HWSAS, Heriot-Watt University, Edinburgh
The measure of mortality
Stephen Richards
8th March 2016
Copyright c Longevitas Ltd. All rights reserved. This presentation may be freely distributed, provided it is unaltered and has this
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Overview
1. About the speaker
2. Risk factors
3. Why longevity risk is different
4. Model risk
5. Conclusions
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1 About the speaker
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1 About the speaker
Independent consultant on longevity risk since
2005.
Founded longevity-related software businesses in
2006:
Joint development with Heriot-Watt University in
2009:
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1 Connection to Heriot-Watt
Graduated twice from Heriot-Watt: 1990 and 2012.
Honorary Research Fellow
Longevitas sponsors prize for survival models.
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2 Risk factors
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2 Risk factors
Mortality by age. Richards et al. (2013).
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2 Risk factors
Mortality by health at retirement. Richards et al. (2013).
log(crude mortality hazard)
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Normal age retirements
Ill−health early retirements
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Age
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2 Risk factors
Survival curves for males and females. Richards et al. (2013).
Kaplan−Meier survival curve
1.0
0.8
0.6
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Females
Males
0.0
60
70
80
90
100
Age
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2 Risk factors
Survival curves by pension size (males only). Richards et al.
(2013).
Kaplan−Meier survival curve
1.0
0.8
0.6
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Highest income (size band 3)
Lowest income (size band 1)
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100
Age
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2 What factors can you use?
Pricing.
Risk management and reserving.
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2 Pricing
The following cannot be used in pricing individual
insurance benefits:
Gender.
Race or ethnicity.
Sexual orientation (including gender reassignment).
Religion or belief.
Pregnancy or maternity status.
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2 Risk management
However. . .
. . . regulators still expect insurers to use gender in risk
management and reserving.
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2 Impact of risk factors I
UK annuitants from Richards and Jones (2004):
Risk
factor
Change
Base case
Gender
Lifestyle
Duration
Pension size
Region
Female→male
Top→bottom
Short→long
Largest→smallest
South→North
Overall
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Annuity
factor
13.39
12.14
10.94
9.88
9.36
8.90
Relative
change
-9.3%
-9.9%
-9.7%
-5.2%
-4.9%
-33.6%
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2 Impact of risk factors II
German pensioners from Richards et al. (2013):
Risk
factor
Change
Base case
Gender
Retirement health
Pension size
Region
Employer type
Female→male
Normal→ill-health
Largest→smallest
B→P
Private→public
Overall
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Annuity
factor
16.11
14.53
12.97
11.72
11.02
10.60
Relative
change
-9.8%
-10.7%
-9.7%
-5.9%
-3.9%
-34.2%
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2 Impact of risk factors
Different portfolios have different risk factors
available.
Important to use risk factors relevant to your
business processes.
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2 Risk factors: lifestyle
Q. What was “Lifestyle” for the UK annuitants?
A. Profile based on the annuitant’s address or
postcode. . .
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2 Digression: UK postcodes
UK has a hierarchical postcode structure.
Each piece of postcode narrows in on a
geographical area.
Hierarchical postcodes in UK, USA, Canada and
the Netherlands.
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2 Digression: UK postcodes
Anatomy of a UK postcode
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2 Digression: UK postcodes
Compare the postcodes EH4 4SP and EH3 6BX.
Both in Edinburgh.
Life expectancy “1.1 years less than the UK
average”1
1 Punter Southall, Postcode Life Expectancy Tool, accessed on 5th May 2015.
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2 Digression: UK postcodes
EH4 4SP. Source: Google Maps, accessed 5th May 2015.
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2 Digression: UK postcodes
EH3 6BX. Source: Google Maps, accessed 5th May 2015.
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2 Digression: UK postcodes
There are around 1.7 million residential postcodes.
We can’t use Google Maps every time
Solution is to map each postcode to a
geodemographic type code. . .
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2 Digression: UK postcodes
Mosaic family tree
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2 Digression: UK postcodes
EH4 4SP → K46 Municipal Challenge, High-Rise
Residents.
EH3 6BX → A01 City Prosperity, World-Class
Wealth.
1.7 million residential postcodes become 67
lifestyle codes.
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2 Geodemographic profiling
Works in:
UK.
USA.
Canada.
The Netherlands.
Does not appear to work in France.
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3 Why longevity risk is different
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3 Why longevity risk is different
Opposing interests.
Time frame over which risk operates.
Limited information.
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3.1 Opposing interests
Life insurance: neither side wants insured event to
occur.
Longevity insurance: pensioner wants exact
opposite of what the insurer wants.
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3.1 Opposing interests
Pensioners, their relatives, their doctors, medical
science and government are all working to reduce
the risk of death and increase longevity.
Insurers hope their pricing assumptions are
adequate.
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3.2 Time frame
“Whereas a catastrophe can occur in an
instant, longevity risk takes decades to unfold”
The Economist
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(2012)
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3.2 Time frame
Mortality shocks are easy to spot.
Longevity shocks much less so. . .
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3.2 1918 influenza pandemic
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3.2 1918 influenza pandemic
m̂ x,1918 /m̂ x,1917 for Swedish males, HMD data2 .
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2 m̂ is the estimated central death rate at age x last birthday.
x
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3.2 When does a trend change?
m̂ 70 for Swedish males, HMD data.
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3.2 Time frame
Can only detect a trend change several years after
it has already started. . .
Longevity risk not a natural fit to “1:200 over one
year” approach.
Run-off is the appropriate way to view this risk. . .
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3.3 Limited information
“As there is not currently a deep and liquid
market for longevity risk, firms are required to
derive their longevity assumptions from first
principles”
Bank of England
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Prudential Regulatory
Authority (2015)
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3 Market forecast for interest
Yield curve for UK non-index-linked gilts without accrued interest
(DMO data for 2015-04-16).
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3 Market forecast for inflation
Yield curve for UK index-linked gilts (DMO data for 2015-04-16).
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3.3 Limited information
Market forecasts exist for economic variables on a
near-daily basis.
There is no market forecast for mortality rates or
longevity.
Population mortality data published once a year.
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3.3 Limited information
Without a “deep and liquid market” to provide
market views, benchmarking projections is tricky.
Longevity-related assumptions can be seen as a
malleable item in reserving.
Pressure to back-solve longevity assumptions from a
given level of capital, rather than the other way
around.
Greatest risk of back-solving lies in models with
lots of subjective assumptions.
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4 Model risk
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4 Model risk
Many options available for mortality projections:
Deterministic scenarios v. stochastic models.
All-cause mortality v. cause-of-death.
Targeting methods v. extrapolation.
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4 Model risk
Different models produce different capital
requirements. . .
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4 Model risk
Stressed−trend 99.5% capital requirement
Run-off capital requirements by age for four stochastic models.
Source: Richards et al. (2014).
7%
6%
5%
4%
Lee−Carter (1992)
Cairns−Blake−Dowd (2006)
Age−Period−Cohort
2D age−period (2004)
3%
55
60
65
70
75
80
85
90
Age
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4 Model risk
The best way to deal with model risk is to not rely
on a single model.
The PRA itself works with:
“four commonly used families of
stochastic longevity risk models”
Bank of England Prudential
Regulatory Authority (2015)
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4 Expert judgement
“The advantage of expert opinion is the
incorporation of demographic, epidemiological
and other relevant knowledge, at least in a
qualitative way. . .”
Booth and Tickle (2008)
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4 Expert judgement
“. . .The disadvantage is its subjectivity and
potential for bias. The conservativeness of
expert opinion with respect to mortality decline
is widespread, in that experts have generally
been unwilling to envisage the long-term
continuation of trends, often based on beliefs
about limits to life expectancy.”
Booth and Tickle (2008)
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4.2 Cause-of-death models
Considerable technical challenges discussed by
Continuous Mortality Investigation (2004).
Drawbacks discussed by Richards (2010)3.
3 More details at
www.longevitas.co.uk
www.longevitas.co.uk/site/informationmatrix/?tag=cause+of+death
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4.2 Cause-of-death models
UK PRA did not use any cause-of-death models:
“due to their greater complexity, data
requirements and the need for a greater level of
expert judgement to be exercised. In particular
we were concerned that the correlations
between causes of death were not easily
measured and would not be stable over time”
Bank of England Prudential Regulatory
Authority (2015)
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4.2 Correlated causes of death?
Mortality rates due to influenza and CHD. Source: Massachusetts
Department of Public Health Registry of Vital Records and
Statistics.
700
CHD mortality rate
Influenza mortality rate
Rate per 100,000
600
500
400
300
200
100
0
1850
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1900
1950
Year
2000
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4.2 Cause-of-death models
Cause-of-death models often structured with a few
broad “independent” categories.
This is at best a simplifying assumption.
At its worst, it ignores important correlations.
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5 Conclusions
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5 Conclusions
Insurers constrained in what risk factors they can
use in pricing.
Longevity risk has unique features compared to
other demographic risks.
Model risk handled by using multiple models.
Stick to openly published models in peer-reviewed
journals.
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References I
Bank of England Prudential Regulatory Authority
(2015, March). Solvency II: matching adjustment
update. Letter to UK-regulated insurers and
reinsurers.
Booth, H. and L. Tickle (2008). Mortality modelling
and forecasting: a review of methods. Annals of
Actuarial Science 3(I/II), 3–44.
Continuous Mortality Investigation (2004). Projecting
future mortality: A discussion paper. Continuous
Mortality Investigation.
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References II
Richards, S. J. (2010). Selected issues in modelling
mortality by cause and in small populations. British
Actuarial Journal 15 (supplement), 267–283.
Richards, S. J., I. D. Currie, and G. P. Ritchie (2014).
A value-at-risk framework for longevity trend risk.
British Actuarial Journal 19 (1), 116–167.
Richards, S. J. and G. L. Jones (2004). Financial
aspects of longevity risk. Staple Inn Actuarial Society
(SIAS), London.
Richards, S. J., K. Kaufhold, and S. Rosenbusch (2013).
Creating portfolio-specific mortality tables: a case
study. European Actuarial Journal 3 (2), 295–319.
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References III
The Economist (2012). The ferment of finance. Special
report on financial innovation February 25th 2012, 8.
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