Credit risk measurement: avoiding unintended results: part 2: weighting on defaults—knowing your institution's default metrics

RMA Journal, The, May, 2004 by Peter O. Davis, Darrin Williams

Probability of default is one of the most fundamental metrics in credit analysis. It is used to calculate expected credit loss--a concept central to dual ratings systems, loan loss reserves, economic capital frameworks, and, potentially, regulatory capital under Basel II. The calculation of probability of default is generally unambiguous and straightforward. As shown in this article, the application of default rates may be less so.

Default risk can be measured in two ways. First, we can measure the probability that an obligor will default over a given time horizon. A 2% default rate would indicate that two out of 100 obligors are expected to default over a given period. This incidence-based default rate measures the number of borrowers that are likely to default. Alternatively, we can measure the probability that a certain amount of obligations will be defaulted on over a given time horizon. In this case, a 2% default rate would indicate that $2 out of every $100 are likely to go to default over a given time horizon. This exposure-weighted metric provides a measure of the dollars expected to go to default over a given time period. In recent years, large defaults, such as Enron and WorldCom, have demonstrated how different these two metrics can be. While these two firms only counted as two "incidents," they represented over $30 billion in defaulted corporate bond obligations, driving up the dollar-based corporate bond default rate in 2001 and 2002.

While these two metrics are clearly different, they may not necessarily produce different results. If the average balance on defaulted loans is equal to the average balance on outstanding loans, incidence-based and dollar-based default rates will be the same. However, in cases where this is not true, using the two metrics interchangeably may result in a significant mismeasurement of credit risk. Given that default probabilities are a foundation input to calculations of credit risk, misstating default risk will cause all other dependent metrics (such as expected loss and credit capital) to be off significantly.

Measuring Default Risk

Default models are designed to measure the likelihood that an obligor will default over a given time horizon. This is true both for judgment-based grading frameworks and model-driven default frameworks. Default grades/models assess the likelihood that an obligor will fail to meet its financial obligations. While there is a link between a lender's exposure to a given borrower and the assessment of that borrower's default risk (reflected in the borrower's leverage), default assessments are generally an incidence-based measure. For example, a large corporate customer may be rated a four on a lender's internal rating scale, regardless of whether the amount lent to that borrower was $3 million or $30 million.

Default models are typically validated at the time of development and back-tested over time to ensure that the realized default probabilities on an incidence basis fall within a predefined range established by risk-rating band. This default validation process says nothing about whether incidence-based default rates equal dollar-based default rates for a given lender.

Using Default Rates

It is not uncommon for institutions to assume that dollar-based and incidence-based default rates are equal. The standard expected loss formula is shown in Exhibit 1 (for disbursed closed-end loans). Using an incidence-based default probability in this formula implicitly assumes that the two default metrics are equal. These dollar-based expected loss figures are often applied to loan loss reserves, economic capital frameworks, and various portfolio risk analyses and reporting.

[ILLUSTRATION OMITTED]

The challenge with using incidence-based default probability for expected loss calculations is that it says nothing about the dollar-weighted default rate. A portfolio with exposure to 100 borrowers--99 for $10,000 and one for $1 million--could lose over half its dollar value (assuming zero recovery) and still have only a 1% incidence-based default rate.

Moreover, the incidence-based rate cannot be compared directly with the historical loss since it implies a loss of $19,900 (1% of $1.99 million), not the $1 million that was actually lost.

Expected loss frameworks based on incidence rates of default may implicitly assume that the underlying portfolios are perfectly granular--in other words, the portfolio is reasonably "fine-grained" with exposures being evenly spread out across a large number of obligors. If commercial portfolios were perfectly granular, incidence-based and dollar-weighted default rates would always be the same.

Since commercial portfolios are not perfectly granular, banks using incidence-based default rates to calculate expected loss in dollars have to assume that there is not a significant difference between the size of defaulted credits and other credits in the portfolio. The question is, how well does this assumption hold?

Addressing differences in the two metrics seems obvious: When calculating expected loss, use dollar-weighted rather than incidence-based default probabilities. Unfortunately, incidence-based probabilities are the primary basis for the quantification of defaults: in third-party credit models, internal ratings systems, vendor default databases, and ratings agencies' bond default studies. Further, the use of a dollar-weighted default rate creates complications when working with usage given default (UGD) assumptions for unused commitments. If a dollar-weighted default rate is applied, the impact future draws have on expected loss is already captured, making it difficult to appropriately measure UGD for unused commitments.