Professeur, École d’actuariat Louis Adam 2006-09-22 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

Outline Introduction: Modified AA scale OK ? Trend of Pensioner Mortality in Canada Proposed Projection Scale 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

Part 1- Introduction Conclusion to be announced Modified Scale AA Proposed scale 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

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 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

Modified Scale AA (CLIFR, October 2005) 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

Projection Scale: Male 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

Projection Scale: Female 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

Reference for Scale AA « Scale AA is wholly based on the historic experience of the CSRS and of Social Security--1977 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 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

Issues with Scale AA U.S. data only Experience ends in 1993 Current standard Is it similar to recent Canadian experience? 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

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 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

Proposal for a new scale Canadian data 1967-2003 Period CPP + QPP Pensioners (over age 60) Only those with pensions > 35 % Maximum Pension ( exclude low earnings) Average rate of decrease, with adjustment 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

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 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

Part 2- Mortality Trend Projection Scale: q70 ×(1-Rate70)#years Weights given to each year Length of period ending 2003 10 years (5-10-15-20-25 ??) Maximum allowed by data ? Implicit assumption: future trend similar to “a part of the past experience” 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

Evolution of q70 over time 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

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 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

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 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

2003 10-yr AA 70 for q70 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

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

Weighted Rate of Decrease 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

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 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

Alternate values for AA70 Louis Adam 2006-09-22 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. 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement CIA AA Seminar, PD 11 CLIFR Topics II Mortality Improvement

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 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

Unweighted Rate: 2.46 %, Weighted Rate: 2.54 % (15-year) 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

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) 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

95 % Confidence Interval: 10-year, Male 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

95 % Confidence Interval: Maximum Period, Male 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

95 % Confidence Interval: 25-Year Period, Male 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

95 % Confidence Interval: 10-year, Female 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

95 % Confidence Interval: Maximum Period, Female 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

95 % Confidence Interval: 25-Year Period, Female 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

Male, Various Periods: Mean 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

Female, Various Periods: Mean 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

Male Projection Factors 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

Female Projection Factors 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

Projection Scale: Male 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

Projection Scale: Female 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement

Some comments Does qx decrease over time ? Yes ! Louis Adam 2006-09-22 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 ? 2006-09-22 Louis Adam, CIA AA Seminar, PD 11 CLIFR Topics II, Mortality Improvement CIA AA Seminar, PD 11 CLIFR Topics II Mortality Improvement

Thank you ! Questions ?