Longevity Risk in the United Kingdom - CiteSeerX

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.

Slide 1

www.richardsconsulting.co.uk

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.

Slide 2


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,

Slide 3

4th

November 2004.


Prologue—odds • The bookmaker used a survival probability of 1%.

Slide 4


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.

Slide 5


Life-expectancy calculations • Can actuaries do any better than bookmakers?

Slide 6


Life-expectancy calculations • Can actuaries do any better than bookmakers? • They must!

Slide 7


Life-expectancy calculations • Can actuaries do any better than bookmakers? • They must! • And here’s why. . .

Slide 8


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.

Slide 10


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


Mortality improvements • Much analysis of mortality improvements over past five years.

Slide 12


Mortality improvements • Much analysis of mortality improvements over past five years. • Mortality improvement defined by Willets (1999): 1−

Slide 13

qx,t qx,t−1



qx,t qx,t−1

• Improvements are not constant over time or age.

Slide 14



qx,t qx,t−1

• Improvements are not constant over time or age. • Improvements strongly related to year of birth, or cohort.

Slide 15



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).

Slide 16


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


Possible causes of cohort mortality patterns

Slide 18


Possible causes of cohort mortality patterns • Changes in smoking incidence.

Slide 19


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



Slide 21


Possible causes of cohort mortality patterns • Changes in smoking incidence. • . . . but this cannot be the whole explanation.

Slide 22


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



Slide 24


Possible causes of cohort mortality patterns • Changes in smoking incidence. • Early-life exposure to pathogens.

Slide 25


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


Direction of future mortality improvements • Circumstantial evidence suggests improvements are accelerating.

Slide 27


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. . .

Slide 29


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


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


Direction of future mortality improvements • Previous ‘model’ was simplistic.

Slide 32


Direction of future mortality improvements • Previous ‘model’ was simplistic. • Need formal statistical aproach.

Slide 33


Direction of future mortality improvements • Previous ‘model’ was simplistic. • Need formal statistical aproach. • Use penalised-spline regression—see Eilers and Marx (1996).

Slide 34


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).

Slide 35


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).

Slide 36


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%