1. Professeur, École d’actuariat
Louis Adam
Session # PD-11 CLIFR Topics II Expected Annuitant Mortality Improvement
Louis Adam, f.s.a., f.i.c.a.
Professeur, École d’actuariat
Université Laval
Toronto, September 22, 2006
Temps alloué de 1h30
De 10h30 à 12h00
I will focus on results of a reseach project involving only Canadian data for pensioners.
CIA AA Seminar, PD 11 CLIFR Topics II Mortality Improvement

2. Outline Introduction: Modified AA scale OK ?
Trend of Pensioner Mortality in Canada
Proposed Projection Scale
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

3. Part 1- Introduction Conclusion to be announced Modified Scale AA
Proposed scale
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

4. Announced conclusion
Proposed scale is higher than Modified AA scale (see next slides for conclusion)
Results will show how figures are achieved
Methodology debatable, not the data
No crystal ball for the future
Mirror-image: Short-term future assumed to mimic recent past
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

5. Modified Scale AA (CLIFR, October 2005)
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

6. Projection Scale: Male
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

7. Projection Scale: Female
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

8. Reference for Scale AA
« Scale AA is wholly based on the historic experience of the CSRS and of Social Security through 1993, by age and sex--with a minimum 0.5% per year improvement at ages under 85. The period 1977 through 1993 was considered a representative historical period on which to base future mortality projections. »
THE UP-94 AND GAR-94 TABLES: ISSUES IN CHOOSING THE APPROPRIATE TABLE, TSA XLVII, 1995, page 797
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

9. Issues with Scale AA U.S. data only Experience ends in 1993
Current standard
Is it similar to recent Canadian experience?
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

10. Modified AA Scale CIA, CLIFR, October 2005
Changes at various ages, from AA scale
Female: minimum rate of 1 % from age 60 to age 80
Still below recent Canadian experience, according to this data set
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

11. Proposal for a new scale
Canadian data
Period
CPP + QPP Pensioners (over age 60)
Only those with pensions > 35 % Maximum Pension ( exclude low earnings)
Average rate of decrease, with adjustment
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

12. New scale features Proposed figures based on past Canadian experience
Future experience might vary
Slight differences in point estimates based on specific method of calculation
Confidence intervals shown for one method
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

13. Part 2- Mortality Trend Projection Scale: q70 ×(1-Rate70)#years
Weights given to each year
Length of period ending 2003
10 years ( ??)
Maximum allowed by data ?
Implicit assumption: future trend similar to “a part of the past experience”
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

14. Evolution of q70 over time
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

15. Detailed calculation Trend over past 10 years Annual decrease of q70
Probabilities, rate of decrease, weights
Rate of decrease is not constant over time: recent acceleration
Arithmetic average of weighted rate of decrease
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

16. 2003 10-year Rate, q70 Explain how 2.98 % is obtained
q1994 / q1993 = 1 - rate (1994)
Weight(1994) = 1 / Var(q1994)
Calculate rate(1994)… rate(2003)
2.98 % = Weighted average
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

17. yr AA 70 for q70
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

18. 2003 10-yr Least-square Rate 2006-09-22
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

19. Weighted Rate of Decrease
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

20. Long-Term Rate Average over longest possible period
Vary by age (C/QPP inception, etc.)
Age 60: from 1984 to 2003, 20 values.
70: 1967 – 2003, 37 values
80: 1976 – 2003, 28 values
90: 1986 – 2003, 18 values
100: 1996 – 2003, 8 values
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

21. Alternate values for AA70
Louis Adam
Alternate values for AA70
Weighted avg.: 2.98 %
Unweighted average of 10 figures from 1994 to 2003 : 2.76 %
Least-square, unweighted: 2.97 %
Least-square, weighted: 3.02 %
95 % Confidence Interval:
From 2.49 % to 3.55 % (± 0.5 % )
R2 = 94.7 %
This is important ! : significant difference with AA scale.
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement
CIA AA Seminar, PD 11 CLIFR Topics II Mortality Improvement

22. Alternative methods Unweighted least squares Example: 15-yr rate, q70
Arithmetic avg, unweighted: 2.53 %
Arithmetic avg, weighted: 2.78 %
Least Squares (next slide): 2.46 %
Least Square, weighted: 2.54 %
95% Confidence Interval: 2.21 % to 2.88 %
(± 0.3 % )
Mortality decreases over time
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

23. Unweighted Rate: 2.46 %, Weighted Rate: 2.54 % (15-year)
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

24. Impact of Confidence Interval
Next slides show, for various time-periods:
Weighted least-square regression avg rate of decrease of mortality
Lower and upper bounds for rate of decrease
Modified Scale AA
My 2005 Proposal (based on arithmetic avg)
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

25. 95 % Confidence Interval: 10-year, Male
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

26. 95 % Confidence Interval: Maximum Period, Male
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

27. 95 % Confidence Interval: 25-Year Period, Male
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

28. 95 % Confidence Interval: 10-year, Female
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

29. 95 % Confidence Interval: Maximum Period, Female
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

30. 95 % Confidence Interval: 25-Year Period, Female
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

31. Male, Various Periods: Mean
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

32. Female, Various Periods: Mean
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

33. Male Projection Factors
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

34. Female Projection Factors
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

35. Projection Scale: Male
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

36. Projection Scale: Female
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

37. Some comments Does qx decrease over time ? Yes !
Louis Adam
Some comments
Does qx decrease over time ? Yes !
Rate of decrease not constant by age
Higher at age 65, lower at age 90
Negative decrease over age 90 ?
Varies from year to year
Rates for female lower than male
Recent rates of decrease are higher than in the past
Proposal is relatively simple (straight line sought)
Will the future be like the past ?
Is it applicable to your block of business ?
Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement
CIA AA Seminar, PD 11 CLIFR Topics II Mortality Improvement

38. Thank you !
Questions ?