Jul 20, 2005 - Longevity Risk in the United Kingdom ... www.richardsconsulting.co.uk .... Mortality rates by broad cause of death. 1920. 1940. 1960. 1980.
Institut f¨ ur Finanz- und Aktuarwissenschaften, Universit¨ at Ulm
Longevity Risk in the United Kingdom
Stephen Richards 20th July 2005
c Stephen Richards. All rights reserved. Electronic versions of this and other Copyright freely available papers and presentations can be found at www.richardsconsulting.co.uk
Prologue • Jennifer Strover collects £12,500 after winning a bet that her motherin-law would live to 100.
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Prologue • Jennifer Strover collects £12,500 after winning a bet that her motherin-law would live to 100. • She placed a bet of £100 at 100-1 odds 11 years ago, and a year later staked another £50 at 50-1 odds.
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Prologue • Jennifer Strover collects £12,500 after winning a bet that her motherin-law would live to 100. • She placed a bet of £100 at 100-1 odds 11 years ago, and a year later staked another £50 at 50-1 odds. • Her mother-in-law, Rosalind, celebrates her birthday at a party paid for with the winnings.
Source: BBC News,
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4th
November 2004.
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Prologue—odds • The bookmaker used a survival probability of 1%.
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Prologue—odds • The bookmaker used a survival probability of 1%. • He should have used a figure five times greater: 5.48%.
Source: Own calculations using 1992–1994 GAD interim life table for females in England and Wales.
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Life-expectancy calculations • Can actuaries do any better than bookmakers?
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Life-expectancy calculations • Can actuaries do any better than bookmakers? • They must!
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Life-expectancy calculations • Can actuaries do any better than bookmakers? • They must! • And here’s why. . .
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Financial significance of life expectancy • Following its first mortality analysis for a decade, British Aerospace announced a £2.1bn increase in pension liabilities (17%)1 .
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Financial significance of life expectancy • Following its first mortality analysis for a decade, British Aerospace announced a £2.1bn increase in pension liabilities (17%)1 . • Following the adoption of International Financial Reporting Standards (IFRS), British Airway’s net assets fell from £2.7bn to £1.4bn as the pension-scheme deficit came the balance sheet2 .
Source:
1
British Aerospace: 2004 preliminary results, page 25.
2
British Airways: Release
of Financial Information 2004/5 under IFRS, page 3.
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Retirement life expectancy by socio-economic group 18
18 I
Male life expectancy at age 65 in years
17
17 II
16
16 IIIN
15
15 IIIM IV
14
13
14
13 V
12
12
11
11
1972−76
1977−81
1982−86
1987−91
1992−96
1997−99
Source: ONS Longitudinal Survey. Slide 11
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Mortality improvements • Much analysis of mortality improvements over past five years.
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Mortality improvements • Much analysis of mortality improvements over past five years. • Mortality improvement defined by Willets (1999): 1−
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qx,t qx,t−1
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Mortality improvements • Much analysis of mortality improvements over past five years. • Mortality improvement defined by Willets (1999): 1−
qx,t qx,t−1
• Improvements are not constant over time or age.
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Mortality improvements • Much analysis of mortality improvements over past five years. • Mortality improvement defined by Willets (1999): 1−
qx,t qx,t−1
• Improvements are not constant over time or age. • Improvements strongly related to year of birth, or cohort.
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Mortality improvements • Much analysis of mortality improvements over past five years. • Mortality improvement defined by Willets (1999): 1−
qx,t qx,t−1
• Improvements are not constant over time or age. • Improvements strongly related to year of birth, or cohort. • For more details, see Willets (2004) and Richards and Jones (2004).
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Mortality improvements by year of birth Annual percentage mortality improvement
4
3 Males 2
1
Females
0
−1 1910
1920
1930
1940
1950
Year of birth
Source: Own calculations with GAD interim life tables for 2000–2002 and 2001–2003. Slide 17
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Possible causes of cohort mortality patterns
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Possible causes of cohort mortality patterns • Changes in smoking incidence.
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800
80−84 75−79
600
CCTCC by age band
Lung cancer mortality by age
Lung-cancer mortality rates (left) and lifetime consumption of cigarettes (right) by year of birth
70−74 65−69
400 60−64
200
55−59 50−54
80−84
200
55−59
150
50−54
100 50
0 1870
1890
1910
1930
1870
1890
Year of birth
1910
1930
Year of birth
Source: Lee et al (1990), Forey et al (1993) and ONS data. Slide 20
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Possible causes of cohort mortality patterns • Changes in smoking incidence.
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Possible causes of cohort mortality patterns • Changes in smoking incidence. • . . . but this cannot be the whole explanation.
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Cohort survival curves for life-long non-smokers Percentage surviving from age 35
100
80
60 1900−1909 1910−1919 1920−1929
40
20
60
65
70
75
80
85
90
95
Age
Source: Doll et al (2004). Slide 23
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Possible causes of cohort mortality patterns • Changes in smoking incidence.
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Possible causes of cohort mortality patterns • Changes in smoking incidence. • Early-life exposure to pathogens.
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Mortality rates by broad cause of death 800 Circulatory diseases Cancer Respiratory diseases Infectious diseases
Mortality per 100,000
600
400
200
0 1920
1940
1960
1980
2000
2020
Year
Source: Own calculations using ONS data. Slide 26
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Direction of future mortality improvements • Circumstantial evidence suggests improvements are accelerating.
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Direction of future mortality improvements • Circumstantial evidence suggests improvements are accelerating. • Look again the pattern of mortality rates over the past century. . .
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Direction of future mortality improvements • Circumstantial evidence suggests improvements are accelerating. • Look again the pattern of mortality rates over the past century. . . • . . .and consider the implications of circulatory-disease mortality continuing its linear downward trend. . .
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Mortality rates by broad cause of death 800 Circulatory diseases Cancer Respiratory diseases Infectious diseases
Mortality per 100,000
600
400
200
0 1920
1940
1960
1980
2000
2020
Year
Source: Own calculations using ONS data. Slide 30
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Annual percentage improvement
Smoothed annual mortality improvement 8
8
6
6
4
4
2
2
0
0
−2
−2
−4
−4
−6
−6 1920
1940
1960
1980
2000
2020
Year
Source: Five-year moving average. Own calculations using ONS data. Slide 31
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Direction of future mortality improvements • Previous ‘model’ was simplistic.
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Direction of future mortality improvements • Previous ‘model’ was simplistic. • Need formal statistical aproach.
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Direction of future mortality improvements • Previous ‘model’ was simplistic. • Need formal statistical aproach. • Use penalised-spline regression—see Eilers and Marx (1996).
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Direction of future mortality improvements • Previous ‘model’ was simplistic. • Need formal statistical aproach. • Use penalised-spline regression—see Eilers and Marx (1996). • For specific application to two-dimensional mortality data, see Durban, Currie and Eilers (2002).
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Direction of future mortality improvements • Previous ‘model’ was simplistic. • Need formal statistical aproach. • Use penalised-spline regression—see Eilers and Marx (1996). • For specific application to two-dimensional mortality data, see Durban, Currie and Eilers (2002). • For application to mortality projections, see Currie, Durban and Eilers (2003) and CMIB (2005).
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Mortality improvements 1920
1930
1940
1950
1950
1920
1930
1940
1950
2000
1950
1990
3−4%
1940
1980
2000
>4%
1990
1930
1980
Year of Observation
1920
2−3%
1970
1970
0−1%
