Turning the tables

Traditional actuarial mortality analysis was done by expressing a portfolio's mortality experience relative to a reference mortality table (a so-called A/E analysis).  In modern actuarial work the A/E analysis is supplemented (or even replaced) with a multi-factor statistical model; besides age and gender, common risk factors include pension size, geodemographic profile and early-retirement status.  However, when it comes to communicating results, it is still often necessary to express the result in terms of a reference mortality table.  Ideally this would be the same mortality table as the A/E analysis for comparison.  Another reason for needing a percentage of a reference table is that many pricing and valuation systems can only support mortality rates varying by age and gender.

However, one question in all cases is "which reference mortality table"?  In the UK there are a couple of options:

  1. A mortality table produced by the CMI, or
  2. A mortality table produced by a national statistics office, such as the ONS.

There are pros and cons of each.  CMI mortality tables are created from the experience of particular classes of business, and so are potentially more relevant than population-based tables.  However, CMI tables are no longer freely available, hence the use of "reference table" instead of "published table" in this blog.  CMI tables are also typically somewhat out-of-date — the "latest" S3 pensioner tables have an effective date of 1st January 2013, i.e. almost seven before the time of writing.

In contrast, population tables are public and can be freely downloaded from the website of the relevant national statistics office.  They are available in a variety of options, covering differing constituent parts of the UK and for varying time periods.  The latest national life tables are for 2016–2018, i.e. with an effective year of 2017, so they are considerably more up-to-date than the CMI tables.  And if you are really concerned about being current, there are even single-year life tables, with 2018 being the most recent.  However, national life tables also have drawbacks — they tend to stop at age 100, whereas actuaries working with pensions and annuities need rates up to 120 (say) to close-out their calculations.  National life tables are typically also unsmoothed, so mortality rates can drop from one age to the next.

However, there is a third option available: produce your own mortality tables.  This has the double advantage of (i) being as up-to-date as your experience data, and (ii) of being exactly relevant because they are for the portfolio of interest.  Producing your own mortality tables is far more straightforward than it sounds — in Richards, Kaufhold & Rosenbusch (2013) we showed how this was done for a portfolio of pensioners in German occupational pension schemes.  You also need less data than you think — in Richards (2019) I showed how an eight-factor model could be created for a medium-sized pension scheme with 16,780 lives and 3,488 historic deaths.  When so much can be done with a multi-factor model, producing your own reference table by age and gender is a realistic option for many portfolios.

References

Richards, S. J., Kaufhold, K. and Rosenbusch, S. (2013) Creating portfolio-specific mortality tables — a case study, European Actuarial Journal, Volume 3, Issue 2, pages 295–319, DOI: 10.1007/s13385-013-0076-6.

Richards, S. J. (2019) A Hermite-spline model for post-retirement mortality, Scandinavian Actuarial Journal, DOI: 10.1080/03461238.2019.1642239.

 

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Stephen Richards
Stephen Richards is the Managing Director of Longevitas
Table generation in Longevitas
Longevitas automatically generates rate tables corresponding to each fitted model.  Alternatively, for complicated models, Longevitas can also generate a rate table for each life in the portfolio.  These individual-member rate tables are specific to the exact age and risk combination of each life.