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www.moodys.com

Credit Policy Moodys

Special Comment

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 Moodys Annual and Quarterly Adjustment at the Portfolio Level 8 Comparison of Moodys Adjustment at the Portfolio and Issuer Levels 10 Comparison of Moodys 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 Rates 15 Conclusion 21 References 23 Moodys 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

March 2008

Comparing Withdrawal Adjustment Methods: An Application of Moodys 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A recurring issue in the calculation of default and transition rates is the treatment of withdrawn securities.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 Five years later, we see that 10 of the bonds have defaulted, and 20 have had their ratings withdrawn shortly after the beginning of the observation period, perhaps because they were liquidated and were no longer at risk of default or because they simply exited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Another answer is to be agnostic about the fate of those 20 withdrawn securities and allow for the possibility that they, too, might have defaulted if they had continued to remain at risk.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%.

2 March 2008 Special Comment Moodys Credit Policy Comparing Withdrawal Adjustment Methods: An Application of Moodys Credit Transition Model

Special Comment Moodys Credit Policy

Comparing Withdrawal Adjustment Methods: An Application of Moodys Credit Transition Model

Moodys 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

0%

10%

20%

30%

40%

50%

60%

70%

80%

Aaa Aa1 Aa2 Aa3 A1 A2 A3 Baa1Baa2Baa3 Ba1 Ba2 Ba3 B1 B2 B3 Caa1Caa2Caa3 Ca C

Unadjusted Adjusted

Moodys 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 Moodys current method of adjusting annual cohorts. The second is essentially the Moodys method applied in quarterly steps. The third is a conditional transition probability which can only be calculated within Moodys 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 For a thorough discussion of Moodys adjustment method and its rationale, see Cantor and Hamilton (2007). 2 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. 3 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.

3 March 2008 Special Comment Moodys Credit Policy Comparing Withdrawal Adjustment Methods: An Application of Moodys Credit Transition Model

Special Comment Moodys Credit Policy

Comparing Withdrawal Adjustment Methods: An Application of Moodys Credit Transition Model

There is little difference between applying the Moodys 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 Moodys adjustment. In particular, the CTMs 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 Moodys 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.

4 March 2008 Special Comment Moodys Credit Policy Comparing Withdrawal Adjustment Methods: An Application of Moodys Credit Transition Model

Special Comment Moodys Credit Policy

Comparing Withdrawal Adjustment Methods: An Application of Moodys 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 readil

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