PrefBlog

This post was originally intended to be part of the report of the BoE Financial Stability Report … but it got too interesting and too long! So here it is … an introduction to Loan Default Correlation:

Box 2 of the report, Valuing sub-prime RMBS, provides a primer on the pricing of loan pools. Of great importance is the correlation of the default probability … we might say, for instance, that a sub-prime borrower has a 15% chance of defaulting and be perfectly correct, as far as that goes. It would be a mistake to construct detailed probability charts of default proportion within the pool, however, because this 15% default probability is not an asystemic risk that can be diversified away – there is a great deal of systemic risk in the pool.

For instance, while 5% of the total 15% default probability might be due to factors unique to the individual borrower – he loses his job, or gets sick or whatever – 10% of the total might be a response to broader factors that will affect the entire pool in much the same way – an economic depression causes unemployment to rise sharply, a pandemic makes everybody get sick, or whatever.

Thus, correlation must be estimated. The Bank reports:

Scenario C is the same as Scenario B except that it also has a higher rate of default correlation. As Chart A shows, this increases the chance of extreme outcomes, raising the price of the BBB tranche and reducing the price of the AAA tranche.

Comparing Table 1 with Chart 1.9 suggests that expectations about both default rates and correlations may have increased during July and early August, as the prices of both junior and senior RMBS tranches fell sharply. Views about default correlation may subsequently have been revised down, however, with prices of senior tranches recovering while the prices of junior tranches have continued to fall.

The correlation of 5% used for their base-case and for their scenarios A and B is consistent with research presented to a Fed Conference by Cowan & Cowan; scenario C increased the correlation to 15%. The Cowan & Cowan reports states:

This paper presents the first formal study of default correlation within a subprime mortgage loan portfolio. We find generally that default correlations for the specific portfolio studied are insignificant until the portfolio is segregated into appropriate risk groups. We analyze six month default correlation using both actual default (foreclosure) and a more broad definition of delinquency which is consistent with previous literature. Contrary to our expectations, actual defaults generally result in higher default correlations than delinquencies. As anticipated, the magnitude of default correlation increases as the internally assigned risk grade declines.

Briefly reviewing the results from actual defaults, we obtain a six month default correlation of 6.2% for CC-rated borrowers as compared with a miniscule 0.1% for AArated borrowers. If loans are grouped by occupancy type, the default correlation increases to 8.7% for second home loans and 2.6% for non-owner occupied homes. In contrast, classification by property type results in a maximum default correlation of 4.6% for multi-unit properties.

If default correlations are very low within subprime portfolios, then an expensive investigation of default correlations is not an efficient use of resources. However, our findings, combined with the findings of Loffler (2003) that lower grade portfolios are more sensitive to changes in default correlations, suggest that the industry needs to focus on this issue. Although it represents but one lender, it clearly provides sufficient insight to suggest a direction for further investigation. If, as Carey (2000) suggests, bad tail loss rates are understated by estimating portfolio loss distributions by equally weighting events in each database year, then our results should compel both subprime lenders and regulators to further investigate the impact of default correlation.

This entry was posted on Friday, October 26th, 2007 at 2:17 pm and is filed under Interesting External Papers. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.