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«STRUCTURED FINANCE Rating Methodology Moody's Revisits its Assumptions Regarding Structured Finance Default (and Asset) Correlations for CDOs **AUTHORS: ...»

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Moody's Revisits its Assumptions Regarding Structured

Finance Default (and Asset) Correlations for CDOs

**AUTHORS: I. Summary

Olivier Toutain II. Moody's Prior Correlation Assumptions for Multisector CDOs

VP-Senior Analyst

III. Alternative Approaches for Measuring Structured Finance Credit

(331) 5330-1042


Olivier.Toutain@moodys.com IV. Moody's Again Prefers Asset Correlations Inferred from Ratings David Rosa VP-Senior Analyst Transitions (4420) 7772-5341 V. Estimates Derived from the DRTM Approach: Major Structured David.Rosa@moodys.com Sectors Yvonne Fu VI. Extrapolation to All Structured Finance Sectors and "Tree" Senior Vice President Representation (212) 553-7732 Yvonne.Fu@moodys.com VII. Extensions to Account for Regional, Vintage, Key Agent and Paul Mazataud Same-Transaction Effects Managing Director VIII. Conclusion (331) 5330-1037 Paul.Mazataud@moodys.com Appendices Guillaume Jolivet Associate Analyst I. SUMMARY (331) 5330-5978 Late last year, Moody's published a correlation framework for corporate instruGuillaume.Jolivet@moodys.com ments that we now apply to synthetic CDOs.1 The framework consists of a set of Laurent Lassalvy asset correlations derived primarily from co-movements in Moody's ratings, and is Associate Analyst (4420) 7772-8634 implemented via an additive factor ("tree") scheme. Asset correlations vary for Laurent.Lassalvy@moodys.com pairs of firms within and across industries, as well as by geographic region.

Julien Sieler Since CDOs are increasingly backed by, or if synthetic, reference, structured instruSenior Associate ments, it is important to have a corresponding set of asset correlation assumptions (331) 5330-1077 for asset-backed securities (ABS), residential-mortgage backed securities (RMBS), Julien.Sieler@moodys.com Gareth Levington commercial mortgage-backed securities (CMBS), as well as CDO tranches themManaging Director selves. Moody's has, in fact, developed such a framework for use within its (4420) 7772-5506 CDOROM™ model. We describe this framework over the balance of this article.

Gareth.Levington@moodys.com Gary Witt II. MOODY'S PRIOR CORRELATION ASSU

–  –  –

June 27, 2005

• In the case of REIT debt-and only in this case-an active equity market existed from which it was possible to infer default correlations. Specifically, by relating equity return correlations to ratings, we were able to measure asset correlations for REITs from various subsectors, from which default correlations were then inferred.

• In the case of CDOs, it was possible to develop an 'observed' set of default correlations by simulating the performance of pairs of CDOs with collateral pools that were somehow related. The degree to which the pools were related was expressed in terms of the overlap by industry and obligor across the pools. Hence for different CDO sectors, we calculated typical industry and obligor overlaps, simulated cash flows for typical structures, and measured the incidence of joint default.

• For other structured sectors, a lack of similar data required a more ad hoc approach. For these asset classes, we relied on an extensive set of interviews with Moody's expert analysts for each sector. Frequent comparisons across asset classes ensured that the rank ordering of correlation levels was appropriate in the eyes of the structured finance analysts.

Recognizing that default correlations should vary with default probability, we varied default correlation assumptions as the investment-grade (IG) or non-investment grade (NIG) status of a particular pair of credits varied.

Since early resecuritizations were generally backed by Baa-rated credits, the IG assumptions were geared toward this rating level. However, those assumptions are quite conservative for pools of highly-rated credits, which increasingly back (or are referenced by) multisector CDOs.



As in the case of corporate obligations, there are several different approaches for inferring either default or asset

correlations for structured credits4:

• The behavior of credit spreads

• The joint behavior of the asset pools that underlay structured transactions

• Co-movements in ratings

Each of these has advantages and disadvantages:

Drawing Inferences from Credit Spreads As in the corporate context, credit spreads may be an attractive source of information for inferring credit correlations because they are market measures that reflect market views regarding default and loss. Spreads are available for most, though certainly not all, structured finance sectors.

The chief obstacle here is also the primary problem in the corporate context-it is very difficult to separate the credit-related component of the spread from other components, such as liquidity effects, tax effects, risk aversion, etc. The task is made more difficult because the contributions of these non-credit factors to spreads almost certainly vary over time.

Indeed, the problem is exacerbated in the structured finance context because structured instruments are generally quite illiquid.5 Because structured tranches trade infrequently, it is thus difficult to observe true market spreads. Spreads are much more likely to be the result of 'matrix pricing' that effectively imposes its own noncredit-related correlation matrix on various structured asset classes. Moreover, while the "cleanest" credit spread data in the corporate context are probably drawn from the credit default swap (CDS) market, there is no meaningful CDS market for structured instruments.

Drawing Inferences from the Behavior of the Underlying Assets A more promising approach that is empirical, but not market driven, is to relate the performance of the assets that back structured transactions to the credit correlations of structured finance tranches. This approach requires two sets of information: the behavior of the underlying collateral, and the structures of transactions for each asset class. For example, it isn't sufficient to know the correlation between, say, credit card receivables and residential mortgage delinquencies. Rather, one needs to understand how the performance of the asset pools (delinquencies, nonperforming loans, recoveries, prepayments, etc.) is related for the two asset classes, as well as the way in which collateral performance affects losses associated with credit card ABS and RMBS tranches.

4 One approach that is relevant for corporate obligors-inferring asset correlations from equity behavior within a variant of the Merton model-is not directly relevant in the structured finance context.

5 Although this is often true, there are, of course exceptions. For example, standard Aaa-rated credit card ABS tranches may be quite liquid. But even in that case the issues similar to those encountered with the use of correlations from corporate spreads (spread reflecting liquidity and/or herd investment) will still occur here.

2 • Moody’s Investors Service Moody's Revisits its Assumptions Regarding Structured Finance Default (and Asset) Correlations for CDOs The only apparent method for implementing this approach is to simulate the joint behavior-in all its dimensionsof the underlying pools, while "running the asset performance through" actual structures (tranching and cashflow waterfalls) for credit card and RMBS structures. This is theoretically possible, but the data issues are rather daunting. For many less traditional asset classes, collateral performance data are inadequate to allow a meaningful simulation. Moreover, even this exercise would not capture the potential for event risk, which may have a significant impact on correlation (and which we address via the 'Key Agent' concept below).

Drawing Inferences from Co-Movements in Ratings The third approach is essentially what we have implemented in the corporate context: inferring asset correlations from joint rating transitions. Of course, in the structured finance context, we define our "industries" to be asset sectors like ABS, RMBS, CMBS and CDOs, rather than corporate industries.

As in the case of corporates, the advantages of the ratings-based approach are consistency with the modeling of defaults and recoveries (which are also ratings-based) and fairly wide coverage. But as with other approaches, the data will tend to be sparse for the newer or more exotic sectors within structured finance. It can at least be said that rating co-movements are fairly easy to observe for these exotic sectors, while meaningful credit spreads or historical pool performance data may be quite difficult to produce.



Echoing our choice in the corporate sector, Moody's prefers to rely on the Directional Ratings Transition Matrix (DRTM) approach to derive a set of asset correlations for structured credits. The choice of the DTRM is based on:

1. The availability of data-as noted above, rating transitions are available for the major structured finance sectors and are readily accessible. Moreover, they will be readily accessible in the future for the purpose of updating and extending parameter estimates. One important extension is the application of the technique to assess correlations between structured and corporate instruments, to which the DRTM is well suited.

2. Consistency with other aspects of Moody's CDO ratings-one state to which a rating may transition is default. The DRTM yields asset correlation estimates that are thus consistent with the ratingsbased measures of default and loss that Moody's uses to model CDOs.

The preference for using asset, rather than default correlations, is identical to that in the corporate context:

1. Asset correlations are much easier to work with within a simulation framework, such as Moody's CDOROM model. More specifically, one can mathematically describe joint events of default in a computationally convenient and widely used way.

2. The reliance on asset correlations gives rise to a consistent set of default correlations that can be applied within the BET or another non-simulation framework. That is, by first choosing a set of asset correlations for entities within or across sectors, the implied default correlations are appropriately scaled for the default probabilities of the pair of obligations.6 3. The asset correlation approach is also quite natural in the structured finance context, where tranche performance clearly depends on the performance of the assets in the collateral pool, which may be correlated across transactions.

The actual application of the DRTM to structured finance ratings differs somewhat from that in the corporate sector. The reason is simply the availability of data: the structured finance market is much less mature than the corporate bond market, thus providing a much shorter history of rating transitions. Furthermore, structured finance ratings of particularly important sectors like RMBS have tended to be more stable than corporate ratings, suggesting that there have been fewer observed transitions per rated credit per year. The sparse data on structured finance rating transitions requires the application of a different technique to infer asset correlations than was applied in the corporate context. The details of the estimation process are described in Appendix 1.

6 One could use these correlations to derive discrete distributions for use in cash-flow CDOs. We are about to publish a Special Report explaining how the correlated BET methodology determines the default distribution.

Moody's Revisits its Assumptions Regarding Structured Finance Default (and Asset) Correlations for CDOs Moody’s Investors Service • 3


Regardless of approach, any meaningful estimation of asset correlations requires extensive data. Within the structured finance world, sufficient (multi-year) transition data exist for the major sectors: consumer-related ABS, RMBS, CMBS, high-yield (HY) corporate and other CDOs. Further distinctions can be made based on a priori views about the relationships between more refined or more exotic structured finance sectors, but the data are simply not sufficient to provide reliable estimates.

To arrive at robust correlation estimates, we examined rating co-movements in the major sectors over the last twenty years. By choosing this period, we were able to observe at least 1000 rating actions within each sector.

The numbers of observations (all rating actions including the initial assignment of a rating) in each asset class during the sample period is presented in Figure 1 below.

–  –  –

Application of the DTRM approach over the sample period, as described in Appendix 1, gives rise to the following asset correlation matrix (Figure 2):

–  –  –

The relatively low intra-sector correlation level for the 'other CDOs' bucket reflects the aggregation of the different types of CDOs (resecuritization, synthetic arbitrage and emerging market) within this classification. In effect, these figures should be interpreted as inter-, rather than intra-sector, correlation numbers between resecuritization, synthetic arbitrage and emerging market CDOs. The low intra-sector correlation level for CMBS can also seem a bit awkward, but looking only at IG tranches the correlation is closer to 30%. That difference stems from

two elements:

• The paydown structure of those CMBS implies that historically, we have seen cases where the Aaa /Aa tranches were upgraded due to high repayment and at the same time, the junior tranches, being mostly NIG, were downgraded because of defaults (although limited);

• Large loan CMBS have issued only IG tranches and their rating histories differ from the usual diversified CMBS pool.

4 • Moody’s Investors Service Moody's Revisits its Assumptions Regarding Structured Finance Default (and Asset) Correlations for CDOs



The data above provide substantial guidance toward selecting a full asset correlation framework. But because of the limited scope of the data-the fact that we can't derive asset correlations for each pair of narrowly-defined structured finance categories-we must supplement the estimates by imposing a set of assumptions within a well-reasoned scheme.

In the corporate context, it is natural to develop a scheme around industrial and geographic sectors, which is indeed the approach that we have adopted. For structured finance assets, the choices are somewhat less clear, but it makes intuitive sense that any classification scheme should be related to the underlying assets for each transaction type. We have thus developed a set of increasingly refined sector definitions, within which we would expect the performance of the underlying assets to be increasingly linked.

To be more precise, we first define a set of 'meta' categories within which there is a modest degree of linkage of the underlying assets. Beneath each of the meta sectors, there are broad sectors within which the underlying assets may be more tightly linked. Each broad sector is comprised of a set of narrow sectors.7 In general, if a pair of structured finance tranches are classified within the same meta sector, but are in different broad sectors, they will have only modest correlation. The correlation would be somewhat higher if credits have a common broad sector, and higher still if they have a common narrow sector.

We enforce these relationships by employing a 'tree' structure in which pair-wise correlation can be described by the extent to which two credits are on the same 'branch' of the tree, as well as the 'narrowness' (sector specificity) of the branch (Figure 3).

–  –  –

7 See Appendix 4 for a list of narrow sectors. Appendix 4 also specifies ranges of FICO credit scores for classification of three RMBS narrow sectors.

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