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The IRB approach to capital requirements of the New Basel Accord makes the internal ratings a critical building block of the credit risk management within banks. Banks adopting the standardized approach rely only on external ratings, plus the uniform 100% weight for all unrated entities. Since the majority of bank transactions are usually with unrated entities, the standardized approach does not remedy the major drawback of the old system, that of not being risk-sensitive enough. When moving to the foundation and advanced approaches, ratings become the basis for defining default probabilities.

The simplest technique is to map internal ratings to external ratings and use the correspondence between external ratings and default probabilities to obtain the missing link from internal ratings to default probabilities (Figure 35.2). Such techniques assume that the mapping of internal to external ratings is correct and that the mapping of agency ratings to default probabilities is also.

It is easy to challenge both assumptions. Internal rating scales differ from agency rating scales, in terms of what ratings represent, and the correspondence is judgmental. The mapping process necessitates grouping some categories in order to match given external classes. Agency ratings relate to severity of losses, a combination of default probability and recovery rate. Unsecured senior ratings should relate better to default frequencies. However, default probability models (Chapter 37) suggest a significant variance of default frequencies of firms within the same rating class.

The expected loss is the product of the default probability and the loss given default:

For instance for the same default probability, say 0.2%, the recovery rate could be 0% or 80% depending on the specifics of a debt issue. The expected losses are respectively 0.2% x 100% = 0.2% and 0.2% x 20% = 0.04%. The expected loss quantifies the severity of loss, which agencies capture synthetically in their ratings. The merit of the

simple expected loss equation is that it illustrates how to separate the issuers risk from the issue risk. A second application is to assign an equivalent rating from expected loss calculations of debt issues, given their recovery rates. For instance, from Table 36.1, a 0.2% default probability in the simplified rating scale corresponds roughly to a Baa rating and a 0.04% default rate is close to an Aa rating. This allows assigning ratings from expected loss calculations. The 0.2% expected loss percentage maps to a senior unsecured Baa rating. The 0.04% value maps to an equivalent Aa senior unsecured rating. Note that, in this second case, the default probability, 0.2%, remains the same, corresponding to the Baa rating. Because of the higher recovery rate, however, the equivalent rating moves significantly up in the rating scale to a higher grade.

Credit Risk: Historical Data

Historical statistics of rating agencies are a first source of data on defaults and migrations based on bond issues. Defaults occur when a borrower fails to comply with a payment obligation. A migration, or a transition, is a change of risk class. Historical data for loans also exists in banks. This chapter refers to publicly available data from rating agencies.

Historical data report risk statistics as frequencies (numbers or percentages) of a reference population sample. Percentages are either arithmetic or weighted averages, notably for default rates, using size of defaulting bonds as weights. Agencies group data by risk class, defined by rating, to report default and migration rates over a given period for all ratings. Default and migration rates are historical statistics, as opposed to the predicted expected default frequency (Edf ©) as defined by KMV Corporation. Many applications use such rates as proxies of default and migration probabilities, although historical data are backward looking while probabilities are forward looking.

Rating systems combined with statistics on defaults allow us to relate them to default and migration frequencies. Public historical credit risk statistics include: yearly default rates by rating class; cumulative default rates over time; annualized cumulated default rates; yearly default rate volatilities; transition matrices; averaged recovery rates. Internal bank data warehouses might have detailed credit risk data by borrower and transaction. Banks map their internal ratings to external default frequencies, using an intermediate mapping between their own ratings and those of external agencies.

Some major empirical findings include: default frequencies increase much more than proportionally when moving from good to high risk classes; cumulative default rates increase less than proportionally with horizon for high ratings, and more than proportionally for lower rating classes; default rates relate inversely to the default rate volatility of each risk class.

Transition matrices provide the frequencies of migration between any pair of rating classes, for varying horizons. They serve for valuing migration risk. The value of downside migrations (riskier ratings) results from the wider credit spreads embedded in market rates for discounting future flows when marking to market loans on bonds. The value of the transaction becomes lower than the current value, resulting in a loss. Both cumulative and marginal default rates are useful to characterize default risk through a succession of future periods. Forward default rates are frequencies of default of firms having survived up to a specified date for subsequent periods beyond this starting date.

The first two sections describe the main types of available statistics. The third section addresses migrations across risk classes. The last section addresses the term structure of default rates with cumulative rates over different horizons and marginal default rates, or forward default rates, between any two dates in the future.