Modelling Annuitant Mortality:
UK v. France
Hélène Queau and Stephen Richards
Copyright © UMR and Stephen Richards Consulting Ltd
Overview
1.
2.
3.
4.
5.
6.
Regional variation in France.
Modelling regional mortality with UMR data.
Socio-economic group in UK.
Annuitant longevity in UK.
Does UK-style analysis work for UMR data?
Conclusions and questions.
1. Regional variation in France
Region
Figures are
period life
expectancies in
2007.
Rhône-Alpes
Midi-Pyrénées
Poitou-Charentes
Île-de-France
Pays de la Loire
Corse
Aquitaine
Centre
Provence-Alpes-Côte d'Azur
Languedoc-Roussillon
Limousin
Franche-Comté
Bourgogne
Basse-Normandie
Alsace
Auvergne
Bretagne
Haute-Normandie
Champagne-Ardenne
Lorraine
Picardie
Nord-Pas-de-Calais
Female life expectancy Difference
85.2
85.0
85.0
84.9
84.9
84.8
84.7
84.6
84.6
84.5
84.5
84.4
84.3
84.2
84.0
83.9
83.8
83.6
83.5
83.1
82.4
82.2
0.3
0.1
0.1
0.0
0.0
-0.1
-0.2
-0.3
-0.3
-0.4
-0.4
-0.5
-0.6
-0.7
-0.9
-1.0
-1.1
-1.3
-1.4
-1.8
-2.5
-2.7
Sources : Insee, État-civil (données domiciliées), estimations localisées de population.
1. Regional variation in France
•
•
Do UMR annuitants have these same
differentials?
The answer lies in building a statistical
model and fitting it to some experience
data…
2. Modelling mortality
Mortality model
•
•
•
Survival model for force of mortality, x.
16 models considered (Richards, 2010).
Best-fitting model is Makeham-Perks:
•
α, β and ε are estimated from the data.
2. UMR portfolio data
•
•
•
•
•
Mainly educational professionals.
130,468 records of anuitants over age 60.
582,922 life-years of exposure.
8,949 deaths.
99.2% of annuitants have French address.
2. Region
•
•
•
24 regions, including overseas territories
and foreign addresses.
Île-de-France has most annuitants, so treat
this as the baseline to measure against.
On average one department will appear
significantly different just by chance: (241)*5%=1.15.
2. Region as risk factor in UMR
Source: UMR and Longevitas Ltd. Île-de-France is the baseline and the parameter for this is implicitly zero.
Other parameters — such as Age, Gender and Time — are not shown for reasons of space.
2. Regional variation in UMR data
•
•
•
1 region has significantly lighter mortality:
Provence-Alpes-Côte d'Azur.
3 regions have significantly heavier
mortality: Lorraine, Pays de la Loire, and
Picardie.
4 significant differences v. 1.15 expected.
2. Regional variation
•
•
•
Results for Lorraine and Picardie match
population data.
Can we do better than using region?
What about using socio-economic group?
3. Socio-economic group
3. Socio-economic group in UK
•
•
Socio-economic status determined by
occupation.
Significant variation in life expectancy…
Source: ONS data from longitudinal study on population data.
3. Socio-economic group
•
•
•
•
Socio-economic status determined by
occupation.
Occupation often not available or reliable.
Question: How to include in annuity pricing?
Answer: Use variables which are correlated
with socioeconomic group or replace it.
3. Socio-economic group
•
Two possible replacements:
1. Pension size, i.e. indicator of wealth and
income.
2. Geodemographic type, i.e. a direct profile of
lifestyle based on location.
3. Geodemographic profile
•
•
•
•
Grouping of people with shared
characteristics.
Based on address or postcode …
…using information about the people who
live there (housing type, car ownership etc)
In the UK this is based on postcode …
3. Structure of a UK postcode
3. Postcodes
•
•
•
•
•
Each postcode covers 15–17 households
1.7 million postcodes in UK
Too many to use directly!
Use geodemographic type
Example: Mosaic from Experian
3. Mosaic classification
4. Annuitant mortality in UK
4. Annuitant mortality in UK
•
Richards & Jones (2004) found several risk
factors:
•
•
•
•
•
•
Age
Gender
Pension size
Postcode
Duration since retirement
Region
Source: Richards and Jones (2004) using life-company annuitant mortality experience.
Importance of socio-economic group
Factor
Step change
Gender
Female→male
Reserve
change
-11.5%
Lifestyle
Top→bottom
-11.4%
Duration
Short→long
-10.8%
Income
High→low
-5.9%
Region
South→North
-5.9%
Source: Richards and Jones (2004) “Financial aspects of longevity risk”, SIAS, p39
4. Annuitant mortality in UK
•
Postcodes have been confirmed as risk
factors in other works: Richards (2008) and
Madrigal et al (2009).
5. Does this apply to UMR data?
5. UMR log(mortality) by age
Source: UMR and Longevitas Ltd
5. log(mortality) by age and gender
Source: UMR and Longevitas Ltd
5. UMR mortality by pension size
Source: UMR and Longevitas Ltd. Crude mortality rate per decile with 1 being smallest 10% of
pensions and 10 being the 10% with the largest pensions.
5. Risk factors for UMR annuitants
•
As in the UK, the following are risk factors:
1. Age
2. Gender
3. Pension size
•
But not geodemographic type!
5. Geodemographics in France
•
•
•
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Geodemographic type based on Îlot.
An Îlot covers around 90 households in
Paris…
…but can cover an entire town or village in
rural areas (commune).
A UK postcode covers 15–17 households.
5. Geodemographics and UMR data
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•
•
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54 geodemographic types.
Expect two or three to appear significant by
chance: (54-1)*5%=2.65.
F25 has largest exposure time, so make this
the baseline.
Only two geodemographic types have
significantly different mortality.
5. Why is geodemographic type not
significant here?
•
Some possibilities:
1. UK postcode has finer granularity than French
Îlot.
2. UMR portfolio is homogeneous with respect to
occupation: educational professionals.
3. France is more egalitarian than the UK.
6. Conclusions and questions
1. Pension size a significant rating factor, but
not as strong as in UK.
2. Geodemographic type not significant for
UMR data.
3. Copies of papers available from Stephen (in
English, sorry!)
References
MADRIGAL ET AL 2009 What longevity predictors should be
allowed for when valuing pension-scheme liabilities?,
British Actuarial Journal (to appear).
RICHARDS, S. J. AND JONES, G. L. 2004 Financial aspects of
longevity risk, SIAS.
RICHARDS, S. J. 2008 Applying survival models to pensioner
mortality data, British Actuarial Journal, Vol 14, Part II, No.
61.
RICHARDS, S. J. 2010 A handbook of parametric survival
models for actuarial use, Scandinavian Actuarial Journal
(to appear).