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15 April 2023 2
Disclaimer
The following presentation is for general information, education and discussion purposes only.
Views or opinions expressed, whether oral or in writing do not necessarily reflect those of PartnerRe nor do they constitute legal or professional advice.
15 April 2023 4
Artifact (or should it be Artefact?)
“an unintentional pattern in data, arising from processes
of collection and management”
© Fotolia.com
15 April 2023 5
Where have all the men gone?
© Fotolia.comhttp://news.bbc.co.uk/2/hi/uk_news/magazine/3601493.stm
15 April 2023 6
Discussion Topics
• Projection Basics
• Smoothing
• Basis Risk
• Migration Impact
• International Comparison
• External Factors and Volatility
Progr
ess
Comm
unity
Sessio
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eetin
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Educa
tion
Wor
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parti
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Volunt
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Resea
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Shapin
g th
e fu
ture
Networ
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Profe
ssion
al su
ppor
t
Enter
prise
and
risk
Lear
ned
socie
ty
Oppor
tunit
y
Inte
rnat
ional
prof
ile
Jour
nals
Suppo
rting
Exper
tise
Spons
orsh
ip
Thoug
ht le
ader
ship
15 April 2023
Mortality Projections 101
15 April 2023 11
Heat Map
20
24
28
32
36
40
44
48
52
56
60
64
68
72
76
80
84
88
92
96
100
1991 2001 2011 2021 2031 2041 2051 2061
4.75%-5.25%4.25%-4.75%3.75%-4.25%3.25%-3.75%2.75%-3.25%2.25%-2.75%1.75%-2.25%1.25%-1.75%0.75%-1.25%0.25%-0.75%-0.25%-0.25%-0.75%--0.25%-1.25%--0.75%-1.75%--1.25%
ProjectedActual
Source: CMI 2013
15 April 2023 12
Heat Map
20
24
28
32
36
40
44
48
52
56
60
64
68
72
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80
84
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92
96
100
1991 2001 2011 2021 2031 2041 2051 2061
4.75%-5.25%4.25%-4.75%3.75%-4.25%3.25%-3.75%2.75%-3.25%2.25%-2.75%1.75%-2.25%1.25%-1.75%0.75%-1.25%0.25%-0.75%-0.25%-0.25%-0.75%--0.25%-1.25%--0.75%-1.75%--1.25%
ProjectedActual
Source: CMI 2013
Cohort Effect
15 April 2023 13
Heat Map
20
24
28
32
36
40
44
48
52
56
60
64
68
72
76
80
84
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92
96
100
1991 2001 2011 2021 2031 2041 2051 2061
4.75%-5.25%4.25%-4.75%3.75%-4.25%3.25%-3.75%2.75%-3.25%2.25%-2.75%1.75%-2.25%1.25%-1.75%0.75%-1.25%0.25%-0.75%-0.25%-0.25%-0.75%--0.25%-1.25%--0.75%-1.75%--1.25%
ProjectedActual
Source: CMI 2013
Cohort Effect
PeriodEffect
15 April 2023 16
Potential Complications
What assumptions are we making here?
)1,(),(5.0
21
txPtxP
x, tPE(x,t)
Progr
ess
Comm
unity
Sessio
nal M
eetin
gs
Educa
tion
Wor
king
parti
es
Volunt
eerin
g
Resea
rch
Shapin
g th
e fu
ture
Networ
king
Profe
ssion
al su
ppor
t
Enter
prise
and
risk
Lear
ned
socie
ty
Oppor
tunit
y
Inte
rnat
ional
prof
ile
Jour
nals
Suppo
rting
Exper
tise
Spons
orsh
ip
Thoug
ht le
ader
ship
15 April 2023
To Smooth or not to Smooth?
15 April 2023 19
Russia Smoothed
Source of Data: Human Mortality Database. University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). Available at www.mortality.org or www.humanmortality.de.
PartnerRe Own Calculations
15 April 2023 20
Russia Smoothed
Source of Data: Human Mortality Database. University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). Available at www.mortality.org or www.humanmortality.de.
PartnerRe Own Calculations
15 April 2023 24
UK – No Smoothing
See Andrew Cairns’ talk and paper for more on this
Source: HMD (own calculations)
15 April 2023 25
Longevity Portfolio
• Over 1 million lives
• Gender differentiated
• Full date of birth available
How are dates of birth distributed?
15 April 2023 29
Longevity Portfolio
Source: PartnerRe
First World War Ends
Nov 11, 1918
Second World War Ends Sep
2, 1945
15 April 2023 31
Longevity Portfolio
Source: PartnerRe
First World War Ends
Nov 11, 1918
Second World War Ends Sep
2, 1945
15 April 2023 32
Longevity Portfolio
Source: PartnerRe
First World War Ends
Nov 11, 1918
Second World War Ends Sep
2, 1945
Downwards trend???
Progr
ess
Comm
unity
Sessio
nal M
eetin
gs
Educa
tion
Wor
king
parti
es
Volunt
eerin
g
Resea
rch
Shapin
g th
e fu
ture
Networ
king
Profe
ssion
al su
ppor
t
Enter
prise
and
risk
Lear
ned
socie
ty
Oppor
tunit
y
Inte
rnat
ional
prof
ile
Jour
nals
Suppo
rting
Exper
tise
Spons
orsh
ip
Thoug
ht le
ader
ship
15 April 2023
Basis Risk
15 April 2023 40
U.S. Example
• Consider data from the Centers for Disease Control and Prevention (CDC)
• Gender differentiated
• Individual Age
• Calendar Years 1999 – 2011
• … also includes ethnic origin
15 April 2023 47
U.S. Example
Source: CDC - Accessed Oct 2014
~ 2.5% p.a
~ 2.2% p.a~ 1.5% p.a
~ 1.1% p.a
Progr
ess
Comm
unity
Sessio
nal M
eetin
gs
Educa
tion
Wor
king
parti
es
Volunt
eerin
g
Resea
rch
Shapin
g th
e fu
ture
Networ
king
Profe
ssion
al su
ppor
t
Enter
prise
and
risk
Lear
ned
socie
ty
Oppor
tunit
y
Inte
rnat
ional
prof
ile
Jour
nals
Suppo
rting
Exper
tise
Spons
orsh
ip
Thoug
ht le
ader
ship
15 April 2023
Migrations
15 April 2023 50
2 Populations
Cat LandNo mortality improvement
Dog LandNo mortality improvement
© Fotolia.com
15 April 2023 51
2 Populations
Cat LandNo mortality improvement
Dog LandNo mortality improvementq(x) is 900% of that in Cat Land
© Fotolia.com
15 April 2023 52
Example 1
• Residents of Dog Land migrate to Cat Land
• 1% population growth – Per annum
– Over 4 years
– Over the age range 30 – 50
• Dogs don’t trend to local mortality experience
15 April 2023 59
Example 2
• Residents of Dog Land migrate to Cat Land
• 1% population growth – Per annum
– Over 4 years
– Over the age range 30 – 50
• Dogs take on cat characteristics over 10 years
15 April 2023 67
Low Immigrant Mortality or Data Artifact?
• Low mortality for most immigrant groups compared to natives in the host country1
• Often attributed to beneficial health selection processes
• Could it be data artifacts?
• Explored in recent paper by Wallace and Kulu2
1NZ - Hajat et al., 2010, U.S. - Abraido-Lanza et al., 1999; Palloni and Arias, 20042Wallace and Kulu, 2014
15 April 2023 68
Potential Data Artifacts
Misreporting of Age
Misclassifying Nationality
Emigrations under-
registered
Deaths undercounted
Mobility Bias
15 April 2023 69
Potential Data Artifacts
Misreporting of Age
Misclassifying Nationality
Emigrations under-
registered
Deaths undercounted
Mobility Bias
“This study supports low mortality among immigrants … results are not a
data artefact.” (Wallace and Kulu)
Progr
ess
Comm
unity
Sessio
nal M
eetin
gs
Educa
tion
Wor
king
parti
es
Volunt
eerin
g
Resea
rch
Shapin
g th
e fu
ture
Networ
king
Profe
ssion
al su
ppor
t
Enter
prise
and
risk
Lear
ned
socie
ty
Oppor
tunit
y
Inte
rnat
ional
prof
ile
Jour
nals
Suppo
rting
Exper
tise
Spons
orsh
ip
Thoug
ht le
ader
ship
15 April 2023
One True History?
Progr
ess
Comm
unity
Sessio
nal M
eetin
gs
Educa
tion
Wor
king
parti
es
Volunt
eerin
g
Resea
rch
Shapin
g th
e fu
ture
Networ
king
Profe
ssion
al su
ppor
t
Enter
prise
and
risk
Lear
ned
socie
ty
Oppor
tunit
y
Inte
rnat
ional
prof
ile
Jour
nals
Suppo
rting
Exper
tise
Spons
orsh
ip
Thoug
ht le
ader
ship
15 April 2023
The Changing Seasons
15 April 2023 90
6,000
8,000
10,000
12,000
14,000
16,000
18,000
20,000
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014
2008/9 Flu epidemic
Seasonality – weekly death registrations
Source: ONS
1999/2000 Flu epidemic
15 April 2023 91
-
1,000
2,000
3,000
4,000
5,000
6,000
2010 2011 2012 2013 2014
Seasonality – Age 85+ (CMI)
Source: CMI
15 April 2023 92
-
1,000
2,000
3,000
4,000
5,000
6,000
2010 2011 2012 2013 2014
Seasonality – bank holiday effect
Source: CMIQueen’s Jubilee
3 day week
August bank holiday
Christmas
Royal wedding
15 April 2023 93
Seasonality – weekly death registrations
Source: ONS & MetOffice4 week moving average
Deaths
Temperature
-40
-30
-20
-10
-
10
20
0
2000
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10000
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14000
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18000
20000
2000 2001 2002 2003 2004 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
Deaths Temperature
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014
15 April 2023 94
Seasonality – conventional approach
• Seasonality normally ignored
• Deaths by calendar year
• Mid-year population estimates
Interval Average improvement in
mortality
Standard deviation in
annual improvement
12 months ending December
2.3% 2.3%
Ten year time series
15 April 2023 95
Seasonality – choice of interval
Source: ONS data & own calculations
Conventional methodVol = 2.3%
12 months ending 30 SeptemberVol = 1.5%
15 April 2023 96
Seasonality – choice of interval
Interval Average improvement
Standard deviation in annual improvement
12 months ending December
2.3% 2.3%
12 months ending September
2.3% 1.5%
• Calendar year interval overstates underlying volatility
• Stochastic models - Lee Carter, CBD, RH etc
Source: ONS data & own calculations
15 April 2023 98
Standardized mortality rate
Source: Wikipedia
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
3.5%
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number of pirates SMR (UK)
15 April 2023 99
Standardized mortality rate
Source: Wikipedia
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
3.5%
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number of pirates SMR (UK)
15 April 2023 100
Expressions of individual views by members of the Institute and Faculty of Actuaries and its staff are encouraged.
The views expressed in this presentation are those of the presenter.
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