Actuarial Assumptions

Lars Billberg, Chief Actuary Moscow, 2012-09-14

Actuarial Assumptions

2012-09-14

1

Two components in the Public Pension Income Pension • Notional defined contribution (NDC)

Premium Pension • Defined contribution (DC)

• Pay-as-you-go

• Pre-funded system

• Return: wage index

• Return: financial market

• Automatic balancing

Income Pension Premium Pension Actuarial Assumptions

2012-09-14

2

Retirement • Flexible from the age of 61, no upper limit • Income Pension or Premium Pension, or both • Premium Pension: – Single life or joint life – Variable (VA) or With Profit (WPA) annuity

• Guaranteed Pension from 65

Actuarial Assumptions

2012-09-14

3

Annuity factor I

• Annuity factor (a) = Capital needed now to pay out 1 SEK life-long • One pensioner: a = 1 + 1 + 1 + ….. = ? • Statistical approach - 1 000 pensioners: 1000 * a = 1000 + 990 + 979 + ….. • One statistical pensioner: a = 1 + 0,990 + 0,979 + ….. = 21,05 • Future payments discounted with assumed rate of return: a = 1 + 0,990 / 1,039 + 0,979 / (1,039 * 1,039) + ….. = 13,80

Actuarial Assumptions

2012-09-14

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Annuity factor II

•

Annuity factor = Capital needed now to pay out 1 SEK life-long

• So, if I have 13,80 I can pay a statistical pensioner 1 per year • If I have 13 800 I can pay 13 800/13,80 = 1000 per year etc. • That is: Yearly amount = Capital / Annuity factor • Annuity factor depends on: • Expected life length/mortality • Expected rate of return of investment

Actuarial Assumptions

2012-09-14

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Annuity factor III The exact formula for the annuity factor ax at age x years is ∞

a x = ∫ e −δ t ⋅ 0

l(x + t) dt l ( x)

where l(x) is the survival function x

l ( x) = e

− ∫ ⋅µ ( t ) dt 0

and µ(x) is the mortality function µ

µ ( x) = a + b ⋅ e c⋅x For x > w, µ(x) merges with a straight line with a slope of k.

This formula applies to single life, i.e. no co-insured.

Actuarial Assumptions

2012-09-14

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Pension amounts

• Pension amount: Yearly amount = Capital / Annuity factor •

If exacty 65 years old (single life): 3 066 SEK/year = 50 000 SEK 3 624 SEK/year = 50 000 SEK 3 053 SEK/year = 50 000 SEK 2 100 SEK/year = 50 000 SEK

/ / / /

16,31 13,80 16,38 23,81

Actuarial Assumptions

(Income Pension) (Premium Pension - VA) (Premium Pension - WPA) (Premium Pension - WPA guaranteed)

2012-09-14

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Assumptions for Annuity factor

Mortality

Income

Premium

Premium

Premium

Pension

Pension -

Pension -

Pension – WPA

VA

WPA

guaranteed

Observed last 5

Prognosis

Prognosis

Prognosis

years before

Main

Main

Low

retirement

(21,0 from 65)

(21,0 from 65)

(23,5 from 65)

Prognosis

Prognosis

Fixed

1,6%

4,0 %

2,3%

0%

-

Prognosis

Prognosis

Prognosis

0,1%

0,1%

0,1%

(19,4 from 65)

Rate of

Real income

return

growth

Costs

Actuarial Assumptions

2012-09-14

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Discussion points I

• Mortality: • Observed or prognosis? • Which prognosis? • Rate of return: • Front or end loaded pensions? • Who decides?

Actuarial Assumptions

2012-09-14

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Pension amount over time I 5% actual rate of return

Amount paid out

Actual mortality (survival bonus) same as assumed

3% assumed rate of return Guaranteed amount

0% assumed rate of return

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Pensionsår Pension year

Actuarial Assumptions

2012-09-14

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Pension amount over time II 3% actual rate of return

Actual mortality (survival bonus) same as assumed

Amount paid out 3% assumed rate of return Guaranteed amount

0% assumed rate of return

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Pensionsår Pension year

Actuarial Assumptions

2012-09-14

11

Pension amount over time III 0% actual rate of return

Actual mortality (survival bonus) same as assumed If WPA: Amount paid out = Guaranteed amount!

3% assumed rate of return

Guaranteed amount

0% assumed rate of return

Amount paid out 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Pensionsår Pension year

Actuarial Assumptions

2012-09-14

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Higher guaranteed amounts 5% actual rate of return

Amount paid out

Actual mortality (survival bonus) same as assumed

3% assumed rate of return Guaranteed amount

0% assumed rate of return

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Pensionsår Pension year

Actuarial Assumptions

2012-09-14

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Discussion points II

• Guarantees: • With or without? • Level and construction? • Who pays for it? • Matching of liabilities and assets (ALM): • When is it possible?

Actuarial Assumptions

2012-09-14

14

Observed and expected life lengths

Pehr Wargentin (1717-1783)

Actuarial Assumptions

2012-09-14

15

Years

90 Female

Life expectancy 1861 – 2011

80

At birth

Male

70 60 50 40 Age 50 30 20

Age 65 Age 75

10

Age 85 Source: Statistics Sweden

0 1860 1880 1900 1920 1940 1960 1980 2000 Actuarial Assumptions

2012-09-14

16

300

Deaths per 1000 born alive

Infant mortality 1750-2010 by gender (per 1000)

250

200

150

100

50 Boys Girls 0 1750

1800

1850

1900

1950

2000

Source: Statistics Sweden Actuarial Assumptions

2012-09-14

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1

Age

Mortality same period.

f40 m40 f50 m50 f60 m60

0,1

f70

Use of trend 1980-2010 gives higher female mortality in the future!

m70 f80 m80 f90 m90

Not realistic – different approach needed.

Source: Statistics Sweden

0,01

0,001

0,0001 1860 1880 1900 1920 1940 1960 1980 2000 Year Actuarial Assumptions

2012-09-14

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Yearly change of death rate for different death reasons per gender and age between 1980 and 2010 Percent 2

Neoplasms

Diseases of circulatory system 2

1 0 -1 -2

1 0

Female (23 %) Male (27 %)

-2

-3

-3

-4

-4

-5

-5

20–24 30–34 40–44 50–54 60–64 70–74 80–84 90+ Age Source: Statistics Sweden

-1

(41 %) (40 %) 20–24 30–34 40–44 50–54 60–64 70–74 80–84 90+

Accidents, suicide

Other reasons

2

2

1

1

0 -1

(32 %)

0

(7 %)

-1

-2

-2

-3

-3

(4 %)

-4

(27 %)

-4

-5

-5 20–24 30–34 40–44 50–54 60–64 70–74 80–84 90+

20–24 30–34 40–44 50–54 60–64 70–74 80–84 90+

Actuarial Assumptions

2012-09-14

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Assumed yearly reduction of death rate per gender, age and period Percent 0,0

Female

0,0

-0,5

-0,5

-1,0

-1,0

-1,5

Male

2045– -1,5 2013–2040

-2,0

-2,0

-2,5

-2,5

-3,0

-3,0 0 10 20 30 40 50 60 70 80 90 100

2045– 2013–2040

0 10 20 30 40 50 60 70 80 90 100

Age Source: Statistics Sweden Actuarial Assumptions

2012-09-14

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Death rate per gender and age 1960-2011 and Logarithmic scale projection 2012-2060 Deaths per 1 000

1000

Female

Male Age

1000

100

100 100

90

100

80

80

Source: Statistics Sweden

10

1

10

70

70

60 0 50

60 0 50

1

40 0,1

90

40 20,30

20,30 0,1 10

10

0,01 0,01 Actuarial Assumptions 2012-09-14 1960 1980 2000 2020 2040 2060 1960 1980 2000 2020 2040 2060

21

Life expectancy at birth 1960-2011 and projection 2012-2060 Years

90 Prognos Projection

88,8

Kvinnor Female

86,7 85

83,7

Source: Statistics Sweden

80

Män Male

79,8

75 74,9

71,2 70

65 1960

1970

1980

1990

2000

2010

2020

Actuarial Assumptions

2030

2040

2050 2012-09-14

2060 22

Mortality rate 1

Year of 1770 1775 1780 1785 1790 1795 1800 1805 1810 1815 1820 1825 1830 1835 1840 1845 1850 1855 1865 1870 1875 1880 1885 1890 1895 1900 1905 1910 1915 1920 1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

0,1

0,01

Source: Statistics Sweden

0,001

0,0001

1E-05 0

20

40

60

80

Actuarial Assumptions

100

A

Female mortality. Cohorts 17702005.

2012-09-14

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Expected return on investments

4,2%

4,0%

+3,5%

6,5%

Equity premium

Global equities

-1,0% 3,0%

UFR

Long term bonds

Long term premium

Short term bonds Actuarial Assumptions

2012-09-14

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Prognosis of Rate of returns Rate

Premium

Premium

Pension - VA

Pension - WPA

Equities

6,3%

90%

30%

Bonds

3,5%

10%

70%

Inflation

2,0%

4,0%

2,3%

Portfolio real return

Actuarial Assumptions

2012-09-14

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Discussion points III

• How do we adapt to all this? • Future life expectancy: • Russia / Sweden / Europe / Japan • Trends, death reasons, cohorts, base period • Medical cost for living longer • Future return on investments: • Risk vs. return • Free choice of assets • Default solutions Actuarial Assumptions

2012-09-14

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