Session 6A, Mortality Improvement Approaches Moderator: Jean Marc Fix, FSA, MAAA Presenters: Laurence Pinzur, FSA
Session 6A Mortality Improvement Models 6 January 2017 Laurence Pinzur, PhD, FSA Aon Hewitt
Agenda The Challenge Some Basics Deterministic Models used in the US Deterministic Models used in the UK and Canada Assessing Model Effectiveness Questions LT100 January 2017 2
The Challenge Prediction is very difficult, especially about the future. Niels Bohr
The Challenge = 1.0% = 1.6% Source: SOA; Mortality Improvement Scale MP 2016 Report LT100 January 2017 4 4
The Challenge LT100 January 2017 5 5
The Challenge: Signal vs Noise LT100 January 2017 6 6
Some Basics
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 LT100 January 2017 8 8
Age Only vs Two Dimensional Age only projection scales consist of (genderspecific) 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)) LT100 January 2017 9 9
Static vs Generational Mortality Calendar Year Static Age 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 60 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) LT100 January 2017 10 10
Deterministic 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.)
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. LT100 January 2017 12 12
AG38 MI (Life Insurance) LT100 January 2017 13
G2 (Individual Annuity) LT100 January 2017 14
AA (Group Annuity Reserves) LT100 January 2017 15
Explanation for AA s Shape LT100 January 2017 16
BB (Retirement Plan Obligations) LT100 January 2017 17
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%) LT100 January 2017 18
Comparison (Males) LT100 January 2017 19
Comparison (Females) LT100 January 2017 20
2D 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 LT100 January 2017 21 21
Heatmap: Scale MP 2016 LT100 January 2017 22 22
2D 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) LT100 January 2017 23 23
Heatmap: SSA MI Scale LT100 January 2017 24 24
Summary of US MI Scales Scale Type Latest Basis Update AG38 MI Age only 2016 SSA actual (2003 2013) + SSA (Alt. II) assumed MI (2014 2034) G2 Age only 2011 SSA actual (1990 2006) + SSA (Alt. II) assumed MI through 2022 + a bit extra AA Age only 1994 SSA & CSRS; retrospective only (1977 1993) BB Age only 2012 (Scale BB 2D): SSA; assumed LTR = 1.0%¹ MP 2016 2D 2016 SSA; assumed LTR = 1.0%¹ SSA (Alt. II) 2D 2016 Age dependent assumed LTR² based on cause of death projections ¹ MP 2016 LTR equals 1.0% for all ages up to 85; then tapers to 0% by age 115. ² Average LTRs in 2016 Trustees Report are 0.90% for ages 15 49, 1.07% for ages 50 64, 0.74% for ages 65 84, and 0.49% for ages 85+. LT100 January 2017 25 25
Deterministic Models Used in the UK and Canada
Current CMI Graduated Historical MI Age Period Cohort Residual LT100 January 2017 27 27
Current CMI Convergence Periods (CP) Vary In Current CMI Methodology A P A/P 100% of LTR C C Zero LT100 January 2017 28 28
Current CMI Historical MI Interpolation LTR Attained A/P 100% of LTR + C Zero + Residuals LT100 January 2017 29 29
CMI_2015 Example Mortality improvements from CMI_2015_M [1.5%] Source: The Future of the CMI Mortality Projections Model (October 2015) LT100 January 2017 30 30
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) LT100 January 2017 31 31
CPM B (MI Scale) Males LT100 January 2017 32 32
Assessing Model Effectiveness Essentially, all models are wrong, but some are useful. George Box
Desirable MI Model Features Features to consider Stability Historical Fit Backtesting Forecast Accuracy (Predictive Power) Smoothness Parsimony Simplicity 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 LT100 January 2017 34 34
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? LT100 January 2017 35 35
Stability vs Fit: Historical Smoothing LT100 January 2017 36
Long Term Rate (LTR) How long is long term? SSA: 25 years MP 2016: 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 LT100 January 2017 37 37
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 our 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) LT100 January 2017 38 38
Inherent Volatility For a specific fixed age, let m(t) represent the central mortality rate for that age at time t Let s assume: log m(t) = S(t) + Z(t), where S(t) is some smooth, slowly varying, deterministic underlying trend and Z(t) is a standard normal random variable Variance for log m(t), Mortality Improvement (MI) and Direction of Travel (DoT) (log ( )) = 2 ( ( )) = ( Δ log ( )) = (Δ log ( )) = 2 2 ( ( )) = ( Δ 2 log ( )) = (Δ 2 log ( )) = 6 2 Source: CMI Working Paper #91; Section 5.3 LT100 January 2017 39 39
Questions 40