Default and transition analysis of corporate debt rating.
Bajaj, Richa Verma
Introduction
[ILLUSTRATION OMITTED]
The Basel Committee on Banking Supervision had released the
guidelines on 'New Capital Adequacy Framework' in June 1999.
The Committee proposes two approaches, viz., Standardized and Internal
Rating Based (IRB) approach for estimating regulatory capital. Under the
'standardized approach', the capital computation is based on
the external rating agency's assessment of risk and same is
function of various risk elements under Foundation and Advanced IRB
Approach. These elements are: probability of default (PD), loss given
default (LGD), exposure at default (EAD), and maturity (M). These
estimates enter into a formula yields credit risk capital requirement.
PD, among these estimates, has the greatest differential impact on
determining risk capital. The sophisticated banks under the foundation
and advanced approaches are required to report estimated one year
probability of default (PD) for their credit exposure. Probability of
default (PD) is a quantitative measure of default risk. Basel has
defined default as: (i) Borrower is unlikely to pay its debt obligation
in full; (ii) the borrower is past due more than 90 days on any credit
obligation. Transition Matrix (TM) is used as a tool to study the
migration of a bond/loan from one rating grade to other. The PD
increases when an obligor's credit rating downgrades. The
probabilities of rating transition, in particular the default state, act
as an important input in credit risk models.
Basel Committee have recommended that PD estimates must be long-run
average of one-year realized default rates for borrowers in each rating
grade and they must depend upon historical experience and empirical
evidence. Hence, the bank must use historical observation period of at
least five years. To fulfill regulatory requirements, PD estimates needs
to be mapped to risk grade or risk rating of the borrower and it should
be estimated for each borrower's industry-wise or rating
class-wise. Given this background, the present study is undertaken
primarily to view the distribution of rating transitions conditional on
credit rating of the long term debt issuers, economic activities of the
issuer and macro-economic environment, for the period from January 1994
to January 2009.
II. Review of Literature
The first empirical credit rating migration model was developed by
Jarrow et al. (1 997) who used firm data to construct a matrix of credit
rating transitions probabilities. The rating agencies like Moody's
and Standard and Poor's have been the exclusive providers of rating
transition information for many years. The studies which have documented
the fact that the rating transition matrices vary according to the stage
of business cycle, the industry of the obligor and the length of the
time that has elapsed since the issuance of the bond are presented
below:
Altman (1989 a, b) attempted to identify the estimated probability
of default and loss from default over a specific time horizon given a
bond rating. The author maintained that prevailing methods for
calculating multi-year bond default rates were unsuitable because they
failed to account for maturities, calls, and other early redemptions
that occur prior to the end of a given measurement horizon. Asquith et
al. (1989) also observe that age of a bond is an important factor that
assumed to influence conditional probabilities of credit migration. The
authors find that default rates are lower immediately after issue and
rise over time. Aging effects are also looked at by Jonsson et al.
(1996) and Helwege et al. (1996).
The studies by Altman et al. (1992 a, b) further suggest that
rating migration may be time sensitive. The author addresses the
importance of the economic sector of the firm in the credit migration
process. They analyze the propensity for bonds to experience multiple
rating changes and the direction of those changes by industry sector.
Nagpal et al. (2001) approach is to assume that the rating transition is
a Markov process i.e., future ratings depend only on the current rating.
However, historical data suggest that recently upgraded or downgraded
companies are more likely to continue this trend in the near future
compared to companies whose ratings have been more stable. Wilson (1997
a, b) find cyclical PDs, especially in the case of economic downturns
when PDs increase dramatically. Carey (1 998) documents significant
differences in default rates for "good" years, as compared to
"bad" years. Bangia et al. (2000) and Figlewski et al. (2006)
find evidence of macroeconomic and industry effects on rating
transitions. They also found that ratings down-gradation and defaults
are more likely during downturns in economic activity. Lando et al.
(2002) propose an estimator for a time-inhomogeneous transition matrix
(i.e. transition matrix changes with time, for example with economic
fluctuations).
Jafry et al. (2003) compare the three approaches on S&P
transition data. They develop a statistical framework to test the
difference between matrices calculated using the cohort approach as well
as the time-homogeneous and in homogeneous continuous time methods.
Frydman et al. (2007) and Kadam et al. (2008) demonstrated that rating
migration probabilities are highly correlated with issuer
characteristics such as the industry of activity and domicile.
Shcherbakova (2008) focuses on estimating credit rating migration
probabilities. The results of this study confirm the previous empirical
finding in that obligor characteristic and business cycle stages have a
strong effect on the dynamics of credit ratings, with a stronger effect
observed in longer-horizon models.
On making review of the previously conducted studies, it is clear
that the PD changes with time and economic activity of the issuer. The
present study titled, "Default and Transition Analysis of Corporate
Debt Rating" has been conducted to examine this link for corporate
in India.
This paper is divided into five sections. Introduction of the
problem is described in Section I and review of previous studies is
presented in Section II. While the database and methodology is presented
in Section III, empirical results are reported in Section IV Conclusion
is available in the final Section of the paper.
III. Data Base and Methodology
In the present paper, an attempt has been made to study the
distribution of rating transitions. The secondary data was collected to
achieve the above-mentioned objective of the study. The CRISIL's
annual ratings of long term debts issued by 578 corporate (Manufacturing
Companies) formed the basis of the analysis. For estimating the
migration in corporate debt instruments, the period from January 1994 to
January 2009 i.e. of 16 years have been taken. Using CRISIL rating
history, an attempt has been made to find answer to the following
questions:
* What are the estimates of migration probabilities, default
probabilities and cumulative probability for the period January 1994 to
January 2009?
* What are the transition probabilities for each rating grade and
on the basis of economic sectors of the company?
The CRISIL's rating scales are divided into fifteen categories
i.e. AAA to C. But the present study analyzed major letter categories
rating scales i.e. AAA, AA, A, BBB, BB, B and C. The rating scales with
+ and--signs have been combined with the main rating grades. The grade D
represents default which is defined as a credit event where the
underlying firm has missed payment. In order to make the analysis more
meaningful, the corporate are divided into ten broad categories
(Textiles (T), Chemicals (C), Metal and metal products (M), Non-mettalic
products (N.M), Machinery (My), Transport Equipment (T.E), Food and
Beverages (F), Miscellaneous Manufacturing (M.M), Diversified (D) and
Service (S) sector) based on their economic activities. The data for the
same have been collected from CRISIL's Monthly Bulletin and PROWESS
database of CMIE. The default risk analysis has been made for all rating
grades together and by each sector individually. An attempt has also
been made to study the migration in Investment and Non-Investment Grades
(NIG) issuers. The IG issuers correspond to rating from AAA to BBB,
while NIG grade are ratings from BB to C. The methodology for estimating
default probabilities is based on the approach developed by Altman et
al. (1991) and De Servigny et al. (2004).
Default probabilities can be calculated by studying the migration
in credit ratings of the issuers. It can be analyzed and monitored
through "Transition Matrix (TM)". TM represents the moving
(Transition) probabilities from one rating level to all other rating
levels with in time span of one year. It indicates that borrower's
credit quality is improving or worsening. It is studied as--Transfer
Frequencies divided by Numbers of original firms in each risk class.
Features of a Transition Matrix (TM) are: (i) for designing TM
information at only two dates for each year of borrowers is necessary,
(ii) last column of transition matrix represents PD, (iii) higher
transition frequencies occur mostly in the neighboring classes of
rating, (iv) concentration is their along the first diagonal of the
Matrix, (v) all probabilities sum to 1 across rows because each row
lists all possible final states, inclusive of default state.
To start with, mortality rate analysis (historical default rate
experience of a bond/loan) of cohorts of companies to find the number of
firms in each rating class in each cohort moving towards default
category (D) is conducted. Each cohort comprises of all the companies
which have a rating outstanding at the start of the cohort year. From
these cohorts, year-wise default probabilities (Marginal Mortality Rate,
probability of a bond/loan defaulting in any given year) for different
rating grades and for different industries is computed. Like, there are
[T.sub.i,D] number of firms migrating to Default category out of N
number of firms in the ith rating grade over a one-year period, where, i
represents the rating grade at the start of the period, and D represents
Default. One year PD of the ith rating grade is estimated by counting
the frequencies: T i, D/N i (1)
Further, mortality rate analysis of yearly cohorts of companies for
at least two years is computed, to find the number of firms in each
rating class in each cohort moving towards default category (D). The
average one year default probability for the ith rating grade is
obtained by weighted average, Where, w' = --N-- "" ^
,t'd
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
weights are the number of firms in the ith rating class in a
particular year divided by the total number of firms in all the years.
These weights represent the relative importance of a given year. Altman
(1989a) has cited in his paper that the mortality rate is a
value-weighted rate for the particular year after issue, rather than
un-weighted average. If we were simply to average each of the year-one
rates, year-two rates, etc. our results would be susceptible to
significant specific-year bias. If, for example, the amount of new issue
is very small and the defaults emanating from that year are high in
relation to the amount issued, the un-weighted average could be
improperly affected. The weighted- average technique correctly biases
the results towards the larger-issue years, especially the more recent
years.
An attempt has also been made to calculate Cumulative default rate
(Cumulative Mortality Rate-CMR). CMR indicates the probability of
transition of loan/bond to default rating class within n years or over a
specified multiyear period. It is calculated by dividing the number of
issuers that defaulted at a specific time horizon by the number of
issuers that survived to that point of time. It is arrived at by
subtracting the product of the surviving population of each of the
previous year from one. [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN
ASCII] (3)
where [PI] is the geometric product, SR1 *SR2*......*SRn and N
denotes the no of years over which CMR is calculated.
IV. Empirical Results
Default is one state into which debt issuer can transfer when their
credit quality changes i.e. migration from standard to sub-standard
rating grade. However, the rating can be upgraded, downgraded or remain
unchanged. Changes in the distribution of rating in a given year add to
the changes in the credit quality of the borrowers. The rating
transition rates are considers as the representations of the historical
behavior of ratings. In contrast, rating stability is the ability to
resist change or migration.
Marginal Mortality Rate (MMR) and Cumulative Mortality Rate (CMR)
The Table-1 presents the marginal mortality rate (individual year)
and cumulative mortality rate (multi-year) estimates of the long term
debts issuers (578 corporate) as per rating grades over January 1995 to
January 2009 periods (as no defaults from January 1994 to January 1995).
These mortality rates are after adjustment, as suggested by Altman (1989
a, b). The table depicts that the mortality (default) rates are low for
the higher rated issuers and high for lower rated ones. The default
percentages ranges from 1 5 percent (2001) to 54 percent (1999) for BB
rating grade and it has increased to 33 percent (2002) to 100 percent
(2005) for C rated issuer during the study period. The table clearly
presents that during 2008-09, the transition from BBB to Default was 50
percent. In contrast, there is no default in low rating grade issuers
during the same period.
The table also presents estimated cumulative default rates for all
the long term debt issuers conditional on their ratings. The
methodologies detailed in Altman's (in 1989 and 1992) various
papers was adopted and CMR is arrived at by subtracting the product of
the surviving population of each of the previous year from one In
general, the cumulative default probability increases for longer horizon
and it is found low in the higher rating class than the lower ones.
During the study period, same is observed for rating grades. The high
default rates in low rating grade under study clearly presents that
"PD sensitivity to time is very much".
Average One Year Transition Matrix
Average one year transition matrix displays all rating movements
between categories from the beginning of the year through the end of the
year. The Table-II depicts the average one year transition rates for the
annual cohorts for various rating grades from January 1994 to January
2009, where each annual cohort is weighted by the size of the cohorts
(no. of issuers). The studies by Altman (1992 a, b), Nagpal (2001),
Lando (2002), Jafry (2003) and Shcherbakova (2008) form the basis of the
analysis. The table clearly indicates since 1994, an issuer started with
rating of AAA and ended with the same rating 97.34 percent of the time
and 2.66 percent of entries were downgraded to AA in the same period.
CRISIL even reported that no AAA rated entity has ever been downgraded
to a rating lower than AA. One can see from the table that no default
for AAA can be observed in last 16 years. The probability for AA ratings
remaining stable over a one-year period is 91.28 percent. The matrix
further presents that out of all A rated issuers at the beginning of the
year, 84.05 percent have remained in the A category by the year-end,
while 3.49 percent have been upgraded to AA. At the same time 7.51
percent have been downgraded to BBB, 2.41 percent to BB and so on. Also,
out of all the A rated companies at the beginning of the year, 3.48
percent have been downgraded to the speculative (NIG) category. As a
rule, the higher ratings have been less likely to be revised over one
year in contrast to low rating grades. The probability of stable rating
in BBB rating category over one year is 71.57 percent and it has reduced
to 60.17 percent for BB rating grade issuer. The issuer that began the
year with B rating, ended with the same rating 56 percent of the time
and default rate reached to 28 percent. The increasing trend for default
probability was observed from BBB (5.02 percent) to C (44.19 percent)
rating grade during the study period. The results clearly presents that
as the rating declines (credit quality worsens), the stability
probability declines and default probability increases. As one moves
down the rating scale, the likelihood of a multi-notch changes or up or
down increases. The above analysis clearly presents the correlation
between default rates and rating changes in line with Wilson (1997 a,
b), Carey (1998), Bangia et al. (2000) and Figlewski et al. (2006).
Conditional Transition
The empirical results further present the effects of cyclical
fluctuations on the rating migration over the study period (1994-95 to
2008-09). Altman, (1989 a, b) suggested that Default rates are
calculated on an average annual basis, with individual rates for each
year combined with the rates for other years over some longer time
horizon to form the estimate for the average annual rate. The average
annual default rate for the period 1995-96 to 2008-09 was 2.85 percent.
The Table-III presents that on an average, 3.25 percent of
investment grade issuers were down-graded to non-investment grade and
1.14 percent of them have defaulted over the study period. In contrast,
the up-grades were 4.30 percent from NIG to IG. The non-investment grade
rating categories showed relatively lower stability over the study
period. On sector-wise analysis it was found that the rating stability
is higher in services sector (90.33 percent) followed by Transport
Equipments sectors (83.58 percent). In contrast, the rating stability
was observed lowest in Metal Sector (56.99 percent) followed in upside
by non-metal sector (69.43 percent). However, higher transition i.e. the
up-gradation and down-gradation were observed in metal and non-metal
sector. On the basis of the above results, I also agree with Blume et
al. (1991) that rating changes and defaults are primarily a function of
the economic climate and are less dependent on the individual
characteristics of the bonds.
Sector-wise One-year Probability of Default
In line with Altman (1992 a, b) the following analysis present the
multiple rating changes and the direction of those changes by industry
sector. The Table-IV presents the average default probabilities for each
of the 10 sectors. The default probabilities are observed higher in low
rating grade issuers like BB, B and C. All C rating grade issuers have
defaulted on an average in last sixteen years in Non-metal, Machinery
and Miscellaneous Manufacturing sectors. In contrast, defaults are zero
for low rated issuers in Transport Equipment sector under study.
V. Conclusion
The present study is undertaken primarily to view the distribution
of rating transitions conditional on credit rating of the long term debt
issuers and economic activities of the issuer. The CRISIL's annual
ratings of long term debts issued by corporate (Manufacturing Companies)
formed the basis of the analysis. The reference period for the study
ranges from January 1994 to January 2009 i.e. 1 6 years.
It is found from the analysis that the mortality rate was observed
low for high rated issuer and high for low rated ones. The analysis
clearly indicates that as the rating declines, stability probability
declines and default probabilities increases. The mortality rate
analysis clearly presents that during 1994-95 to 1998-99, ratings were
less stable and the incidences of defaults were high. This clearly
reflects the impact of Asian crises. The most recent period of the study
(2004-05 to 2008-09) was positive for rating change, except the year
2008-09. This confirms the period of strong macro-economic fundamentals.
The cumulative mortality rate increases for longer horizon and it was
found low in higher rating class than lower ones for all time horizons.
The least (more) stable retention rate was found in non-investment grade
(investment grade) and low (high) rating grade issuers. In the better
rating grades the down grades exceeded upgrades for every rating grade.
B rating grade was an exception to the upgrade/ downgrade imbalance
during the study period. The annual average default rate was observed
2.85 percent for the entire study period. On sector-wise analysis, we
found that the rating stability was found higher in Service sector and
lowest in Metal and Metal products sector. The Transport Equipment
sector experienced no defaults during the study period.
From the above analysis, we found that the approach of evaluating
default risk through rating migration is very attractive because of its
simplicity. It is also observed that ratings transition is cyclical in
nature and so the default probability. It clearly proves the Basel
assumption that the default depends upon common factors. The findings of
the present study have a number of practical implications for credit
risk management.
References
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Performance', Journal of Finance, September, Vol. 44, pp. 909-922,
1989a.
* Altman, E.I., 'Default Risk Mortality Rates and the
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Richa Verma Bajaj
Assistant Professor,
National Institute of Bank Management,
Pune.
Table--I
MMR and CMR (%)--January 1996 to January 2009
1996 1997 1998 1999 2000 2001 2002
AAA MMR 0.0 0.0 0.0 0.0 0.0 0.0 0.0
CMR 0.0 0.0 0.0 0.0 0.0 0.0 0.0
AA MMR 0.0 0.0 0.0 2.0 0.0 0.0 0.0
CMR 0.0 0.0 0.0 2.0 2.0 2.0 2.0
A MMR 0.0 3.0 1.0 6.0 0.0 2.0 0.0
CMR 0.0 3.0 3.9 9.7 9.7 11.5 11.5
BBB MMR 2.0 0.0 0.0 23.0 6.0 8.0 6.0
CMR 2.0 2.0 2.0 24.5 29.1 34.7 38.7
BB MMR 17.0 20.0 20.0 54.0 30.0 15.0 29.0
CMR 17.0 33.6 46.9 75.6 82.9 85.5 89.7
B MMR 0.0 0.0 50.0 0.0 33.0 17.0 60.0
CMR 0.0 0.0 50.0 50.0 66.5 72.2 88.9
C MMR 0.0 0.0 50.0 43.0 57.0 44.0 33.0
CMR 0.0 0.0 50.0 71.5 87.7 93.1 95.4
2003 2004 2005 2006 2007 2008 2009
AAA 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0
AA 0.0 0.0 0.0 0.0 0.0 0.0 0.0
2.0 2.0 2.0 2.0 2.0 2.0 2.0
A 4.0 0.0 0.0 0.0 0.0 0.0 0.0
15.1 15.1 15.1 15.1 15.1 15.1 15.1
BBB 0.0 20.0 0.0 0.0 0.0 0.0 50.0
38.7 50.9 50.9 50.9 50.9 50.9 75.5
BB 0.0 0.0 0.0 0.0 0.0 0.0 0.0
89.7 89.7 89.7 89.7 89.7 89.7 89.7
B 0.0 0.0 0.0 0.0 0.0 0.0 0.0
88.9 88.9 88.9 88.9 88.9 88.9 88.9
C 67.0 0.0 100.0 0.0 0.0 0.0 0.0
98.5 98.5 100.0 100.0 100.0 100.0 100.0
Table--II
One year average transition matrix (1994-95 to 2008-09)
AAA AA A BBB BB B C D
AAA 97.34 2.66 0.00 0.00 0.00 0.00 0.00 0.00
AA 2.75 91.28 5.14 0.60 0.00 0.12 0.00 0.12
A 0.00 3.49 84.05 7.51 2.41 0.40 0.67 1.47
BBB 0.00 1.00 5.69 71.57 11.37 2.01 3.34 5.02
BB 0.00 0.85 0.00 3.39 60.17 3.39 6.78 25.42
B 0.00 0.00 0.00 8.00 0.00 56.00 8.00 28.00
C 0.00 0.00 0.00 2.33 0.00 0.00 53.49 44.19
D 0.00 0.00 0.00 0.57 0.85 0.00 0.28 98.30
Table--III
One year conditional transition
Years Upgrade Downgrade Default (D) No change
Overall 2.85 7.15 2.85 87.14
Investment Grade (IG) and Non-Investment Grade (NIG) wise
IG 0.00 3.25 1.14 95.61
NIG 4.30 0.00 30.11 65.59
Sector-wise
Textiles 1.32 7.93 16.74 74.01
Chemicals 3.45 7.04 11.49 78.02
Metal 6.09 9.68 27.24 56.99
Non-Metals 4.46 8.92 17.20 69.43
Machinery 1.82 8.39 20.07 69.71
Transport Equipment 1.87 7.09 7.46 83.58
Food 2.44 6.50 27.64 63.41
Miss. Manu. 2.88 6.47 17.27 73.38
Diversified 1.67 10.00 24.17 64.17
Services 2.26 3.70 3.70 90.33
Table--IV
Sector-wise average one-year probability of default (PD)
Textile Chemical Metal Non Machinery
Metal
AAA - 0.00 0.00 0.00 0.00
AA 0.00 0.00 1.37 0.00 0.00
A 0.00 0.53 2.22 4.55 1.10
BBB 10.34 2.17 11.11 0.00 10.71
BB 25.00 18.52 30.77 66.67 21.05
B 50.00 33.33 75.00 0.00 0.00
C 66.67 30.00 40.00 100.00 100.00
Transport Food Miss. Diversified Services
Equipment Manufacturing
AAA 0.00 0.00 0.00 0.00 0.00
AA 0.00 0.00 0.00 0.00 0.00
A 2.86 3.45 1.25 2.13 0.00
BBB 5.56 0.00 0.00 8.33 0.00
BB - 40.00 29.41 12.50 20.00
B 0.00 - - 16.67 -
C 0.00 50.00 100.00 33.33 50.00
