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The Actuary The magazine of the Institute & Faculty of Actuaries
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Understanding pensioner longevity

The topic of pensioner longevity has
dramatically increased in significance
in recent years. At the same
time as FRS17 disclosed large deficits
in corporate pension schemes, a slew of new
insurers in the UK has increased the market
capacity for bulk buyouts. It has never been
more important to understand differentials in
pensioner longevity. Fortunately there have
been great advances in the techniques and
resources available to actuaries advising on pensioner
liabilities.
On the one hand, profiling tools from
consumer-database companies have greatly
enhanced companies’ ability to understand
who their pensioners and annuitants are and
what characteristics they have. On the other
hand, the move to using advanced statistical
models enables actuaries to get more out of
their data than ever before. This article shows
how the two combine to give a more detailed
picture of pensioner longevity.
About the data
The data used in this article comprised around
a quarter of a million life-office pensioners,
including both holders of individual annuities
and pensioners from bulk-purchase annuities
(bulk buyouts). Using a commercially available
profiling tool from Experian, the pensioners
were classified for their mortality group using
their addresses. The tool was able to identify the
mortality group for 78% of pensioners, as
shown in table 1.
In addition to profiling for mortality group,
the same tool is also able to profile for likely
marital status. This is important for the pricing
and valuation of spouses’ benefits in final-salary
schemes, and is therefore useful to insurers in
the bulk buyout market.
Table 2 shows that the tool was able to classify
67.0% of cases according to likely marital
status. The remaining lives split into 1.6% of
pensioners who were matched by the profiling
tool but whose marital status could not be modelled,
and also 31.3% of pensioners who were
not matched at all due to incomplete name or
address details.
The total proportion of unknown and
unmatched marital statuses (32.9%) is larger
than the number of unknown socio-economic
groups (21.3%). This is because the latter can
also be driven by postcode: where a household
is not matched by the tool, a socio-economic
group can still be assigned using the dominant
group for the postcode.
Methodology
Many life offices use generalised linear models
(GLMs) to analyse pensioner mortality. However,
GLMs have a number of drawbacks, chief
of which is their inefficient use of available data
and the restricted ability to model only a single
year’s data. As a result some life offices are
switching to a more powerful set of techniques,
called survival models. Survival models make
better use of available data, and they are preferable
to GLMs in most circumstances as a result.
A survival model can be defined very simply.
In this example, each life i is observed alive at
1 January 2005 at exact age xi, and survives ti
years. We distinguish between deaths and survivors
using an indicator variable, di, which
takes the value of 1 on death and 0 on survival.
The probability that life aged x survives t years
is tpx, while the force of mortality at age x + t is
denoted ?x + t . The likelihood function for a survival
model is as follows:
L ??
n
i =1
t i pxi ?di
xi
+ ti
where n is the number of lives, ?ti is the total
time lived, and ?di is the number of deaths. ?ti
is known to actuaries as the ‘central exposed to
risk’, whereas it is called the ‘waiting time’ in
survival modelling. All that remains is to define
tpx and ?x. In this case, we use a simple Gompertz
model for the force of mortality, namely:
?x = e?+?x
where the values of ? and ? will be built up individually
from risk components for each life i.
We also use the general result linking the force
of mortality to the survival probability:
tpx = exp ( ?t
0
?x + s ds)
where the integral is called the integrated hazard
function. Fortunately there is software available
to do all the calculations for us (we have used
the Longevitas system here, which can fit survival
models and GLMs, as well as other models).
Results for socio-economic group
As expected, the model produced parameters
for age and gender with the highest level of
significance. In socio-economic group 1 the
model life expectancy at age 65 of a female was
25.1 years, whereas for an equivalent male in
the same group it was 23.1 years. Also, as
expected, the model produced wide socioeconomic
differentials, as shown in table 3. A single male aged 65 in socio-economic group 1
had a life expectancy of 23.1 years, while a similar
single male in group 4 could expect to live
21.8 years. A male in group 7 could expect to
live just 20.6 years.
It is instructive to express these differentials
in terms of the pricing assumption a life office
might use for an annuity or bulk buyout. To do
this we can use the ready reckoner on p54 of
the SIAS paper ‘Financial aspects of longevity
risk’.(1) The difference between the life expectancies
of socio-economic groups 1 and 4 is
1.3 years, and this equates to more than a 1%
difference in interest rate under current investment
conditions. Since a life office pricing margin
is typically much less than 1%, not knowing
the socio-economic profile of an annuity portfolio
could be fatal to profitability.
Results for marital status
Population studies have repeatedly shown that
married people have longer life expectancies
than unmarried people. However, there is a correlation
with socio-economic group: the better
off a person is, the more likely they are to be married.
Thus the population observation of longer
life expectancy for married people might simply
be because married people as a group contain
disproportionately more better-off people. In
this example we have already controlled for
socio-economic group explicitly, so we can fit
and test marital status as a predictor of longevity.
Intriguingly, marital status does still prove to be
a significant rating factor for mortality as well,
albeit not as strong as socio-economic group.
Table 4 shows the impact of marital status on
the life expectancy and mortality of males in
the middle socio-economic group.
The difference in life expectancy between
single and married people is around two
months for males in group 4, which roughly
equates to a 0.07%, or seven basis points (bps),
change in interest rate. While this does not
sound like much, 7 bps is a significant proportion
of a typical bulk buyout pricing margin,
which might be around 5070 bps at the time
of writing. However, this understates the importance
of marital status in bulk annuity pricing:
as married people are more likely to be drawn
from the better off, their financial weighting in
a scheme may be more significant than the
above analysis implies.
A final word is necessary about the dramatically
shorter life expectancy of those annuitants
who were unmatched for marital status. One
possibility could be due to the age profile of the
unmatched group: if they were substantially
older and from an earlier birth cohort, they
might have heavier mortality for that reason.
However, table 2 shows that there is no obvious
material difference between the marital statuses
with regard to age. Another possible source of
difference is that the matching process depends
on having full name and address: without
either, a pensioner cannot be profiled for marital
status. We note, however, that there are two
kinds of bulk buyout: those that are individual
policies held by named members (individual
buyout), and those that are a single policy held
by the scheme (group buyout). In the latter case
the individual member’s details may not be
known to the life office as all correspondence
and administration is with the scheme, not the
member. Thus, the short life expectancy of the
unmatched marital status may be because of the
more downmarket socio-economic profile of
this office’s group buyout business.
Improved efficiency
The advent of new profiling services enables
actuaries to gain richer detail on the mortality
differentials among pensioners and annuitants.
More powerful survival models can circumvent
the inefficiencies and limitations of traditional
GLMs. With these new tools for both data
profiling and data modelling, actuaries can now
apply greater rigour to the pricing and reserving
of annuities and bulk buyouts.

Reference
(1) Richards SJ and Jones GL (2004) ‘Financial
aspects of longevity risk’, SIAS.

Table 1 Breakdown by mortality
group
Proportion of:
Mortality Lives Deaths Exposure
group (%) (%) (%)
1 19.0 13.8 19.0
2 25.7 20.9 25.8
3 13.9 12.4 14.0
4 5.4 4.7 5.4
5 5.1 6.2 5.0
6 7.2 8.6 7.2
7 2.5 3.0 2.4
Unknown 21.3 30.3 21.2
Total 100.1 99.9 100.0

Table 2 Breakdown by likely marital status
Proportion of:
Marital status Mean age Lives Deaths Exposure
(%) (%) (%)
Married 69.7 41.1 24.0 41.4
Single 71.9 25.9 23.9 26.0
Unknown 70.6 1.6 1.5 1.6
Unmatched 72.3 31.3 50.6 30.9
All 71.1 99.9 100.0 99.9

Table 3 Mortality for social groups
(single males aged 65)
Force of mortality:
Social e65 (i) 1000 ?65 (ii) as %
group group 1
1 23.1 3.64 100
4 21.8 6.10 168
7 20.6 9.35 257


Table 4 Mortality by marital status
(males aged 65 in group 4)
Force of mortality:
Marital e65 (i) 1000 ?65 (ii) as %
status married
value
Married 21.9 4.94 100
Single 21.8 6.10 124
Unmatched 16.3 14.26 289

07_11_26-27.pdf