www.moodys.com
Moody’s
Special Comment
Credit Policy
March 2008
Table of Contents:
Why Support Multiple Adjustment Methods?
4
Defining the Withdrawal Methods
4
Should We Expect Different Results?
7
Forecast Methodology
7
Comparison of Moody’s Annual and
Quarterly Adjustment at the Portfolio Level 8
Comparison of Moody’s Adjustment at the
Portfolio and Issuer Levels
10
Comparison
of
Moody’s
Issuer-Level
Adjustment and the CTM Conditional
Forecast for New (Unseasoned) Issuers 12
Comparison of Methods for Upgraded,
Downgraded and Seasoned Issuers
14
Comparing the Impact on Transition Rates15
Conclusion
21
References
23
Moody’s Related Research
23
Analyst Contacts:
New York
1.212.553.1653
28 Albert Metz
Senior Credit Officer
Nilay Donmez
Product Strategist
Richard Cantor
Team Managing Director
Comparing Withdrawal
Adjustment Methods:
An Application of Moody’s
Credit Transition Model
A recurring issue in the calculation of default and transition rates is the treatment
of withdrawn securities. It is perhaps easiest to illustrate with an example.
Suppose we are tracking a cohort of B rated bonds for five years. To be concrete,
assume there are initially 100 such bonds. Five years later, we see that 10 of the
bonds have defaulted, and 20 have had their ratings withdrawn shortly after the
beginning of the observation period, perhaps because they were liquidated and
were no longer at risk of default or because they simply exited from the public
bond market. What should our estimate of the five year default rate be for this
cohort? A simple answer is “10%” – since we observed 10 of 100 bonds
defaulting. But this implicitly assumes that the 20 that withdrew would not have
defaulted if they had continued to have public debt outstanding.
Another answer is to be agnostic about the fate of those 20 withdrawn securities
and allow for the possibility that they, too, might have defaulted if they had
continued to remain at risk. Absent any more information, a reasonable guess is
to assume that those 20 would have defaulted at the same rate as the bonds we
fully observed. In this example, we fully observed the fate of 80 bonds and saw
that 10 defaulted, implying a default rate of 12.5%.
Moody’s Credit Policy
Special Comment
Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Moody’s routinely adjusts its default statistics for withdrawal, though not exactly in the manner described
above, while other agencies typically do not. 1 The result is, all else equal, higher default rate estimates. From
our point of view, the appropriateness of adjusting for withdrawal depends on the question to be answered. If
by a “five year default rate” we mean the risk of default in an exposure which is expected to last at least five
years, then it is crucial to adjust the numbers for withdrawal. If instead we mean the risk of default over the
next five years in an exposure which may last less than five years, then another measure is needed. 2 Our
preference for adjusted numbers reflects the fact that, in most cases, the former question in more relevant.
Investors usually have an opinion about the expected life of their exposures and seek default rate estimates
for the corresponding tenor.
This is not merely an academic issue. Exhibit 1 compares by rating category the unadjusted with the adjusted
five year default rates. If investors were to use the unadjusted numbers as estimates of the “five year default
rate” for an exposure which was going to last at least five years, they would underestimate the true risk by, in
some cases, nearly half. 3
Exhibit 1:
5-Year Cumulative Default Rate, North American Issuers
80%
70%
60%
50%
40%
30%
20%
10%
0%
Aaa Aa1 Aa2 Aa3 A1 A2 A3 Baa1Baa2Baa3 Ba1 Ba2 Ba3 B1
Unadjusted
B2
B3 Caa1Caa2Caa3 Ca
C
Adjusted
Moody’s Credit Transition Model provides forecast transition probabilities for individual issuers over variable
horizons. These cover not only the probabilities of transitioning to all the rating states, but also to the default
and withdrawal states. An example for a single issuer is presented in Exhibit 2 below. Since an explicit
withdrawal forecast is provided, users of the model may decide whether, and how, to adjust the model output
for these withdrawal probabilities. Several different options are available. The purpose of this Special
Comment is not to defend the practice of adjustment per se, but simply to compare the quantitative differences
of these different adjustment methods.
We consider three adjustments, defined in greater detail below. The first is Moody’s current method of
adjusting annual cohorts. The second is essentially the Moody’s method applied in quarterly steps. The third
is a conditional transition probability which can only be calculated within Moody’s Credit Transition Model
(CTM). This adjustment has a certain logical appeal, but there is no analogous adjustment that can be made
to the historical data making comparisons problematic. We also compare these adjustments when applied first
to individual issuers, and second to the portfolio average. Our principle findings are:
1
2
3
2
For a thorough discussion of Moody’s adjustment method and its rationale, see Cantor and Hamilton (2007).
The simple unadjusted default rate, however, would be the appropriate benchmark only if the rate of withdrawal in the estimation sample happened to match
the early call rate on the bond in question.
Even in those cases when some form of prepayment exists such that the real credit exposure might be less than the stated maturity, if that prepayment
process is modeled explicitly, using the unadjusted numbers would again result in an underestimate of the default risk.
March 2008 „ Special Comment „ Moody’s Credit Policy – Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Moody’s Credit Policy
Special Comment
Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
„
There is little difference between applying the Moody’s method annually and applying its quarterly variant.
For ratings above B3, there is virtually no difference with the CTM conditional adjustment as well.
„
For ratings Caa1 and below there can be a material difference between the conditional probabilities
produced by the Credit Transition Model and the Moody’s adjustment. In particular, the CTM’s conditional
probabilities imply higher default rates and “better behaved” transition probabilities.
„
To the extent that default and withdrawal probabilities covary positively, the average of individually
adjusted default rates will be greater than the adjusted average default rate. However, in the cases we
examine, the difference is slight.
Exhibit 2:
Cumulative Transition Probabilities for a new B2 Issuer
1q
4q
8q
12q
16q
20q
Aaa
0
0
0
0
0
0
Aa1
0
0
0
0
0
0
Aa2
0
0
0
0
0
0
Aa3
0
0
0
0
0
0
A1
0
0
0
0
0
0
A2
0
0
0
0
0
0
A3
0
0
0
0
0
0
Baa1
0
0
0
0
0
0
Baa2
0
0
0
0
0
0
Baa3
0
0
0
0
0
1
Ba1
0
0
0
1
1
1
Ba2
0
0
1
1
1
1
Ba3
0
1
2
3
3
3
B1
0
3
6
8
7
6
B2
96
80
57
36
24
16
B3
1
4
7
8
7
6
Caa1
0
2
4
5
5
4
Caa2
0
1
2
3
3
2
Caa3
0
0
1
1
1
1
Ca
0
0
1
1
1
1
C
0
0
0
0
0
0
WR
2.8
6.8
12.0
19.9
28.2
36.2
Def
0.0
1.7
6.3
11.5
16.2
19.7
Sample output from Moody’s Credit Transition Model. A new issuer rated B2 has a 96% probability of being rated B2 one
quarter from now. Five years from now, there is only a 16% probability of its being rated B2, with a 19.7% probability of
having defaulted and a 36.2% probability of having withdrawn.
3
March 2008 „ Special Comment „ Moody’s Credit Policy – Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Moody’s Credit Policy
Special Comment
Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Why Support Multiple Adjustment Methods?
Before defining the adjustment methods, it is natural to ask why there are different options. The answer, of
course, is that there are multiple purposes, and different purposes suggest different approaches.
Users of the Credit Transition Model often want to produce forecasted default rates for their portfolios which
can be compared directly to the historical record. This can be readily accomplished by applying the Moody’s
adjustment to their portfolios’ average default and withdrawal rates. This is analogous to how Moody’s
calculates historical rates, and we will call it Moody’s Adjustment – Portfolio.
One potential drawback is that by adjusting the portfolio average, we lose the subadditivity of the portfolio. Put
differently, if we calculate the adjusted default rate for portfolio A, for portfolio B and finally for portfolio A ∪ B,
we would not be able to exactly reconcile the results.
We can remedy this by applying the Moody’s adjustment to each individual issuer in the portfolio, and then
taking averages over different subsets as desired. Call this method Moody’s Adjustment – Issuer. Now, our
results for portfolios A, B and A ∪ B will reconcile perfectly. However, this is no longer exactly analogous to
the historical record. The resulting default rates will usually be higher than the portfolio adjustment. A
question we will study below is, how much higher?
A second potential drawback is that the Moody’s adjustment is applied annually and hence loses the benefits
of the quarterly forecasts from the Credit Transition Model. We can apply the method quarterly rather than
annually. When doing so, we will remove a bias adjustment so that the resulting method will be recognized
exactly as the Kaplan-Meier product limit estimate. We can do this again at either the individual or portfolio
level. Call these Moody’s Quarterly – Issuer and Moody’s Quarterly – Portfolio, respectively. The drawback
now is that this is not exactly how Moody’s adjusts the historical data. Again, a purpose of this Special
Comment is to test the magnitude of the difference.
Finally, the Credit Transition Model offers us a truly unique opportunity to pose a particular question: what are
the default and transition probabilities of an issuer conditional on its rating not otherwise withdrawing? This is,
logically, what we seek from withdrawal-adjusted numbers. The drawback is that there is no historical analog
to this type of adjustment. Aside from the fact that we obviously cannot adjust individual histories by individual
“probabilities,” the observed historical data are drawn from a process where withdrawal is an option. While the
model permits us to perform the counter-factual experiment of “what rating transitions would be if withdrawal
were not an option,” the experiment is exactly that – counter-factual.
Defining the Withdrawal Methods
The Moody’s adjustment is essentially the Kaplan-Meier estimator applied in annual steps with a bias
correction for withdrawal. Imagine beginning with a cohort of N0 bonds on date 0. Define Dt as the number
who default at time t and Wt as the number who withdraw. Clearly then (and ignoring any other form of
censoring):
N t +1 = N t − Dt − Wt .
1
We calculate the default hazard rate in the first year of the cohort as:
H1 = D1 / ( N1 − .5 ⋅W1 ) .
2
Why do we adjust the risk set by half the withdrawn issuers? Another reasonable definition would be
H1 = D1 / N1. This presupposes that the issuers who withdrew in the first year, W1, were at no risk of default in
the first year. This strikes us as an optimistic assumption. Alternatively, we could define H1 = D1 / (N1 – W1).
This assumes that the withdrawn issuers were at an identical risk of default as all other issuers. When
considering a time interval of a full year, this may be unduly pessimistic. The truth is probably somewhere in
between: those issuers that withdrew did so more or less evenly throughout the year, hence some had the
4
March 2008 „ Special Comment „ Moody’s Credit Policy – Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Moody’s Credit Policy
Special Comment
Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
same default risk as the observed pool (those that withdrew towards the beginning of the year), others had no
default risk (those that withdrew at the end of the year), and most were in between. On balance, we assume
that their risk was about half of the observed pool, hence the bias correction in equation 1.
In general, we define the default hazard in year t as:
H t = Dt / (N t − .5 ⋅ Wt ) ,
3
where, again, Nt satisfies equation 1.
Given this sequence of hazard rates, we calculate the cumulative default rate as:
T
FT = 1 − ∏ (1 − H t ) .
4
t =1
In the context of the Credit Transition Model, N0 is 1, Dt is the probability of default in period t and Wt is the
probability of withdrawal in period t.
The periods under study need not be years – they could be quarters. As the time interval shrinks the bias
adjustment becomes unnecessary, so we define Ht = Dt / (Nt – Wt). Everything else is unchanged. This will be
recognized as the Kaplan-Meier estimator.
Nothing in the above formalism depends on whether these are the probabilities of an individual issuer, or the
average probabilities taken over a portfolio of issuers. The directional difference between the two is
indeterminate. Consider for simplicity a portfolio of two issuers, and consider the default hazard for the first
period. Let Di and Wi be the default and withdrawal probabilities, respectively, for the ith issuer for the first
period. The average of the individual adjusted default rates is given in equation 5, while equation 6 gives the
adjustment for average probabilities.
ha = .5 ⋅
hb =
D1
D2
.5 ⋅ ( D 1 + D 2 ) − .5 ⋅ D 1 ⋅ W 2 − .5 ⋅ D 2 ⋅ W 1
+
.
5
⋅
=
1−W 1
1−W 2
1 − W 1 − W 2 + W 1 ⋅W 2
,
.5 ⋅ ( D 1 + D 2 )
.
1 − .5 ⋅ (W 1 + W 2 )
5
6
Obviously the denominator in equation 6 is always greater than the denominator in equation 5, but just as
obviously so is the numerator – hence we cannot determine whether ha is greater or less than hb. Equality
between the two can be established as: 4
ha = hb ⇔ D 1 (1 − W 2 ) = D 2 (1 − W 1 ) .
7
Imagine beginning with a set of default and withdrawal probabilities such that equation 7 is satisfied. Now
imagine perturbing the default rates by a positive amount c while leaving the withdrawal rates unchanged.
Specifically, let D1 = D1* - c and D2 = D2* + c. By construction, hb is unchanged. But whether ha increases or
decreases depends on whether W2* is greater or less than W1*. Heuristically, when D2 > D1, ha will tend to be
2
1
greater than hb if W > W . Since both default rates and withdrawal rates correlate with ratings, we would
expect this to be true more often than not. Consequently, while it certainly may be the case that the adjusted
average portfolio default rate exceeds the average of adjusted default rates, we generally would expect the
opposite.
The above equations only pertain to adjusting default rates – not other rating transition rates. The difference is
that default is an absorbing state, with a well-defined cumulative probability. Rating states are not absorbing
4
5
That is assuming that D ≠ D and W ≠ W . If the withdrawal rates are equal, then the ha = hb. If the withdrawal rates are unequal but the default rates are
equal, then ha > hb.
1
2
1
2
March 2008 „ Special Comment „ Moody’s Credit Policy – Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Moody’s Credit Policy
Special Comment
Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
states, hence the above equations cannot be applied to, say, the “probability of being rated Aa3.” Absent
other information, all we can do is distribute the remaining probability across the rating states in their given
proportions. For example, suppose at period 1 a given issuer (or portfolio of issuers) has a 10% probability of
being rated A, 35% probability of being rated B, a 20% probability of being rated C, a 20% probability of
withdrawing and a 15% probability of defaulting. The adjusted default probability is 0.15 / (1 - 0.20), or
18.75%. We set the withdrawal probability to 0 of course. That leaves 16.25% probability mass
“unaccounted” for. Our approach is to distribute that mass across the rating states in the proportions 2:7:4 as
given by the observed rating probabilities. The results for this issuer (or portfolio) would thus be:
Unadjusted
Adjusted
A
10%
12.5%
B
35%
43.75%
C
20%
25.0%
WR
20%
-0-
Def
15%
18.75%
100%
100%
The opportunity offered by the Credit Transition Model is that it does calculate the hazard rate of all transitions
– even to the other rating states. We can therefore calculate these transition probabilities conditional on an
issuer’s not withdrawing. We’ll proceed a bit informally. Define Pr(x) as the probability of x, and Pr(~x) as the
probability of not-x, and allow x to include D (default) and W (withdrawal). Imagine an issuer that is currently
rated, and consider the distribution of states one quarter later. It is tautologically true that:
1 = Pr(~ D, ~ W )+ Pr( D, ~ W ) + Pr(W ) .
8
Of course, Pr(~D, ~W) is the probability of not defaulting and not withdrawing – in other words, the probability
of still being rated. Pr(D, ~W) is the probability of defaulting and not withdrawing, or the probability of being
observed to default. Finally, Pr(W) is just the probability of withdrawing. All of these are given directly by the
Credit Transition Model. These probabilities allow us to make the following conditional calculations:
Pr(~ D |~ W ) ≡
Pr( D |~ W ) ≡
Pr(~ D, ~ W )
Pr(~ W )
Pr( D, ~ W )
Pr(~ W )
9
10
Quite simply, we can calculate the rating and default transitions all conditional on not withdrawing. These are
naturally objects of interest, and correspond to our thought experiment, what is the default rate for an exposure
which will otherwise remain outstanding? But how does this compare to another question, what is the
probability of default (as distinct from the probability of being observed to default)? The probability of default
may be decomposed as:
Pr( D ) = Pr( D, ~ W ) + Pr( D, W )
11
The problem is that we only observe the first term, not the second: we do not know the probability of default
for issuers whose ratings are withdrawn. If we make the identifying assumption that rating withdrawal is
neutral with respect to default probabilities, then:
Pr( D ) = Pr( D | W ) = Pr( D |~ W )
6
March 2008 „ Special Comment „ Moody’s Credit Policy – Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
12
Moody’s Credit Policy
Special Comment
Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
which means that the conditional probabilities the CTM can produce are equal to the simple “probability of
default.”
Should We Expect Different Results?
We fully expect that different adjustment methods will yield different results, so the question really is, can we
understand why the results differ in the way they do, and can we therefore have a preference – can we say
which adjustment method is “correct?”
The difference between applying the Moody’s adjustment annually or quarterly is the usual difference in
applying the Kaplan-Meier estimator at different intervals. As the interval shrinks, the results converge. We
cannot say a priori whether the difference will be “large” or in what direction it will be – that is one of the
purposes of this Special Comment.
As mentioned above, we know that adjusting each issuer and then taking portfolio averages will result in
different default rate estimates than adjusting the portfolio average itself. We might have a slight preference
for the individual adjustments, since it preserves the subadditivity of a portfolio. The only drawback is that we
cannot make a similar adjustment to the historical data. Another purpose of this Comment is to quantify the
difference: if it is “slight,” we might decide to make the individual adjustments anyway and disregard the
discrepancy with the historical treatment.
The conditional transition forecasts calculated within the Credit Transition Model offer arguably the most
logically appealing alternative. We generally expect that the resulting default rate estimates will be greater
than those given by applying the Moody’s adjustment (either quarterly or annually). The reason is that while
there is evidence that withdrawal is a neutral event with respect to default (e.g., a withdrawn B3 issuer has the
same default risk as an identical-but-rated B3 issuer), we know that withdrawal is not neutral with respect to
rating: lower ratings are more likely to withdraw. Hence, when calculating rating transition paths within CTM
conditional on not withdrawing, we should find that issuers are more likely to occupy the lower ratings than
otherwise. Over a long-horizon forecast we should see increased default risk. This may be seen as a result of
the fact that the CTM adjustment is able to condition on more information than is available under the Moody’s
adjustment.
The drawback again is that we cannot adjust the historical data in an analogous manner. Using the CTM
conditional adjustment is going to result in default rates which at least in principle are somewhat apples-tooranges when compared with history. This Comment will document the difference. Again, if it is slight, we
might prefer to use this adjustment. If it is not slight, users will have to weigh the tradeoff.
We expect to see the greatest difference between the conditional CTM adjustment and the Moody’s
adjustment in the calculation of rating transition probabilities. Here the CTM adjustment strikes us, all else
equal, as preferable, since the other adjustment methods require the counter-factual assumption that
withdrawal is neutral with respect to rating level. Generally speaking, the most likely rating an issuer will have
in the future is its current rating; put differently, the diagonal of a rating transition matrix should be the largest
rating value. When examining the implications for rating transition forecasts, we see that the CTM adjustment
results in “better behaved” estimates for the very low (Caa1 and lower) rating categories in the sense that the
modal forecasted rating continues to be the initial rating. This is not true when applying the Moody’s
adjustment which tends to overestimate the probability that surviving ratings will rise over time.
Forecast Methodology
This paper concerns itself with the output of Moody’s Credit Transition Model. There are no historical data
presented below – they are all forecasts. The Credit Transition Model generates these forecasts by
conditioning on certain issuer-specific features and on an expected future path of the macroeconomy. The
issuer-specific features include:
7
„
Current rating,
„
Whether the issuer was upgraded or downgraded into its current rating,
March 2008 „ Special Comment „ Moody’s Credit Policy – Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Moody’s Credit Policy
Special Comment
Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
„
Elapsed time in the current rating, and
„
Elapsed time since the issuer’s first rating was assigned.
To simulate an issuer in CTM, we must specify all these dimensions. Unless otherwise stated, we will always
be simulating new issuers, e.g. issuers who were neither upgraded nor downgraded into their current rating
and who have spent no time in this or any other rating before. We will also test variations of this to see if any
of our conclusions are sensitive to these points.
The macro-economic drivers the model conditions on are two: the U.S. unemployment rate, and the high yield
spread over Treasuries. 5 To run a simulation we must also have a forward view on these drivers. Throughout
this special comment, we restrict ourselves to a naïve forecast and assume that these two series remain
constant at their 20 year averages (about 5.6 and 530 bps, respectively).
We stress that none of the numbers presented below should be used as “forecasts” of anything other than our
highly stylized issuers run through our highly stylized macroeconomy.
Comparison of Moody’s Annual and Quarterly
Adjustment at the Portfolio Level
In this section we study the difference between applying the Moody’s adjustment at the portfolio level in either
annual (which is Moody’s standard) or quarterly intervals. To determine if the results are sensitive to the
portfolio composition, we study four different portfolios:
„
All North American Issuers
„
North American Investment-Grade issuers
„
North American Speculative-Grade Issuers
„
North American Issuers rated below B3
In all cases, the portfolio default and withdrawal probability is the simple average of the constituent issuers.
We then adjust this average default probability by the average withdrawal probability by applying Moody’s
standard adjustment in either annual or quarterly steps. The results are presented in Exhibits 3a, 3b, 3c and
3d below. As an example, Exhibit 3a presents the cumulative default rate for years one through five for the
entire North American universe under the two different adjustment methods. As a cumulative rate it is of
course increasing in the time horizon, but what strikes us is that there is no appreciable difference between the
annual and the quarterly adjustment. The difference (defined as the quarterly adjusted value less the annual
adjusted value) is labeled in each exhibit.
For the entire North American issuer universe, the adjusted 5-year default rate is 10.63% when adjusted
annually or 10.75% when adjusted quarterly. For the IG universe, the numbers are 0.79% and 0.79%,
respectively, while for SG issuers they are 27.77% and 28.28%. Restricting attention to issuers rated below
B3, the subset with both the highest default and withdrawal rates, the difference in adjustment methods is
more consequential: the annually adjusted 5-year default rate is 43.84%, the quarterly 44.85%.
In sum, applying the Moody’s adjustment annually always results in lower default rates than applying it
quarterly. The difference between the two increases in the lower ratings because, generally, those issuers
have higher withdrawal rates. For all but the lowest rated credits, the difference strikes us as immaterial.
5
8
Spread data re provided by Lehman’s index on U.S. high yield corporates.
March 2008 „ Special Comment „ Moody’s Credit Policy – Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Moody’s Credit Policy
Special Comment
Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Exhibit 3a:
Cum. Def. Rate
Cumulative Default Rate, All North American Issuers
20%
15%
10%
5%
0.08%
0.05%
0.10%
0.11%
0.03%
0%
1
2
3
Years
Moody's Annual
4
5
Moody's Quarterly
The difference between cumulative default rates using Moody’s Quarterly and Moody’s Annual adjustment is
calculated for all time horizons. The 5-Year cumulative default rate adjusted quarterly is 0.11% greater than
when adjusted annually.
Exhibit 3b:
Cumulative Default Rate, North American Investment-Grade Issuers
Cum. Def. Rate
20%
15%
10%
5%
0.08%
0.05%
0.10%
0.11%
0.03%
0%
1
2
3
Years
Moody's Annual
4
5
Moody's Quarterly
The difference between cumulative default rates using Moody’s Quarterly and Moody’s Annual adjustment is
calculated for all time horizons. The 5-Year cumulative default rate adjusted quarterly is 0.01% greater than
when adjusted annually.
Exhibit 3c:
Cum. Def. Rate
Cumulative Default Rate, North American Speculative-Grade Issuers
30%
0.43%
0.50%
0.34%
20%
0.23%
10%
0.11%
0%
1
2
3
Years
Moody's Annual
4
5
Moody's Quarterly
The difference between cumulative default rates using Moody’s Quarterly and Moody’s Annual adjustment is
calculated for all time horizons. The 5-Year cumulative default rate adjusted quarterly is 0.50% greater than
when adjusted annually.
9
March 2008 „ Special Comment „ Moody’s Credit Policy – Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Moody’s Credit Policy
Special Comment
Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Exhibit 3d:
Cum. Def. Rate
Cumulative Default Rate, North American Caa-C Issuers
50%
40%
0.72%
30%
20%
0.89%
1.00%
0.51%
0.25%
10%
0%
1
2
3
4
5
Years
Moody's Annual
Moody's Quarterly
The difference between cumulative default rates using Moody’s Quarterly and Moody’s Annual adjustment is
calculated for all time horizons. The 5-Year cumulative default rate adjusted quarterly is 1.00% greater than
when adjusted annually.
Comparison of Moody’s Adjustment at the Portfolio and
Issuer Levels
In this section we study the difference between adjusting the portfolio average default rate versus adjusting the
default rate of each individual issuer and then taking the average. The former corresponds to Moody’s method
of adjusting historical data; the latter allows us to reconcile the default rate estimates of different subsets of
portfolios. We continue to study the portfolios defined in the previous section and consider annual
adjustments. 6
The results (cumulative default rates for the first five years) are presented in Exhibits 4a through 4d. By year
five for the entire North American universe, the portfolio-adjusted default rate is, again, 10.63%, but the issueradjusted rate is almost 150 bps higher at 12.11%. The data are the same in both cases; the difference is
simply the order of averaging and adjusting. For the IG subset, the portfolio-adjustment is 0.79%, while the
issuer-adjustment is 0.78%. For the SG subset, the 5-year cumulative default rate estimates are 27.77% and
28.33%, respectively. Finally, for the C-rated subset, the difference is fairly modest, being either 43.84% when
adjusting the portfolio or 43.64% when adjusting each issuer first. In this case we have the somewhat
unexpected result that the portfolio adjustment is greater than the individual.
Exhibit 4a:
Cum. Def. Rate
Cumulative Default Rate, All North American Issuers
20%
15%
0.56%
10%
5%
0.04%
0.99%
1.48%
0.24%
0%
1
2
3
4
5
Years
Moody's Portfolio
Moody's Issuer
The difference between cumulative default rates using Moody’s Issuer and Moody’s Portfolio adjustment is
calculated for all time horizons. The 5-Year cumulative default rate adjusted at the issuer level is 1.48%
greater than when adjusted at the portfolio level.
6
10
The results using quarterly adjustments are essentially identical.
March 2008 „ Special Comment „ Moody’s Credit Policy – Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Moody’s Credit Policy
Special Comment
Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Exhibit 4b:
Cum. Def. Rate
Cumulative Default Rate, North American Investment-Grade Issuers
2.0%
1.5%
0.00%
1.0%
0.5%
0.00%
0.00%
1
2
0.00%
0.00%
0.0%
3
4
5
Years
Moody's Portfolio
Moody's Issuer
The difference between cumulative default rates using Moody’s Issuer and Moody’s Portfolio adjustment is
calculated for all time horizons. The 5-Year cumulative default rate adjusted at the issuer is not measurably
different from when adjusted at the portfolio level.
Exhibit 4c:
Cum. Def. Rate
Cumulative Default Rate, North American Speculative-Grade Issuers
30%
25%
20%
15%
10%
5%
0%
0.55%
0.33%
0.17%
0.06%
0.01%
1
2
3
4
5
Years
Moody's Portfolio
Moody's Issuer
The difference between cumulative default rates using Moody’s Issuer and Moody’s Portfolio adjustment is
calculated for all time horizons. The 5-Year cumulative default rate adjusted at the issuer level is 0.55%
greater than when adjusted at the portfolio level.
Exhibit 4d:
Cum. Def. Rate
Cumulative Default Rate, North American Caa–C Issuers
60%
50%
40%
30%
20%
10%
0%
-0.06%
-0.08%
-0.19%
-0.20%
-0.05%
1
2
Moody's Portfolio
3
Years
4
5
Moody's Issuer
The difference between cumulative default rates using Moody’s Issuer and Moody’s Portfolio adjustment is
calculated for all time horizons. The 5-Year cumulative default rate adjusted at the issuer level is 0.20% less
than when adjusted at the portfolio level.
Exhibit 5 summarizes the results thus far. It compares the 5-year cumulative default rate for the North
American universe under four different adjustment methods: annual (A) or quarterly (Q) adjustments to either
issuers or the portfolio average. We see that there is really no difference between the annual or quarterly
adjustment. The issuer adjustment results in higher default rate estimates, but only at longer horizons. Note
11
March 2008 „ Special Comment „ Moody’s Credit Policy – Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Moody’s Credit Policy
Special Comment
Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
that Moody’s standard method – adjusting the portfolio average in annual steps – always results, in these
cases, in the lowest default rate estimates.
Exhibit 5:
Cum. Def. Rate
Cumulative Default Rate, All North American Issuers
15%
13%
10%
8%
5%
3%
0%
1
2
3
4
5
Years
Moody's Portfolio A
Moody's Portfolio Q
Moody's Issuer A
Moody's Issuer Q
Comparison of Moody’s Issuer-Level Adjustment and
the CTM Conditional Forecast for New (Unseasoned)
Issuers
We now compare Moody’s issuer-level adjustments (applied both quarterly and annually) with the conditional
default forecast which the Credit Transition Model is capable of providing. Exhibit 6a plots the 1-year adjusted
default rate forecast for new issuers in rating categories B3 and higher. We see that for this set of ratings
there is no difference between the three methods. For lower rated issuers, the CTM conditional forecast and
the Moody’s quarterly adjustment continue to correspond closely, but the Moody’s annual adjustment results in
lower default rate estimates as shown in Exhibit 6b.
Exhibit 6a:
Cum. Def. Rate
1-Year Cumulative Default Rate, New Issuer Aaa-B3
4%
3%
2%
1%
0%
Aaa Aa1 Aa2 Aa3
A1
A2
A3
Baa1 Baa2 Baa3 Ba1
Ba2
Ba3
B1
B2
B3
Years
Moody's Annual
12
Moody's Quarterly
CTM
March 2008 „ Special Comment „ Moody’s Credit Policy – Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Moody’s Credit Policy
Special Comment
Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Exhibit 6b:
Cum. Def. Rate
1-Year Cumulative Default Rate, New Issuer Caa-C
4%
3%
2%
1%
0%
Caa1
Caa2
Caa3
Ca
C
Years
Moody's Annual
Moody's Quarterly
CTM
Differences become more pronounced at longer horizons. Exhibit 7a and 7b are analogous to 6a and 6b but
present the adjusted 5-year default rate, again for hypothetical new issuers running through our hypothetical
static economy. As before, there is essentially no difference between the adjustment methods for ratings of
B3 or higher. For lower rating categories, the standard Moody’s Annual adjustment again results in the lowest
estimates, but now we observe a non-negligible wedge between the Moody’s Quarterly adjustment and the
CTM conditional estimate, with the latter always greater than the former. For the lowest rating category, the
Moody’s Annual adjustment results in an estimated 5-Year default rate of 45%, the Moody’s Quarterly
adjustment 48%, and the CTM conditional adjustment 51%.
Exhibit 7a:
Cum. Def. Rate
5-Year Cumulative Default Rate, New Issuer Aaa- B3
60%
50%
40%
30%
20%
10%
0%
Aaa Aa1 Aa2 Aa3
A1
A2
A3
Baa1 Baa2 Baa3 Ba1
Ba2
Ba3
B1
B2
B3
Years
Moody's Annual
Moody's Quarterly
CTM
Exhibit 7b:
Cum. Def. Rate
5-Year Cumulative Default Rate, New Issuer Caa-C
60%
50%
40%
30%
20%
10%
0%
Caa1
Caa2
Caa3
Ca
C
Years
Moody's Annual
13
Moody's Quarterly
CTM
March 2008 „ Special Comment „ Moody’s Credit Policy – Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Moody’s Credit Policy
Special Comment
Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Comparison of Methods for Upgraded, Downgraded and
Seasoned Issuers
Are these conclusions sensitive to our assumption of new issuance? What about seasoned issuers, or
recently upgraded or downgraded issuers? Qualitatively our conclusions are robust to these different cases,
but the magnitude of the differences can change. Exhibit 8 plots adjusted 5-Year default rates for seasoned
issuers, Exhibit 9 plots recently upgraded issuers, and Exhibit 10 plots recently downgraded issuers. We see
that in this last case – downgraded issuers – the three adjustment methods imply very similar estimates.
The default rate pattern of seasoned issuers is similar to that of new issuers. Of course a seasoned issuer’s
default rate is much higher than that of a new issuer. The difference between the three adjustment methods is
substantial for rating categories below B3, as shown in Exhibit 8.
Exhibit 8:
Cum. Def. Rate
5-Year Cumulative Default Rate, Seasoned Issuer
80%
60%
40%
20%
0%
Aaa
Aa2
A1
A3
Baa2
Ba1
Ba3
B2
Caa1
Caa3
C
Years
Moody's Annual
Moody's Quarterly
CTM
The pattern for upgraded issuers is different from that of new and existing issuers, especially for ratings below
B3. 7 There remains a substantial difference across the three adjustment methods for ratings below B3, as
shown in Exhibit 9.
Exhibit 9:
5-Year Cumulative Default Rate, Upgraded Issuer
Cum. Def. Rate
50%
40%
30%
20%
10%
0%
Aaa
Aa2
A1
A3
Baa2
Ba1
Ba3
B2
Caa1
Caa3
C
Years
Moody's Annual
Moody's Quarterly
CTM
Exhibit 10 presents 5-year default probabilities for recently downgraded issuers. The pattern across ratings is
more familiar. Interestingly, the various withdrawal adjustment methods now have no real difference at any
rating level.
7
14
Because upgrades are rare for issuers below B3, when they do occur they signal a significantly improved credit profile – in other words, subsequent default
probabilities are sharply reduced.
March 2008 „ Special Comment „ Moody’s Credit Policy – Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Moody’s Credit Policy
Special Comment
Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Exhibit 10:
5-Year Cumulative Default Rate, Downgraded Issuer
Cum. Def. Rate
100%
80%
60%
40%
20%
0%
Aaa
Aa2
A1
A3
Baa2
Ba1
Ba3
B2
Caa1
Caa3
C
Years
Moody's Annual
Moody's Quarterly
CTM
Comparing the Impact on Transition Rates
In addition to adjusting default rates, the withdrawal adjustments can be applied to all rating transitions.
Exhibit 11 presents a typical 5-year transition matrix which includes transitions to the withdrawal sate (e.g., an
unadjusted transition matrix). For low ratings, the withdrawal state is more significant than the default state,
and taken together it is clear that most issuers rated B3 or lower will, for one reason or the other, no longer be
rated five years hence.
If we are interested in the dynamics of a rated portfolio under the assumption that our credit exposures will
persist for at least five years, a matrix such as Exhibit 11 is of little help. We need an adjusted matrix. We
have seen above that, for the most part, our different methods for adjusting default rates lead to similar
estimates. We next explore whether that remains true for other rating transitions.
Exhibit 12 is based on the same underlying data as Exhibit 11, but applies the Moody’s annual withdrawal
adjustment. The Moody’s quarterly adjustment is presented in Exhibit 13, while the CTM conditional
transitions are shown in Exhibit 14.
15
March 2008 „ Special Comment „ Moody’s Credit Policy – Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Special Comment
Moody’s Credit Policy
Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Exhibit 11:
5-Year Transition Matrix, North American Issuers – Unadjusted
16
Aaa
Aa1
Aa2
Aa3
A1
A2
A3
Baa1
Baa2
Baa3
Ba1
Ba2
Ba3
B1
B2
B3
Caa1
Caa2
Caa3
Ca
C
Aaa
61%
11%
7%
3%
1%
1%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
16%
0%
Aa1
9%
43%
13%
10%
3%
1%
1%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
19%
0%
Aa2
4%
12%
29%
15%
6%
3%
1%
1%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
29%
0%
Aa3
1%
3%
7%
38%
10%
5%
2%
1%
1%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
31%
0%
A1
0%
1%
2%
10%
36%
12%
6%
3%
2%
1%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
26%
0%
A2
0%
0%
1%
4%
10%
37%
11%
7%
4%
2%
1%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
21%
0%
A3
0%
0%
0%
1%
4%
12%
30%
12%
9%
5%
2%
1%
1%
0%
0%
0%
0%
0%
0%
0%
0%
20%
1%
Baa1
0%
0%
0%
1%
1%
5%
10%
32%
14%
8%
3%
2%
1%
1%
1%
0%
0%
0%
0%
0%
0%
20%
1%
Baa2
0%
0%
0%
0%
1%
3%
4%
10%
31%
12%
5%
3%
2%
1%
1%
1%
0%
0%
0%
0%
0%
23%
2%
Baa3
0%
0%
0%
0%
1%
2%
2%
6%
13%
28%
7%
4%
3%
2%
2%
1%
1%
0%
0%
0%
0%
24%
3%
Ba1
0%
0%
0%
0%
1%
1%
2%
3%
7%
12%
15%
5%
5%
3%
3%
2%
1%
1%
0%
0%
0%
34%
5%
Ba2
0%
0%
0%
0%
0%
1%
1%
2%
4%
7%
7%
10%
5%
4%
4%
3%
2%
1%
0%
0%
0%
40%
9%
Ba3
0%
0%
0%
0%
0%
1%
1%
1%
2%
4%
4%
4%
11%
5%
5%
3%
2%
1%
1%
0%
0%
43%
11%
B1
0%
0%
0%
0%
0%
0%
0%
1%
1%
2%
2%
3%
5%
11%
6%
4%
3%
2%
1%
1%
0%
45%
14%
B2
0%
0%
0%
0%
0%
0%
0%
0%
1%
1%
1%
2%
3%
5%
12%
5%
3%
2%
1%
1%
0%
43%
19%
B3
0%
0%
0%
0%
0%
0%
0%
0%
0%
1%
1%
1%
1%
3%
4%
9%
4%
3%
1%
1%
0%
44%
27%
Caa1
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
1%
1%
2%
3%
4%
7%
2%
2%
1%
0%
50%
28%
Caa2
0%
0%
0%
0%
0%
0%
0%
0%
0%
1%
0%
0%
1%
1%
2%
3%
2%
4%
1%
1%
0%
47%
35%
Caa3
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
1%
1%
1%
2%
2%
1%
3%
1%
0%
50%
36%
Ca-C
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
1%
1%
1%
2%
1%
1%
1%
1%
0%
54%
37%
March 2008 „ Special Comment „ Moody’s Credit Policy – Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
WR Default
Special Comment
Moody’s Credit Policy
Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Exhibit 12:
5-Year Transition Matrix, North American Issuers – Moody’s Annual Adjustment
17
Aaa
Aa1
Aa2
Aa3
A1
A2
A3
Baa1
Baa2
Baa3
Ba1
Ba2
Ba3
B1
B2
B3
Caa1
Caa2
Caa3
Ca
C
Default
Aaa
72%
13%
8%
4%
1%
1%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
Aa1
11%
53%
16%
12%
4%
2%
1%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
Aa2
6%
17%
40%
21%
8%
4%
2%
1%
1%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
Aa3
1%
5%
11%
55%
14%
8%
4%
2%
1%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
A1
0%
1%
3%
14%
49%
16%
8%
4%
2%
1%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
A2
0%
0%
1%
4%
13%
47%
14%
9%
5%
3%
1%
1%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
A3
0%
0%
1%
1%
5%
16%
38%
15%
11%
6%
2%
1%
1%
1%
0%
0%
0%
0%
0%
0%
0%
1%
Baa1
0%
0%
0%
1%
2%
7%
12%
40%
17%
10%
4%
2%
1%
1%
1%
1%
0%
0%
0%
0%
0%
1%
Baa2
0%
0%
0%
1%
1%
3%
6%
13%
40%
16%
6%
4%
3%
2%
1%
1%
1%
0%
0%
0%
0%
2%
Baa3
0%
0%
0%
0%
1%
2%
3%
7%
17%
36%
9%
5%
5%
3%
2%
2%
1%
1%
0%
0%
0%
4%
Ba1
0%
0%
0%
0%
1%
2%
2%
5%
11%
19%
23%
7%
7%
4%
4%
3%
2%
1%
0%
0%
0%
6%
Ba2
0%
0%
0%
0%
1%
1%
1%
3%
6%
12%
12%
17%
9%
7%
7%
5%
3%
2%
1%
1%
0%
12%
Ba3
0%
0%
0%
0%
1%
1%
1%
2%
4%
8%
8%
8%
20%
9%
9%
6%
4%
2%
1%
1%
0%
15%
B1
0%
0%
0%
0%
0%
1%
1%
1%
2%
3%
4%
6%
9%
22%
11%
9%
5%
3%
1%
1%
0%
19%
B2
0%
0%
0%
0%
0%
0%
0%
1%
1%
2%
2%
3%
6%
10%
24%
10%
6%
4%
2%
1%
0%
26%
B3
0%
0%
0%
0%
0%
0%
0%
1%
1%
1%
1%
2%
3%
7%
9%
19%
8%
6%
3%
2%
1%
37%
Caa1
0%
0%
0%
0%
0%
0%
0%
0%
1%
1%
1%
1%
2%
5%
7%
10%
18%
6%
4%
3%
1%
40%
Caa2
0%
0%
0%
0%
0%
0%
0%
0%
1%
2%
1%
1%
2%
4%
5%
8%
6%
12%
3%
3%
1%
50%
Caa3
0%
0%
0%
0%
0%
0%
0%
0%
1%
1%
1%
1%
2%
4%
4%
7%
5%
5%
10%
3%
1%
52%
Ca-C
0%
0%
0%
0%
0%
0%
0%
0%
0%
1%
1%
1%
3%
4%
5%
7%
4%
4%
5%
5%
1%
57%
March 2008 „ Special Comment „ Moody’s Credit Policy – Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Special Comment
Moody’s Credit Policy
Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Exhibit 13:
5-Year Transition Matrix, North American Issuers – Moody’s Quarterly Adjustment
18
Aaa
Aa1
Aa2
Aa3
A1
A2
A3
Baa1
Baa2
Baa3
Ba1
Ba2
Ba3
B1
B2
B3
Caa1
Caa2
Caa3
Ca
C
Default
Aaa
72%
13%
8%
4%
1%
1%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
Aa1
11%
53%
16%
12%
4%
2%
1%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
Aa2
6%
17%
40%
21%
8%
4%
2%
1%
1%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
Aa3
1%
5%
11%
55%
14%
8%
3%
2%
1%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
A1
0%
1%
3%
14%
49%
16%
8%
4%
2%
1%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
A2
0%
0%
1%
4%
13%
47%
14%
9%
5%
3%
1%
1%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
A3
0%
0%
1%
1%
5%
16%
38%
15%
11%
6%
2%
1%
1%
1%
0%
0%
0%
0%
0%
0%
0%
1%
Baa1
0%
0%
0%
1%
2%
7%
12%
40%
17%
10%
4%
2%
1%
1%
1%
1%
0%
0%
0%
0%
0%
1%
Baa2
0%
0%
0%
1%
1%
3%
6%
13%
40%
16%
6%
4%
3%
2%
1%
1%
1%
0%
0%
0%
0%
2%
Baa3
0%
0%
0%
0%
1%
2%
3%
7%
17%
36%
9%
5%
5%
3%
2%
2%
1%
1%
0%
0%
0%
4%
Ba1
0%
0%
0%
0%
1%
2%
2%
5%
11%
19%
23%
7%
7%
4%
4%
3%
2%
1%
0%
0%
0%
6%
Ba2
0%
0%
0%
0%
1%
1%
1%
3%
6%
12%
11%
17%
9%
7%
7%
5%
3%
2%
1%
1%
0%
12%
Ba3
0%
0%
0%
0%
1%
1%
1%
2%
4%
8%
8%
8%
20%
9%
9%
6%
4%
2%
1%
1%
0%
15%
B1
0%
0%
0%
0%
0%
1%
1%
1%
2%
3%
4%
6%
9%
22%
11%
9%
5%
3%
1%
1%
0%
20%
B2
0%
0%
0%
0%
0%
0%
0%
1%
1%
2%
2%
3%
6%
10%
24%
10%
6%
4%
2%
1%
0%
27%
B3
0%
0%
0%
0%
0%
0%
0%
1%
1%
1%
1%
2%
3%
6%
9%
19%
8%
6%
3%
2%
1%
38%
Caa1
0%
0%
0%
0%
0%
0%
0%
0%
0%
1%
1%
1%
2%
5%
7%
10%
17%
6%
4%
2%
1%
41%
Caa2
0%
0%
0%
0%
0%
0%
0%
0%
1%
2%
1%
1%
2%
4%
5%
8%
6%
12%
3%
3%
1%
51%
Caa3
0%
0%
0%
0%
0%
0%
0%
0%
1%
1%
1%
1%
2%
4%
4%
7%
5%
5%
10%
3%
1%
54%
Ca-C
0%
0%
0%
0%
0%
0%
0%
0%
0%
1%
1%
1%
3%
4%
5%
7%
4%
4%
4%
5%
1%
59%
March 2008 „ Special Comment „ Moody’s Credit Policy – Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Special Comment
Moody’s Credit Policy
Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Exhibit 14:
5-Year Transition Matrix, North American Issuers – CTM Adjustment
19
Aaa
Aa1
Aa2
Aa3
A1
A2
A3
Baa1
Baa2
Baa3
Ba1
Ba2
Ba3
B1
B2
B3
Caa1
Caa2
Caa3
Ca
C
Default
Aaa
71%
13%
9%
4%
1%
1%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
Aa1
11%
51%
17%
13%
4%
2%
1%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
Aa2
6%
16%
41%
22%
8%
4%
2%
1%
1%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
Aa3
1%
5%
12%
55%
13%
7%
3%
1%
1%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
A1
0%
1%
3%
16%
48%
15%
8%
4%
2%
1%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
A2
0%
0%
1%
5%
13%
46%
14%
9%
5%
3%
1%
1%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
A3
0%
0%
1%
2%
5%
16%
37%
15%
11%
6%
2%
1%
1%
1%
1%
0%
0%
0%
0%
0%
0%
1%
Baa1
0%
0%
0%
1%
2%
7%
12%
39%
17%
10%
4%
2%
2%
1%
1%
1%
0%
0%
0%
0%
0%
1%
Baa2
0%
0%
0%
1%
1%
3%
6%
13%
39%
16%
6%
4%
3%
2%
2%
1%
1%
0%
0%
0%
0%
2%
Baa3
0%
0%
0%
0%
1%
2%
3%
7%
17%
35%
9%
6%
5%
3%
3%
2%
1%
1%
0%
0%
0%
4%
Ba1
0%
0%
0%
0%
1%
2%
2%
5%
11%
18%
25%
7%
7%
4%
4%
3%
2%
1%
0%
0%
0%
6%
Ba2
0%
0%
0%
0%
1%
1%
1%
3%
6%
11%
12%
19%
9%
7%
7%
5%
3%
2%
1%
1%
0%
12%
Ba3
0%
0%
0%
0%
0%
1%
1%
2%
4%
7%
8%
8%
23%
8%
9%
6%
4%
2%
1%
1%
0%
15%
B1
0%
0%
0%
0%
0%
1%
1%
1%
2%
3%
4%
6%
10%
24%
10%
8%
5%
3%
1%
1%
0%
19%
B2
0%
0%
0%
0%
0%
0%
0%
1%
1%
2%
2%
3%
6%
10%
25%
9%
6%
4%
2%
1%
0%
26%
B3
0%
0%
0%
0%
0%
0%
0%
0%
1%
1%
1%
2%
3%
6%
9%
21%
7%
6%
3%
2%
1%
37%
Caa1
0%
0%
0%
0%
0%
0%
0%
0%
0%
1%
1%
1%
2%
4%
6%
9%
21%
6%
4%
3%
1%
40%
Caa2
0%
0%
0%
0%
0%
0%
0%
0%
1%
1%
1%
1%
2%
3%
4%
7%
5%
16%
3%
3%
1%
51%
Caa3
0%
0%
0%
0%
0%
0%
0%
0%
0%
1%
1%
1%
2%
3%
3%
5%
4%
4%
16%
3%
2%
55%
Ca-C
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
1%
1%
2%
2%
3%
5%
2%
3%
4%
13%
2%
63%
March 2008 „ Special Comment „ Moody’s Credit Policy – Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Moody’s Credit Policy
Special Comment
Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
The main differences between these exhibits are seen in the default rate column and along the diagonal,
which is the probability of staying in the current rating. We have already discussed the default rate; in this
section we will focus on the diagonal of the matrix.
Exhibit 15 plots the diagonal for the different adjustment methods. In short, we are comparing the probability
of remaining in the same rating for five years (the “stability probability”). We see that the CTM conditional
transition results in a greater 5-year stability probability for ratings below B3. For the other rating categories
there is no substantial difference between adjustments. Exhibit 16 is an analogous presentation of 1-year
stability probabilities. As expected, at this shorter horizon there is no difference across the adjustment
methods.
Exhibit 15:
5-Year Stability Probability, All North American Issuers
5-Year Stability Prob.
80%
70%
60%
50%
40%
30%
20%
10%
0%
Aaa
Aa2
A1
A3
Baa2
Moody's Annual
Ba1
Ba3
B2
Moody's Portfolio
Caa1
Caa3
Caa1
Caa3
CTM
Exhibit 16:
1-Year Stability Probability, All North American Issuers
1-Year Stability Prob.
100%
80%
60%
40%
20%
0%
Aaa
Aa2
A1
A3
Moody's Annual
Baa2
Ba1
Moody's Quarterly
Ba3
B2
CTM
Exhibit 17 compares the probability of upgrading over five years by rating category. Here the bias of the
Moody’s adjustment is even clearer, as it overestimates the probability that low ratings will rise over time. The
reason is fairly straightforward. Recall that the Moody’s adjustment grosses up the observed distribution of
rating states to compensate for the “missing” withdrawal state. But withdrawal is not independent of rating
level - in particular it is more common among lower rated issuers. Therefore the observed surviving rating
states are biased toward the high ratings. The conditional transitions calculated within the Credit Transition
Model do not suffer from this problem.
20
March 2008 „ Special Comment „ Moody’s Credit Policy – Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Special Comment
Moody’s Credit Policy
Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Exhibit 16:
5-Year Upgrade Prob.
5-Year Probability of Upgrading, All North American Issuers
50%
40%
30%
20%
10%
0%
Aaa
Aa2
A1
A3
Baa2
Moody's Annual
Ba1
Ba3
Moody's Portfolio
B2
Caa1
Caa3
CTM
Conclusion
In this paper we have presented three different methods of adjusting default rates and rating transition
probabilities for withdrawal: Moody’s adjustment applied annually, applied quarterly and the conditional
transitions of Moody’s Credit Transition Model. Our purpose was to compare the quantitative difference
across these methods, and the difference between applying the adjustment methods to individual issuers or to
portfolio averages.
We observed only very slight differences between applying the Moody’s method annually and applying its
quarterly variant. For ratings above B3, there is virtually no difference with the CTM conditional adjustment as
well. For ratings Caa1 and below there can be a material difference between the conditional probabilities
produced by the Credit Transition Model and the Moody’s adjustment. In particular, the CTM’s conditional
probabilities imply higher default rates and “better behaved” transition probabilities. Finally, it was usually the
case that adjusting the issuers rather than just the portfolio average results in higher default rate estimates, but
this is not universally true.
Exhibit 18 summarizes our findings.
Exhibit 18:
Is There a Difference between Moody’s Standard Adjustment and Other Adjustment
Methods?
Duration Adjustment Method
Default Rates
% Difference¹
Default Rates
All Issuers
1 Year
5 Year
21
% Difference¹
IG Issuers
Moody's Annual Portfolio
2.19%
0.05%
Moody's Annual Issuer
2.23%
2%²
0.05%
0%
Moody's Quarterly Portfolio
2.22%
1%
0.05%
1%
Moody's Quarterly Issuer
2.29%
4%
0.05%
1%
CTM Issuer
2.27%
4%
0.05%
1%
Moody's Annual Portfolio
10.63%
Moody's Annual Issuer
12.11%
14%
0.78%
0%
Moody's Quarterly Portfolio
10.75%
1%
0.79%
1%
Moody's Quarterly Issuer
12.35%
16%
0.79%
0%
CTM Issuer
12.24%
15%
0.81%
3%
0.79%
March 2008 „ Special Comment „ Moody’s Credit Policy - Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Special Comment
Moody’s Credit Policy
Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Is There a Difference between Moody’s Standard Adjustment and Other Adjustment
Methods?
Duration Adjustment Method
Default Rates
% Difference¹
Default Rates
SG Issuer
1 Year
5 Year
% Difference¹
Caa-C
Moody's Annual Portfolio
5.36%
11.08%
Moody's Annual Issuer
5.37%
0%
11.02%
0%
Moody's Quarterly Portfolio
5.47%
2%
11.33%
2%
Moody's Quarterly Issuer
5.49%
2%
11.30%
2%
CTM Issuer
5.46%
2%
11.24%
1%
Moody's Annual Portfolio
27.77%
Moody's Annual Issuer
28.33%
2%
43.64%
0%
Moody's Quarterly Portfolio
28.28%
2%
44.85%
2%
Moody's Quarterly Issuer
28.90%
4%
44.69%
2%
CTM Issuer
28.60%
3%
44.78%
2%
43.84%
¹ The % difference is calculated as the difference between the cumulative default rates adjusted by a WR method other than
Moody’s Annual Portfolio and that adjusted by Moody’s Annual Portfolio, divided by Moody’s Annual Portfolio.
² For instance, 2% is the percentage difference between the one-year default rate when adjusted either at the issuer or at
the portfolio level: 0.02 = (0.0223 – 0.0219) / 0.0219.
22
March 2008 „ Special Comment „ Moody’s Credit Policy - Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Special Comment
Moody’s Credit Policy
Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
References
Cantor, R. and D. Hamilton (2007). “Adjusting Corporate Default Rates for Rating Withdrawals,” Journal of
Credit Risk, vol 3, no 2, pg 3-25.
Moody’s Related Research
Special Comment:
„
A Cyclical Model of Multiple-Horizon Credit Rating Transitions and Default, August 2007 (103869)
„
Introducing Moody’s Credit Transition Model, August 2007 (104290)
To access any of these reports, click on the entry above. Note that these references are current as of the date
of publication of this report and that more recent reports may be available. All research may not be available to
all clients.
23
March 2008 „ Special Comment „ Moody’s Credit Policy - Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Special Comment
Moody’s Credit Policy
Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model
Report no.: 108085
Authors
Production Associates
Albert Metz
Nilay Donmez
Cassina Brooks
Wing Chan
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reserved. ALL INFORMATION CONTAINED HEREIN IS PROTECTED BY COPYRIGHT LAW AND NONE OF SUCH INFORMATION MAY BE COPIED OR
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24
March 2008 „ Special Comment „ Moody’s Credit Policy - Comparing Withdrawal Adjustment Methods: An Application of Moody’s Credit Transition Model