Self-prophesying models

A phenomenon to watch for is that of the "self-prophesying model".  It occurs when a variable is too specific to the mortality experience of a reference portfolio to have wider application.  It has been claimed that the risk of this increases for smaller data sets and more lifestyle categories. In fact, the error is actually most likely where there is a small number of lives in each sub-group prior to grouping.  This is simply because the impact of random variation is largest in very small groups.

As an illustration of this, consider the apparently reasonable alternative of using postcode sector instead of a geodemographic type.  The postcode sector is basically everything except the last two characters of a UK postcode, so EH11 2 is the postcode sector for our full postcode EH11 2AS.  Postcode sectors are free, so they appear to have a cost advantage over geodemographic types, which require a licence from a third-party provider.

However, this cost "advantage" is wholly illusory.  Using a medium-sized annuity portfolio, we found that the median number of lives per Mosaic type code was 3,950.  This is unlikely to result in a self-prophesying model, as random fluctuations will not be unduly influential for such large numbers of lives.  The same cannot be said for a model based on postcode sector: for the same data set, the median number of lives per sector was just 4.  Any model based on postcode sector will therefore suffer from being a self-prophesying model, and will be inapplicable to other portfolios as a result.  Indeed, such a model will not even be applicable to the same portfolio in the near future.