## Currency devaluation

I have written before on aspects of the CMI's new deterministic projection model (some comments I made at a public meeting in January 2011 are available on the right).  One hoped-for goal was that the CMI 2010 model would become a "common currency" for communicating mortality-improvement bases (Working Paper 41, sections 2.1–2.4).

The CMI 2010 model is now being used in company financial statements. A recent example is Prudential's statement about its allowance for future mortality improvements for annuities in the UK:

"The Continuous Mortality Investigation (CMI) model and Core Projection parameters have been reviewed and a custom parameterisation of the CMI model has been made where some aspects of the pattern of convergence from current rates of improvements to long-term rates of improvement have been altered."

Source: Prudential plc's EEV statement of 9th March 2011, page 15, note (b)

Reading this sounds like Prudential is very much aware of the core model's unfortunate behaviour of immediately projecting a sharp reversal of mortality improvements. But what does "custom parameterisation" mean for the reader? The CMI 2010 model has no fewer than 524 parameters for controlling "aspects of the pattern of convergence". This is on top of 262 parameters controlling the component split of the initial rates of improvement, and a further 262 for long-term period and cohort improvements. That makes 1,048 parameters (not counting the 131 base rates and the 2,227 initial rates of improvement, which are also modifiable).

The obvious problem with this situation is that the reader is completely in the dark as to precisely what the improvement assumption actually is. Companies will feel obliged to use the new model, yet users of financial statements have no prospect of comparing bases across companies if there are 1,048 parameters to customise.  In addition, the CMI's model changed between the 2009 and 2010 versions, so it is not even clear how an individual company's improvement basis has changed from one year to the next.  This confusion makes it hard for the CMI's model to function as a "common currency" for communicating mortality-improvement bases.

As it happens there is a solution to this communication problem, and one which still allows actuaries to use any basis they like internally. This is described in an earlier blog on equating bases.  The method is timeless, consistent and free to use.  It makes it easy for users of financial statements to compare bases across companies, and also to track changes across time for the same company.

Assume we have a random variable, $$X$$, with expected value ... Read more