Subprime CDO Ratings and the Current Financial Crisis: A Modeling Perspective: Models Used by Rating Agencies Were Inadequate to Assess the Credit Risks of Subprime Mortgages in a Turbulent Housing Market. A Model Based on Housing Market Price Risks Might Be an Alternative to the Rating Agencies' Models

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UNLIKE PAST DOWNTURNS in the housing market cycle, this one has caused havoc in financial markets because of write-offs on securities linked to subprime mortgages. Write-downs could reach as high as $400 billion. The International Monetary Fund (IMF) said recently that the cost of the crisis might approach $1 trillion. There is plenty of blame to go around. Investors, lenders, borrowers, and rating agencies all bear responsibility.

Given the size of the market failure, it's fair to question the methodology that the rating agencies used to assign credit ratings to subprime collateralized debt obligation (CDO) tranches. Between 2005 and the third quarter of 2007, about 80% of all subprime mortgages were converted into AAA pools. A vehicle backed by subprime mortgages could borrow 80% of notional amount at AAA rates. One may wonder how it is possible to create AAA-rated instruments out of B-rated paper.

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The secret recipe for this magical conversion is that there are many junior-class notes rated lower than AAA. In fact, there must be at least one class note known as the equity piece that is not even rated (and thus rated lower than B). Cash flows from mortgages are paid to the most senior notes first, then to the next senior notes, and so on. On the other hand, if home owners default, the most junior notes get hit. And if the most junior notes cannot absorb the losses completely, then the next junior notes are affected, and so on, climbing up the ladder. Of course, the most junior notes receive the highest interest rate to compensate for absorbing risk.

CDO Rating Models

The rating agencies relied on CDO rating models in slicing/ dicing and assessing the credit risks of CDO tranches. CDO rating models are ratings-based mathematical models that, to most investors, in some way mysteriously generate ratings.

In the past, CDO rating models were used mostly for evaluating CDOs for corporate debt. Moody's first developed a CDO rating model, the binomial expansion technique (BET), which became the most popular tool for rating CDO products, including CDOs for subprime mortgages. The model generates the number of defaulted loans/ bonds in a pool with the frequency of occurrences if loans/ bonds of the collateral are more or less homogeneous in probability of default (PD) and exposure, and if defaults of loans/bonds are independent events. For example, for a pool of 100 loans, the probability of only one loan default over the maturity is very low, and so is the probability that 99 loans will default. In reality, the underlying pools are not homogeneous, and there is a tendency for many loans to default at the same time.

The key idea of BET is to map the real portfolio into a hypothetical homogeneous portfolio by calculating the average PD of the exposures and the diversity score. The diversity score summarizes the degree of homogeneity of the real portfolio. More importantly, it reflects the default correlation among loans by replacing the number of loans in the pool. From the previous example, if the diversity score is 50, the frequency of the number of defaulted loans is calculated as if there are only 50 loans in the pool. All the model requires to set the calculation are ratings or PDs of loans/bonds. Other rating models, some more sophisticated than others, also operate based on ratings or PDs.

For corporate credits, ratings-based CDO models performed adequately. After all, corporate creditworthiness is well researched by rating agencies; it's their primary job. The question is whether these models can be applied to evaluate default risks of subprime CDO tranches.

Ratings of Subprime CDO Tranches in CDO Rating Models

If assigning ratings required familiarity with mathematical models, it would be impossible for general investors to assess creditworthiness of subprime CDO notes. Using ratings assigned by rating agencies, however, allows investors to benchmark what they paid for. …