#SIASJun15 The Nature of Longevity Risk Sacha Dhamani Demographic Risk Actuary, Partnership Assurance 9 June 2015
Agenda • Conceptual Framework • Systemic Behaviours • Specific Behaviours • Variation in Longevity Exposure 2 03 July 2015
Conceptual Framework 03 July 2015
Why is a Conceptual Approach Important ? 4 03 July 2015
Longevity Risk Universe 5 03 July 2015
Direct Mathematical Approach 6 03 July 2015
Conceptual Modelling Approach 7 03 July 2015
Overly Simplistic Approach 8 03 July 2015
Conceptual Framework • Trend Uncertainty • Trend Volatility • Catastrophe • Basis Risk • Underwriting Risk • Mis-estimation Risk • Statistical Volatility 9 03 July 2015
Foundation Assumptions • Uncertainty & Volatility – Uncertainty: the risk of getting the average wrong – Volatility: the risk of getting the average right, but being unlucky • Systemic & Specific – Systemic: risk arising in the reference population – Specific: risk arising in the portfolio 10 03 July 2015
Division of Risk Behaviours Uncertainty in Volatility in setting the “right” experience relative to assumptions the “right” assumptions Systemic (or population risks) Specific (or portfolio risks) 11 03 July 2015
Division of Risk Behaviours Uncertainty in Volatility in setting the “right” experience relative to assumptions the “right” assumptions Systemic Trend Uncertainty Trend Volatility (or population Catastrophe risks) Specific Mis-Estimation Volatility (or portfolio Basis risks) Underwriting 12 03 July 2015
Systemic Behaviours 03 July 2015
Systemic Longevity Risk Trend Uncertainty Uncertainty in the trend of mortality improvements Trend Volatility Volatility in the trend of mortality improvements Catastrophe A “catastrophic shift” in mortality rates 14 03 July 2015
Trend Uncertainty Trend uncertainty is the risk relating to the ability to predict mortality rates in the future as mortality is influenced by a range of drivers such as: • Development in medical treatments 110% • Lifestyle factors 100% • Economic circumstances Percentage of 2014 Mortality 90% • Public policy 80% • Etc . . . 70% 60% 50% 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 Age Male - CMI Male - MBC Female - CMI Female - MBC 15 03 July 2015
Trend Volatility Two Scenarios : 1.1 1. The survival curve is 1 shifted to the right – 0.9 permanent increase Surival Probability 0.8 in LE 0.7 2. The future survival 0.6 curve is unchanged after the period of 0.5 volatility – temporary 0.4 increase in LE 0.3 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Projection Year BE Scenario 1 Scenario 2 16 03 July 2015
Catastrophe ??? 17 03 July 2015
Catastrophe 18 03 July 2015
HIV and AIDS in 1990s 19 03 July 2015
Comparison of Systemic Shapes 100.000% Reduction in Mortality Rates 95.000% 90.000% 85.000% 80.000% 75.000% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Projection Year Trend Uncertainty Trend Volatility Catastrophe 20 03 July 2015
Specific Behaviours 03 July 2015
Provider Variation 0.3 Population Standard Provider 0.25 Postcode Rated Annuity Provider Enhanced Annuity Provider 0.2 0.15 0.1 0.05 0 0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9 4.1 4.3 4.5 4.7 4.9 5.1 5.3 5.5 5.7 5.9 6.1 6.3 6.5 6.7 6.9 7.1 7.3 7.5 7.7 7.9 8.1 8.3 8.5 8.7 8.9 9.1 9.3 9.5 9.7 9.9 Increasing number of years of life lost 22 03 July 2015
Managing Longevity Risk Longevity Risk is managed using information from three source: • External mortality experience or related analysis from a reference population – E.g. base tables, trend assumptions, postcode rating, scheme rating, etc • Individual life information – Medical underwriting, lifestyle underwriting, etc • Past mortality experience of the portfolio This leads to residual risks . . . 23 03 July 2015
Specific Longevity Risk Mis-estimation Statistical error in the calibration of the mortality basis to past experience Uncertainty in the assumptions drawn from Basis “external” experience Uncertainty in the assumptions from Underwriting specific information by the individual Volatility Random chance of portfolio deaths These are portfolio specific and will vary by the nature of the annuity provider 24 03 July 2015
Specific Longevity Risk Underwriting Mis- Risk Estimation Risk Basis Risk 25 03 July 2015
Specific Longevity Risk Underwriting Mis- Risk Estimation Risk Basis Risk 26 03 July 2015
Specific Longevity Risk And don’t forget the model risk! Underwriting Mis- Risk Estimation Risk Basis Risk 27 03 July 2015
Basis Risk • Relevance • Heterogeneity • Selection Risk • Survivorship Bias • Risk Factor Weighting Bias 28 03 July 2015
Basis Risk • Relevance • Heterogeneity • Level • Trend • Selection Risk • Shape • Survivorship Bias • Model • Risk Factor Weighting Bias . . . All add up to the assumptions not being appropriate to the lives they are being applied to 29 03 July 2015
Mis-Estimation Risk • Parameter • Model Relevance, whilst a basis risk, is a critical aspect of utilising past experience 30 03 July 2015
Credibility of Experience A 1 J B 0.8 0.6 0.4 I C 0.2 0 H D G E F 31 03 July 2015
Credibility of Experience A 0.6 J B Area of credible experience 0.4 0.2 I C 0 H D G E F 32 03 July 2015
Underwriting Risk Interpretation of Individual Life Details Life Specific Measure of Mortality Assessment of Individual Rating Factors 33 03 July 2015
Underwriting Risk Interpretation of Individual Life Details Life Specific Measure of Mortality Assessment of Individual Rating Factors 34 03 July 2015
Underwriting Risk • Starting Point • Trends in Risk Factor Effect • Data Quality & Reporting Bias • Relevance 35 03 July 2015
Underwriting Risk • Starting Point • Trends in Risk Factor Effect • Data Quality & Reporting Bias • Relevance 36 03 July 2015
Comparison of Frameworks IAA Risk Behaviours Richards Risk Behaviours Proposed Risk Behaviours Volatility Idiosyncratic Statistical Volatility Catastrophe N/a Catastrophe Volatility Trend Volatility Trend Trend Uncertainty Trend Uncertainty Model Basis Basis Mis-estimation Mis-estimation Level Uncertainty N/a Underwriting Sources: A Global Framework for Insurer Solvency Assessment, A value-at-risk framework for longevity trend risk, Richards, Currie and Ritchie, 2012 37 03 July 2015
Variation in Longevity Risk 03 July 2015
Variation in Longevity Risk • Mortality Rating Approach • Credibility of Experience • Size of Portfolio • And many others! 39 03 July 2015
Mortality Rating Approach • “Standard” provider; – no account is taken of the mortality differences resulting health status or geographical location and the mortality basis is likely to be a modified base and trend. • Postcode rating provider; – account is taken of the geographical variation as a proxy for health and socio-economic variation. • Underwriting provider; – account is taken of individual health status 40 03 July 2015
Insurance Company Example (1) • Time 1 – Company A buys an annuity company (with existing liability and active in the market) – comes with no experience and limited policy holder information (dob, gender, postcode, premium). – assumptions are derived from external sources of information • Time 2 – Adopts an underwriting approach – For all lives (past and new) medical information is available to base the mortality assumptions on. • Time 3 – Underwriting assumptions are experience rated • Time 4 – Externally derived assumptions are experience rated 41 03 July 2015
Insurance Company Example (2) Risk Time 1 Time 2 Time 3 Time4 Population 50 50 50 50 Volatility 10 10 10 10 Basis 60 30 30 20 Underwriting 0 30 20 20 Mis-estimation 0 0 10 20 Total 120 120 120 120 42 03 July 2015
Insurance Company Example (3) Undiversified Diversified Undiversified Diversified Undiversified Diversified Undiversified Diversified 1 2 3 4 Population Volatility Basis Underwriting Mis-estimation Diversified calculated using the Euler Method assuming independence 43 03 July 2015
Insurance Company Example (4) Undiversified Diversified Undiversified Diversified Undiversified Diversified Undiversified Diversified 1 2 3 4 Population Volatility Basis Underwriting Mis-estimation Diversified calculated using the Euler Method assuming independence 44 03 July 2015
Size of Portfolio 45 03 July 2015
Final Thoughts 03 July 2015
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