are compared using the Log-Rank test. Where the hypothesis of
equality between two curves is not rejected (p-value over 5%), the breaks are
reclustered and the tests are run anew.
The Graphic 4 and Table 2 below illustrate the test and the clusters’ behavior
over time relative to the survival curve.
Graphic 4 illustrates the survival curves of five homogeneous clusters found. Table 2 shows the Logrank
test to check whether all survival curves are distinct when paired.
3. Conclusion
When applied to credit risk models, survival analysis usually performs
well from the angle of explaining de-
■ Graphic 4: Survival curves by homogeneous cluster.
■ Table 2: Logrank test – illustrative.
Cluster Cluster
Chi-squared
p-value
1
2
q12
<0.0001
1
3
q13
<0.0001
1
4
q14
<0.0001
1
5
q15
<0.0001
2
3
q23
<0.0001
2
4
q24
<0.0001
2
5
q25
<0.0001
3
4
q34
<0.0001
3
5
q35
<0.0001
4
5
q45
<0.0001
fault at a specific point in time – considering curve after 365 days, in this
case. The methodology’s benefit compared to the usual logit regression is
the ability to preview defaulting individuals over different horizons. The main
point of improvement was the ability to
add the traditional practitioner concept
with the concept of time to the event,
which was possible because all the
analyses done on the predictive variables focused on the two aspects, lending stability and accuracy to the adjustment.
Authors
30
Melissa Sousa
Has a Bachelor’s degree in Statistics from Universidade Estadual de Campinas and an MBA in Finance
from FIA/USP. Currently an Analytics consultant at Serasa Experian, her experience includes credit risk
modeling, CRM, and Analytics solutions. She has worked in modeling areas devoted to several kinds of portfolios, focusing on financial performance, always in the banking industry. Sousa can be contacted by e-mail: [email protected].
Tiago Lima
Has a Bachelor’s degree in statistics from Universidade Estadual de Campinas and a Master’s degree in
statistics from Universidade de São Paulo. Currently an expert in econometric credit risk models development. His experience includes time-series projection models and multivariate analysis. Lima can be contacted by e-mail: [email protected].
Wanderson Rocha
Has a Bachelor’s degree in Statistics from Universidade Federal do Paraná and is a post-graduate student
of Analytical Intelligence at FIA/USP. He has been with the Serasa Experian Analytics area since 2012. His
experience includes credit risk modeling and Basel II in particular. Previously, he worked in a major financial institution’s Corporate Credit Risk – Basel II area for 3 years. Wanderson can be contacted by e-mail:
[email protected].
31
Spatial Correlation
of Corporate Defaults
Rinaldo Artes
32
Abstract
In recent decades, measuring credit risk has been
a constant concern for financial institutions; credit scoring are important tools for this purpose. The national and
local economic situation may affect a company’s or an
individual’s credit risk. Several indices exist to measure a
country’s economic risk, but the same is not true of business and individual risk. Local economic effects may provide information on the default rates of companies or people that operate/live in the respective areas; this can be
measured using spatial statistical analysis techniques. In
this paper, we use Moran’s I to evaluate the spatial correlation of default for companies in the State of São Paulo.
We perform a time analysis and suggest a structure associated with the granularity level. The main results are evidence of the presence of a spatial correlation and the relationship between Moran’s I and the market rate of default.
Keywords: Spatial Correlation, Rate of Default,
Moran’s I, Credit Risk.
1. Introduction
One of the objectives of Basel
II (BCBS, 2006) is to encourage measurement of the credit-risk to which
each financial institution is exposed
and propose calculating the capital to
be allocated in order to prevent against
losses. The Vasicek (2002) model is regarded as the basis for the required capital formula. The model assumes that
a company’s probability of default (PD)
depends on its idiosyncratic characteristics and on a macro-economic factor
common to all companies.
Small and medium-sized businesses in particular are more heavily
influenced by regional/local economic
factors. The effect can be observed
in small areas such as region, sub-re-
gion, or even sector and sub-sector, according to Brazilian Post Office (“Correios”) postal code (“CEP”) digit classification (http://www.correios.com.br/
servicos/cep/cep_estrutura.cfm).
The economic activity indices
currently published in Brazil do not reach this level of information capillarity. Therefore, inclusion of these effects
into a PD model is not possible. However, although such regional factors cannot always be observed, their
effects can be identified by means of
spatial analysis of default.
In this paper, we use Moran’s I
to study the evolution of the spatial dependence of the default of small and
medium-sized companies between São
Paulo state regions defined according
33
to CEP numbers, from December 2007
to August 2010. We considered three
regionalization criteria. In addition, we
correlated Moran’s I with SME default
rates observed in the state of São Paulo during the relevant period.
2. Literature Review
Probability of default may be
conditioned on several risk factors, of
which the location of an applicant relative to other obligors may be a potentially relevant factor, as Stine (2011)
points out. In this article the author
analyzes real-estate credit risk in the
United States pre- and post-2008 crisis, based on county-level default rate
data.
Figure 1 was extracted from this
paper and shows the change in default
in 2005-2009 (the full paper analyzes
the 1993-2010 period). Figure 1 uses
warm colors to represent counties with
high default rates and cool colors for
those where the rates are low.
Spatial default-rate correlation
is clearly visible. Default rises intensively in the West Coast during period.
In this case, a county’s rate increase
appears to be related with the increase in neighboring counties.
Cotterman (2001) analyzes the impact of local characteristics on consumer
property credit risk in the United States.
The neighborhood’s ethnic make-up and
income are associated with default risk
factors. Cotterman (2001) thus attempts
to capture the causative effect of the spatial correlation based on neighborhood
socio-demographic characteristics.
■ Figure 1 Evolution of default in the USA by county.
(Source: Stine - 2011)
34
The paper’s conclusions include evidence that the effects of local
factors (income and race) lose strength when the model is conditioned on
other characteristics for the applicant,
operation and macro-economic environment.
Cotterman’s paper focuses specifically on property credit securitized
by the Federal Housing Administration
(FHA), the US Government agency for
mortgage securitization. Cotterman
(2001) incorporates the spatial correlation by means of postal code clusters.
In the following years, several
papers came out on the spatial correlation of credit risk, but always conditioned on the distance between applicants and creditors. Grunert and Weber (2009), Degryse and Ongena (2005),
Carling and Lundberg (2005) and, later,
Argawal and Hauswald (2007) use empirical evidence to approach the correlation between default rates and the
applicant-creditor distance.
Deng, Pavlov and Yang (2005)
model the cause of mortgage foreclosure and incorporate spatial heterogeneity into their model. Some of the variables that influence foreclosure are
often latent: culture, access to information, etc. According to Deng, Pavlov
and Yang (2005), individuals with those latent characteristics agglomerate
in neighborhoods, which enables modeling the cause of foreclosure.
Deng, Pavlov e Yang (2005)
address three causes of foreclosure:
refinancing, property sale and default.
Non-foreclosed contracts are regar-
ded as censures. In this paper the model assumes that each individual has a
choice: refinance, sell, or default. The
correlation structure between co-variables and the response variable depends on the type of neighborhood, through which the authors introduce spatial
information into the model.
Deng, Pavlov and Yang (2005)
propose a competitive risks model for
the causes of mortgage foreclosures.
The model’s parameters are variant, in
an attempt to capture the effect of latent variables shared by individuals in
a certain region.
In a 2012 paper, Agarwal et al.
identify the presence of spatial default
correlation by analyzing mortgages in
the US. Their study estimates the increase in the risk of default of residents
of regions with higher foreclosure rates.
However, controlling for other
individual factors, the concentration of
sub-prime mortgages does not increase the credit risk of a non-defaulting
neighbor. Only higher risk operations
such as hybrid ARMs (Fabozzi, 2006) or
documents with incomplete documentation show this spatial correlation.
In essence Argawal et al. (2012),
Deng et al. (2005) and Cotterman (2001)
propose the presence of latent unobserved factors resulting in a spatial
correlation among individuals. Stine
(2011), on the other hand, proposes a
pragmatic analysis of the spatial correlation structure via the spatial correlation for areas known as Moran’s I (Moran, 1950).
35
3. Methodology
Type 1) wik = 1/dik, where
Moran’s I (I-Moran) is a correlation metric that incorporates the two
dimensions involved in a spatial phenomenon: latitude and longitude. As defined in Moran (1950), the index is given
by the Equation 1:
I
=
ƩƩ
N
ƩƩ
i
i
k
w
ik
where yi is the yth observational
unit’s default, ȳ is the mean default, N
is the number of observations and wik
is the weight related to the distance
between units i and k. Note that wik lacks a rigid, single form; therefore different structures will result in different
Moran’s I values.
Moran’s I is widely used in studies where the observational units are
areas. Some illustrative examples of w_
ik given this context include:
dik is the distance between observations i and k.
2
Type 2) wik = 1/dik ,
{
Type 3) wik=
k
1, where i and k are neighboring regions
0,otherwise
w (y i – ȳ) (y k – ȳ)
ik
Ʃ (y – ȳ)
i
i
2
,
(1)
3. Results
Stine (2011) shows that for individuals, revolving, installment and mortgage credit portfolios show a strong
spatial correlation, with Moran’s I ranging between .25 and. 65, depending on
the portfolio and the period. Graphic 1
shows this variation over time.
It is worth pointing out that the
spatial correlation depends on the macro-economic scenario. The 2000-2006 period
shows increased spatial correlation, but
■ Graphic 1 Spatial correlation – Moran’s I
(Source: Stine - 2011)
36
even after the 2008 crisis, although there
is a drop in Moran’s I, spatial default-rate dependence persists among US counties. Stine (2011) formulated the weights
schedule as being type three with neighborhoods of up to two layers, that is, adjoining counties or counties separated by up
to one county have weight 1.
In this paper, we evaluate Moran’s
I using type-2 weight, that is, the inverse of
the squared distance between regions. In
this case, the region’s centroid was used to
calculate distances. The first selected region level was the CEP region, represented
by the code’s first two numerals. Figure 2
shows the State of São Paulo’s 19 regions.
The first map shows the nine coastal and
interior regions, the second shows the six
greater São Paulo regions, and, finally, the
city of São Paulo’s fur regions. Additional
details on the regions denoted by the first
two CEP numerals can be found in MundoGeo (2013) and NeoGeographiká (2013).
However, analysis of Moran’s I for
these 19 regions in the relevant period showed low spatial correlation results. Graphic 2 shows that Moran’s I does not exceed .1 in this case. Analyzing sub-regions,
that is, areas determined by the first three
CEP numerals, spatial correlation increases and ranges between .15 and .21. Finally,
when sector (first four CEP numerals) is
■ Figure 2 Illustration of nineteen regions of the state of São Paulo.
■ Graphic 2 Moran’s I by CEP granularity level.
37
taken into consideration for Moran’s I calculation purposes, the correlation rises to
around .55. Greater granularity would require calculating the distances among 20
thousand areas and be subject to computing limitations.
As in Stine (2011), Moran’s I varies
over time. In our study, variation over time
is smaller due to the shorter period involved: 3 years, as opposed to 19. Still, one
can discern a rising trend in spatial correlation (sector and sub-region levels) over
time. The correlation between market
default rate (BACEN Website, 2013) and
Moran’s I is of around .65. In other words,
there are indications that increased spatial correlation occurs together with increased market defaulting.
As for SMEs, the presence of
spatial correlation is intuitively consistent. Small and medium-size companies (SMEs) in particular show greater spatial correlation with nearby business firms. Firms of this size exist to
serve their region’s population and larger companies. This may result in spatial dependence, as a cooling economy
and the resulting increase in defaults
cause the credit risk of a given company in the region to rise.
4. Closing remarks
The spatial correlation among
small and medium-sized enterprises
may be due to a failure to observe local economic activity factors. The correlation level depends on the definition
of the analyzed regions and this paper
found a weak spatial correlation as measured by Moran’s I for the 19 São Paulo state regions (the first two CEP numerals). However, when the area definition is based on the state’s sectors
(first four CEP numerals), Moran’s I indicates the presence of significant spatial correlation. Should this information be disregarded while developing a
credit risk model – the so-called biased due to the endogeneity created by
omitted variables.
Furthermore, it is worth noting
that the correlation between the rate of
default and Moran’s I is moderate, with
a Pearson coefficient of .65. A cause-and-effect relationship does not necessarily exist, but in periods of high
defaulting, credit scoring models that
fail to incorporate the spatial correlation present in the data will be more
liable to lose performance.
One topic for future research
is how to include information from the
spatial correlation into credit scoring
models. One direct means would be
through the variances and co-variances matrix, but in this case the issue
of computing limitation must be taken
into consideration. Another front, approached by Fernandes (2012), would
be to estimate spatial risk through techniques such as Kriging.
Finally, the time correlation
found between spatial dependence
and market rate of default suggests a
future detailed study to evaluate the
vulnerability of credit portfolios.
Authors
38
Guilherme Fernandes has a Bachelor’s degree in Statistics from Universidade Federal de São Carlos and a Master’s
degree in Economics from Insper-SP, and is a Doctor of Statistics candidate at ICMC-USP/DEs-UFSCar. He is currently
responsible for Serasa Experian’s Analytics Innovation area, where he has been since 2010. His experience focuses on
credit and fraud risk modeling. He was previously employed for four years in the corporate credit risk area of a major
Brazilian bank. Fernandes may be contacted by email at [email protected].
Prof. Dr. Rinaldo Artes
Prof. Dr. Rinaldo Artaes is a Bachelor, Master and Doctor of Statistics from Universidade de São Paulo. He
is currently a full-time professor at Insper Instituto de Ensino e Pesquisa. His main areas of research include
References
multivariate analysis, circular data and estimation equations.
BAGARWAL, S. E HAUSWALD, R.B.H. (2007): Distance and information asymmetries in lending decisions. Proceedings, Federal Reserve Bank of Chicago, issue May, pp. 183-204.
AGARWAL, S.; AMBROSE, B.W; CHOMSISENGPHET, S. e SANDERS, A.B. (2012): Thy Neighbor’s Mortgage: Does
Living in a Subprime Neighborhood Affect One’s Probability of Default?, Journal of Real Estate Economics, American Real Estate and Urban Economics Association, vol. 40, No. 1, pp. 1-22.
Banco Central do Brasil: Consulta ao site https://www3.bcb.gov.br/sgspub/localizarseries/ às 13:50 do dia 28/Abril/2013.
Série utilizada: Operações de crédito aos setores público e privado - recursos livres - inadimplência – PJ.
Basel Committee on Canking Supervision (2006): International Convergence of Capital Measurement and Capital
Standards – A Revised Framework. Bank of International Settlements.
CARLING e LUNDBERG (2005): Asymmetric information and distance: an empirical assessment of geographical
cretit rationing, Jounal of Economics and Business. Vol. 57, pp. 39-59.
COTTERMAN, R.F. (2001): Neighborhood effects in mortgage default risk. Relatório encomendado por U.S. Department of Housing and Urban Development. Download feito de http://www.huduser.org/portal/publications/hsgfin/defaultrisk.html na data de 20/03/2012.
DEGRYSE, H. e ONGENA, S. (2005): Distance, Lending Relationships, and Competition, Journal of Finance, American Finance Association, Vol. 60, No. 1, pp. 231-266.
DENG, Y.; PAVLOV, A.D. e YANG, L. (2005): Spatial Heterogeneity in Mortgage Terminations by Refinance, Sale
and Default, Journal of Real Estate Economics, American Real Estate and Urban Economics Association, vol.
33, No. 4, pp. 739-764.
FERNANDES, G. (2012): Mensuração do risco de crédito espacial e sua incorporação nos modelos de credit scoring. Dissertação de Mestrado, Insper,São Paulo, SP.
GRUNERT, J. e WEBER, M. (2009): Recovery Rates of Commercial Lending: Empirical Evidence for German Companies. Journal of Banking and Finance, Vol. 33, pp. 505-513.
MORAN, P.A.P. (1950): Notes on Continuous Stochastic Phenomena. Biometrika. Vol 37, No. 1, pp. 17–23.
MundoGeo (2013): Acesso feito à página http://mundogeo.com/blog/1998/08/02/geonegocios-8/ em 30 de abril de 2013.
Neogeographiká (2013): Acesso feito à página http://neogeographika.blogspot.com.br/2012/08/ken-mapas-e-plantas.
html em 30 de abril de 2013.
STINE, R. (2011): Spatial temporal models for retail credit. Credit Scoring and Credit Control Conference 2011, Edimburgo, Reino Unido.
39
Infrastructure
Credit and
Financing in Brazil
Frederico A. Turolla
Márcio F. Gabrielli
Igor J. C. Gondim
40
Introduction
A window of opportunity has opened for a leap ahead in infrastructure investment after the developments for
the Brazilian economy in the 1990s and 2000s. In this period,
and in the 1990s in particular, the country underwent a ranging review of key elements in its institutional environment.
The sweeping reforms addressed areas of broad impact, such as prices stabilization, the introduction of more
modern competition protection mechanisms, a review of
bankruptcy and corporate recovery laws, and the restructuring of public debt at all levels of government. They also included important industry-specific elements, with new regulatory frameworks and changes to infrastructure business
models, including concession mechanisms, de-nationalization and the restructuring of government-owned entities.
Keywords: Infrastructure Assets, Financing Risk, Information Asymmetry.
The 1994 prices stabilization and
the 2002 political transition played a key
role in the Brazilian economy’s transformation. The former eliminated the main
source of long-term economic unpredictability. The latter significantly reduced the political risks that had previously inhibited long-term investments or
made them significantly more expensive. On the macroeconomic level at least,
the pillars that ensured economic stability
and policy continuation were maintained
for almost ten years, despite some deterioration, starting in 2003, in terms of regulatory independence and the promotion of competition within industries.
The fact that the world experienced a period of ample supply of funds for
investment in emerging countries, in different moments, is relevant for infrastructure. Firstly, the 2000s were a period
of remarkable growth worldwide, with re-
latively risk perception around the globe.
After the 2008 financial crisis in the US
and the subsequent European crisis, the
expansionist monetary policy in developed countries led to funds overflowing to
emerging economies as a side effect, in a
movement that led to the generalized appreciation of currencies operating on flexible foreign exchange regimens. Brazil
was an important beneficiary of this flow
of funds, as it enjoyed, at the time, significant global attention as a result of the
broad reforms had in the previous period
and the smooth political transition, as discussed earlier.
This array of institutional changes
and the global environment significantly
raised not only the potential for investment
in Brazil’s infrastructure but also credit supply and private-sector financing (both domestic and international) to the industries
involved. However, in spite of the extraor-
41
dinary window of opportunity and the announcement of a major Federal-Government plan, Brazilian infrastructure failed
to take off as expected. The opportunities
were therefore under-exploited.
There are at least two reasons for
the performance to prove itself dissatisfactory despite such a highly propitious
environment. The first reason is related to
the very nature of infrastructure assets:
projects in this area require massive volumes of capital and would face significant financing challenges in any country.
Such challenges are magnified in an economy such as Brazil’s. The second reason concerns the increase in political risk
since the past decade, due to greater political intervention in technical decisions,
which again made projects more expensive and reduced investor propensity to accept them.
This article discusses the Brazilian infrastructure-financing environment, as well as its main challenges. Section one addresses the typical characteristics of infrastructure assets, which
are relevant to their financing. We then
address the old state-support Vs. marketplace dichotomy, which is strongly associated with the role of the National Bank
for Economic and Social Development
(BNDES) and other institutions that have
historically concentrated the supply of
funds in this area. We next provide comments on the financial and capital markets and then evaluate infrastructure financing risks. The final section highlights
some of the most important challenges
remaining in the arena.
Characteristics of
Infrastructure Assets
Generally speaking, infrastructure assets have specific characteristics
that vary significantly among industries
– power, transport, sanitation and telecommunications – and also within each
industry. Depending on an activity’s position on the industry chain, the characteristics may vary significantly. On the power chain, for example, cable segments
(transmission and distribution) have marked natural-monopoly characteristics
that require strict regulation, while the
energy segments (generation and commercialization) operate in more competitive environments.
The table next summarizes characteristics of the various infrastructure
industries.
■ Table 1: Characteristics of the various infrastructure industries.
Consequence
Typical response
High fixed cost
Natural monopoly issues
Public operation or concessions; regulation
Specific assets
Discourages investment
Long-maturity contracts
Positive
externalities
Public policy characteristics
Access and universalization policies
Long life
Operator-change issues
Operator selection, renewal and
replacement processes
Stable demand
Defensive assets
Source: developed by the authors
42
One typical response to these characteristics is the heavy weight of
public-sector operation and, even in the
case of private or partnered operation,
the financing of infrastructure projects
shows high public-sector concentration
worldwide. Public operation is being increasingly replaced by an increase in various forms of private-sector participation. In Brail, this is seen mainly in contracts under the Concessions Act (Law
No. 8.987 of 1995) and the Public-Private Partnerships Act (Law No. 11.079 of e
2004), among other mechanisms.
In recent decades, there has
been a strong global trend of implementing institutional risk-mitigation
mechanisms, such as independent regulation and long-term planning. These enable significantly encouraging
not only private investment, but also
private-sector financing of infrastructure projects. Brazil, too, has made significant headway in this direction, with
the definition of industry frameworks
and relatively autonomous regulatory
entities, all of which face the dual challenge of being on the first phase of the
institutional learning curve and being
under constant attack from politicians
interested in decisions of high economic and electoral worth.
In addition to institutional issues, the financing system has several specific aspects of is own. To illustrate, in the presence of strong information asymmetry for the extension
of financing, a common form of defense for finance providers often materializes as requiring warranties that may
be real (mortgage, chattel mortgage,
commercial pledge, or collateral depo-
sit) or personal (sureties and bonds),
with the frequent accumulation of either. The difficulty or cost involved in
obtaining such warranties may cause
companies with viable projects and the
willingness to repay financing to lose
access to funding. BNDES itself requires high warranties. Given this context,
warranties become an important competitiveness-inhibiting factor for several important industries, in addition to
inhibiting investments towards universalization.
State-support vs.
the Marketplace:
the Old Argument
In brazil and many other countries, infrastructure credit is highly
concentrated on public-sector development sources. In the power industry, for example, according to Sabattini (2012, p. 121), development entities –
BNDES and Banco do Brasil in particular – are the main individual credits
of the majority of conglomerates active in this industry in Brazil. In sanitation, Caixa Econômica Federal, succeeds the former Banco Nacional da Habitação in representing a significant portion of the interest-bearing funds made
available to the industry.
Several development entities
and official institutions provide infrastructure in Brazil: Banco Nacional
de Desenvolvimento Econômico e Social (BNDES), Caixa Econômica Federal (CEF), Banco do Brasil (BB), Banco
do Nordeste do Brasil (BNB), Banco da
Amazônia (BASA), Financiadora de Estudos e Projetos (FINEP), and state-level development agencies, which ope-
43
rate state-level funds as well as pass-throughs from BNDES itself.
In addition, there are international development entities, which include, chiefly the World Bank, the International Finance Corporation (IFC),
the Inter-American Development Bank
(IADB), Corporación Andina de Fomento (CAF), to name a few.
Given the importance of infrastructure for economic development
and the volume of funds involved, governments are typically directly involved in the financing process. In many
cases, however, they fail to ask a crucial
question: to what point to development
and market-based credit products are
substitute or complementary goods?
On other words, when governments
play a direct role in the financing process, are they simply crowding out private-sector financing and thereby unnecessarily transferring risks and any
subsidies to the taxpayer? This question, although of great economic and
social import, is also very difficult to
answer.
The Financial and
Capital Markets
The financial and capital markets fund infrastructure projects in several ways, with both debt and equity.
Financing environments include corporate finance, which creates liabilities
directly on the service provider organizations’ balance sheets, and project finance, which is intended for Specific
Purpose Entities (“Sociedades de Propósito Específico” – SPE). The corporate mode is more traditionally used
in Brazilian infrastructure, particularly
due to the massive state-owned companies that prevailed in the operational
arena for decades.
In this context, own funds generation was an important investment
finance instrument, as seen in the
economy’s various industries in an environment of high macroeconomic instability and low capital markets development. Under the Planasa basic-sanitation system for example, public-sector financing was provided by the
Banco Nacional da Habitação (BNH),
together with the state governments
that controlled the operational companies, in the belief that such companies would become self-sustainable
and start generating the funds to sustain their future expansion and operation. However, in the 1970s and ‘80s, in
several infrastructure segments, utility
bills started to be used as macroeconomic policy instruments in an attempt to
keep inflation in check, sacrificing internally-generated financing.
More recently, the Brazilian
marketplace’s institutional development and the new Public-Private Partnership instruments of recent decades have incremented the role of project financing. Even major infrastructure operators have been engaging in
SPE-based financing schemes.
One important program concerns the development of Infrastructure Debentures and Receivables Investment Funds (“Fundos de Investimento em Direitos Creditórios” – FIDC),
Incentivized Debenture Funds, and Infrastructure Investment Participation
Funds (“Fundos de Investimentos em
Participação em Infraestrutura” – FIP-
44
-IE), which rely on tax benefits.
The private equity and venture
capital (PE/VC) industry is often mentioned as a potential investor in infrastructure. But opinions vary as to the feasibility of investment from this source. For one thing, the typical PE/VC investment cycle – with exit in 3-5 years
– does not match the lengthy return periods of typical infrastructure projects.
The same critics of the role of
private equity and venture capital funds mention that the returns on infrastructure projects ten to be controlled,
at least ex-ante, by the public sector
by means of the concession process
models. To obtain higher returns, investors usually seek out environments
with less institutional security, which
may disproportionally increase risks,
reducing attractiveness.
However, one may argue that
these characteristics do not imply a
natural incompatibility between PE/VC
funds and the infrastructure industry,
nor do they severely limit the kinds of
projects the industry might be willing
to finance within the context of infrastructure.
In this sense, private equity and
venture capital expert Leonardo de
Lima Ribeiro recently noted that some
of the best PE/VC investments in Latin
America were done precisely in infrastructure or related industries, such as:
Mills, Cemar, GasAtacama, CPFL, Gol,
ALL, among others. For Ribeiro:
“the secret lies in investing mainly in the companies that develop projects
in the industry, and not necessarily in the
projects themselves. And to seek out turnaround opportunities, when the initial
investment has already been made but
at some point the company got into debt
and had to be sold by the original investor. Or privatizations. In fact, with the recent change in power industry bills, I foresee a new round of investments ready
to take place soon. Also on the power industry, it is perhaps the segment with
the greatest opportunity for private equity investment directly in projects. After
all, you can sell power in the long-term
via PPAs and get credit to build the developments, which greatly leverages the
return on equity. You can also exploit variations in power prices (enter into PPAs
when prices are high and purchase power
from the market at a lower price) although this has led to the demise of at least
one company, a Campanario/Tierra Amarilla). Finally, power includes the issue of
environmental risk. You can use equity to
develop a project and sell it after securing
the required licenses”
(Mr. Leonardo de Lima Ribeiro, in an exclusive
statement for this article, April 19th, 2013).
Financing in the
Partnerships Arena
Partnerships between the public and private sectors are among the
most important vehicles to enable new
infrastructure investments, particularly given fiscal and budgetary constraints. In Brazil, the law that governs
public-private partnerships includes
classes that may be regarded as ordinary, administrative, or sponsored concessions. In the former case, Law No.
8.987 of 1995 applies; for the latter two,
Law No. 11.079 of 2004. The two complement one another and are in turn
complemented by the Bidding Act
45
(Law NO. 8.666 of 93). Generally speaking, the former two address self-sustainable projects with financial flows
arising from billings, whereas the law
that became known as the “PPP Act”
is concerned with project where public funds are required. Finally, there
is the overall legal regimen, the discussion about legal tradition and the capital markets, and a large number of aspects associated with the credit market
and bankruptcy laws.
In the Brazilian case, in practice, the framework for public-public and
public-private contracts has been enabling a significant increase in the range of possibilities in terms of the provision and financing of infrastructure services, allowing new forms of cooperation among a wide array of public
and private actors.
As an example of partnership
and financing institutions in the Brazilian case, the Graphic 1 below illustrates a hypothetical infrastructure projects portfolio. The vertical axis represents the projects’ private rate of return; the horizontal axis shows their
social rate of return, which represents
the volume of externalities generated
by unit of investment. Each sphere represents one project, where the volume of the sphere may be taken as the
relative size of the project.
The best projects are those in
the Northeasternmost part of the first
quadrant, as they represent a fortunate
combination of high private return and
high social return. Sadly, projects like
these, which do not require public funds and add great collective benefits, are
rare. They are candidates for operation
■ Graphic 1: A hypothetical infrastructure projects portfolio.
Source: developed by the authors
46
via ordinary concession, under Law No.
8.987 of 95, or Concessions Act.
The projects that lie close to the
horizontal axis and to the East of the
vertical axis show good social return
but low private return. For these, the
typical instrument is Law No. 11.079 of
2004 (Public-Private Partnerships Act).
These contracts ma also operate with
public subsidies, as, despite their social
interest, they do not offer sufficient private-sector return to stimulate autonomous execution by private investors.
Law No. 12.766 of 2012 (resulting from the congressional approval
of Provisional Decree No. 575) created
the latest PPP-related developments
with the establishment of public investment in projects, which is relevant
to project financing insofar as it avoids
the need to obtain financing for investments. The Law was regulated by Federal Revenue Service Instruction No.
1.342 which provides special tax treatments for public-entity investments
inPPPs.
Infrastructure
Credit Risks
It is worth pointing out, however, that the kinds of risks taken in the
infrastructure area may differ from those in more traditional commercial areas. For example, public-sector risk is
usually higher, subject to adverse decisions involving regulation, billing, technical standards and other. These characteristics may require a more specialized research structure and more intensive legal advice to protect against
risks, for example via analysis of the
concessions’ insurance and warranties
schedule, or more intense survey of local, idiosyncratic characteristics of the
sub-national governments and political
environments.
Risks in the infrastructure industry are directly related to the institutional environment, both macro- –
nationally and locally – and microeconomically. In terms of the national macroeconomic environment, there have
been significant gains for infrastructure projects in the past two decades.
These changes include addressing the
needs for public-sector financing, in
the late 1990s, by means of a set of reforms that included the refinancing of
sub-national debt, the Fiscal Stability
Program, and the Fiscal Responsibility
Act; the consolidation of price stability
after severe tests involving emerging-economy crises; and the reduction of
political risk as an important consequence of the continued economic policy regimen after the 2002 transition.
The achievement of investment grade
was associated with these factors, which brought about not only reduced public and foreign financing needs, but
also increased financing security, with
a drop in the perceived probability of
solvency crises.
Regulatory aspects have also
improved significantly in Brazil in recent decades, especially in the latter
half of the 1990s and the early 2000s.
The creation of regulatory frameworks
based on self-governed entities with
independent mandates is a true structural departure from the preceding
period’s practice. This independence, however, has proved itself fragile in
practice, given the political interest in
47
maintaining decisions of high electoral
and economic worth under the direct
control of the Executive Branch and
politically appointed cabinet members.
There has also been an important
evolution – especially at the state level – in
terms of projects with private involvement
and governed by the Concessions and
Public-Private Partnership (PPP) Acts.
Among the important developments, we
may name the concessions’ risk matrices,
which have been covering important risks
that are now more clearly established in
the projects.
Infrastructure
Financing Challenges
Based on the above discussion, certain relevant challenges stand
out facing the expansion of infrastructure financing in Brazil. Next, we offer
a non-exhaustive discussion of these
challenges.
Firstly, we must evaluate the
cost-to-benefit ratio involved in taking
major fiscal risks as a result of the public financing mechanisms now available. The public sector’s sustainability
is a global challenge.
Secondly, we must determine
whether public- and private-sector financings are substitute or complementary goods. It is possible that development-agency funding effectively displaces private-sector capital, as some
suggest, which would require clearly urgent in-depth studies. Naturally, if
they are substitute goods, they will create fiscal risks and bring about undesi-
rable effects for the economy. It is therefore worth reviewing development-agency funding in a holistic manner,
as well as the role of bank credit and of
the capital markets in the Brazilian infrastructure financing.
Thirdly, achieving greater leverage, that is, a larger share of credit relative to equity in infrastructure projects. Typically, this involves more intense use of project finance-related
instruments, including concessions
and public-private partnerships. The
country has already made significant
legislative progress in this sense, but
there is still much to do.
Fourth, we must review the institutional environment as concerns the
most relevant industry risks, in particular relative to stability and the introduction of competition. The stable macroeconomic environment that has prevailed since the late 1990s and proved itself clearly favorable to investments is
dwindling as a result of more discretionary and short-term oriented policies.
Likewise, the industry regulation environment is increasingly subject to interventions, in many cases devoid of
long-term planning and occasionally
aligned with an electoral agenda. Promoting competition wherever possible,
embracing the best elements of international experience, would enable safe
gains for users.
These are complex, inter-related challenges that involve crucial
answers for Brazil’s development.
Authors
48
Frederico Araujo Turolla
Frederico Araujo Turolla is a Doctor of Corporate Economics, a Professor of the ESPM International Management
Master’s Program, and a partner at Pezco Microanalysis – e-mail [email protected]
Márcio Fernandes Gabrielli
Márcio Fernandes Gabrielli is a Maser of Business Administration with emphasis in Finance, a Finance Professor at FGV
and ESPM, and an associate at Pezco Microanalysis – e-mail [email protected]
Igor J. C. Gondim
Igor J. C. Gondim is a Doctoral Candidate, Finance, at FGV, and a consultant at Pezco Microanalysis – e-mail
Bibliography
[email protected]
SABBATINI, Rodrigo. Financiamento do investimento no setor de energia elétrica. In: IPEA. Infraestrutura e Planejamento no Brasil: Coordenação estatal da regulação dos incentivos em prol do investimento - o caso do setor elétrico.
IPEA, Relatório de Pesquisa, 2012.
TUROLLA, Frederico A. Financiamentos e garantias. Revista Conjuntura da Infraestrutura (FGV e ABDIB). Março de
2010.
VALENTE, Paulo Gurgel. Financiamento de longo prazo: um roteiro prático para o BNDES, IFC, FINEP e outras
instituições. Rio de Janeiro: Campus Elsevier, 2012.
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