1. Longevity risk: asset or liability? Stephen Richards, Longevitas Ltd Society of Actuaries webcast, 9 th December 2011

2. Contents 1.About the speaker 2.Why care about longevity risk? 3.Investing in longevity risk 4.Underwriting longevity risk 5.Longevity tail risk 6.Conclusions Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk

3. 1. About the speaker Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk

4. 1. About the speaker Consultant on longevity risk since 2005 Founded two longevity-related software businesses in 2006: Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk Joint venture with Heriot-Watt University in 2009:

5. 2. Why care about longevity risk? Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk

6. 2. Why care about longevity risk? “ By providing financial protection against the major 18th- and 19th- century risk of dying too soon, life insurance became the biggest financial industry of that century […] Providing financial protection against the new risk of not dying soon enough may well become the next century's major and most profitable financial industry." Drucker (1999) Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk

7. 2. Why care about longevity risk? Sensitivity of reserves to longevity risk has increased dramatically As interest rates fall, relative change in annuity factor increases Errors in estimating longevity have more impact than in the past… Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk

8. 2. Why care about longevity risk? Gilt yields (left) and change in a 65 from 20% mortality reduction (right): Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk Source: End-year yields from British Government Stock (10-year nominal par yield, series IUAMNPY from Bank of England) and own calculations for a 65 using S1PA (males) and same yields.

9. 3. Investing in longevity risk Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk

10. 3. Spot the insurance company Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk CompanyLongevity liability (£ billions) BT43.3 Royal Dutch Shell42.1 Prudential plc36.5 Source: Figure are 2010 pension-scheme liabilities sourced from LCP's “Accounting for pensions 2011" report. The figure for Prudential includes the end-2010 annuity liabilities in the PAL and PRIL subsidiaries.PALPRIL

11. 3. Investing in longevity risk Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk Equity investors often already long in longevity risk How well underwritten and managed is it…?

12. 4. Underwriting longevity risk Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk

13. 4. Underwriting longevity risk Traditional actuarial risk factors for underwriting longevity risk: Age Gender Pension size Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk

14. 4. Underwriting longevity risk Challenges to traditional underwriting approach: 1.Gender banned as pricing factor in EU from December 2012 1 2.Pension size is becoming less reliable as a proxy for wealth and socio-economic group Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk 1 Group contracts are unaffected as long as gender does not determine an individual’s benefits or premiums.

15. 4. Longevity and occupation Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk Source: ONS Longitudinal Study. Strong and persistent differences in life expectancy by occupation:

16. 4. Longevity and pension size Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk Source: Longevitas Ltd. Mixed impact of pension size due to fragmented provision:

17. 4. Underwriting longevity risk Pension size imperfect proxy for wealth or income Use postcodes to counter weaknesses of pension size Postcodes now routinely used for pricing annuities… Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk

18. 4. Structure of UK postcode Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk Source: Longevitas Ltd

19. 4. Postcodes 1.6 million residential postcodes in UK Not used directly in underwriting Instead, each postcode maps to a geodemographic type… Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk

20. 4. Geodemographic profiling Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk Source: Mosaic “family tree”, Experian Ltd

21. 4. Underwriting longevity risk Use postcodes to counter weaknesses of pension size Expand risk factors to adapt to loss of gender in underwriting Use statistical models to avoid double-counting of impact Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk

22. 5. Longevity tail risk Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk

23. 5. Longevity tail risk Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk Solvency II is about reserving for tail risk Stochastic models particularly useful for estimating a 99.5 th percentile…

24. 5. Longevity tail risk Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk Source: Own calculations of log(mortality) for males aged 70 in England & Wales, with sample paths from ARIMA projection under model of Delwarde, Denuit and Eilers(2007).

25. 5. Longevity tail risk Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk Beware of models with artificial limits to mortality reduction Such models are inappropriate for estimating tail risk…

26. 5. Longevity tail risk Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk Source: Own calculations of log(mortality) for males aged 70 in England & Wales, with sample paths from ARIMA projection under model of Delwarde, Denuit and Eilers(2007) subject to artificial reduction limit.

27. 5. Longevity tail risk Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk Model risk: how do you know your projection model is correct? What are the consequences if it is not? Critical to use more than one projection model… …and to avoid models with tail restrictions!

28. 6. Conclusions Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk

29. 6. Conclusions Equity investors already exposed to substantial longevity risk How well is it managed? Statistical models and postcodes now essential for underwriting Stochastic projection models essential to manage uncertainty Dangerous (negligent?) to rely on a single projection model Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk

30. References Delwarde, A., Denuit, M. and Eilers, P.H.C. 2007 Smoothing the Lee-Carter and Poisson log-bilinear models for mortality forecasting: a penalized likelihood approach, Statistical Modelling, 7, pages 29–48. Drucker, P. 1999 Innovate or die, The Economist, September 23 rd 1999.Innovate or die Richards, S. J. 2008 Applying survival models to pensioner mortality data, British Actuarial Journal, Volume 14, Part I, pages 257–326. Richards, S. J. 2011 A head for tails, Longevitas blog.A head for tails Copyright © 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.ukwww.longevitas.co.uk