CDO evaluator and portfolio benchmarks.

• Author: Bergman, Sten

Standard & Poor's new CDO Evaluator refines CDO default analysis. This new model uses Monte Carlo statistical methodology to evaluate the credit quality of a portfolio of CDO assets and to provide scenario-default rates for the portfolio at each rating level. The CDO Evaluator system is used to determine the credit risk of a portfolio of assets both for cash flow and for synthetic CDOs.

1. STANDARD & POOR'S CDO EVALUATOR

   Standard & Poor's new CDO Evaluator refines CDO default analysis. This new model uses Monte Carlo statistical methodology to evaluate the credit quality of a portfolio of CDO assets and to provide scenario-default rates for the portfolio at each rating level.

   The CDO Evaluator system is used to determine the credit risk of a portfolio of assets both for cash flow and for synthetic CDOs. The direct result is a probability distribution of potential default rates for the portfolio assets in aggregate. These potential default rates range from 0% (no assets in the portfolio default by maturity) to 100% (all assets in the portfolio default by maturity). The more likely outcome is that some, but not all, assets default. The portfolio default rate is computed as the total dollar amount of assets defaulted by maturity, divided by the total principal amount of the portfolio.

   The probability distribution describes the likelihood of the occurrence of any particular default rate of the portfolio. Chart 1 below presents an example histogram of a probability distribution for a highly diverse pool of 50 corporate bonds rated 'BB', each with a 10-year maturity and the same principal balance. It shows that the likelihood that 24% of the assets in the portfolio would default is approximately 7%, which means that the odds that exactly 12 bonds of the 50 bonds default by maturity is seven out of 100. Similarly, it shows that the probability of defaults in the portfolio exceeding 28% is less than 3% (calculated as the sum of the probabilities of default rates greater than 28%, which are represented by the bars on the Exhibit 1).

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   After calculating the probability distribution associated with a given portfolio, we can derive a set of Scenario Default Rates (SDRs). This set of SDRs is used in determining, for each credit rating, the default rate that a CDO tranche with that rating should be able to withstand under the various cash flow scenarios encompassed by Standard & Poor's rating criteria. The determination of these SDRs is a two-step process. First, for a given tranche credit rating, determine the portfolio default rate such that the probability of defaults in the portfolio exceeding this portfolio default rate is be no greater than the probability of default of a corporate bond with that rating. Second, multiply this portfolio default rate by an adjustment factor designed for the specific tranche rating. This adjustment factor, which may be either greater than or less than 1.0, depending upon the specific tranche rating, partly reflects the fact that the assumed probabilities of default for each asset are only estimates of the likelihood of default--not the eventual default experience of that particular asset class prior to the maturity of the portfolio.

   For example, based on historical default rates, the probability of default for a 10-year 'A' rated corporate bond is estimated to be 3.0%. We therefore want to determine the portfolio default rate for which there is no greater than a 3% chance that it will be exceeded by the observed default rate by maturity. For the highly diverse pool underlying chart 1, this portfolio default rate is 28%. That is to say, the probability of exceeding a 28% default rate is no greater than 3.0%. But, since we are working with estimated probabilities of default for the assets in the portfolio, we multiply the 28% by an adjustment factor, which is 1.02 at the 'A' rating category. This yields an 'A' SDR of 28.56% for the portfolio. A consequence of this methodology for this rating category is that if a tranche can survive defaults less than or equal to the 'A' SDR, then its probability of default would be no greater than 3.0%, as would be appropriate for an 'A' rating.

   The CDO Evaluator replaces the Risk Tabulator Model and the CDO Structuring Model, respectively, used for CDOs backed by ABS (asset-backed securities) and corporate bonds/loans. Unlike these two models, the CDO Evaluator does not use notching penalties for high industry concentration. Instead, it relies on the effects of correlation upon the SDRs to inhibit industry concentration. In addition, it can work with hybrid portfolios of both ABS and corporates. Moving beyond the traditional task of determining SDRs, the CDO Evaluator computes new CDO benchmarks, which may prove useful in describing the credit quality of a portfolio. These include industry friendly measures of default, variability, and correlation. (These measures are explained in Standard & Poor's Structured Finance Special Report entitled "New Benchmarks Overcome Shortcomings of Traditional CDO Evaluations").

   1. Conceptual Framework

   Although the CDO Evaluator methodology is the same for all types of collateral, the conceptual framework is best understood in the context of a specific example. For ease of reference we chose an ABS CDO transaction. Exhibit 2 is a schematic of an ABS CDO supported by a number of ABS securities. The ABS securities are securitizations of asset-pools, consisting of credit card receivables, auto loans, mortgages, or other pools of financial instruments. For the purpose of the example, we will assume that an ABS security will default because the underlying pool of assets is experiencing too many defaults. In general, the probability of the ABS security defaulting is assumed to be the one implied by its Standard & Poor's credit rating. For example, based on historical studies Standard & Poor's uses a default probability of 8% for a 'BB' ABS security (see Exhibit 2).

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   Given that ABS securities derive their performance largely from the asset pools that collateralize them, it follows that the default correlation that exists between such securities is primarily a consequence of the performance correlation between the asset pools that support them. In general, asset-pool correlation reflects the increased likelihood that one pool will perform poorly (or well) given that another has performed poorly (or well). This may be based on the impact of general economic conditions, as well as on issuer or industry specific conditions or events. For example, the performance of auto loans and credit card receivables may be adversely affected by higher unemployment. If this is the case, then the auto ABS security and the credit card ABS security collateralized by these kinds of asset pools will tend to default together and thus are also correlated.

   The framework described above in the context of ABS securities is equally applicable to corporate securities. In this case, the economic performance of an obligor (typically a corporation) would generally be correlated with that of other obligors belonging to similar industry sectors or to industries that may be affected by general economic events in the same manner.

   The CDO Evaluator addresses correlation primarily at the underlying obligor/asset-pool level and assumes that it can be expressed in terms of a pair-wise sector correlation table. The advantage of studying correlation at the obligor/asset-pool level, rather than the portfolio level, is that it allows issuers and investors to focus on the general correlation assumptions governing the performance of industries, broad asset-pool classes and the economy as a whole, rather than on the considerably less transparent relationship between securities or tranches with different positions within the capital structure of their respective issuing entities.

   The emphasis placed on modeling correlation in the CDO Evaluator is due to the profound effect that correlation can have on the level of SDR for various credit ratings. Exhibit 3 vividly shows the effects of correlation on the entire probability distribution of default rates for an ABS CDO consisting of 50 assets, from five different sectors, assuming all securities are rated 'B'. As can be seen in the exhibit, the mean remains unchanged, but extreme values become more likely. Most affected are the SDR for the higher credit rating categories. For example, with no correlation the 'AA' SDR is 31%. Assuming our current ABS sector correlations, the 'AA' SDR increases to 49%.

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2. MONTE CARLO SIMULATION

   To properly model the effect of correlation on the CDO asset pool, Standard & Poor's has adopted a Monte Carlo approach to estimating the probability distribution of default rates. Within this approach, a number of independent trials are simulated. Each trial generates a vector of random numbers equal in length to the number of assets and having the desired correlation structure. For each trial, each asset represented in this vector is then determined to have either defaulted or not, based on the...