Credit Modeling Innovations: A Number of Conceptual Innovations Have Been Central to the Transformation of Credit Risk Theory and Practice over the Past 25 Years. the Most Significant of These Contributions Are Reviewed in This Article

By Rowe, David M.; Day, Thomas | The RMA Journal, November 2007 | Go to article overview

Credit Modeling Innovations: A Number of Conceptual Innovations Have Been Central to the Transformation of Credit Risk Theory and Practice over the Past 25 Years. the Most Significant of These Contributions Are Reviewed in This Article


Rowe, David M., Day, Thomas, The RMA Journal


[ILLUSTRATION OMITTED]

In the 1960s a young academic named Ed Altman turned his attention to improving the rigor of credit risk analysis. Focusing on accounting statements, he developed a weighted average of five financial ratios, which he called a Z-score. (1) The five ratios and the weights were chosen to maximize the resulting index's discriminatory power in predicting default over the one and two years following the date of the statements.

In effect, Altman brought rigorous statistical techniques to the task of defining a credit quality index. In practice, a Z-score was generally supplemented by more qualitative factors like absolute market size, market growth prospects, the level and trend in a firm's market share, the existence of legal or logistical barriers to entry for competitors, and threats from new technological possibilities. Over the past 40 years, various manifestations of the Altman Z-score have continued to play an important role in fundamental credit analysis. (2)

Credit Migration Approach

Just as Ed Altman's analysis was a rigorous extension of traditional approaches to credit risk assessment, so the credit migration approach builds on historical data for credit ratings. A transition matrix displays all rating classes in the headers for both the columns and the rows. The elements of this matrix indicate the probability that an obligor starting a period with a rating corresponding to the row will end the period with the rating corresponding to the column. The largest probabilities tend to lie along the diagonal, indicating the high likelihood that a firm's rating will be unchanged during the period.

In its simplest form, this approach makes the aggressive assumption that the probability of a firm migrating to another rating is the same for all firms in a given rating class. For multi-period analysis, it is possible to introduce momentum factors for one or more periods if the data is available to support this level of detail. In this case, entities that migrated in the previous period or periods are deemed to have different future transition probabilities than those with ratings that have been stable. In addition, it is possible to apply different transition matrices depending on the projected state of the economy.

Extending the transition approach to modeling multiple holdings requires some means of imposing correlations on the migration behavior. The approach implemented by CreditMetrics involves simulating the value of each firm's assets against a grid that maps simulated asset values to corresponding credit ratings. This mapping preserves the migration probabilities of the applicable transition matrix. Historical correlations among each firm's equity-value changes are used as proxies for asset correlations, and these are imposed on the simulation process. Future cash flows are then discounted in each simulation based on rates appropriate to the credit rating implied for each instrument in that scenario. Repeating this simulation many times produces an estimated distribution of future portfolio values from which a credit value-at-risk (CVaR) estimate can be derived.

The KMV Approach to the Merton Model

In 1974, Robert Merton pointed out that the legal structure surrounding a limited liability corporation implies that debt holders have effectively written a put on the firm's assets to the benefit of the equity holders. The strike price for this put is the book value of the liabilities. If the market value of the unleveraged assets falls below the book value of the liabilities, the equity holders have the option to "put" the assets to the debt holders. This effectively limits the downside loss of the equity holders, simultaneously leaving them with unlimited upside potential--identical to the payoff of an asset owner with a put option.

Unfortunately, the market value of a firm's assets is not observable. The market value of the equity can be observed, but it reflects the value of the assets in excess of the liabilities plus the value of the implicit put option on those assets. …

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