1 survivor products: managing longevity risk & mortality improvements professor david blake...
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Survivor Products: Managing longevity risk & mortality improvements
Professor David BlakeDirector
Pensions InstituteCass Business School
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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