ARCH 2013.1 Proceedings August 1- 4, 2012 Louis Adam Actuarial - PDF document

Article from: ARCH 2013.1 Proceedings August 1- 4, 2012 Louis Adam

Actuarial Research Conference, Winnipeg, Session P4A, Projection Scales 2012-08-03 Outline 1. Introduction Mortality Improvement for 2. Phases of Study Canadian Pensioners: 3. Methodology & Results, Phase II P Proposed Projection Scales d P j ti S l 4. Mortality Improvement Rate: Formulas Louis Adam, FSA, FCIA 5. Projection Scales: Proposal Université Laval, Quebec City, QC 6. Conclusion 47 th Actuarial Research Conference Winnipeg, Manitoba, 2012 ‐ 08 ‐ 03 ARC, Winnipeg. Mortality Improvement for Canadian Pensioners: Proposed Projection Scales 2 1. Introduction CCPME Acknowledgements : • Created in 2008 by CIA – Financial support from Canadian Institute of • Commissioned two studies in 2009 Actuaries, and formerly from Chaire d’actuariat, • Data collected in 2010 Université Laval and SOA • Data analysis and review 2010 and 2011 – Data and support: • Reports drafted and reviewed: • Office of the Chief Actuary (CPP) • Régie des rentes du Québec (QPP) – Registered Pension Plan Study in 2012 – CIA CCPME: Committee on Canadian Pensioners – CPM Study in 2011 and 2012 Mortality Experience • CIA Annual Meeting: June 2012 Presentation – and many reviewers, colleagues, students ARC, Winnipeg. Mortality Improvement for Canadian Pensioners: Proposed Projection Scales 3 ARC, Winnipeg. Mortality Improvement for Canadian Pensioners: Proposed Projection Scales 4 Louis Adam, FSA, FCIA, Université Laval 1

Actuarial Research Conference, Winnipeg, Session P4A, Projection Scales 2012-08-03 CPM Messages, CIA June 2012 Session • Canadian Pensioners Mortality = CPM 1. It is time to change the Canadian standard for • Pensioner data only, from CPP and QPP mortality tables for pension plans: Canadian administrators evidence for this – Separate and combined results Separate and combined results 2. Income is important for pensioner mortality 2 Income is important for pensioner mortality – Data comprehensive and high quality (with time, gender, age, source) – Data segmented by pension income level 3. Mortality trend: Higher improvements rates – Almost 8 million exposed lives (86.9 M life ‐ years observed in recent past= troubling news exposure from 1967 to 2008) – pensions payable since 1967 4. Impact might be material for many plans ARC, Winnipeg. Mortality Improvement for Canadian Pensioners: Proposed Projection Scales 5 ARC, Winnipeg. Mortality Improvement for Canadian Pensioners: Proposed Projection Scales 6 2. CPM Study Phases 3. Methodology & Results, Phase II 1: Get high quality data: CPP + QPP = CAN • Deaths & Exposure measured 2: Measure qx at recent point in time: • 5 variables: source, gender, age, income , year – 2005 ‐ 2007, centered in 2006 • Exact age, constant force of mortality for 31 t 2012 – Phase II Report : May 31 st , 2012 Ph II R M fractional ages f i l 3: Measure mortality trends: projection scales • Exact age compares to “Nearest Birthday” – With recent experience over 15 years for short • Provides point estimate and confidence term scale: 1992 ‐ 2007 2006 to 2021 intervals – Long term scale based on C/QPP Actuarial Reports • Graduation: Gompertz, modified at extreme – Phase III Report : Draft July 17 th , 2012 ages, values within bounds of 1 std dev. ARC, Winnipeg. Mortality Improvement for Canadian Pensioners: Proposed Projection Scales 7 ARC, Winnipeg. Mortality Improvement for Canadian Pensioners: Proposed Projection Scales 8 Louis Adam, FSA, FCIA, Université Laval 2

Actuarial Research Conference, Winnipeg, Session P4A, Projection Scales 2012-08-03 Income Results shown here • 5 income classes • Ratios of q(x) : CPM ‐ CAN/ UP ‐ 94 @ 2006 + • Split in % of C/QPP Maximum Pension • 2006: No projection for CPM ‐ CAN – 1 : <35%, 2 : 35% ‐ 94%, 3 : >95% • 2012: 6 ‐ Year Projection with short term scale • Remove lower pensions (Class 1) to get proxy • UP ‐ 94: Scale AA, static proj. to 2006 or 2012 for mortality of pension plans members • Class 4 = Class 2 (mid) + Class 3 (high) • Class 5 = All income ARC, Winnipeg. Mortality Improvement for Canadian Pensioners: Proposed Projection Scales 9 ARC, Winnipeg. Mortality Improvement for Canadian Pensioners: Proposed Projection Scales 10 CPM vs UP ‐ 94 in 2006 : ratios q(x) Male CPM vs UP ‐ 94 in 2012 : ratios q(x) Male 120% 120% 110% 110% 100% 100% 90% 90% Class 2= 35% ‐ 94% Class 2= 35% ‐ 94% 80% 80% Maximum Pension Maximum Pension Class 3= 95% ‐ 100% Class 3= 95% ‐ 100% 70% 70% Maximum Pension Maximum Pension 60% Class 4= 35% ‐ 100% 60% Class 4= 35% ‐ 100% Maximum Pension Maximum Pension 50% 50% 60 65 70 75 80 85 90 95 60 65 70 75 80 85 90 95 ARC, Winnipeg. Mortality Improvement for Canadian Pensioners: Proposed Projection Scales 11 ARC, Winnipeg. Mortality Improvement for Canadian Pensioners: Proposed Projection Scales 12 Louis Adam, FSA, FCIA, Université Laval 3

Actuarial Research Conference, Winnipeg, Session P4A, Projection Scales 2012-08-03 CPM vs UP ‐ 94 in 2006 : ratios q(x) Female CPM vs UP ‐ 94 in 2012 : ratios q(x) Female 120% 120% 110% 110% 100% 100% 90% 90% Class 2= 35% ‐ 94% Class 2= 35% ‐ 94% 80% 80% Maximum Pension Maximum Pension Class 3= 95% ‐ 100% Class 3= 95% ‐ 100% 70% 70% Maximum Pension Maximum Pension 60% Class 4= 35% ‐ 100% 60% Class 4= 35% ‐ 100% Maximum Pension Maximum Pension 50% 50% 60 65 70 75 80 85 90 95 60 65 70 75 80 85 90 95 ARC, Winnipeg. Mortality Improvement for Canadian Pensioners: Proposed Projection Scales 13 ARC, Winnipeg. Mortality Improvement for Canadian Pensioners: Proposed Projection Scales 14 CPM vs UP ‐ 94: 2006 and beyond CPM ‐ CAN 2005 ‐ 2007 Male: Classes 2, 3 & 4 130% Class 2 ‐ Low • Male: depends on income class, but lower Class 2 ‐ High 120% Class 2 ‐ Grad. than UP ‐ 94 in 2012 until age 84 Class 3 ‐ Low – Class 4 ages 74 ‐ 77: under 102%; 110% Class 3 ‐ High Class 3 ‐ Grad. – Wide gap between income classes, Wide gap between income classes 100% Class 4 ‐ Low • For Female: CPM mortality is lower (age< 87 ) Class 4 ‐ High 90% • Projected to 2015, 2020: lower ratios Class 4 ‐ Grad. • Next Charts: compare Classes 2, 3 & 4 only 80% • Also: compare Sources CPP, QPP, CAN 70% 60 65 70 75 80 85 90 ARC, Winnipeg. Mortality Improvement for Canadian Pensioners: Proposed Projection Scales 15 ARC, Winnipeg. Mortality Improvement for Canadian Pensioners: Proposed Projection Scales 16 Louis Adam, FSA, FCIA, Université Laval 4

Actuarial Research Conference, Winnipeg, Session P4A, Projection Scales 2012-08-03 4. Mortality Improvement Rate, Source 2005 ‐ 07 Male: CAN, CPP, QPP Formulas 104% Next Slide show formulas for reference 102% Charts follow and illustrate trends 100% Excerpts from Phase III Draft Report (2012 ‐ 07) Canada 98% Canada Pension Plan Quebec Pension Plan 96% 60 65 70 75 80 85 90 95 ARC, Winnipeg. Mortality Improvement for Canadian Pensioners: Proposed Projection Scales 17 ARC, Winnipeg. Mortality Improvement for Canadian Pensioners: Proposed Projection Scales 18 Formulas: force, prob., weights Formulas: Regression D μ ˆ = E x ( ) _ + _ × − t x Improvement rate : = 1 Deaths and exposure (exact): init year t init year q q IR x x x x - μ q =1-e ˆ Regression on ln(qx): linear form Probability of death, from force: ˆ x x ( ( ) ) ( ( ) ) ( ( ) ) Variance of force, and of prob.: _ + _ + × − ln = ln ln 1 init year t init year q q q q t IR x x x x x x μ D D ( ) ˆ ˆ σ = Var μ = 2 x = x β + β × ˆ = y x x μ ˆ E 2 E x 0 1 i i x x ( ) ( ) 2 ( ) − ˆ μ Var q = e × Var μ Weighted Linear Regression (Min W, find slope): ˆ x ˆ x x n Weight: ∑ ( ) 2 ( ) 2 = × − β − β × E 1 W w y x 0 1 x w = = i i i ( ) ( ) = ˆ 2 1 t Var q i 1-q ˆ ×D x x x ARC, Winnipeg. Mortality Improvement for Canadian Pensioners: Proposed Projection Scales 19 ARC, Winnipeg. Mortality Improvement for Canadian Pensioners: Proposed Projection Scales 20 Louis Adam, FSA, FCIA, Université Laval 5