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Survivor Products: Managing longevity risk & mortality improvements

Professor David BlakeDirector

Pensions InstituteCass Business School

d.blake@city.ac.uk

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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.

The problem

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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.

The problem

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Mortality improvements over time

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Mortality improvements over time

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

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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.

Stochastic nature of mortality improvements

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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

Longevity risk

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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.

Longevity risk

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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.

Longevity risk

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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.

Longevity 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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Reinsurers (eg Swiss Re) have stopped reinsuring

longevity risk of life offices!

Significant concern!

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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

Survivor Products

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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).

Survivor Products

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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

BNP Paribas Longevity Bond

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BNP Paribas Longevity Bond

Mortality swap

Floating S(t)

BNP

Interest-rate swap

Issue price

Issue price

EIB

Bond holders

Partner Re

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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.

Advantages of longevity bond

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Longevity Bond Annuity

Partial hedging of the longevity risk

Full hedging of longevity risk

Low credit risk of EIB (rated AAA)

Higher credit risk of the insurer but there is additional protection through the government compensation scheme

Fixed term of 25 yearsCovers the full term of the

liability

Only level pensions matchedDifferent annuities can be

used to match non - level pensions

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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)

Survivor Products

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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

Swiss Re Bond 2003

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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

Influenza pandemics

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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

Influenza pandemics

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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

Influenza pandemics

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2005-06 Started in SE Asia H5N1 virus Closely related to 1918 Spanish virus

Influenza pandemics

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$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

Swiss Re Bond 2003

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Swiss Re Bond 2003

Swiss Re Bond holders SPV (Vita Capital)

Check terminal mortality

index value

Up to $400m if extreme mortality is not experienced

Up to $400m if extreme mortality is experienced

Annual coupons (USD LIBOR + 135bps)

Principal payment $400m

Off balance sheet

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Swiss Re Bond 2003

100% - 90% -

70% -

60% - 50% - 40% - 30% - 20% - 10% -

0% -

80% -

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6

Mortality Index Level (q)

Prin

cipa

l Rep

aym

ent (

%)

Atta

chm

ent p

oint

Exh

aust

ion

poin

t

Capital erosion

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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

Swiss Re Bond 2003

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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)

Survivor Products

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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

Survivor Products

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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.

Demand side of market

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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

Demand side of market

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Government: Securitising social security budget

Corporates long longevity risk: Pharamceuticals

Supply side of market

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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.

Barriers to development in cash market

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Reasons why BNP bond did not launch:

design issues which make bond an imperfect hedge for longevity

risk

pricing issues

institutional issues

Barriers to development in cash market

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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.

Design issues

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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.

Design issues

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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.

Design issues

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Need to forecast mortality index MI’s Need to estimate r’s Correlation between MI and r:

Anticipated to be low

Pricing issues

31 22 3

1 2 3

.. .

(1 ) (1 ) (1 )

d MId MI d MIP

r r r= + + +

+ + +

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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)

Pricing issues

31 22 3

1 2 3

.. .

(1 ) (1 ) (1 )

d MId MI d MIP

r r r= + + +

+ + +

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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

Pricing issues

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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.

Institutional issues

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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.

Institutional issues

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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.

Barriers to development in futures market

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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.

Barriers to development in futures market

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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.

Barriers to development in futures market

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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.

Barriers to development in futures market

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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.

Failure of futures contracts

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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.

Failure of futures contracts

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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.

Failure of futures contracts

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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.

Important lessons for development of mortality-linked futures market

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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.

Important lessons for development of mortality-linked futures market

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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.

Important lessons for development of mortality-linked futures market

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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!

Conclusion

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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

Conclusion