Turning the tables

(Nov 8, 2019)

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…

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Tags: A/E, standard table

Spotting quality issues with limited data

(Mar 10, 2014)

In an earlier posting I showed how to use the Kaplan-Meier function to identify subtle data problems.  However, what can you do when you don't have the detailed information to build a full survival curve?  In a recent consulting engagement we were only provided with crude aggregate mortality rates for five-year age bands. This is a nuisance, because such summarisation loses important details in the data.

We had a strong suspicion that the data were of poor quality, and that the problem once again lay with the male-female mortality differential.  We therefore calculated the survival rates for males and females in five-year intervals for the portfolio in question and compared the survival differential with…

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Tags: data validation, survival rates, standard table

Tables turned

(Nov 9, 2010)

Two years ago I asked the question whether we needed standard tables any more.  The question arose because most life offices and even many pension schemes have enough mortality-experience data to create their own portfolio-specific models.  Since these models can allow for more risk factors than just age and gender, and can allow for portfolio-specific variation by age, they are typically superior to standard tables.

However, I recently came across a rather rarified example where standard tables could still play a useful role.  The scenario in question involved a portfolio where retirals had only relatively recently been permitted into the fund.  The volume of data was respectable enough to create bespoke…

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Tags: standard table

Personal Standards

(Nov 30, 2009)

Love them or loathe them, actuaries cannot get by without standard tables in some shape or form. Even when performing analysis of your own experience data to avoid basis risk, standard tables are often used as a kind of lingua franca between parties, a convenient way to express approximate results in a way everyone can understand.

The use of standard tables in experience analysis brings its own issues of course: Mortality moves on after a table is published, and even those that are not too outdated may still be innappropriate for the population under study. In any case the rates from a standard table will often require significant transformation in order to achieve something vaguely similar to your actual experience.…

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Tags: technology, standard table

Table talk

(Dec 18, 2008)

When valuing a portfolio, an actuary must often make a decision as to what tables to use for the risk.  The ideal is to use tables which have been created from the portfolio's own experience, preferably using a statistical model to account for the various risk factors.  It is even possible to generate an individual mortality table or survival curve for each member of the portfolio.

Not every portfolio is large enough to warrant such an approach, of course, and the actuary will have to fall back on some kind of standard table.  But how to pick which one?  In theory, it doesn't matter much which table is used due to the equivalent-reserve calculation described in the SIAS paper, "Financial aspects of longevity…

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Tags: standard table

Do we need standard tables any more?

(Nov 1, 2008)

Actuaries are long used to using standard tables. In the UK these are created by the Continuous Mortality Investigation Bureau (CMIB), and the use of certain tables is often prescribed in legislation. As actuaries increasingly move to using statistical models for mortality, it is perhaps natural that they should first consider incorporating standard tables into these models. But are standard tables necessary, or even useful, in such a context?

Although we normally prefer to model the force of mortality, here we will use a model for the rate of mortality, qx, since this is how many actuaries still approach mortality. Our model is actually a generalised linear model (GLM) where the rate of mortality is:


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Tags: standard table, GLM, survival models

New SAPS tables

(Nov 1, 2008)

On 31st October 2008 the CMIB published the new SAPS S1 mortality tables based on the mortality of defined-benefit pension schemes. These tables follow the previous release of the '00 Series' mortality tables based on the mortality of life-office pensioners.  It is instructive to compare the life expectancies under the two series.

One drawback is that there are rather a lot of tables in the S1 series: ten in total.  We will use the so-called amounts tables, i.e. mortality as weighted by the size of the annual pension, as this gives a better indication of the financial importance. The life expectancies below are calculated using the S1PMA and S1PFA tables from SAPS S1, and the slightly older PCA00 table.

  PCA00 S1PA Change

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Tags: standard table

Degrees of freedom

(Sep 16, 2008)

In an earlier post questioning whether we still need standard tables, we used the AIC to choose between models.  For the AIC we assign a "cost" to the inclusion of extra parameters, and I had counted each mortality rate actually used in the model-fitting as a parameter.  However, there is no set approach for this, and there are a number of arguable positions which could be taken:

  1. Count each mortality rate in the table as a parameter.  This would arise because the selection of the table is supposed to be done before fitting any model.  However, it seems harsh to count rates which are not actually used.
  2. Count each mortality rate actually used as a parameter.  This is my preferred approach, but the rates themselves…

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Tags: degrees of freedom, AIC, standard table

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