Скачать или смотреть Low Default Portfolios (Part 1)

A Low Default Portfolio (LDP) is a portfolio characterized by a low number of defaults.
Too simple?

Citing the BCBS (Basel Committee on Banking Supervision):

Several types of portfolios may have low numbers of defaults. For example, some portfolios historically have experienced low numbers of defaults and are generally—but not always— considered to be low-risk (e.g. portfolios of exposures to sovereigns, banks, insurance companies or highly rated corporates). Other portfolios may be relatively small in size, either globally or at an individual bank level (e.g. project finance, shipping), or a bank may be a recent market entrant for a given portfolio. Other portfolios may not have incurred recent losses, but historical experience or other analysis might suggest that there is a greater likelihood of losses than is captured in recent data (e.g. retail mortgages in a number of jurisdictions).

Why are LDPs a problem? Why should we complain about a few defaults?

The answer is simple: regulations require banks to estimate the PD of all their counterparties. But what happens if the data we have are not sufficient to have reliable estimates?
For some of these counterparties, such as for example very good quality borrowers, the historical information about past defaults may be missing, or it may be clustered in specific downturn periods, while for other long periods almost no default is observed.
Default rates may thus become extremely volatile and unreliable.

Since we observe (almost) no default for AAA bonds, can we really assume that the probability of default is zero? Do we seriously want to be victims of such a trivial historical bias?
Do you remember Lehman Brothers? Before September 15, 2008, no one had ever seen such a bankruptcy in the US... The impact was huge.

Luckily, there are techniques we can use to deal with the problem of zero defaults in data.
Some of these methods come from reliability theory and engineering, some others make use of Bayesian statistics and expert judgements.

Unfortunately, there is no first-best solution. Each method has its own weaknesses and we have to cope with that.
For example, when using experts judgements, via the elicitation of some prior distribution on the PD of a given counterparty (or group of counterparties), we immediately see that more than one distribution could be used, generating different results. And in any case, whatever prior we choose, it will be probably subject to criticism by people with other beliefs.
And when using methods deriving from hypothesis testing, the significance level we choose will always influence the estimates we get, notwithstanding the necessity of checking if the basic hypotheses are verified.

Dealing with LPDs requires being ready to fully motivate our modeling choices, preparing detailed documentations, and trying to be as transparent as possible.

Despite dating back to 2005, the BCBS document "Validation of low-default portfolios in the Basel II Framework" is still valid, especially when it states that both regulators and the industry are still struggling to define a good way of dealing with LDPs, in particular under the IRB framework.

For those interested, I suggest reading the following documents:

BCBS (2005): https://www.bis.org/publ/bcbs_nl6.pdf
EBA (2014): https://tinyurl.com/bdf25p82