Mortality Studies GPV Workshop

(1)

Actuarial Experience Studies:

Mortality

By

(2)

Mortality Experience Studies - Content

• Use of Mortality Experience

• Source of Mortality Studies

• Best Estimate Assumptions

• Margin for Adverse Deviation

• Experience Studies

• Exposure Measurement • Credibility

(3)

Use of Mortality Experience

•

Valuation

•

Pricing

•

Products without mortality Risk?

• Still needed as mortality could be a contingency with respect to persistency

•

Life insurance

•

Life annuity

(4)

Source of Mortality Studies

•

Industry Studies / Mortality Tables

• Representative of your Company’s experience?

• Indonesia vs Other Countries (e.g. US Society of Actuaries (SOA) mortality tables)

• May not be representative due to differences in underwriting standards, socio economic factors, etc

•

Population Mortality

• Not representative of insured mortality (re: underwriting)

•

Reinsurers’ experience

•

Own experience

• Most Relevant

• Credibility

•

Important to understand the experience underlying the mortality table

• Insured mortality

• Basis of the table (e.g. SOA tables are valuation tables and include “built in” margins)

• Period of observation – experience may be dated and mortality improvements / deterioration may be required to make the table current

(5)

Best Estimate Assumption – Data Differentiation

•

Life insured’s/Annuitant’s age, sex, smoking habit, health, lifestyle

•

Duration since issue of policy

•

Plan of insurance (e.g. term, whole life) and its benefit provided

•

Company’s underwriting practice

•

Size of policy

•

Company’s distribution system (e.g. agency, brokerage, etc.) and marketing

practice

•

Each “cell” should be as homogeneous as possible

(6)

Margin for Adverse Deviation(MfAD)

• MfAD should increase the liability – requires testing of “direction” of MfAD (i.e. increasing or reducing the best estimate assumption)

• Size of MfAD reflects the degree of uncertainty of the best estimate assumption

• Uncertainty relates to misestimation of and deterioration from the best estimate assumption

• Canadian Standard for life insurance: K / e_x per 1,000 lives

• High Margin: K = 15

• Low Margin: K = 3.75 (i.e. 25% of High Margin) • Canadian Standard for annuities

• High Margin: -20%

• Low Margin: -5%

• Selection of High or Low margin depends on “Significant Considerations”

(7)

Margin for Adverse Deviation(MfAD) - continued

• Significant Considerations – Misestimation of best estimate assumption:

• Low credibility of the Company’s own experience

• Lack of homogeneity

• Unrefined method used to determine best estimate assumption (e.g. using single equivalent age for joint policies instead of each individual age)

• Change in underwriting practice in the Company

• Significant Consideration – Deterioration of best estimate assumption:

• Anti-selection is present (e.g. re-entry products; underwriting, sales force)

• Unfavourable mortality developments have emerged (e.g. AIDS)

• Persistency rate of product is low

• Premium structure does not recognize mortality differentials as precisely as the rest of the market (e.g. unisex rates; no distinction between smokers/non-smokers)

• Similar considerations apply to annuity business

• But favourable mortality developments would be important consideration

(8)

Experience Studies – Best Estimate Assumption

•

q

_x

= Deaths / Exposure

•

Exposure to risk

• Critical Element of experience studies

•

Deaths refer to Actual Claims

• Reconcile to Claims registry/P&L

• Use annuity payments for annuitant mortality experience

•

Compute based on count (i.e. number of deaths) and amount

(9)

Exposure - Measurement

• Study Period

• Include all policies exposed to risk during the period

• Need to determine entry point and exit point

• Entry Point:

• Start of exposure period for policies in-force at the beginning of the study period

• Issue date of policy for new business • Exit Point:

• End of exposure period for policies in-force at the end of the study period

• Date of termination for other policies

• Cause of Termination is an important consideration

• Death claims exposed to the end of the year of death

• Lapses/surrenders – exposed to the date of termination

• This would be reversed if doing lapse study: lapsed policies exposed for the full period but terminations due to death/surrender exposed only date of termination

• Treatment of late reported claims?

• Included in the year of study

• Best to perform study a few months after close of observation period to reduce the number of late reported claims

(10)

Exposure – Measurement

Beginning

A lives, age x

Ending

B lives, aged x+1

D deaths during the period

New Entrants

n lives, aged x+r

Withdrawals

w lives, aged x+s

0

r

s

1

(11)

Exposure – Measurement

Beginning

A lives, age x

Ending

B lives, aged x+1

New Entrants

n lives, aged x+r

Withdrawals

w lives, aged x+s

0

r

s

1

D = A * q

_x

+ n *

_1-r

q

_x+r

– w *

_1-s

q

_x+s

(12)

Exposure – Mortality for periods less than 1 year

• Balducci formula:

1-t qx+t= (1-t) * q x, 0 ≤ t ≤ 1 • Simple assumption to compute exposure

• Alternate Formulas:

• Uniform distribution of deaths

• _tq_x= t * q _x, 0 _≤ t _≤ 1

• _1-tq_x+t= (1-t) * q _x, / (1-t*q_x) 0 ≤ t ≤ 1

• Constant force of mortality

• _tq _x= 1- (1-q_x) t_, ₀_≤_t_≤₁

• _1-tq _x+t = 1- (1-q_x) (1-t) _, ₀_≤_t_≤₁

(13)

Exposure – Measurement

Beginning

A lives, age x

Ending

B lives, aged x+1

New Entrants

n lives, aged x+r

Withdrawals

w lives, aged x+s

0

r

s

1

D = A * q

_x

+ n *

_1-r

q

_x+r

– w *

_1-s

q

_x+s

Using Balducci,

D = A * q

_x

+ n * (1-r) * q

_x

– w * (1-s) q

_x

D = q

_x

* [ A + n * (1-r) – w * (1-s) ]

With q

_x

= D / E, we have

(14)

Exposure – Measurement – Example 1

Beginning

A lives, age x

Ending

B lives, aged x+1

New Entrants

n lives, aged x+r

Withdrawals

w lives, aged x+s

0

r

s

1

In the above observation period, we have:

A = 1,000

(15)

Exposure – Measurement – Example 1 - Solution

Beginning

A lives, age x

Ending

B lives, aged x+1

New Entrants

n lives, aged x+r

Withdrawals

w lives, aged x+s

0

r

s

1

Solution:

First Step: Determine Number of Deaths D

B = A + n – w – D

D = A + n – w - B

D = 1,000 + 40 – 30 - 990

D = 20

(16)

Beginning

A lives, age x

Ending

B lives, aged x+1

New Entrants

n lives, aged x+r

Withdrawals

w lives, aged x+s

0

r

s

1

Solution:

Second Step: Determine Exposure assuming Balducci

E = A + (1-r) * n – (1-s) * w

(17)

Beginning

A lives, age x

Ending

B lives, aged x+1

New Entrants

n lives, aged x+r

Withdrawals

w lives, aged x+s

0

r

s

1

Solution:

Third Step: Calculate q

_x

q

_x

= D / E

q

_x

= 20 / 1,020

q

_x

≈

0.0196

(18)

Example

• Calculate Exposure contributed for each of the following lives.

• Observation period begins March 1, 2000.

• Balducci hypothesis is assumed.

Case

Birth Date

Other Facts

1

Oct. 1, 1980

Withdrew Feb. 1, 2002

2

Dec. 1, 1981

Died Apr. 1, 2003

3

Apr. 1, 1979

Died May 1, 2004

4

Mar. 1, 1980

Died Apr. 1, 2000

(19)

Example 2 - Solution

Case

Birth Date

Other Facts

1

Oct. 1, 1980

Withdrew Feb. 1, 2002

19 Exposure Period - Calendar Year

Year

Number of

Months Description

2000 10 Mar 1 - Dec 31 2001 12 Jan 1 - Dec 31 2002 1 Jan 1 - Jan 31

Total 23

Age at Entry 19 5/12

Exposure Period - By Age

Age

Number of

19 7 Mar 1, 2000 - Sept 30, 2000 20 12 Oct 1, 2000 - Sept 30, 2001 21 4 Oct 1, 2001 - Jan 31, 2002

Total 23

Oct 1, 1999

Entry Mar 1, 2000

Exit Feb 1, 2002

(20)

Example 2 - Solution

Case

Birth Date

Other Facts

2

Dec 1, 1981

Died April 1, 2003

Exposure Period - Calendar Years Year

Number of

2000 10 Mar 1 - Dec 31

2001 12 Jan 1 - Dec 31

2002 12 Jan 1 - Dec 31

2003 11 Jan 1 - Nov 30

Total 45 Age at Entry 18 3/12

Exposure Period - By Age Age

Number of

18 9 Mar 1, 2000 - Nov 30, 2000 19 12 Dec 1, 2000 - Nov 30, 2001 20 12 Dec 1, 2001 - Nov 30, 2002 21 12 Dec 1, 2002 - Nov 30, 2003

Total 45

Dec 1, 1999

Entry Mar 1, 2000

Died Apr 1, 2003

Dec 1, 2000 Dec 1, 2001 Dec 1, 2002 Dec 1, 2003

(21)

Example 2 - Solution

Case

Birth Date

Other Facts

3

Apr 1, 1979

Died May 1, 2004

21 Note: Since the termination is by death, we give a full year of exposure in the year of death

Exposure Period - Calendar Years

Year

Number of

Months Description 2000 10 Mar 1 - Dec 31 2001 12 Jan 1 - Dec 31 2002 12 Jan 1 - Dec 31 2003 12 Jan 1 - Dec 31 2004 12 Jan 1 - Dec 31 2005 3 Jan 1 - Mar 31

Total 61

Age at Entry 20 11/12

Age

Number of

20 1 Mar 1, 2000 - Mar 31, 2000 21 12 Apr 1, 2000 - Mar 31, 2001 22 12 Apr 1, 2001 - Mar 31, 2002 23 12 Apr 1, 2002 - Mar 31, 2003 24 12 Apr 1, 2003 - Mar 31, 2004 25 12 Apr 1, 2004 - Mar 31, 2005

Total 61

Apr 1, 1999 Entry Mar 1, 2000

Died May 1, 2004

Apr 1, 2000 Apr 1, 2001 Apr 1, 2002 Apr 1, 2003

Exit Apr 1, 2005

(22)

Example 2 - Solution

Case

Birth Date

Other Facts

4

Mar 1, 1980

Died Apr 1, 2000

Exposure Period - Calendar Years

Year

Number of

2000 10 Mar 1 - Dec 31 2001 2 Jan 1 - Feb 28

Total 12

Age at Entry 20

Age

Number of

20 12 Mar 1, 2000 - Feb 28, 2001

Total 12

Mar 1, 2000

Entry Mar 1, 2000

Died Apr 1, 2000

Mar 1, 2001

(23)

Example 2 - Solution

Case

Birth Date

Other Facts

5

Nov 1, 1980

Withdrew Aug. 1, 2004

23

Exposure Period - Calendar Years

Year

Number of

2000 10 Mar 1 - Dec 31

2001 12 Jan 1 - Dec 31

2002 12 Jan 1 - Dec 31

2003 12 Jan 1 - Dec 31

2004 7 Jan 1 - Jul 31

Total 53

Age at Entry 19 4/12

Age

Number of

19 8 Mar 1, 2000 - Oct 31, 2000 20 12 Nov 1, 2000 - Oct 31, 2001 21 12 Nov 1, 2001 - Oct 31, 2002 22 12 Nov 1, 2002 - Oct 31, 2003 23 9 Nov 1, 2003 - Jul 31, 2004

Total 53

Nov 1, 1999

Entry Mar 1, 2000

Nov 1, 2000 Nov 1, 2001 Nov 1, 2002 Nov 1, 2003

Exit Aug 1, 2004

(24)

Credibility

•

Function of number of claims

• CIA Educational Note sets 100% credibility at 3,007 death claims (based on Poisson distribution; 90% confidence interval with 3% margin of error)

•

Use to blend own experience with industry experience

• Assumption that Industry Tables are 100% credible

•

Blended q

_x

= Z * own experience + (1-Z) * Industry experience

•

Z is credibility factor = minimum { (Number of Claims / 3007) ^ (1/2) , 1 }

•

Examples of Credibility Factors

Number

of

Claims

(25)

Example 3

• Calculate Actual-to-Expected experience by number of lives and by amounts based on the following data

• Calculate Credibility at age 22, assuming 3,007 claims for full credibility

• If e₅₂= 28.89, calculate the Margin for Adverse Deviation (MfAD) for High Margin situations and total “valuation” mortality at age 52 based on Canadian Actuarial Standards of Practice

Exposure

Actual Claims

Age

1000 q

_x

Number

Amount

Number

Amount

22

.67

471,797

17,119,826

196

6,685

37

.90

660,127

29,317,759

661

23,777

52

2.91

1,549,048

93,872,023

4,506

228,785

67

16.32

1,098,383

36,781,306

12,720

335,609

82

64.87

534,162

8,686,284

28,878

430,786

(26)

• Step 1 – Calculate Expected Claims

• Expected Claims = Exposure * q_x

Age

1000 q

x

Number

Amount

Number

Amount

22

0.67

471,797

17,119,826

316

11,470

37

0.90

660,127

29,317,759

594

26,386

52

2.91

1,549,048

93,872,023

4,508

273,168

67

16.32

1,098,383

36,781,306

17,926

600,271

82

64.87

534,162

8,686,284

34,651

563,479

(27)

• Step 2 – Actual to Expected

• A / E = Actual Claims divided by Expected Claims

27

Age

Number

Amount

Number

Amount

Number

Amount

22

196

6,685

316

11,470

62%

58%

37

661

23,777

594

26,386

111%

90%

52

4,506

228,785

4,508

273,168

100%

84%

67

12,720

335,609

17,926

600,271

71%

56%

82

28,878

430,786

34,651

563,479

83%

76%

TOTAL

46,961

1,025,642

57,995

1,474,774

81%

70%

(28)

Example 3 – Solution

•

Calculate Credibility at age 22, assuming 3,007 claims for full

credibility

•

Solution:

•

Credibility = minimum { (Actual Claims / 3007) ^ 0.5, 100%}

•

Actual Claims [22] = 196

•

Credibility = minimum { (196 / 3007) ^ 0.5 , 100%}

(29)

•

If e

₅₂

= 28.89, calculate the Margin for Adverse Deviation (MfAD) for

High Margin situations and total “valuation” mortality at age 52

based on Canadian Actuarial Standards of Practice

•

Solution:

•

MfAD [x] = K / e

_{x ,}

per 1,000, with k = 15 for High Margin situations

•

MfAD [52] = 15 / 28.89 per 1,000

•

MfAD [52] = 0.52 per 1,000

•

Total Valuation Assumption = Best Estimate Assumption + MfAD (*)

•

Total q

₅₂

= 2.91 per 1,000 + 0.52 per 1,000

•

Total q

₅₂

= 3.43 per 1,000

29

(30)

Best Estimate Assumption – Additional Considerations

•

Persistency

• Anti-selective lapses

•

Underwriting Practices

• Medical

• Non-medical

•

Mortality Improvement

• Project current mortality from dated studies

• Required for annuity business

• Accepted practice in Canada

• Typical approach:

• q_x,n = q_x * (1 – improvement) n_{, where n is number of years since the study of the}

underlying q_xwas performed

•

“Back-to-Back” contracts

(31)

Example 4

• You are given the following q_x for males based on a mortality study centered in 2010

• Assuming 2% annual mortality improvement, calculate the q_x for a policy issued in 2012 for a male aged 25 at issue

Age

1000 q

_x

Adjusted 1000 q

_x

25

.76

26

.78

27

.80

28

.81

29

.82

(32)

• Step 1 – Determine number of elapsed years since the mortality study

Age

Attained Year

Elapsed Years

25

2012

2

26

2013

3

27

2014

4

28

2015

5

(33)

• Step 2 – Determine mortality improvement factor by elapsed year since study

Age

Elapsed

Years

Improvement

25

2

Improvement factor [2] = (1-2%) ^ 2 = 0.9604

26

3

27

4

28

5

29

6

(34)

Example - Solution

• Step 3 – Calculate the adjusted q _x

• Adjusted q_x,n= base q_x * improvement factor [n], where n is the elapsed number of years since the mortality study.

Age

Base

1000 q

_x

Improvement

Factor

Adjusted 1000 q

_x

25

.76

0.9604

.730

26

.78

0.9412

.734

27

.80

0.9224

.738

28

.81

0.9039

.732

(35)

Sources of Information

• Canadian Institute of Actuaries Standards of Practice

• Canadian Institute of Actuaries Educational Notes:

• Expected Mortality: Fully Underwritten Canadian Individual Life Insurance Policies

• Margins for Adverse Deviation

• Society of Actuaries Mortality Table Construction (Batten) , Prentice Hall, 1978