Pricing Longevity Risk - Richards Consulting

Pricing Longevity Risk - Richards Consulting

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

Copyright 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.uk 1. About the speaker Consultant on longevity risk since 2005 Founded two longevity-related software businesses in 2006:

Joint venture with Heriot-Watt University in 2009: Copyright 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.uk 2. Why care about longevity risk? Copyright 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.uk

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.uk 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.uk 2. Why care about longevity risk? Gilt yields (left) and change in a65 from 20% mortality reduction (right): 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.

Copyright 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.uk 3. Investing in longevity risk Copyright 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.uk 3. Spot the insurance company Company

Longevity liability ( billions) BT 43.3

Royal Dutch Shell 42.1 Prudential plc 36.5

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

Copyright 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.uk 4. Underwriting longevity risk Copyright 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.uk 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.uk 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 1 Group contracts are unaffected as long as gender does not determine an individuals benefits or premiums.

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

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

Source: Longevitas Ltd Copyright 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.uk 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.uk 4. Geodemographic profiling Source: Mosaic family tree, Experian Ltd Copyright 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.uk 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.uk 5. Longevity tail risk

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

5. Longevity tail risk 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). Copyright 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.uk 5. Longevity tail risk Beware of models with artificial limits to mortality reduction

Such models are inappropriate for estimating tail risk Copyright 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.uk 5. Longevity tail risk 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.

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

Copyright 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.uk 6. Conclusions Copyright 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.uk 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.uk 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 2948. Drucker, P. 1999 Innovate or die, The Economist, September 23rd 1999. Richards, S. J. 2008 Applying survival models to pensioner mortality data, British Actuarial Journal, Volume 14, Part I, pages 257326. Richards, S. J. 2011 A head for tails, Longevitas blog.

Copyright 2011 Longevitas Ltd. All rights reserved. www.longevitas.co.uk

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