Download Financial and Monetary Economics

Survivor Products:
Managing longevity risk &
mortality improvements
Professor David Blake
Director
Pensions Institute
Cass Business School
[email protected]
1
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.
2
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.
3
Mortality improvements over time
4
Mortality improvements over time
5
What is longevity risk?
(Broken limits to life expectancy – Oeppen & Vaupel)
6
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.
7
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
8
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.
9
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.
10
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.
11
Longevity risk in UK pension
provision, £billion of total liabilitiesbroad estimates: end 2003
Figure 5.17 p181
12
Significant concern!
Reinsurers (eg Swiss Re)
have stopped reinsuring
longevity risk of life
offices!
13
Survivor Products


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
14
Survivor Products



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).
15
BNP Paribas Longevity Bond







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
16
BNP Paribas Longevity Bond
Bond holders
Floating S(t)
Issue price
Interest-rate swap
EIB
BNP
Issue price
Mortality swap
Partner Re
17
18
Advantages of longevity bond

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.
19
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 years
Covers the full term of the
liability
Only level pensions matched
Different annuities can be
used to match non - level
pensions
20
Survivor Products



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)
21
Swiss Re Bond 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
22
Influenza pandemics



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
23
Influenza pandemics

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
24
Influenza pandemics

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
25
Influenza pandemics

2005-06
 Started
in SE Asia
 H5N1 virus
 Closely related to 1918 Spanish virus
26
Swiss Re Bond 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
27
Swiss Re Bond 2003
Off balance
sheet
Swiss Re
Annual coupons
(USD LIBOR + 135bps)
SPV (Vita
Capital)
Bond holders
Principal
payment $400m
Up to $400m if
extreme
mortality is
experienced
Check
terminal
mortality
index value
Up to $400m if
extreme
mortality is not
experienced
28
100% 90% 80% 70% -
Exhaustion point
60% 50% 40% 30% 20% 10% 0% 1
Capital erosion
Attachment point
Principal Repayment (%)
Swiss Re Bond 2003
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)
29
Swiss Re Bond 2003



Bond valued using Extreme Value Theory
(Beelders & Colarossi (2004))
Assume Generalised Pareto Distribution
Probability of attachment:
 P[MI(t)>1.3MI(2002)]

Probability of exhaustion:
 P[MI(t)>1.5MI(2002)]



= 0.33%
= 0.15%
Expected loss = 22bp < 135bp
A good deal for investors!
Bond trading at Libor + 100bp in June 2004
30
Survivor Products


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)
31
Survivor Products





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
32
Demand side of market

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.
33
Demand side of market

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
34
Supply side of market

Government:
 Securitising

social security budget
Corporates long longevity risk:
 Pharamceuticals
35
Barriers to development in cash market

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.
36
Barriers to development in cash market

Reasons why BNP bond did not launch:
 design
issues
 which
make bond an imperfect hedge for longevity
risk
 pricing
issues
 institutional
issues
37
Design issues

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.
38
Design issues



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.
39
Design issues

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.
40
Pricing issues
d .MI 3
d .MI1
d .MI 2
P=
+
+
+
2
3
(1+ r1 ) (1+ r2 )
(1 + r3 )



Need to forecast mortality index MI’s
Need to estimate r’s
Correlation between MI and r:
 Anticipated
to be low
41
Pricing issues
d .MI 3
d .MI1
d .MI 2
P=
+
+
+
2
3
(1+ r1 ) (1+ r2 )
(1 + r3 )


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)
42
Pricing issues



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
43
Institutional issues




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.
44
Institutional issues





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.
45
Barriers to development in futures market

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.
46
Barriers to development in futures market


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.
47
Barriers to development in futures market


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.
48
Barriers to development in futures market

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.
49
Failure of futures contracts



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.
50
Failure of futures contracts



Futures contract on Treasury inflationprotected 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.
51
Failure of futures contracts


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.
52
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.
53
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.
54
Important lessons for development of mortality-linked
futures market

Potential weak point in longevity bond market is
on the supply side:


Futures contract would be effective in reducing
aggregate risk,:


since few natural issuers on supply side.
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.
55
Conclusion


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!
56
Conclusion

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

57