Credit Policy. Comparing Withdrawal Adjustment Methods: An Application of Moody s Credit Transition Model. Special Comment. Moody s.

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1 Special Comment Moody s 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 Rates 15 Conclusion 21 References 23 Moody s Related Research 23 Analyst Contacts: New York 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s Credit Transition Model A recurring issue in the calculation of default and transition rates is the treatment of withdrawn securities.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 Five years later, we see that 10 of the bonds have defaulted, and 20 have had their ratings withdrawn shortly after the beginning of the observation period, perhaps because they were liquidated and were no longer at risk of default or because they simply exited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 1 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 Another answer is to be agnostic about the fate of those 20 withdrawn securities and allow for the possibility that they, too, might have defaulted if they had continued to remain at risk.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 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 Aaa Aa1 Aa2 Aa3 A1 A2 A3 Baa1Baa2Baa3 Ba1 Ba2 Ba3 B1 B2 B3 Caa1Caa2Caa3 Ca C Unadjusted 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: 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. 2 March 2008 Special Comment

3 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 Aa Aa Aa A A A Baa Baa Baa Ba Ba Ba B B B Caa Caa Caa Ca C WR Def 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

4 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 N 0 bonds on date 0. Define D t as the number who default at time t and W t as the number who withdraw. Clearly then (and ignoring any other form of censoring): N = N D W t+1 t t t. 1 We calculate the default hazard rate in the first year of the cohort as: H ( N. ) 1 = D1 / 1 5 W1. 2 Why do we adjust the risk set by half the withdrawn issuers? Another reasonable definition would be H 1 = D 1 / N 1. This presupposes that the issuers who withdrew in the first year, W 1, were at no risk of default in the first year. This strikes us as an optimistic assumption. Alternatively, we could define H 1 = D 1 / (N 1 W 1 ). 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

5 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 t ( N. W ) = D 5 /, 3 t where, again, N t satisfies equation 1. t Given this sequence of hazard rates, we calculate the cumulative default rate as: ( 1 ) F T = H t T 1. 4 t= 1 In the context of the Credit Transition Model, N 0 is 1, D t is the probability of default in period t and W t 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 H t = D t / (N t W t ). 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 D i and W i 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. h a 1 D =.5 1 W 1 2 D W 2.5 ( D = D ).5 D W W W + W D 2 W 2 W 1, ( D + D ) h b ( W + W =. 6 2 ) 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 h a is greater or less than h b. Equality between the two can be established as: 4 h a = h D (1 W ) = D (1 W ). 7 b 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 D 1 = D 1* - c and D 2 = D 2* + c. By construction, h b is unchanged. But whether h a increases or decreases depends on whether W 2* is greater or less than W 1*. Heuristically, when D 2 > D 1, h a will tend to be greater than h b if W 2 > W 1. 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 That is assuming that D 1 D 2 and W 1 W 2. If the withdrawal rates are equal, then the h a = h b. If the withdrawal rates are unequal but the default rates are equal, then h a > h b. 5 March 2008 Special Comment

6 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 1 probability of being rated A, 35% probability of being rated B, a 2 probability of being rated C, a 2 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 % B 35% 43.75% C WR 2-0- Def 15% 18.75% 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(~ W ) 9 Pr( D ~ W ) Pr( D, ~ W ) Pr(~ W ) 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 ) 12 6 March 2008 Special Comment

7 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: Current rating, Whether the issuer was upgraded or downgraded into its current rating, 7 March 2008 Special Comment

8 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 Spread data re provided by Lehman s index on U.S. high yield corporates. 8 March 2008 Special Comment

9 Exhibit 3a: Cumulative Default Rate, All North American Issuers 2 15% 1 5% 0.03% 0.05% 0.08% % 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 0.11% greater than when adjusted annually. Exhibit 3b: Cumulative Default Rate, North American Investment-Grade Issuers 2 15% 1 5% 0.03% 0.05% 0.08% % 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 0.01% greater than when adjusted annually. Exhibit 3c: Cumulative Default Rate, North American Speculative-Grade Issuers % 0.23% 0.34% 0.43% 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 0.5 greater than when adjusted annually. 9 March 2008 Special Comment

10 Exhibit 3d: Cumulative Default Rate, North American Caa-C Issuers % 0.72% 0.51% 0.25% 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 1.0 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: Cumulative Default Rate, All North American Issuers 2 15% 1 5% 0.04% 0.24% Moody's Portfolio 0.56% 0.99% Moody's Issuer 1.48% 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 The results using quarterly adjustments are essentially identical. 10 March 2008 Special Comment

11 Exhibit 4b: Cumulative Default Rate, North American Investment-Grade Issuers % % 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: Cumulative Default Rate, North American Speculative-Grade Issuers 3 25% 2 15% 1 5% 0.55% 0.33% 0.17% 0.06% 0.01% 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: Cumulative Default Rate, North American Caa C Issuers % -0.06% Moody's Portfolio -0.08% -0.19% Moody's Issuer -0.2 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 0.2 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

12 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: Cumulative Default Rate, All North American Issuers 15% 13% 1 8% 5% 3% 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: 1-Year Cumulative Default Rate, New Issuer Aaa-B3 4% 3% 2% 1% Aaa Aa1 Aa2 Aa3 A1 A2 A3 Baa1 Baa2 Baa3 Ba1 Ba2 Ba3 B1 B2 B3 Moody's Annual Moody's Quarterly CTM 12 March 2008 Special Comment

13 Exhibit 6b: 1-Year Cumulative Default Rate, New Issuer Caa-C 4% 3% 2% 1% Caa1 Caa2 Caa3 Ca C 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: 5-Year Cumulative Default Rate, New Issuer Aaa- B Aaa Aa1 Aa2 Aa3 A1 A2 A3 Baa1 Baa2 Baa3 Ba1 Ba2 Ba3 B1 B2 B3 Moody's Annual Moody's Quarterly CTM Exhibit 7b: 5-Year Cumulative Default Rate, New Issuer Caa-C Caa1 Caa2 Caa3 Ca C Moody's Annual Moody's Quarterly CTM 13 March 2008 Special Comment

14 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: 5-Year Cumulative Default Rate, Seasoned Issuer Aaa Aa2 A1 A3 Baa2 Ba1 Ba3 B2 Caa1 Caa3 C 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 Aaa Aa2 A1 A3 Baa2 Ba1 Ba3 B2 Caa1 Caa3 C 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 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. 14 March 2008 Special Comment

15 Exhibit 10: 5-Year Cumulative Default Rate, Downgraded Issuer Aaa Aa2 A1 A3 Baa2 Ba1 Ba3 B2 Caa1 Caa3 C 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 March 2008 Special Comment

16 Exhibit 11: 5-Year Transition Matrix, North American Issuers Unadjusted Aaa Aa1 Aa2 Aa3 A1 A2 A3 Baa1 Baa2 Baa3 Ba1 Ba2 Ba3 B1 B2 B3 Caa1 Caa2 Caa3 Ca C WR Default Aaa 61% 11% 7% 3% 1% 1% 16% Aa1 9% 43% 13% 1 3% 1% 1% 19% Aa2 4% 12% 29% 15% 6% 3% 1% 1% 29% Aa3 1% 3% 7% 38% 1 5% 2% 1% 1% 31% A1 1% 2% 1 36% 12% 6% 3% 2% 1% 26% A2 1% 4% 1 37% 11% 7% 4% 2% 1% 21% A3 1% 4% 12% 3 12% 9% 5% 2% 1% 1% 2 1% Baa1 1% 1% 5% 1 32% 14% 8% 3% 2% 1% 1% 1% 2 1% Baa2 1% 3% 4% 1 31% 12% 5% 3% 2% 1% 1% 1% 23% 2% Baa3 1% 2% 2% 6% 13% 28% 7% 4% 3% 2% 2% 1% 1% 24% 3% Ba1 1% 1% 2% 3% 7% 12% 15% 5% 5% 3% 3% 2% 1% 1% 34% 5% Ba2 1% 1% 2% 4% 7% 7% 1 5% 4% 4% 3% 2% 1% 4 9% Ba3 1% 1% 1% 2% 4% 4% 4% 11% 5% 5% 3% 2% 1% 1% 43% 11% B1 1% 1% 2% 2% 3% 5% 11% 6% 4% 3% 2% 1% 1% 45% 14% B2 1% 1% 1% 2% 3% 5% 12% 5% 3% 2% 1% 1% 43% 19% B3 1% 1% 1% 1% 3% 4% 9% 4% 3% 1% 1% 44% 27% Caa1 1% 1% 2% 3% 4% 7% 2% 2% 1% 5 28% Caa2 1% 1% 1% 2% 3% 2% 4% 1% 1% 47% 35% Caa3 1% 1% 1% 2% 2% 1% 3% 1% 5 36% Ca-C 1% 1% 1% 2% 1% 1% 1% 1% 54% 37% 16 March 2008 Special Comment

17 Exhibit 12: 5-Year Transition Matrix, North American Issuers Moody s Annual Adjustment 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% Aa1 11% 53% 16% 12% 4% 2% 1% Aa2 6% 17% 4 21% 8% 4% 2% 1% 1% Aa3 1% 5% 11% 55% 14% 8% 4% 2% 1% A1 1% 3% 14% 49% 16% 8% 4% 2% 1% A2 1% 4% 13% 47% 14% 9% 5% 3% 1% 1% A3 1% 1% 5% 16% 38% 15% 11% 6% 2% 1% 1% 1% 1% Baa1 1% 2% 7% 12% 4 17% 1 4% 2% 1% 1% 1% 1% 1% Baa2 1% 1% 3% 6% 13% 4 16% 6% 4% 3% 2% 1% 1% 1% 2% Baa3 1% 2% 3% 7% 17% 36% 9% 5% 5% 3% 2% 2% 1% 1% 4% Ba1 1% 2% 2% 5% 11% 19% 23% 7% 7% 4% 4% 3% 2% 1% 6% Ba2 1% 1% 1% 3% 6% 12% 12% 17% 9% 7% 7% 5% 3% 2% 1% 1% 12% Ba3 1% 1% 1% 2% 4% 8% 8% 8% 2 9% 9% 6% 4% 2% 1% 1% 15% B1 1% 1% 1% 2% 3% 4% 6% 9% 22% 11% 9% 5% 3% 1% 1% 19% B2 1% 1% 2% 2% 3% 6% 1 24% 1 6% 4% 2% 1% 26% B3 1% 1% 1% 1% 2% 3% 7% 9% 19% 8% 6% 3% 2% 1% 37% Caa1 1% 1% 1% 1% 2% 5% 7% 1 18% 6% 4% 3% 1% 4 Caa2 1% 2% 1% 1% 2% 4% 5% 8% 6% 12% 3% 3% 1% 5 Caa3 1% 1% 1% 1% 2% 4% 4% 7% 5% 5% 1 3% 1% 52% Ca-C 1% 1% 1% 3% 4% 5% 7% 4% 4% 5% 5% 1% 57% 17 March 2008 Special Comment

18 Exhibit 13: 5-Year Transition Matrix, North American Issuers Moody s Quarterly Adjustment 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% Aa1 11% 53% 16% 12% 4% 2% 1% Aa2 6% 17% 4 21% 8% 4% 2% 1% 1% Aa3 1% 5% 11% 55% 14% 8% 3% 2% 1% A1 1% 3% 14% 49% 16% 8% 4% 2% 1% A2 1% 4% 13% 47% 14% 9% 5% 3% 1% 1% A3 1% 1% 5% 16% 38% 15% 11% 6% 2% 1% 1% 1% 1% Baa1 1% 2% 7% 12% 4 17% 1 4% 2% 1% 1% 1% 1% 1% Baa2 1% 1% 3% 6% 13% 4 16% 6% 4% 3% 2% 1% 1% 1% 2% Baa3 1% 2% 3% 7% 17% 36% 9% 5% 5% 3% 2% 2% 1% 1% 4% Ba1 1% 2% 2% 5% 11% 19% 23% 7% 7% 4% 4% 3% 2% 1% 6% Ba2 1% 1% 1% 3% 6% 12% 11% 17% 9% 7% 7% 5% 3% 2% 1% 1% 12% Ba3 1% 1% 1% 2% 4% 8% 8% 8% 2 9% 9% 6% 4% 2% 1% 1% 15% B1 1% 1% 1% 2% 3% 4% 6% 9% 22% 11% 9% 5% 3% 1% 1% 2 B2 1% 1% 2% 2% 3% 6% 1 24% 1 6% 4% 2% 1% 27% B3 1% 1% 1% 1% 2% 3% 6% 9% 19% 8% 6% 3% 2% 1% 38% Caa1 1% 1% 1% 2% 5% 7% 1 17% 6% 4% 2% 1% 41% Caa2 1% 2% 1% 1% 2% 4% 5% 8% 6% 12% 3% 3% 1% 51% Caa3 1% 1% 1% 1% 2% 4% 4% 7% 5% 5% 1 3% 1% 54% Ca-C 1% 1% 1% 3% 4% 5% 7% 4% 4% 4% 5% 1% 59% 18 March 2008 Special Comment

19 Exhibit 14: 5-Year Transition Matrix, North American Issuers CTM Adjustment 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% Aa1 11% 51% 17% 13% 4% 2% 1% Aa2 6% 16% 41% 22% 8% 4% 2% 1% 1% Aa3 1% 5% 12% 55% 13% 7% 3% 1% 1% A1 1% 3% 16% 48% 15% 8% 4% 2% 1% A2 1% 5% 13% 46% 14% 9% 5% 3% 1% 1% A3 1% 2% 5% 16% 37% 15% 11% 6% 2% 1% 1% 1% 1% 1% Baa1 1% 2% 7% 12% 39% 17% 1 4% 2% 2% 1% 1% 1% 1% Baa2 1% 1% 3% 6% 13% 39% 16% 6% 4% 3% 2% 2% 1% 1% 2% Baa3 1% 2% 3% 7% 17% 35% 9% 6% 5% 3% 3% 2% 1% 1% 4% Ba1 1% 2% 2% 5% 11% 18% 25% 7% 7% 4% 4% 3% 2% 1% 6% Ba2 1% 1% 1% 3% 6% 11% 12% 19% 9% 7% 7% 5% 3% 2% 1% 1% 12% Ba3 1% 1% 2% 4% 7% 8% 8% 23% 8% 9% 6% 4% 2% 1% 1% 15% B1 1% 1% 1% 2% 3% 4% 6% 1 24% 1 8% 5% 3% 1% 1% 19% B2 1% 1% 2% 2% 3% 6% 1 25% 9% 6% 4% 2% 1% 26% B3 1% 1% 1% 2% 3% 6% 9% 21% 7% 6% 3% 2% 1% 37% Caa1 1% 1% 1% 2% 4% 6% 9% 21% 6% 4% 3% 1% 4 Caa2 1% 1% 1% 1% 2% 3% 4% 7% 5% 16% 3% 3% 1% 51% Caa3 1% 1% 1% 2% 3% 3% 5% 4% 4% 16% 3% 2% 55% Ca-C 1% 1% 2% 2% 3% 5% 2% 3% 4% 13% 2% 63% 19 March 2008 Special Comment

20 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 Aaa Aa2 A1 A3 Baa2 Ba1 Ba3 B2 Caa1 Caa3 Moody's Annual Moody's Portfolio CTM Exhibit 16: 1-Year Stability Probability, All North American Issuers 10 1-Year Stability Prob Aaa Aa2 A1 A3 Baa2 Ba1 Ba3 B2 Caa1 Caa3 Moody's Annual Moody's Quarterly 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

21 Exhibit 16: 5-Year Probability of Upgrading, All North American Issuers 5-Year Upgrade Prob Aaa Aa2 A1 A3 Baa2 Ba1 Ba3 B2 Caa1 Caa3 Moody's Annual Moody's Portfolio 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 % Difference¹ All Issuers IG Issuers Moody's Annual Portfolio 2.19% 0.05% Moody's Annual Issuer 2.23% 2%² 0.05% 1 Year 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% 0.79% Moody's Annual Issuer 12.11% 14% 0.78% 5 Year Moody's Quarterly Portfolio 10.75% 1% 0.79% 1% Moody's Quarterly Issuer 12.35% 16% 0.79% CTM Issuer 12.24% 15% 0.81% 3% 21 March 2008 Special Comment -

22 Is There a Difference between Moody s Standard Adjustment and Other Adjustment Methods? Duration Adjustment Method Default Rates % Difference¹ Default Rates % Difference¹ SG Issuer Moody's Annual Portfolio 5.36% 11.08% Caa-C Moody's Annual Issuer 5.37% 11.02% 1 Year Moody's Quarterly Portfolio 5.47% 2% 11.33% 2% Moody's Quarterly Issuer 5.49% 2% % CTM Issuer 5.46% 2% 11.24% 1% Moody's Annual Portfolio 27.77% 43.84% Moody's Annual Issuer 28.33% 2% 43.64% 5 Year Moody's Quarterly Portfolio 28.28% 2% 44.85% 2% Moody's Quarterly Issuer % 44.69% 2% CTM Issuer % 44.78% 2% 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 = ( ) / March 2008 Special Comment -

23 References Cantor, R. and D. Hamilton (2007). Adjusting Corporate Default Rates for Rating Withdrawals, Journal of Credit Risk, vol 3, no 2, pg 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 -

24 Report no.: Authors Albert Metz Nilay Donmez Production Associates Cassina Brooks Wing Chan Copyright 2008, Moody s Investors Service, Inc. and/or its licensors and affiliates including Moody s Assurance Company, Inc. (together, MOODY S ). All rights reserved. ALL INFORMATION CONTAINED HEREIN IS PROTECTED BY COPYRIGHT LAW AND NONE OF SUCH INFORMATION MAY BE COPIED OR OTHERWISE REPRODUCED, REPACKAGED, FURTHER TRANSMITTED, TRANSFERRED, DISSEMINATED, REDISTRIBUTED OR RESOLD, OR STORED FOR SUBSEQUENT USE FOR ANY SUCH PURPOSE, IN WHOLE OR IN PART, IN ANY FORM OR MANNER OR BY ANY MEANS WHATSOEVER, BY ANY PERSON WITHOUT MOODY S PRIOR WRITTEN CONSENT. All information contained herein is obtained by MOODY S from sources believed by it to be accurate and reliable. Because of the possibility of human or mechanical error as well as other factors, however, such information is provided as is without warranty of any kind and MOODY S, in particular, makes no representation or warranty, express or implied, as to the accuracy, timeliness, completeness, merchantability or fitness for any particular purpose of any such information. Under no circumstances shall MOODY S have any liability to any person or entity for (a) any loss or damage in whole or in part caused by, resulting from, or relating to, any error (negligent or otherwise) or other circumstance or contingency within or outside the control of MOODY S or any of its directors, officers, employees or agents in connection with the procurement, collection, compilation, analysis, interpretation, communication, publication or delivery of any such information, or (b) any direct, indirect, special, consequential, compensatory or incidental damages whatsoever (including without limitation, lost profits), even if MOODY S is advised in advance of the possibility of such damages, resulting from the use of or inability to use, any such information. The credit ratings and financial reporting analysis observations, if any, constituting part of the information contained herein are, and must be construed solely as, statements of opinion and not statements of fact or recommendations to purchase, sell or hold any securities. NO WARRANTY, EXPRESS OR IMPLIED, AS TO THE ACCURACY, TIMELINESS, COMPLETENESS, MERCHANTABILITY OR FITNESS FOR ANY PARTICULAR PURPOSE OF ANY SUCH RATING OR OTHER OPINION OR INFORMATION IS GIVEN OR MADE BY MOODY S IN ANY FORM OR MANNER WHATSOEVER. Each rating or other opinion must be weighed solely as one factor in any investment decision made by or on behalf of any user of the information contained herein, and each such user must accordingly make its own study and evaluation of each security and of each issuer and guarantor of, and each provider of credit support for, each security that it may consider purchasing, holding or selling. MOODY S hereby discloses that most issuers of debt securities (including corporate and municipal bonds, debentures, notes and commercial paper) and preferred stock rated by MOODY S have, prior to assignment of any rating, agreed to pay to MOODY S for appraisal and rating services rendered by it fees ranging from $1,500 to approximately $2,400,000. Moody s Corporation (MCO) and its wholly-owned credit rating agency subsidiary, Moody s Investors Service (MIS), also maintain policies and procedures to address the independence of MIS s ratings and rating processes. Information regarding certain affiliations that may exist between directors of MCO and rated entities, and between entities who hold ratings from MIS and have also publicly reported to the SEC an ownership interest in MCO of more than 5%, is posted annually on Moody s website at under the heading Shareholder Relations Corporate Governance Director and Shareholder Affiliation Policy. 24 March 2008 Special Comment -