1. HWSAS, Heriot-Watt University, Edinburgh The measureofmortality Stephen Richards 8th March 2016 Copyright c Longevitas Ltd. All rights reserved. This presentation may be freely distributed, provided it is unaltered and has this copyright notice intact. www.longevitas.co.uk1/57

2. Overview 1.About the speaker 2.Risk factors 3.Why longevity risk is different 4.Model risk 5.Conclusions www.longevitas.co.uk2/57

3. 1 About the speaker www.longevitas.co.uk3/57

4. 1 About the speaker Independent consultant on longevity risk since 2005. Founded longevity-related software businesses in 2006: Joint development with Heriot-Watt University in 2009: www.longevitas.co.uk4/57

5. 1 Connection to Heriot-Watt Graduated twice from Heriot-Watt: 1990 and 2012. Honorary Research Fellow Longevitas sponsors prize for survival models. www.longevitas.co.uk5/57

6. 2 Risk factors www.longevitas.co.uk6/57

7. 2 Risk factors Mortality by age.Richards et al. (2013). 1 ● ● 0 ● ● ● ● ● −1 ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● −2 ● ● ● ● ● −3 ● ● ● ● ● −4 ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● 60708090100110 AgeAge www.longevitas.co.uk7/57 log(crude mortality hazard)

8. 2 Risk factors Mortality by health at retirement.Richards et al. (2013). 1 ● ● 0 ● ● ● ● ● ● ● ● ● −1 ● ●● ● ● ● ● ●●● ● ●● −2 ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● −3 ● ● ● ● ● ● ●●●●●●●●●●●●●●●● −4 ●●●● ● ● Normal age retirements Ill−health early retirements ● ● ● ● ● ● ●● ● ● ● −5 ● ● ● 60708090100110 AgeAge www.longevitas.co.uk8/57 log(crude mortality hazard)

9. 2 Risk factors Survival curves for males and females.Richards et al. (2013). 1.0 0.8 0.6 0.4 0.2 Females Males 0.0 60708090100 AgeAge www.longevitas.co.uk9/57 Kaplan−Meier survival curve

10. 2 Risk factors Survival curves by pension size (males only). (2013). Richards et al. 1.0 0.8 0.6 0.4 0.2 Highest income (size band 3) Lowest income (size band 1) 0.0 60708090100 AgeAge www.longevitas.co.uk10/57 Kaplan−Meier survival curve

11. 2 What factors can you use? Pricing. Risk management and reserving. www.longevitas.co.uk11/57

12. 2 Pricing The following cannot be used in pricing individual insurance benefits: Gender. Race or ethnicity. Sexual orientation (including gender reassignment). Religion or belief. Pregnancy or maternity status. www.longevitas.co.uk12/57

13. 2 Risk management However...... regulators still expect insurers to use gender in risk management and reserving. www.longevitas.co.uk13/57

14. 2 Impact of risk factors I UK annuitants from Richards and Jones (2004): Risk factor Annuity factor Relative change Change Base case Gender Lifestyle Duration Pension size - Female→male Top→bottom Short→long 13.39 12.14 10.94 9.88 9.36 -9.3% -9.9% -9.7% -5.2% Largest→smallest Region South→North 8.90 -4.9% Overall-33.6% www.longevitas.co.uk14/57

15. 2 Impact of risk factors II German pensioners from Richards et al. (2013): Risk factor Annuity factor Relative change Change Base case Gender Retirement health Pension size Region - Female→male Normal→ill-health Largest→smallest 16.11 14.53 12.97 11.72 11.02 -9.8% -10.7% -9.7% -5.9% B→P Employer type Private→public 10.60 -3.9% Overall-34.2% www.longevitas.co.uk15/57

16. 2 Impact of risk factors Different portfolios have different risk factors available. Important to use risk factors relevant to your business processes. www.longevitas.co.uk16/57

17. 2 Risk factors: lifestyle Q. What was “Lifestyle” for the UK annuitants? A. Profile based on the annuitant’s address or postcode... www.longevitas.co.uk17/57

18. 2 Digression: UK postcodes UK has a hierarchical postcode structure. Each piece of postcode narrows in on a geographical area. Hierarchical postcodes in UK, USA, Canada and the Netherlands. www.longevitas.co.uk18/57

19. 2 Digression: UK postcodes Anatomy of a UK postcode www.longevitas.co.uk19/57

20. 2 Digression: UK postcodes Compare the postcodes EH4 4SP and EH3 6BX. Both in Edinburgh. Life expectancy “1.1 years less than the UK average” 1 1 Punter Southall, Postcode Life Expectancy Tool, accessed on 5th May 2015. www.longevitas.co.uk 20/57

21. 2 Digression: UK postcodes EH4 4SP. Source:Google Maps, accessed 5th May 2015. www.longevitas.co.uk21/57

22. 2 Digression: UK postcodes EH3 6BX. Source:Google Maps, accessed 5th May 2015. www.longevitas.co.uk22/57

23. 2 Digression: UK postcodes There are around 1.7 million residential postcodes. We can’t use Google Maps every time Solution is to map each postcode to a geodemographictype code... www.longevitas.co.uk23/57

24. 2 Digression: UK postcodes Mosaic family tree www.longevitas.co.uk24/57

25. 2 Digression: UK postcodes EH4 4SP → K46 Municipal Challenge, High-Rise Residents. EH3 6BX → A01 City Prosperity, World-Class Wealth. 1.7 million residential postcodes become 67 lifestyle codes. www.longevitas.co.uk25/57

26. 2 Geodemographic profiling Works in: UK. USA. Canada. The Netherlands. Does not appear to work in France. www.longevitas.co.uk26/57

27. entent 3 Why longevity risk is differ www.longevitas.co.uk27/57

28. entent 3 Why longevity risk is differ Opposing interests. Time frame over which risk operates. Limited information. www.longevitas.co.uk28/57

29. 3.1 Opposing interests Life insurance: neither side wants insured event to occur. Longevity insurance: pensioner wants exact opposite of what the insurer wants. www.longevitas.co.uk29/57

30. 3.1 Opposing interests Pensioners, their relatives, their doctors, medical science and government are all working to reduce the risk of death and increase longevity. Insurers hope their pricing assumptions are adequate. www.longevitas.co.uk30/57

31. 3.2 Time frame “Whereas a catastrophe can occur in an instant,longevityrisk takes decades to unfold” TheEconomist(2012) www.longevitas.co.uk31/57

32. 3.2 Time frame Mortality shocks are easy to spot. Longevity shocks much less so... www.longevitas.co.uk32/57

33. 3.2 1918 influenza pandemic www.longevitas.co.uk33/57

34. 3.2 1918 influenza pandemic for Swedish males, HMD data 2. ● mˆ x,1918 /mˆ x,1917 ● 3.5 ● 3.0 ● 2.5 ● ● 2.0 ● ● ● ●●●●●● 1.5 ● ● ● ● ● ● ● ● 1.0 ● ● ● ● ● ● ● ● ● ● ● 0.5 020406080 Age 2 mˆ x is the estimated central death rate at age x last birthday. www.longevitas.co.uk 34/57 m ^ x,1918 m ^ x,1917 ● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●

35. ge? 3.2 When does a trend chan mˆ 70 for Swedish males, HMD data. 0.045 ● ● ● ● ● 0.040 ● ● ● ● 0.035 ● ● ● 0.030 ● 0.025 0.020 ● 1950196019701980199020002010 Year www.longevitas.co.uk35/57 m ^ 70 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●

36. 3.2 Time frame Can only detect a trend change several years after it has already started... Longevity risk not a natural fit to “1:200 over one year” approach. Run-off is the appropriate way to view this risk... www.longevitas.co.uk36/57

37. 3.3 Limited information “As there is not currently a deep and liquid market for longevity risk, firms are required to derive their longevity assumptions from first principles” Bank ofEnglandPrudential Regulatory Authority (2015) www.longevitas.co.uk37/57

38. 3 Market forecast for interest Yield curve for UK non-index-linked gilts without accrued interest (DMO data for 2015-04-16). 2.5 ●● ● ●● ● ●●● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●●●●●●●●●●●●●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●●●●●●●●●●●● ●●●●●●●● ●●●●●●●● 2.0 ● ●●●●●● ●●●●●● ●●●●●● 1.5 ● ● ● ● ● ● ● ●●●● 1.0 ● ● ● ● 0.5 ● ● ● 010203040 Term to maturity (years) www.longevitas.co.uk38/57 Yield (%) ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●

39. n 3 Market forecast for inflatio Yield curve for UK index-linked gilts (DMO data for 2015-04-16). ● ● ● ● ● ● ● ● ● ● ● ● ● ● −1.0 −1.2 −1.4 −1.6 01020304050 Term to maturity (years) www.longevitas.co.uk39/57 Yield (%) ●●●●●●●●●●●●●●●●

40. 3.3 Limited information Market forecasts exist for economic variables on a near-daily basis. There is no market forecast for mortality rates or longevity. Population mortality data published once a year. www.longevitas.co.uk40/57

41. 3.3 Limited information Without a “deep and liquid market” to provide market views, benchmarking projections is tricky. Longevity-related assumptions can be seen as a malleable item in reserving. Pressure to back-solve longevity assumptions from a given level of capital, rather than the other way around. Greatest risk of back-solving lies in models with lots of subjective assumptions. www.longevitas.co.uk41/57

42. 4 Model risk www.longevitas.co.uk42/57

43. 4 Model risk Many options available for mortality projections: Deterministic scenarios v. stochastic models. All-cause mortality v. cause-of-death. Targeting methods v.extrapolation. www.longevitas.co.uk43/57

44. 4 Model risk Different models produce different capital requirements... www.longevitas.co.uk44/57

45. 4 Model risk Run-off capital requirements by age for four stochastic models. Source:Richards et al. (2014). 7% 6% 5% 4% Lee−Carter (1992) Cairns−Blake−Dowd (2006) Age−Period−Cohort 2D age−period (2004) 3% 5560657075808590 AgeAge www.longevitas.co.uk45/57 Stressed−trend 99.5% capital requirement

46. 4 Model risk The best way to deal with model risk is to not rely on a single model. The PRA itself works with: “four commonly used families of stochastic longevity risk models” Bank of England Prudential Regulatory Authority (2015) www.longevitas.co.uk46/57

47. 4 Expert judgement “The advantage of expert opinion is the incorporation of demographic, epidemiological and other relevant knowledge, at least in a qualitative way...” BoothandTickle(2008) www.longevitas.co.uk47/57

48. 4 Expert judgement “...The disadvantage is its subjectivity and potential for bias. The conservativeness of expert opinion with respect to mortality decline is widespread, in that experts have generally been unwilling to envisage the long-term continuation of trends, often based on beliefs about limitstolife expectancy.” Booth and Tickle (2008) www.longevitas.co.uk48/57

49. 4.2 Cause-of-death models Considerable technical challenges discussed by Continuous Mortality Investigation (2004). Drawbacks discussed by Richards (2010) 3. 3 More details at www.longevitas.co.uk www.longevitas.co.uk/site/informationmatrix/?tag=cause+of+death 49/57

50. 4.2 Cause-of-death models UK PRA did not use any cause-of-death models: “due to their greater complexity, data requirements and the need for a greater level of expert judgement to be exercised. In particular we were concerned that the correlations between causes of death were not easily measured and would not be stable over time” Bank of England Prudential Regulatory Authority (2015) www.longevitas.co.uk50/57

51. h? 4.2 Correlated causes of deat Mortality rates due to influenza and CHD. Source: Massachusetts Department of Public Health Registry of Vital Records and Statistics. 700 CHD mortality rate Influenza mortality rate 600 500 400 300 200 100 0 1850190019502000 Year www.longevitas.co.uk51/57 Rate per 100,000

52. 4.2 Cause-of-death models Cause-of-death models often structured with a few broad “independent” categories. This is at best a simplifying assumption. At its worst, it ignores important correlations. www.longevitas.co.uk52/57

53. 5 Conclusions www.longevitas.co.uk53/57

54. 5 Conclusions Insurers constrained in what risk factors they can use in pricing. Longevity risk has unique features compared to other demographic risks. Model risk handled by using multiple models. Stick to openly published models in peer-reviewed journals. www.longevitas.co.uk54/57

55. References I Bank of England Prudential Regulatory Authority (2015, March). Solvency II: matching adjustment update. Letter to UK-regulated insurers and reinsurers. Booth, H. and L. Tickle (2008). Mortality modelling and forecasting: a review of methods. Annals of Actuarial Science 3(I/II), 3–44. Continuous Mortality Investigation (2004). Projecting future mortality: A discussion paper. Continuous Mortality Investigation. www.longevitas.co.uk55/57

56. References II Richards, S. J. (2010). Selected issues in modelling mortality by cause and in small populations. British Actuarial Journal 15 (supplement), 267–283. Richards, S. J., I. D. Currie, and G. P. Ritchie (2014). A value-at-risk framework for longevity trend risk. British Actuarial Journal 19 (1), 116–167. Richards, S. J. and G. L. Jones (2004). Financial aspects of longevity risk. Staple Inn Actuarial Society (SIAS), London. Richards, S. J., K. Kaufhold, and S. Rosenbusch (2013). Creating portfolio-specific mortality tables: a case study. European Actuarial Journal 3 (2), 295–319. www.longevitas.co.uk56/57

57. References III The Economist (2012). The ferment of finance. Special reporton financialinnovationFebruary25th2012, 8. www.longevitas.co.uk57/57