Rating Change Probabilities: An Empirical Analysis of Sovereign Ratings
©2013
Textbook
50 Pages
Summary
This study analyzes the determinants of rating changes and the variables' marginal effects on rating change probabilities. Based on the results, it presents transition matrices by computing transition probabilities. Furthermore, this study analyzes subsamples of the data set, conditional on the business cycle and the economic strength of a country, by using interaction effects. The Author of this study thereby verifies whether or how the transition matrices change by including interaction effects. He applies a latent variable approach, using an ordered probit model, to calculate the effects of different variables on the probabilities of rating changes.
Excerpt
Table Of Contents
1 Introduction
Sovereign Ratings are in the center of public attention, in times of sovereign debt crisis.
They are important for countries as they determine their cost of capital (Bissoondoyal-
Bheenick, 2005). And therefore their movements in either direction are observed critically.
Whereas an upgrade can cause a decrease in borrowing cost, a downgrade can imply
a burden and can cause the dependency of external support in case of default. It is
also essential for institutional investors to know the probability of a rating change as it
describes the potential gain or loss in their portfolio.
After Moody's recent announcement of changing the outlook from stable to negative
on long-term ratings of Germany, the Netherlands and Luxemburg, it seems that even
countries which were thought to keep their Aaa credit standing in the sovereign debt crisis
are affected of potential rating changes (Moody's, 2012b). In the same announcement
Moody's affirm that "Finland's unique credit standing" assures the country an ongoing
stable rating outlook. In this case four countries all belonging to the Euro area and
having the same Aaa credit rating, have different exposures to potential rating changes,
according to Moody's.
Standard and Poor's Ratings Services however decided to keep Germany's long-term
rating outlook stable (S & P, 2012). S & P did not change Germany's rating outlook
because they emphasize "its modern, highly diversified, and competitive economy [...] and
expenditure discipline". They also argue that Germany's dealing with historic "economic
and financial shocks, such as the reunification of West Germany with East Germany in
the 1990s and the global recession in 2009" allow them to have a stable outlook. In the
same time, they changed the outlook of the other AAA rated countries Luxemburg, the
Netherlands and Finland to negative. Even though S & P and Moody's have different
rating assessments in this case, their general assessment remains similiar. Differences in
ratings can appear, depending on the agencies' priorities and their assessment of risk.
The exemplary announcements of changes in rating outlooks raise the question which
factors drive a change in the rating outlook or which determinants cause a real credit
rating change. A lot of research has been done on the determinants of ratings. Less
research has focused on the determinants of credit rating changes and the probabilities of
rating transitions.
In my Bachelor thesis I will analyze the determinants of rating changes and the vari-
ables' marginal effects on rating change probabilities. Based on my results, I will present
transition matrices by computing transition probabilities. Furthermore, I will analyze
subsamples of my data set, conditional on the business cycle and the economic strength
of a country, by using interaction effects. I thereby verify whether or how the transition
matrices change by including interaction effects.
I apply a latent variable approach, using an ordered probit model, to calculate the
5
effects of different variables on the probabilities of rating changes. I therefore make use
of the discreteness of rating changes, classifing them by a number which indicates their
change direction and the number of notches moved. I assign an order to the possible rating
changes with eight classes, when considering the coarse rating category. This method is
proposed by Wooldridge to deal with the underlying ordered nature of the ordered probit
model (Wooldridge, 2001, p.506). The non-linearity, assumed by the model, also allows
to treat the difference between the rating changes differently. A linear model would not
account for the ordinal nature of rating changes, but treat the difference between the
rating changes equally (Borooah, 2001, p.5). A further implication of the ordered probit
model is the normal distribution of the error term
it
. This is in contrast to the ordered
logit model, where one assumes a logistic distribution of the error term
it
. Both models
are alternatives to each other and only differ in the tails of their graphs (Borooah, 2001,
p.9). According to Greene (2012, p.729), one can justify the choice between the ordered
probit or logit model with regard to "mathematical convienience", but it is difficult to
justify it with regard to the distributional assumptions. As the ordered probit model
satisfies my mathematical requirements, I choose it for my calculations.
My analysis adds value to most prior work on sovereign rating changes because they
are dated back ten years or more when sovereign ratings were less available, especially on
a global scale. In my Bachelor thesis I account for the increase in availability of sovereign
ratings. In my data set I use the maximum amount of countries that are both included in
the World Bank data set and rated by Moody's. This allows for better legitimacy of the
ordered probit model as the "ordered probit asymptotic properties do not generalise for
small samples" (Afonso et al., 2011). For example the increase in rated countries since
the paper of Hu et al. (2002), who also worked on rating changes, and my paper can be
seen in Tables 3 and 4 in the Appendix. Whereas Hu et al. worked with 487 ratings in
total, I work with 1,837 ratings in total. In 2011, which is my last year of observation,
with a total number of 112 out of 113, nearly every country was rated. In addition to
the extended sample, there is also an increase in rating changes due to the bust of the
international financial crisis and the following sovereign debt crisis which enables a better
estimation of rating changes and therefore allows a better analysis of rating changes.
The remainder of my Bachelor thesis is organized as follows. Chapter two presents
an overview of the existing literature on rating changes. Chapter three illustrates the
definitions of the rating categories and Moody's approach to rating transitions. Chapter
four introduces the ordered probit model. Chapter five explains my data choice and gives
an analysis of the data set. Chapter six presents the estimation results of the determinants
of rating changes. Chapter seven predicts rating change probabilities and presents the
transition matrices with interaction effects. Chapter eight concludes.
6
2 Previous Literature
The research on the determinants of sovereign rating changes is based on the analysis
of the determinants of sovereign ratings. As found in the influencial work of Cantor
and Packer (1996), using an OLS regression, ratings can be determined mainly on the
basis of six variables, which are per capita income, GDP growth, inflation, external debt,
level of economic development, and default history. Afonso et al. (2007) modified the
analysis of underlying fundamentals of sovereign ratings by using panel estimation and
random effects ordered probit approaches in order to account for the ordered nature of
ratings. They find that under the ordered probit model there are the following variables
that determine ratings: GDP per capita, GDP growth, government debt, government
effectiveness indicators, external debt, external reserves, and default history.
It seems reasonable to suppose that changes in the above mentioned variables will lead
to sovereign rating changes. However not every change in those variables will cause a
sovereign rating change, especially not on long-term ratings, as in my case. Sovereign
rating changes occur when certain thresholds in the fundamental values are crossed. The
aim of my Bachelor thesis is to find out the determining variables which are responsible
for the effective rating changes and to estimate those thresholds.
The literature of the determinants of sovereign rating changes often deals with different
methodologies to assess precise rating change probabilities and the creation of precise
transition matrices, given the constraint of low availability of sovereign ratings.
Most studies have been made with reference to corporate ratings because they allow
to have more data and longer rating histories. Even though corporate ratings differ in
their nature from sovereign ratings, some methodologies of their analysis can be helpful
and sometimes be applied, in a different manner, to sovereign ratings. The results from
corporate rating research can give some insights in the nature of rating changes.
Nickell et al. (2000) have estimated transition matrices for 6534 corporate obligors
during the time 1970-1997, using an ordered probit approach. They examined how in-
dustry, country and stage of the business cycle influence the change in ratings. Nickell
et al. (2000) and Bangia et al. (2002) find out that upgrades are more likely in booms
and downgrades are more likely in recessions. Altman and Kao (1992) investigated the
risk of corporate bonds regarding the aging effect, that is the implication of the length of
time since issue. They find that default risk increases in the first three or four years of
an issue's life and disappears afterwards. Hamilton and Cantor (2004) show that obligors
that have been downgraded are nearly 11 times more likely to default than those that
have been upgraded. Other analysis is based on rating heterogeneity within countries, like
serial correlation, which is known as rating drift. According to Altman and Kao (1992),
Kavvathas et al. (1993) ratings possess a memory. This means that future changes not
only depend on the present credit standing but also on prior rating changes: "The prob-
7
ability of a downgrade following a downgrade within one year significantly exceeds that
of an upgrade following a downgrade and vice versa." (Eisenkopf, 2007).
Some studies about rating changes also refer to sovereign rating changes. Hu et al.
(2002) search for determinants of rating transitions and find a method to create sovereign
transition matrices in the case of a short rating history. They analyze both industrial and
emerging market sovereign borrowers, even though the latter category has only few if any
ratings available. Therefore they propose a simultaneous ordered probit model of credit
ratings and default history. The default history adds to the ratings as a further source of
information, in order to prevent biased maximum likelihood estimators. They find that
previous year default, debt to GNP, reserves to imports, inflation, economic development,
lagged debt service to exports and lagged inflation explain rating changes.
Moreover Al-Sakka and ap Gwilym (2009) apply a random effects ordered probit model
and show that watchlist status, existing rating and issuers domicile region are useful
determinants in modeling sovereign rating changes in emerging economies. Al-Sakka and
ap Gwilym (2010) add to their model that the "estimation of sovereign rating migrations
can be improved by considering the sources of heterogeneity, such as rating history, rating
duration and Watchlist status, and cross-section error (country-specific heterogeneity)".
The idea is to make use of the random effects ordered probit model because the cross-
section error term captures factors for developing countries like "geopolitical uncertainty,
political risk and social tensions" which are mostly time-invariant features and cannot
be quantified (Al-Sakka and ap Gwilym, 2010). Also Afonso et al. (2009) find that
the random effects ordered probit model slightly outperforms the simple ordered probit
model.
Even though the approach of random effects ordered probit model by Al-Sakka and ap
Gwilym (2010) adds information to the simple ordered probit model, they do not find out
the true macroeconomic determinants of rating transitions. The watchlist status and the
existing rating are part of the rating agencies' assessment of rating transitions. Therefore
they do not search for the sources of rating changes like Hu et al. (2002) do and like it
is part of my research. My analysis will show which variables of Hu et al.'s selection also
hold for my data set or which additional variables influence rating changes in the case of
longer sovereign rating histories.
8
3 Agencies' rating assessment
Rating agencies emphasize that ratings are based on both quantitative and qualitative
elements. The qualitative approach is supposed to add additional information which is
not incorporated in the quantitative data. Rating agencies have multiple instruments to
disclose obligors' creditworthiness to investors. Besides rating, also outlook and review
serve as additional sources of information for investors. The outlook usually precedes
rating reviews and serves as an indicator as to the direction of the credit assessment in
the medium term. There are four categories ranging from positive, negative, stable and
developing (Moody's, 2012a). "A review indicates that a rating is under consideration for
a change in the near term" ranging from upgrade (UPG), downgrade (DNG) to uncertain
direction (UNC). This section explains the basic rating definitions and introduces the
agencies' methodology to construct rating transition matrices.
3.1 Rating Definitions and Methodology
"Sovereign debt ratings are forward-looking qualitative measures of the probability of
default, given in the form of a code" (Afonso et al., 2009). There are both short- and
long-term ratings. In this Bachelor thesis I will discuss only long-term ratings because
they are better known and because they allow a broader ranking of letter rating categories.
There are 9 coarse rating categories and 21 fine rating categories for long-term ratings,
whereas there are only four short term ratings which are P-1, P-2, P-3 and not prime.
Table 1 in the Appendix shows the order of Moody's ratings with the respective eval-
uation of a corresponding country's credit standing (Moody's, 2012a). Next to Moody's
credit codes, I also added the codes that I use for my analysis, in order to be able to
calculate with them.
Moody's have a three-stage process to determine a sovereign rating (Moody's, 2008).
In the first step, they assess the country's economic resiliency. In the second step, they
assess the government's financial robustness. Finally, in the third step they determine the
rating within the fine rating category.
The first step is described by two factors. The first factor is the economic strength,
which is given by the quantitative values of GDP per capita and the volatility of GDP. The
second factor is the institutional strength of the country, such as "property right, trans-
parency, the efficiency and predictability of government action, the degree of consensus
on the key goals of political action" (Moody's, 2008).
The second step is again described by two factors. The first factor is the financial
strength of the government, such as the sort of debt and the government's ability to
"raise taxes, cut spending, sell assets, obtain foreign currency,..."(Moody's, 2008). The
second factor is the sensibility to event risk. This factor accounts for the country's ability
9
to resist to the "occurrence of adverse economic, financial or political events" (Moody's,
2008).
Due to the last two mentioned steps, Moody's have placed the country in one of the
nine coarse rating categories. The third step defines the fine category from the 21 ratings
by "adjusting the degree of resiliency to the degree of financial robustness".
3.2 Rating Transition Matrices
According to Moody's, a rating change represents a "variation in the intrinsic relative
position of issuers and their obligations" due to "alteration in creditworthiness, or that
the previous rating did not fully reflect the quality of the bond as now seen" (Moody's,
2012c). Even though long-term ratings are supposed to reflect the country's long-term
rating standing, there are cases, in which Moody's change its rating assessment annually or
quarterly. This especially happens in times of economic turmoils like the current sovereign
debt crisis in Europe.
The big three rating agencies S & P, Moody's and Fitch create one and five year credit
transition matrices. Credit transition matrices describe migration probabilities of firms
and countries to change from any initial credit standing to any terminal rating in a future
time. Moody's make use of survival or duration modeling, called "multiple destination
proportional hazards model" to calculate the transition probabilities (Moody's, 2011).
Duration models simulate how long the rating stays the same and whether there will
be an upgrade, a downgrade or a default. The model uses both macroeconomic and is-
suer specific variables to determine the transition probabilities. Moody's have identified
two macroeconomic factors to have general predictive power for the creditworthiness of
countries, which are the unemployment rate forecast and the forecast of the high yield
spread over Treasuries. The unemployment rate is meant to describe the "macroeconomic
health". The high yield spread over Treasuries is meant to incorporate the "market's per-
ception of credit quality and hence credit availability". Additionally the credit transition
matrix takes into account today's and historic issuer-specific elements: "the current rat-
ing, whether the issuer was upgraded or downgraded into its current rating, how long the
issuer has maintained its current rating, how long the issuer has consecutively maintained
any credit rating, and the issuers current outlook or watchlist status" (Moody's, 2011).
10
4 Ordered Probit Model
My model is similiar to the model of Nickell et al. (2000) and Hu et al. (2002) and
is theoretically based on Long and Freese (2001), chapter 5, Greene (2012), chapter 18
and Borooah (2001). As the notations in the ordered probit model differ in Greene and
Borooah with regard to the intercept and the first cut-off point, I will try to combine
the explanations of both approaches. Moreover using Stata 12.0, this implies different
assumptions with regard to the intercept and the cut-off points. I will explain the role
of the cut-off points in the following section. According to Long and Freese (2001) the
ordered probit model has too "many free parameters" and cannot estimate both the cut-
off points and the constant. Therefore one has to decide for estimating either the constant
and assume the first cut-off value to be zero or to omit the constant and to estimate all
cut-off points (Long and Freese, 2001, p.187). Stata does not include an intercept term in
its output because it is absorbed into the cut-off points, whereas Greene does include it
and sets the first cut-off point to zero (Borooah, 2001, p.10). I will stick to the notation
of Borooah in order to be congruent with the Stata output.
In contrast to Nickell et al. (2000) and Hu et al. (2001), I use credit rating changes
as outcomes in the ordered probit model, instead of rating levels. The ordered probit
model is useful in the observation of rating changes because I assign an order to the
different rating changes by notches moved, where 8 upgrades is the highest outcome and
8 downgrades is the lowest outcome. The ordering is the following: +8, +7, +6, +5, +4,
+3, +2, +1, 0, -1, -2, -3, -4, -5, -6, -7, -8, where a plus symbolizes an upgrade and a
minus a downgrade. Also negative outcomes are possible in the ordered probit model, as
long as "larger values are assumed to correspond to "higher outcomes" (Long and Freese,
2001, p.188).
4.1 Mathematical Framework
The sovereign rating from one to another period can be an upgrade, a downgrade or no
change. In the coarse rating category, as there are 9 rating levels, there are always 8
possible rating changes. Considering the two extremes Aaa and C, the lowest level of a
possible rating change is achieved by a downgrade by eight notches and the highest level
of a possible rating change is reached by an upgrade by 8 notches. When also taking into
account the possibility of no rating change, like shown above, this gives
J =17 possible
outcomes of rating changes in total.
Suppose that a country
i's credit rating change in time t is determined by the realization
of a linear unobserved latent variable y
it
. The latent variable is determined by the sum
of
K (k=1,...,K ) independent variables multiplied with the corresponding estimate for
every country in the time horizon 1990-2011 (Borooah, 2001, p.8):
11
y
it
=
K
k=1
k
x
kit
+
it
= Z
it
+
it
(4.1)
, where Z
it
=
K
k=1
k
x
kit
(4.2)
A country is allocated to a rating change outcome y
it
, if the latent variable y
it
falls into
the interval [
i-1
,
i
] (Hu et al., 2002). The 's are the cut-off points which are unknown
parameters that are to be estimated like 's using maximum likelihood estimation. After
the estimation of the parameters, it is possible to assign the fitted values into the intervals
between the
J-1 = 16 cut-off points:
y
it
= U pgrade by 8 notches, if
16
y
it
y
it
= U pgrade by 7 notches, if if
15
< y
it
16
..
.
..
.
..
.
y
it
= U pgrade by 1 notch, if
9
< y
it
10
y
it
= N o change, if
8
< y
it
9
y
it
= Downgrade by 1 notch, if
7
< y
it
8
..
.
..
.
..
.
y
it
= Downgrade by 7 notches, if
1
< y
it
2
y
it
= Downgrade by 8 notches, if y
it
1
(4.3)
The probability of a rating change is given by the standing of the latent variable in
the normal cumulative distribution function. The observed outcome for a given value of
y
it
is the area under the curve between a pair of
J-1 cut-off points . The cumulative
distribution of a standard normal variate
X is (Borooah, 2001, p.12):
P (X < x) = (x) =
x
1
(X)dX =
x
1
(1/2)exp(
-X
2
/2) dX
(4.4)
In the ordered probit model, is the standard normal cumulative distribution function.
Moreover follows a standard normal distribution with
N(0,
2
) and
it
N(0, 1)
(4.5)
If assuming that every possible rating change also occurs, the probabilities for every
outcome are given by the following equations (Borooah, 2001, p.10):
12
P rob
{ y
it
= U pgrade by 8 notches
| x
it
} = 1 - (
16
- ^
Z
it
)
P rob
{ y
it
= U pgrade by 7 notches
| x
it
} = (
16
- ^
Z
it
)
- (
15
- ^
Z
it
)
P rob
{ y
it
= U pgrade by 6 notches
| x
it
} = (
15
- ^
Z
it
)
- (
14
- ^
Z
it
)
..
.
..
.
..
.
P rob
{ y
it
= Downgrade by 8 notches
| x
it
} = (
1
- ^
Z
it
)
(4.6)
For the right assignment of the probabilities, we must have an increasing order for the
cut-off points :
1
<
2
< ... <
16
(4.7)
In my model the cut-off points are extended by negative values because the downgrades
are defined to be negative and upgrades are defined to be positive. But as the increasing
order is still given, my model satisfies the requirement.
4.2 Model parameters
In the ordered probit model, the estimated coefficient ^
k
corresponds to the predicted
probability of the direction of a rating change (Borooah, 2001, p.24). A positive sign of
the coefficient indicates for dummy variables that all other variables constant, countries
with this feature have a higher probability of being upgraded and a lower probability of
being downgraded than countries that do not have this feature (Borooah, 2001, p.24).
A negative sign suggests that, ceteris paribus, countries with this feature have a lower
probability of being upgraded and a higher probability of being downgraded than countries
that do not have this feature. However only the direction of change in the probabilities of
the extreme outcomes can be inferred and not of the intermediate ones (Borooah, 2001,
p.24). The interpretation of the estimates needs caution. However for interpretation
purposes, I will try to interprete the coefficients, as far as this appears reasonable. The
additionally estimated cut-off points are given underneath the ^
k
-coefficients, in contrast
to Stata outputs in OLS regressions.
4.3 Marginal effects
The marginal effect gives the change in the probability of the outcome if the value of one
of the independent variables changes. An important feature of the ordered probit model is
that the marginal effects are not given by the estimated
k
- coefficients. In the following,
I therefore derive the marginal effects.
13
Marginal Effects of Continuous Variables:
If the independent variable is continuous, the marginal effect can be calculated by the
derivative of the probability of an outcome, using the chain rule:
P rob ( y
it
= U pgrade by 8 notches
| x)
x
= (
16
- ^
Z
it
)
P rob ( y
it
= U pgrade by 7 notches
| x)
x
= [(
15
- ^
Z
it
)
- (
16
- ^
Z
it
)]
P rob ( y
it
= U pgrade by 6 notches
| x)
x
= [(
14
- ^
Z
it
)
- (
15
- ^
Z
it
)]
..
.
..
.
..
.
P rob ( y
it
= Downngrade by 8 notches
| x)
x
=
-(
1
- ^
Z
it
)
(4.8)
As one can see from the marginal effects, again only the influence on the probabilities
from the two extreme outcomes will be unambiguously determined (Greene, 2012, p.829).
For the remaining outcomes, marginal effects do not have a clear sign and therefore do
not allow a conclusion about the direction of the change. As a practical analysis one could
investigate how the probability of a rating transition changes, if GDP growth increases.
From the requirement that the probabilities add up to 1, results that the sum of the
marginal effects is zero (Greene, 2012, p.830).
Marginal Effects of Dummy Variables:
If however the independent variable is a dummy variable, then the effect has to be
determined differently. In this case, the effect has to be calculated as the difference in
probabilities between the two variables which are to be compared. So the difference is
calculated between the probabilities of a dummy variable taking the value one and a
dummy variable taking the value zero, keeping all other variables at their means (Long
and Freese, 2001, p.213):
P rob(y
it
|x
it
)
x
it
= P rob(y
it
|x, x
it
= 1)
- P rob(y
it
|x, x
it
= 0)
(4.9)
Like in the case of continuous variables, the interpretation only holds for the extreme
outcomes. A practical example would be the analysis how the probability of a sovereign
rating transition changes if the concerning country is a non-developing country.
14
5 Data
5.1 Data summary
My dataset contains 113 countries rated by Moody's in the period 1990 until 2011. I
chose all countries that Moody's rated until 2011. The ratings were observed on the 31st
of December of each year. Furthermore I chose the time period because of high data
availability at the World Bank. The sovereign ratings refer to the foreign long-term issuer
ratings, which means that it deals with maturities of one year or greater. I chose Moody's
sovereign ratings, representatively for all credit rating agencies. Cantor and Packer (1996)
also state in their work that there is a high correlation between ratings of Moody's and
S & P with marginal differences: "Of the forty-nine countries rated by both Moodys
and Standard and Poors in September 1995, twenty-eight received the same rating from
the two agencies, twelve were rated higher by Standard and Poors, and nine were rated
higher by Moodys. When the agencies disagreed, their ratings in most cases differed by
one notch on the scale, although for seven countries their ratings differed by two notches."
Furthermore my aim is not to investigate the difference between the rating agencies, but
to analyze rating changes, given the agency's decision on a rating change. I assume that
the results do not improve for higher divergencies in opinions about ratings, given the low
differences in ratings from different agencies.
As far as there are withdrawn ratings, I do not consider them for the period that they
are withdrawn.
In the following I will present several tables and figures that are supposed to introduce
my data set and its structure. I especially want to highlight how rating changes appear in
my data set in general and over time. Tables 3 and 5 show that the 113 countries over the
22 years add up to a total number of 1,837 rating observations with 317 rating transitions
in the fine rating category and 157 rating transitions in the coarse rating category. I
have 1,188 investment grade (Aaa-Baa) rating observations and 649 speculative grade
(Ba-C) ratings. Concerning the fine rating category, there were 178 rating changes within
investment grade and 140 rating changes within speculative grade. Tabel 4 shows that in
the dataset of Hu et al. (2002), there are only 487 sovereign rating observations of which
158 have speculative grade observations over the period 1981-1998. That means that the
analysis based on my data set will provide more general results.
Figure 1 illustrates the distribution of Moody's sovereign ratings for July 2012, colored
by credit quality (Chartsbin, 2012). Especially it shows the strikingly low availability of
sovereign ratings in Africa.
Figure 2 shows the distribution of sovereign ratings by rating category in my data set.
It reveals the dominance of investment grade ratings (Aaa-Baa). Moreover there is a low
presence of Caa and Ca rated countries and no C ratings. Figure 3 additionally shows the
15
Details
- Pages
- Type of Edition
- Erstausgabe
- Year
- 2013
- ISBN (PDF)
- 9783954896561
- ISBN (Softcover)
- 9783954891566
- File size
- 574 KB
- Language
- English
- Publication date
- 2014 (February)
- Keywords
- Ratings Probit Model Transition Matrix Rating Agencies Stata
