longevity risk: asset or liability? stephen richards, longevitas ltd society of actuaries webcast, 9...

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

http://www.longevitas.co.uk/

1. About the speaker



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:


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)




• 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…



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 a65 using S1PA (males) and same yields.


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.


http://www.prudential.co.uk/prudential-plc/investors/financialreports/2010/pru-annu-ltd-2010-fsa/pru-annu-ltd-2010-fsa.pdf

http://www.prudential.co.uk/prudential-plc/investors/financialreports/2010/pru-ret-inc-ltd-2010-fsa/pru-ret-inc-ltd-2010-fsa.pdf



• Equity investors often already long in longevity risk

• How well underwritten and managed is it…?


4. Underwriting longevity risk




• Traditional actuarial risk factors for underwriting longevity risk:

• Age

• Gender

• Pension size




• Challenges to traditional underwriting approach:

1. Gender banned as pricing factor in EU from December 20121

2. Pension size is becoming less reliable as a proxy for wealth

and socio-economic group


1Group contracts are unaffected as long as gender does not determine an individual’s benefits or premiums.


4. Longevity and occupation


Source: ONS Longitudinal Study.

Strong and persistent differences in life expectancy by occupation:


4. Longevity and pension size


Source: Longevitas Ltd.

Mixed impact of pension size due to fragmented provision:



• Pension size imperfect proxy for wealth or income

• Use postcodes to counter weaknesses of pension size

• Postcodes now routinely used for pricing annuities…



4. Structure of UK postcode


Source: Longevitas Ltd


4. Postcodes

• 1.6 million residential postcodes in UK

• Not used directly in underwriting

• Instead, each postcode maps to a geodemographic type…



4. Geodemographic profiling


Source: Mosaic “family tree”, Experian Ltd



• 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


5. Longevity tail risk




• Solvency II is about reserving for tail risk

• Stochastic models particularly useful for estimating a 99.5th percentile…



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).



• Beware of models with artificial limits to mortality reduction

• Such models are inappropriate for estimating 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.



• 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!

6. Conclusions


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


References

Delwarde, A., Denuit, M. and Eilers, P.H.C. 2007 Smoothing theLee-Carter and Poisson log-bilinear models for mortality forecasting: apenalized likelihood approach, Statistical Modelling, 7, pages 29–48.

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 257–326.

Richards, S. J. 2011 A head for tails, Longevitas blog.


longevity risk: asset or liability? stephen richards, longevitas ltd society of actuaries webcast, 9...

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