An important basic concept in default analytics is “exposed to risk” by which we mean risk of going into default unless otherwise specified (one might otherwise be studying risk/propensity of churn, cross-sell etc.)

Abbreviated ETR in this note but AFAIK this isn’t common so won’t be added to the abbreviations list.

Often probabilities are estimated by dividing the number of events that did happen by the number of events that could have happened, and ETR is basically that italicised bit i.e. the denominator of the fraction. The ‘hazards’ and risk PDs of default analytics are just special cases of this situation.

A typical setting is when building an Application PD model: the modelling mart will have some number of accounts that started out at open date (MOB=0), and a certain target OW of (say) 24 months; at the simplest level all the accounts are ETR of going into default within the OW.

However, if account #1 opened only 18 months ago and is still not in default, then although it has been ETR for 18 months, it hasn’t been ETR for 24 months and is not quite the same unit of modelling information as an older account #2 that did survive 24 months. Account #1 has reached the horizon and is said to have been censored. Model builders wouldn’t normally be dealing with these out-of-time (OOT) cases because, knowing that 24 months OW was the target, they would have chosen a sample window (SW) that was at least 24 months before the horizon in its entirety.

But what about account #3 that opened 30 months ago but closed good, i.e. without ever going into default, at MOB=18? Account #3, like account #1, was only ETR for 18 months and is not quite like account #2. There was no way it could have contributed a default event for MOB=19-24 as it was not ETR for 19-24.

That segues into the closed good in vs closed good out discussion AWML but meanwhile opinions and contributions would be welcome from those who have views on the issues. People who study mortality risk have similar issues whereby, for example, they study all individuals for a certain time window. People may emigrate and so be ETR for only a portion of the TW, because one can’t reliably trace their subsequent mortality (survive or die?) in another country. But, you don’t assume they survive (or die); rather you use their information appropriately with respect to their lesser overall ETR.

Because application modelling is longitudinal, the focus is on the first default, so ETR is mostly a matter of the account still being open and not ever having previously been in default. For behavioural modelling which is essentially cross-sectional, there is the additional issue of whether an account is ETR of fresh default or whether it is still included in some previous default episode – link to the re-ageing issue AWML.

There may be subleties in the ETR concept, such as deceased account holders, dormant accounts – are these ETR? Or in a product like reverse mortgage, is there a defaul

t risk at all?