Session 158 PD - Living to 100: Modeling of Mortality Improvement. Moderator: Andrew J. Peterson, FSA, EA, FCA, MAAA

Transcription

1 Session 158 PD - Living to 100: Modeling of Mortality Improvement Moderator: Andrew J. Peterson, FSA, EA, FCA, MAAA Presenters: Elena V. Black, FSA, EA, FCA, MAAA Marianne C. Purushotham, FSA, MAAA SOA Antitrust Compliance Guidelines SOA Presentation Disclaimer

2 2017 SOA Annual Meeting & Exhibit LENA BLACK, FSA, CFA, EA, PHD, MAAA, FCA, THE TERRY GROUP MARIANNE PURUSHOTHAM, FSA, MAAA, LIMRA Session 158 Modeling of Mortality Improvement October

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4 Presentation Disclaimer Presentations are intended for educational purposes only and do not replace independent professional judgment. Statements of fact and opinions expressed are those of the participants individually and, unless expressly stated to the contrary, are not the opinion or position of the Society of Actuaries, its cosponsors or its committees. The Society of Actuaries does not endorse or approve, and assumes no responsibility for, the content, accuracy or completeness of the information presented. Attendees should note that the sessions are audio-recorded and may be published in various media, including print, audio and video formats without further notice. 3

5 Agenda The Challenge Some Basics One-dimensional Models used in the US Two-dimensional Models used in the US, UK, and Canada Assessing Model Effectiveness Questions 4

6 The Challenge Prediction is very difficult, especially about the future. - Niels Bohr

7 The Challenge µ = 1.0% σ = 1.6% Source: SOA; Mortality Improvement Scale MP-2016 Report 6

8 The Challenge Heat map Similar to topographical maps: 2D view of 3D information (shown male SSA raw MI rates) % 4.0% 3.0% 2.0% 1.0% 0.0% -1.0% -2.0% -3.0% -4.0% -5.0% % 6.0% 4.0% 2.0% 0.0% -2.0% -4.0% -6.0% -8.0% Improvement rates for 65-year male Horizontally Improvement rates for male cohort born in 1952 Diagonally -10.0% Improvement rates for males % 4.0% 3.0% 2.0% 1.0% 0.0% -1.0% Vertically -2.0% -3.0% Age >3.5% 3%-3.5% 2.5%-3.0% 2.0%-2.5% 1.5%-2.0% 1.0%-1.5% 0.5%-1.0% 0.0%-0.5% -0.5%-0.0% -1.0%--0.5% <-1.0% Horizontally by years for specific age Vertically by year for all ages Diagonally by year for specific birth year cohort 7 7

9 The Challenge: Signal versus Noise Favoring smoothness promote stability Extreme example fit a constant value plane Very Smooth Raw SSA Data Favor Fit Favor Fit promotes good fit to data and reduces errors Extreme example no smoothing at all Trade-off >3.5% 3%-3.5% 2.5%-3.0% 2.0%-2.5% 1.5%-2.0% 1.0%-1.5% 0.5%-1.0% 0.0%-0.5% -0.5%-0.0% -1.0%--0.5% <-1.0%

10 Some Basics

11 Stochastic vs Deterministic Both start with historical mortality experience, but Stochastic mortality improvement (MI) models reflect assumed probability distributions, which permit future volatility to be quantified; some examples: Lee-Carter Cairns-Blake-Dowd (CBD family of models) Deterministic models produce a single answer (based on a given set of inputs); some examples: CMI RPEC 10

12 Static vs Generational Mortality Static Calendar Year Age q(60,2016) q(60,2017) q(60,2018) q(60,2019) q(60,2020) q(60,2021) q(60,2022) q(60,2023) q(60,2024) q(60,2025) 61 q(61,2016) q(61,2017) q(61,2018) q(61,2019) q(61,2020) q(61,2021) q(61,2022) q(61,2023) q(61,2024) q(61,2025) 62 q(62,2016) q(62,2017) q(62,2018) q(62,2019) q(62,2020) q(62,2021) q(62,2022) q(62,2023) q(62,2024) q(62,2025) 63 q(63,2016) q(63,2017) q(63,2018) q(63,2019) q(63,2020) q(63,2021) q(63,2022) q(63,2023) q(63,2024) q(63,2025) 64 q(64,2016) q(64,2017) q(64,2018) q(64,2019) q(64,2020) q(64,2021) q(64,2022) q(64,2023) q(64,2024) q(64,2025) 65 q(65,2016) q(65,2017) q(65,2018) q(65,2019) q(65,2020) q(65,2021) q(65,2022) q(65,2023) q(65,2024) q(65,2025) 66 q(66,2016) q(66,2017) q(66,2018) q(66,2019) q(66,2020) q(66,2021) q(66,2022) q(66,2023) q(66,2024) q(66,2025) 67 q(67,2016) q(67,2017) q(67,2018) q(67,2019) q(67,2020) q(67,2021) q(67,2022) q(67,2023) q(67,2024) q(67,2025) 68 q(68,2016) q(68,2017) q(68,2018) q(68,2019) q(68,2020) q(68,2021) q(68,2022) q(68,2023) q(68,2024) q(68,2025) 69 q(69,2016) q(69,2017) q(69,2018) q(69,2019) q(69,2020) q(69,2021) q(69,2022) q(69,2023) q(69,2024) q(69,2025) 70 q(70,2016) q(70,2017) q(70,2018) q(70,2019) q(70,2020) q(70,2021) q(70,2022) q(70,2023) q(70,2024) q(70,2025) 71 q(71,2016) q(71,2017) q(71,2018) q(71,2019) q(71,2020) q(71,2021) q(71,2022) q(71,2023) q(71,2024) q(71,2025) 72 q(72,2016) q(72,2017) q(72,2018) q(72,2019) q(72,2020) q(72,2021) q(72,2022) q(72,2023) q(72,2024) q(72,2025) 73 q(73,2016) q(73,2017) q(73,2018) q(73,2019) q(73,2020) q(73,2021) q(73,2022) q(73,2023) q(73,2024) q(73,2025) 74 q(74,2016) q(74,2017) q(74,2018) q(74,2019) q(74,2020) q(74,2021) q(74,2022) q(74,2023) q(74,2024) q(74,2025) 75 q(75,2016) q(75,2017) q(75,2018) q(75,2019) q(75,2020) q(75,2021) q(75,2022) q(75,2023) q(75,2024) q(75,2025) 11

13 One-dimensional vs Two-dimensional Age-only projection scales consist of (gender-specific) MI rates that do not vary over time Example: Scale AA Let q(x,y) represent the mortality rate at age x in calendar year y Then q(x,2016+t) = q(x,2016) (1 - AA x ) t Two-dimensional projection scales consist of (gender-specific) MI rates that are functions of both age and calendar year Example: Scale MP-2016 Let f(x, y) represent the MP-2016 rate at age x in calendar year y Then q(x,2018) = q(x,2016) (1 f(x,2017)) (1 f(x,2018)) 12

14 One-dimensional Models used in the US «Tout ce qui est simple est faux, mais tout ce qui ne l'est pas est inutilisable.» - Paul Valéry (Everything simple is false, but everything complex is unusable.)

15 SOA MI Scales Life insurance products: Scale used in conjunction with AG 38 and VM 20 (Scale AG38- MI *) Individual annuity products: Scale G2 Statutory group annuity reserves: Scale AA Measuring retirement plan obligations: 1994 through 2011: Scale AA 2012 and 2013: Scale BB Post 2013: 2D RPEC models (MP-2014, MP-2015, and MP-2016) All age-only scales * No official name given to this mortality improvement scale. 14

16 General Approach to Age-Only Scales Work by independent groups in different areas resulted in similar general approach: 1. Historical data source identified Commonly population data Social Security (SSA), Human Mortality Database (HMD) 2. Projection Basis SSA intermediate projection (Alt 2) for specified period CMI Model or similar approach Stochastic models 3. Projection Period Short, Medium, Long Term depending on use of scale 15

17 General Approach to Age-Only Scales 4. Smoothing/Graduation 5. Approach for oldest ages Grade to zero by specific age Grade to a long-term average at a specific age 16

18 AG38/VM20 MI (Life Insurance) Approach for Oldest Ages Historical Look Back Period: 10 years Projection Basis SSA Intermediate Project (Alt II) Projection Period: 20 years Manual Smoothing/Graduation Grades to.2% annual improvement age 95 Historical Data Historical Basis: SSA Short term purpose but eliminates some noise * Long experience period * Consistent population basis * Issue: Basis Risk Review of New Data Sources New Academic/Research Reports New Data from HMD by Cause Reviewed for additional detail: CDC, HMD, SOA 17

19 AG38-MI (Life Insurance) 18

20 G2 (Individual Annuity) 19

21 AA (Group Annuity Reserves) 20

22 Explanation for AA s Shape 21

23 BB (Retirement Plan Obligations) 22

24 Development of Scale BB Derived from 2D array of smoothed/projected MI rates BB-2D (Males) RPEC backed into Scale BB from a table of deferred-toage-62 annuity values (RP-2000; i = 6%) 23

25 Comparison (Males) 24

26 Comparison (Females) 25

27 Summary of US MI Scales Scale Type Latest Update Basis AG38-MI Age-only 2016 SSA actual ( ) + SSA (Alt. II) assumed MI ( ) G2 Age-only 2011 SSA actual ( ) + SSA (Alt. II) assumed MI through a bit extra AA Age-only 1994 SSA & CSRS; retrospective only ( ) BB Age-only 2012 (Scale BB-2D): SSA; assumed LTR = 1.0%¹ MP D 2016 SSA; assumed LTR = 1.0%¹ SSA (Alt. II) 2D 2017 Age dependent assumed LTR² based on cause-ofdeath projections Discussed in the next section ¹ MP-2016 LTR equals 1.0% for all ages up to 85; then tapers to 0% by age 115. ² Average LTRs in 2017 Trustees Report are 1.01% for ages 15-64, 0.62% for

28 Two-dimensional Models in US, UK, and Canada

29 Conceptual Framework of 2-d MI Models MI Models/Scales transition from current rates to long term rates Key concepts of 2-d models Short-term: best predictor is current (most recent) experience Long-term: based on expert opinion (LTR assumption) Transition from current to LTR Key differences in example models / scales (CMI (UK), RPEC_2014 (USA), SSA (USA), and MI-2017/CPP (Canada) Cohort component treatment Convergence to LTR: direction, speed, and timing Smoothing or graduation of historical data: current rates 28

30 Conceptual Basis of Models Historical MI CP Interpolation LTR Attained Age / Period LTR Period + Cohort LTR Cohort 29

31 2-d MI Scales (US): RPEC_2014 RPEC_2014 Model Basis for MP-2014, MP-2015, and MP-2016 Conceptual framework based on CMI s (current) model Near-term MI rates should reflect recent experience Long-term MI rates (LTRs) should be based on expert opinion Near-term rates should blend smoothly into long-term rates In contrast to the CMI model, RPEC_2014 does not develop explicit A/P/C components Projection along 45 diagonals is meant to simulate cohort effects Smooth blending (from near-term to long-term) accomplished via horizontal and diagonal cubic splines 30

32 Heatmap: Scale MP

33 2-d MI Scales (US): SSA SSA Model Future mortality improvement is one of many demographic assumptions needed to assess the ongoing financial status of Social Security, Medicare and Medicaid Three sets of alternative assumptions (low-, medium-, and high-cost) Long-term rates of MI Based primarily on in-depth cause-of-death analysis Reflect different LTRs for different age ranges ( age gradient ) Interpolation methodology For each gender and age, the starting point of SSA projections is the average MI over the most prior 10 years Purely horizontal; no explicit recognition of cohort effects Quick transition away from near-term rates (towards long-term) 32

34 Heatmap: Example SSA MI Scale (Male) 33

35 2-d MI Scales (UK) Graduated Historical MI Age Period Cohort Residual 34

36 2-d MI Model (UK) A Convergence Periods (CP) Vary In Current CMI Methodology P A/P 100% of LTR C C Zero 35

37 CMI_2015 Example (UK) Mortality improvements from CMI_2015_M [1.5%] Source: The Future of the CMI Mortality Projections Model (October 2015) 36

38 Canadian Pensioners Mortality (CPM) Long-term MI rates equal to C/QPP assumption for 2030 and beyond Flat 0.8% through age 82 Gradual decline to 0% at age 115 Gender-/age-specific MI rates that decrease linearly (to the respective LTR) between 2012 and 2030 No explicit recognition of cohort effects Subcommittee acknowledged that a cohort effect could be observed for Canadian males, but that the impact on most pension valuations would be negligible Source: Final Report: Canadian Pensioners Mortality (February 2014) 37

39 CPM-B (MI Scale) Males 38

40 Canadian MI

41 Comparison of US, UK, and Canadian 2-d MI Scales Scale US MP-2017 US SSA TR 2017 UK CMI 2015 (core) Canada MI-2017 Canada CPP-27 Data/years to 2014 (prelim) 1/1/1975 to 7/1/ Smoothing 2-d Whitteker Henderson year average by age 2-d Age-cohort P-splines 2-d Whitteker Henderson 15-year average by age Recognize cohort effect? Yes No Yes No No Separate cohort effect? No No Yes No No A/P transition period 10 years 25 years Vary: years, years, years 10 years to 40, 20 years for 60+, grading linearly between 20 years A/P transition function Cubic (default 50% convegence by mid-point) Exponential decay, with third recognized by 5 years C transition period 20 years N/A Cubic (default 50% convergence by mid-point) Same as UK CMI Same as UK CMI 40 years for 20-60, years N/A N/A C transition function Same as A/P N/A Same as A/P N/A N/A LTR 1% to 85, grading to 0.85% at 95, to zero at %, and 0.62% for 65+ User Input-no default 1% to 90, to 0.2% at 100 and 0% at % to age 87, grading to 0 at 110 LTR (A/P) Half of LTR LTR LTR LTR LTR LTR (Cohort) Half of LTR N/A Zero N/A N/A 40

42 Assessing Model Effectiveness Essentially, all models are wrong, but some are useful. - George Box

43 Single Most Important Assumption: Long-Term Rate (LTR) How long is long-term? SSA: 25 years MP-2016: 10/20 years CMI Core : 20 years (cohort component 40) CPM-B: 20 years Even once a time frame has been established, determining an appropriate LTR can be problematic How much reliance should be placed on historical trends? Cause-of-death analysis (projected into the future) Expert opinion Unknown unknowns 42

44 Desirable MI Model Features Features to consider Stability Historical Fit Forecast Accuracy (Predictive Power) Smoothness Parsimony Simplicity Backtesting Relative important of the features should depend on the specific actuarial application Increasing the score of one feature often reduces the score of other features 43

45 Updating MI Scales: Recent Lesson Impact on pension liabilities of updating MI Scales in pension mortality assumption 2.5% Lesson on volatility Only last year we updated from AA to new scales: large increase in liabilities One year later: a significant down correction due to update under MP methodology Back-testing Impact of Annual Updates 7.0% 6.0% 5.0% 4.0% 3.0% 2.0% 1.0% 0.0% -1.0% -2.0% -3.0% Impact on Typical Plan Liabilities 6.4% 2.9% -0.3% -1.9% MP Methodology P 10 LTR_SSA 2014 Update 2015 Update 2.0% 1.5% 1.0% 0.5% 0.0% -0.5% -1.0% -1.5% -2.0% -2.5% Is back-testing a Crystal Ball? Back-testing shows volatility reduced with shortening convergence period(s) There are other ways to achieve this result Impact of updates for more years is cumulative Consecutive years often have impact in the same direction MP method minus P 10 LTR_SSA MP method P 10 LTR_SSA 44

46 Stability vs Fit Model stability (with respect to adding new years of data) and goodness-of-fit to historical MI rates tend to be inversely related This is especially true when the model s interpolation methodology reflects a direction of travel Signal vs noise: What is the appropriate amount of historical smoothing? 45

47 Stability vs Fit: Historical Smoothing LT100 January

48 Forecast Accuracy The ability to accurately predict future mortality rates should clearly be a desirable feature of any MI model But the forecast accuracy (or predictive power ) of a given model is turning out to be difficult to assess (!) CMI Working Paper #91 provides some reasons why this seems to be so challenging Inherent volatility of MI, along with no requirement that future drivers of MI must behave the same way as past drivers Interaction with the model s assumed long-term rate of MI Data limitations (with respect to backtesting) 47

49 Forecast Accuracy Back-testing 2.0% 1.5% 1.0% 0.5% 0.0% -0.5% -1.0% -1.5% Criteria here is how well did we predict the long term period average rates Female Age 65 example: Actual = 1.5% MP-model = 0.5%: Error 1.0% CMI-type = 1.3%: Error 0.2% Actual MP-model Projected CMI 5/20 & SSA88 Revisit Average Rates Example: female average MI rates MP-model projected uses data to 1995, with 2 year step back, first projection year 1994 CMI 5/20 model uses CMI-methodology with horizontal and diagonal periods of 5 and 20 respectively and LTR based on SSA averages to % 1.5% 1.0% 0.5% 0.0% For each age, forecast error = difference between average actual and model-based MI rates RMSE (14 years,50-95)= root mean square error across ages 50 to 95: lower error better forecast Graph of RMSE over 14-year period Label 1993: period % 0.25% -0.5% MP Methodology minus CMA 5-20 SSA88 MP Methodology CMA 5-20 SSA88 48

50 Questions?

51