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Survivor Products: Managing longevity risk & mortality improvements. Professor David Blake Director Pensions Institute Cass Business School [email protected] The problem. Nothing is certain in life except death and taxes (B Franklin).

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Survivor products managing longevity risk mortality improvements l.jpg
Survivor Products: Managing longevity risk & mortality improvements

Professor David Blake

Director

Pensions Institute

Cass Business School

[email protected]


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The problem

  • Nothing is certain in life except death and taxes (B Franklin).

  • Over last 20 years, it has become clear that, while death is no less inevitable than before:

    • it is getting later

    • and its timing has become increasingly uncertain.


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The problem

  • When British welfare state began in 1948, men could draw their state pension at 65 and expect to live until 67 and only a few lived beyond 70.

  • At beginning of 21st Century, British men can still draw their pension from age 65 but now live into their early 80s.

  • Significant proportion of women living into their late 80s.




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What is longevity risk?(Broken limits to life expectancy – Oeppen & Vaupel)


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Stochastic nature of mortality improvements

  • Evident for many years that mortality rates have been evolving in apparently stochastic fashion.

  • Sequences do exhibit general trend, but changes have an unpredictable element:

    • not only from one period to next

    • but also over the long run.


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Longevity risk

  • Large number of products in life insurance and pensions have mortality as key source of risk.

  • Products exposed to unanticipated changes over time in mortality rates of relevant reference populations.

  • Eg annuity providers exposed to risk that mortality rates of pensioners will fall at faster rate than accounted for in pricing and reserving calculations:

    • Current pool of annuitants living 2 years longer than anticipated


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Longevity risk

  • Annuities are commoditised products selling on basis of price, profit margins have to be kept low in order to gain market share.

  • If mortality assumption built into price of annuities turn out to be gross overestimate, cuts straight into profit margins of annuity providers.

  • Most life companies claim to lose money on annuity business.


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Longevity risk

  • Yet life annuities are mainstay of pension plans throughout the world:

    • they are the only instrument ever devised capable of hedging longevity risk.

  • Without them, pension plans will be unable to perform their fundamental task of protecting retirees from outliving their resources for however long they live.

  • Real danger that they might disappear from financial scene.


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Longevity risk

  • Equitable Life:

  • Embedded options in annuity contracts became very valuable in 1990's due to combination of falling interest rates and improvements in mortality.

  • Problems avoided if EL could hedge exposures to:

    • interest-rate risk

    • mortality improvement risk.


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Longevity risk in UK pension provision, £billion of total liabilities- broad estimates: end 2003

Figure 5.17 p181


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Significant concern! liabilities- broad estimates: end 2003

Reinsurers (eg Swiss Re) have stopped reinsuring longevity risk of life offices!


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Survivor Products liabilities- broad estimates: end 2003

  • Long-dated survivor bonds:

  • Life annuity bond: coupon payments decline in line with mortality index:

    • Eg based on population of 65-year olds on issue date.

  • As population cohort dies out, coupon payments decline, but continue in payment until the entire cohort dies.

  • Eg, if after one year 1.5% of population has died out, 2nd year’s coupon payment is 98.5% of 1st year’s etc


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Survivor Products liabilities- broad estimates: end 2003

  • Bond holder, eg life office writing annuities, protected from aggregate mortality risk it faces.

  • Based on Tontine Bonds issued by European governments in 17th and 18th centuries

  • Recently revived by Blake and Burrows (2001) and Lin and Cox (2004).


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BNP Paribas Longevity Bond liabilities- broad estimates: end 2003

  • November 2004

  • Issuer: European Investment Bank (AAA)

  • Issue: £540m, 25 year

  • Mortality index: 65 year-old males from England & Wales (ONS)

  • Structurer/manager: BNP Paribas (assumes longevity risk)

  • Reinsurer of lengevity risk: PartnerRe, Bermuda

  • Investors: UK pension funds


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BNP Paribas Longevity Bond liabilities- broad estimates: end 2003


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Advantages of longevity bond liabilities- broad estimates: end 2003

  • Provides better match for liabilities of pension funds and life insurers than other available investments:

    • other than purchasing (re)insurance to cover the longevity risk (i.e annuities)

  • Bond also provides long term interest rate hedge.

  • Longevity index transparent

  • EIB has AAA credit rating.

  • Life insurers holding longevity bond as hedge may be able to hold lower prudential margins.


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Survivor Products liabilities- broad estimates: end 2003

  • Short-dated, mortality-linked securities:

  • Market-traded securities whose payments are linked to mortality index

  • Similar to catastrophe bonds (Schmock, 1999, Lane, 2000, Wang, 2002, and Muermann, 2004)


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Swiss Re Bond 2003 liabilities- broad estimates: end 2003

  • Designed to securitise Swiss Re’s own holding of mortality risk!

  • 3-year contract (matures 1 Jan 2007) which allows issuer to reduce exposure to catastrophic mortality events:

    • severe outbreak of influenza

    • major terrorist attack (WMD)

    • natural catastrophe.

  • Mortality index (MI):

    • US (70%), UK (15%), France (7.5%), Italy (5%), Switzerland (2.5%).

    • Male (65%), Female (35%)

    • Also age bands


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Influenza pandemics liabilities- broad estimates: end 2003

  • All resulted from avian flu virus mutating with human flu virus

  • 11 outbreaks in 300 years

  • 1580

    • First confirmed flu pandemic

  • 1782

    • Summer Flu

    • Started in China

    • Hit young adults

  • 1889

    • Russian Flu

    • Over 20% of world population infected

    • 1m deaths


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Influenza pandemics liabilities- broad estimates: end 2003

  • 1918-19

    • Spanish Flu

    • Started in Kansas

    • Killed 50m people worldwide:

      • 250,000 in UK

    • More than died in WW1, in shorter period

    • 20% of world’s population infected and 1% killed

    • Spread along trade routes and shipping lines


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Influenza pandemics liabilities- broad estimates: end 2003

  • 1957-58

    • Asian Flu

    • 2m deaths

    • Hit teenagers hardest

    • Spread around world in 6 months

  • 1968-69

    • Hong Kong Flu

    • Started in China

    • 1m deaths

    • Spread slowly with moderate symptons


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Influenza pandemics liabilities- broad estimates: end 2003

  • 2005-06

    • Started in SE Asia

    • H5N1 virus

    • Closely related to 1918 Spanish virus


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Swiss Re Bond 2003 liabilities- broad estimates: end 2003

  • $400m, principal at risk ‘if, during any single calendar year, combined mortality index exceeds 130% of baseline 2002 level’.

  • Principal exhausted if index exceeds 150%

  • Equivalent to a call option spread on the index with:

    • Lower strike price of 130%

    • Upper strike price of 150%

  • Investors get quarterly coupons of 3-mo USD Libor + 135bp


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Swiss Re Bond 2003 liabilities- broad estimates: end 2003


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Swiss Re Bond 2003 liabilities- broad estimates: end 2003


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Swiss Re Bond 2003 liabilities- broad estimates: end 2003

  • Bond valued using Extreme Value Theory (Beelders & Colarossi (2004))

  • Assume Generalised Pareto Distribution

  • Probability of attachment:

    • P[MI(t)>1.3MI(2002)] = 0.33%

  • Probability of exhaustion:

    • P[MI(t)>1.5MI(2002)] = 0.15%

  • Expected loss = 22bp < 135bp

  • A good deal for investors!

  • Bond trading at Libor + 100bp in June 2004


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Survivor Products liabilities- broad estimates: end 2003

  • Survivor swaps:

  • Counterparties swap fixed series of payments in return for series of payments linked to number of survivors in given cohort:

    • UK annuity provider could swap cash flows based on UK mortality index for cash flows based on US mortality index from a US annuity provider counterparty

    • Would enable both counterparties to diversify their longevity risks internationally.

  • Dowd et al (2004)


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Survivor Products liabilities- broad estimates: end 2003

  • Annuity futures:

  • Prices linked to specified future market annuity rate

  • Mortality options:

  • Payout depends on underlying mortality table at payment date.

  • Eg, EL guaranteed annuity contract


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Demand side of market liabilities- broad estimates: end 2003

  • Reference population underlying calculation of mortality rates central to both:

    • Viability

    • Liquidity of contracts.

  • Hedging demand from investors (eg life offices) wishing to hedge mortality exposures.

  • If reference population v different from investor’s specific population, then investor will be exposed to significant basis risk:

    • Might conclude that mortality derivative is not worth holding.


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Demand side of market liabilities- broad estimates: end 2003

  • Speculative demand:

    • depends on liquidity.

  • Adequate liquidity will require small number of reference populations:

    • Need to be chosen carefully to ensure that level of basis risk is small for investors with hedging demands.

  • Demand from hedge funds:

    • seeking instruments that have low correlation with existing financial instruments


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Supply side of market liabilities- broad estimates: end 2003

  • Government:

    • Securitising social security budget

  • Corporates long longevity risk:

    • Pharamceuticals


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Barriers to development in cash market liabilities- broad estimates: end 2003

  • After more than year, BNP Paribas longevity bond had not generated sufficient demand to be launched:

    • Has been withdrawn for redesign

  • Suggests significant barriers need to be overcome before sustainable market in survivor products and derivatives emerges.


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Barriers to development in cash market liabilities- broad estimates: end 2003

  • Reasons why BNP bond did not launch:

    • design issues

      • which make bond an imperfect hedge for longevity risk

    • pricing issues

    • institutional issues


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Design issues liabilities- broad estimates: end 2003

  • Small scheme will find it difficult to use bond to match its liabilities:

    • as variance between actual and expected mortality will be quite large.

  • Mortality experience of individual pension funds and life insurers may be different from reference UK population.

  • Bond only provides hedge for longevity of males:

    • pension funds and life insurers also exposed to significant longevity risk from females.


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Design issues liabilities- broad estimates: end 2003

  • Liabilities for pension funds and life insurers give greater weight to the lives receiving larger pensions.

  • Further, significant differences in mortality of those receiving larger pensions compared to those receiving lower pensions.

  • As payments under bond effectively give equal weight to all the lives in the UK population, the already imperfect hedge provided by the longevity bond is worsened.


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Design issues liabilities- broad estimates: end 2003

  • Bond only matches cashflow under level pension

    • while large portion of pensions paid by pension funds and life insurers will be increasing at RPI/LPI.

  • Bond is progressively worse hedge for pension liabilities related to younger or older cohorts.


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Pricing issues liabilities- broad estimates: end 2003

  • Need to forecast mortality index MI’s

  • Need to estimate r’s

  • Correlation between MI and r:

    • Anticipated to be low


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Pricing issues liabilities- broad estimates: end 2003

  • Above model valid only in complete market

  • In incomplete market, need to convert projected deterministic mortality rates into risk-neutral probabilities

    • E.g using Wang transform

    • Lin & Cox (2005)


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Pricing issues liabilities- broad estimates: end 2003

  • Longevity risk premium built into initial price of bond set at 20 basis points.

  • Given that this is first ever bond brought to market, markets have no real feeling as to how fair this figure is.

  • However, concern that up-front capital was too large compared with risks being hedged by bond:

    • longevity and interest rate risks

  • leaving no capital for other risks to be hedged

    • e.g. inflation


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Institutional issues liabilities- broad estimates: end 2003

  • Issue size too small to create liquid market.

  • Consultants reluctant to recommend it to trustees.

  • Fund managers do not currently have mandate to manage longevity risk.

  • Fund managers have not welcomed bond:

    • since believe it would be closely held and they would not make money from it being traded.

  • Partner Re is unlikely to be perceived as being a natural holder of UK longevity risk.


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Institutional issues liabilities- broad estimates: end 2003

  • Last point highly significant

  • Reflects view that key determinant of future issue of longevity bonds is availability of sufficient reinsurance capacity.

  • Neither UK-based nor EU-based reinsurer willing to provide cover for BNP bond

  • Partner Re not prepared to offer cover above issue size of £540m.

  • Has been questioned whether EU’s solvency requirements render reinsurance cover within EU prohibitively expensive.


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Barriers to development in futures market liabilities- broad estimates: end 2003

  • Following factors key to success of particular futures contract:

    • defined as having consistently high volume of trade and open interest:

  • Must be large, active and liquid spot market for underlying with good price transparency:

    • by far the most important factor:

    • indeed no futures contract has ever survived without a spot market satisfying these conditions.


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Barriers to development in futures market liabilities- broad estimates: end 2003

  • Spot prices must be sufficiently volatile to create hedging needs and speculative interest.

  • Relative hedging demand can be measured by level of open interest relative to volume:

    • since former excludes the many speculators who do not hold overnight positions.

  • Low open interest to volume ratio is an indication of high liquidity :

    • another sign of successful futures contract.


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Barriers to development in futures market liabilities- broad estimates: end 2003

  • Underlying must be homogeneous and/or have well-defined grading system.

  • Market in underlying must not be heavily concentrated on either buy or sell side:

    • since this can lead to price manipulation.

  • Futures contract must be effective in reducing risk.


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Barriers to development in futures market liabilities- broad estimates: end 2003

  • Liquidity costs:

    • bid-ask spreads

    • execution risk:

      • risk of adverse price movements before trade execution

  • Liquidity costs in the futures contract must not be significantly higher than those operating in any existing cross-hedge futures contract.


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Failure of futures contracts liabilities- broad estimates: end 2003

  • CPI futures contract listed on US Coffee, Sugar and Cocoa Exchange in June 1985

  • Delisted in April 1987 with only 10,000 contracts traded.

  • Reasons for failure:

    • no inflation-linked securities market at the time.

    • underlying was infrequently published index.

    • no stable pricing relationship with other instruments.


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Failure of futures contracts liabilities- broad estimates: end 2003

  • Futures contract on Treasury inflation-protected securities (TIPS) listed on Chicago Board of Trade in June 1997

  • Delisted before end of the year with only 22 contracts traded.

  • Reasons for failure:

    • TIPS had only started trading five months before.

    • Only a single 10-year TIPS outstanding.

    • Futures contract competed with underlying for liquidity.

    • Uncertainty over fate of TIPS programme.


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Failure of futures contracts liabilities- broad estimates: end 2003

  • CME launched CPI futures contract in February 2004 which is still trading.

  • Reasons for survival:

    • Inflation-linked securities have gained acceptance amongst investors

    • TIPS have evolved into recognised asset class.

    • Well understood pricing relationships allowing for arbitrage possibilities between TIPS, fixed-interest Treasury bonds and CPI futures.

    • US Treasury committed to long-term TIPS issuance.

    • CPI futures do not compete directly with but rather complement TIPS and uses same inflation index.

    • Contract traded on Globex electronic trading platform:

      • automated two-sided price quotes from lead market maker.


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Important lessons for development of mortality-linked futures market

  • Sufficiently large, active and liquid spot market in longevity bonds must be established well before any futures market started.

  • Mortality index behind longevity bond must be fair estimate of true mortality and have minimal time basis risk:

    • CPI index suffers from same potential problems

    • so survival of CPI futures contract on CME suggests these problems can be overcome.


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Important lessons for development of mortality-linked futures market

  • Although mortality indices are calculated infrequently, spot prices of longevity bonds likely to exhibit high degree of volatility on account of bonds’ high duration.

  • Underlying mortality indices must be few in number and well-defined:

    • small number of contracts helps to increase liquidity

    • but also leads to contemporaneous basis risk

      • arising from different mortality experience of population cohort covered by mortality index and cohort relevant to hedger.


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Important lessons for development of mortality-linked futures market

  • Potential weak point in longevity bond market is on the supply side:

    • since few natural issuers on supply side.

  • Futures contract would be effective in reducing aggregate risk,:

    • but small number of mortality indices might well leave substantial basis risk.

  • No reason to suppose liquidity costs in futures contract would be any higher than for other bond futures contracts.


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Conclusion futures market

  • Existence of survivor products:

    • will facilitate the development of annuities markets in the developing world

    • and could well save annuities markets in the developed world from extinction.

  • Essential to prevent annuity providers going bust!


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Conclusion futures market

  • If survivor products fail to be issued in sufficient size:

    • either the state (i.e., the next generation) is forced to bail out pensioners

    • or companies withdraw from pension provision

    • or insurance companies stop selling annuities

    • or pensioners risk living in extreme poverty in old age, having spent their accumulated assets


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