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Evergreens: Pensions and Tontines
Chris Golden & Con KeatingNewton InstituteApril 2005
1050145L.ppt 2
Overview
Stating the problem— The focus on pension funds
– Worker/Retiree ratio– Longevity– Intergenerational vs self-funding
Problems with the problems— Ratios are misleading— Longevity is tractable— Public pensions need not be either or
A potential solution for funded pensions— Evergreens— Tontine: making the mortality rate work for you
1050145L.ppt 3
The Focus on Pensions
The pension “problem” is now high-profile because of— Ratio problems
– i.e. declining birth rates— The longevity problem
– i.e. lengthening life expectancy— The argument about self-funding vs intergenerational funding
The first two are real observations— But with fallacious conclusions
The last is a false argument— The solution is probably a mixture of both
1050145L.ppt 4
The Ratio Problem
Birth Rates in OECD countries are declining
People are living longer
So the population is ageing
Percentage of UK population 65+
0%
5%
10%
15%
20%
25%
1960 2000 2021
65+
Source : OECD & GAD
1050145L.ppt 5
The Ratio Problem
With an ageing population — There are not enough workers to pay the pensions of retirees
Projected Worker/Retirees in the UK
0.0
0.51.0
1.5
2.02.5
3.0
3.54.0
4.5
2000 2025 2050
Worker/Retirees
Source : GAD
1050145L.ppt 6
A False Problem?
The ratios illustrated are correct
But they do not reflect economic dependency
Two key elements are missing — As well as other minor points
Immigration— Which should change the ratio
– Since most immigrants are workers and not retirees
Productivity— For 3.0 workers to produce in 2025 the same as 4.1 workers in
2000– Implies real productivity growth of 1.2% pa– Or 0.72% pa between 2025 and 2050– Or 0.95% pa for the whole 50 year period
The “Black” Economy
1050145L.ppt 7
Ratios: a false problem?
The ratio “problem” is tractable— The problem is not economic— But political
– I.e. how do we transfer economic productivity growth across generations
But it still exists in principle— I.e. economic dependency ratios COULD worsen
– To an unsustainable level
And therefore relying uniquely on intergenerational transfers for public pensions is probably a bad idea in the long run!
1050145L.ppt 8
Longevity
Longevity, or the increase in retirees expected life, is partly a problem of double accounting
The ratios we have examined obviously already include the fact that people live longer
But it is still a practical ALM problem, and a practical political problem
024
68
101214
161820
1928 1960 2000
Life Expectancy at Retirement Men
Life Expectancy at Retirement Women
Years
Source: Dept for Work and Pensions
1050145L.ppt 9
Longevity
We will examine a potential ALM solution to the longevity problem later
The beneficiaries of increasing longevity are both the public and the private sector - the private sector since this reduces future economic uncertainty.
The political problem would seem to be one of recognising that not all of the increase in expected lifespan can be expected to be spent in retirement
Regular but small increases in the retirement age are a solution
— So long as they are expected (ie “part of the landscape”)— And announced well in advance (ie decades)
1050145L.ppt 10
Pensions: Intergenerational vs Self-funded
Paying for today’s pensioners from the pockets of today’s workers
— Is defensible morally and politically— But it is dangerous
The fact that we do not actually have a ratio problem now— Does not mean we never will have
Prudence dictates that we cannot rely on this system entirely
Equally we cannot rely entirely on self-funding— Economic and political cycles can be much longer than a worker’s
lifetime— Self-funding is too exposed to sudden changes (devaluation,
inflation etc)
The sensible solution is probably a mixture of both, with the emphasis on self-funding
1050145L.ppt 11
Stating the problem
Assume that we are self-funding a large (public) pension fund
The emphasis on self-funding is on the individual life— Probably a hangover from assurance/insurance— And from individual portfolios
But from the perspective of a large fund this is misleading
Each person dies once, and unpredictably
But populations decay, and fairly predictably— The fund’s liabilities for any age cohort will ALWAYS be
downward sloping
The true problem is one of the Asset and Liability management of large cash-flows
1050145L.ppt 12
Population Survival is ALWAYS downward sloping
-
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
100,000
1 4 7
10
13
16
19
22
25
28
31
34
Years of retirement
Population Survival rate of 100,000 UK males in 2003
1050145L.ppt 13
Instruments available for ALM of pensions
Equities : traditionally a UK pension favourite— But dramatically poor characteristics from an ALM point of view
– Virtually unpredictable cash-flows except In long-term aggregates
— The advantage stems from historical out-performance— But the risk is seriously high
– As many company pension plans have found recently
Bonds— Have predictable cash-flows— But they are the wrong shape (I.e. NOT downward sloping)— And the wrong maturity
– Long bonds of 50+ years are still VERY rare
A small caution on ALM: This is about the matching of assets and liabilities. The first order measure of risk on an asset or a liability is its proportional rate of change - that is return. Returns matter - and are an order of magnitude more important than their variability.
1050145L.ppt 14
Possible Solution, part 1: the Evergreen
One solution would seem to lie in creating an instrument with fairly unusual characteristics
— Downward sloping cash-flows— Long-dated payments— Capable of long-term forward purchase
– Ie strippable— With long-term fungibility
– The pension demand is “permanent”
Such an instrument does not already exist in the market
But it does exist in theory, and has been studied closely and worked on in practice
It is called an Evergreen Bond
1050145L.ppt 15
Warning! This presentation introduces a new financial product currently known
as Evergreens
But first a few words!— Evergreens are patent pending in the US and Europe— They are now in the public domain. — Evergreens are not purely theoretical: a vast amount of practical
work has been accomplished– In the money markets/repo area– In the settlement area : Key clearing agents are all aware of
the project and would know how to act– Paying agents, information technology vendors and many
others are aware and prepared— Evergreens are a turnkey project waiting to happen, and they
clearly address the pension problem in an original way
Evergreens are the most thoroughly innovative bonds since Zeros
1050145L.ppt 16
Evergreens are exponentially amortising zero-coupon bonds, leading to a constant maturity
An Evergreen is a bond with no coupon and no theoretical maturity
Instead of interest payments the investor receives redemption payments
These payments (for this purpose) are a FIXED percentage of the OUTSTANDING
Thus the holder of £1,000,000 Evergreen paying 10% would receive— £100,000 the first year, leaving £900,000 nominal owned— £90,000 (10% of £900,000) the second year, leaving £810,000— £81,000 the third year, leaving £729,000, and so on
It is thus a (theoretically) infinite series of zero-coupon bonds,or a (theoretically) infinite amortising zero amortising exponentially
The self-similarity of the cash flows over time lead to a very stable average life, where the average life is typically the reciprocal of the pay down rate
1050145L.ppt 17
The Cashflows of an Evergreen…
Are downward-sloping
£0
£1,000,000
£2,000,000
£3,000,000
£4,000,000
£5,000,000
£6,000,000
£7,000,000
£8,000,000
£9,000,000
£10,000,000
1 5 9
13
17
21
25
29
33
37
41
45
49
Generic Evergreen Cashflow Shape : Downward- sloping
Payment Years
1050145L.ppt 18
Evergreens facilitate the issuance of particularly long-dated debt
In theory, Evergreens never mature. In practice they always have a contingent maturity date. Practically they are never undated.
However, £1,000,000,000 20-year would take over 300 years to make its last payment.
Even a £1 bn tranche of a 2-year life Evergreen would still be paying out after 25 years.
A conventional bond paying out to 50 years would have a conventional life of 50 years…..
A 20-year life Evergreen would still be paying out 4% of its nominal in 50 years (and MORE before that), and would have an average life of 20 years and a duration (at 4%) of 11.111 years
1050145L.ppt 19
The same Evergreen can be issued forever
Evergreens are instantly fungible
Thus Evergreens are designed to maintain their essential characteristics over time
And be fungible instantly a new issue is made
So the same Evergreen is always theoretically available for pension fund investment today and in the future
1050145L.ppt 20
Evergreens maintain a stable and relatively constant weighted average life
The mathematical structure of Evergreens is such that the weighted average life of outstanding cash flows will remain stable forever
The “life” (average) of an Evergreen is simply the reciprocal of its redemption rate
In continuous financial mathematics it would remain permanently constant
In real life the range over which the weighted average life will roam depends on the frequency of payment
Thus a 10-year life Evergreen paying annually would actually have an average life ranging from 10 years to 9 years and one day
And a 20-year life Evergreen paying semi-annually would have an average life ranging from 20 years to 19.5 years
1050145L.ppt 21
The Other General Advantages of Evergreens
Benchmarking
Liquidity
Yield-curve Exposure
ALM
Long-dated Cashflows
1050145L.ppt 22
Evergreens allow investors to match typical benchmarks easily (1)
R2 = 0.759
0%
2%
4%
6%
8%
10%
12%
14%
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38
UBSW Sterling Allstock Index Cashflows
Don’t try this with a conventional bond !
1050145L.ppt 23
Evergreens allow investors to match typical benchmarks easily (2)
Over the 60+ months from Dec 96 to Jan 02
A combination of a 10-year and a 20-year Evergreen— Would have matched the cash flows of the UBSW UK corporate
index— With an R-squared ranging from the mid 70%s to the high 80%s
A 10-year alone would have similar results— Fitting the UBSW UK corporate index with an R-squared from
74%-86%
We have proprietary software that can optimise Evergreen use— To match portfolio cash flows in a number of different ways
1050145L.ppt 24
Evergreens provide any portfolio with core liquidity
Liquidity of a traditional bullet bond is determined by— Size of issue— Age of issue— Benchmark status (on-the-run)— Investor focus
An Evergreen bond— Increases in size— Never ages— Is structured to be a permanent benchmark— Re-openings always focus investors on current issue
In addition within any issuance programme the size of any Evergreen should rapidly overtake the size of even the biggest conventional
1050145L.ppt 25
Evergreens allow a structured exposure to the whole yield curve in a simple manner
Cash flow distribution is smooth— Unlike the irregular structure of a bullet bond
Contribution to duration is smooth— No dominant single cash flow
Thus exposure to the yield curve is much smoother than with a conventional bond
— Where almost all the duration is contained in the final payment
1050145L.ppt 26
0.0%
10.0%
20.0%
30.0%
40.0%50.0%
60.0%
70.0%
80.0%
90.0%
Evergreen 10-yr Bullet
Contribution to duration : 10% Evergreen vs 10-year bullet
Payment Year
Evergreen’s Smooth Exposure to Curve
1050145L.ppt 27
Evergreens facilitate Asset/Liability Management in a wide variety of situations
An Evergreen bond is an example of exponential decay
As such it is similar to many natural and man-made examples of the same phenomenon
— The life expectancy of a human population— Interest payments on a mortgage— Long-term project financing: the Hoover Dam was finally paid for
a decade or so ago
The key point is that conventional bonds are most unsuited for anything long-term: the further the final repayment the greater the credit spread usually demanded by the market
In particular, Evergreens are much more suitable to match cohort pension liabilities than conventional bonds
1050145L.ppt 28
Evergreens radically simplify quantitative portfolio analysis
The maths of Evergreens is very straightforward
Some examples:— The price of an Evergreen is its redemption rate divided by its
yield plus its redemption rate— its yield is the redemption rate times one minus the price all
divided by the price— The modified duration is the price times the life; or for those who
prefer division the price over the redemption rate— The average life (or “life”) is the reciprocal of the redemption
rate
None of these could be so easily expressed in English if we were analysing a conventional bond
Incidentally Evergreens have more convexity per unit of duration than any other standard bond other (ironically) pure annuity bonds
1050145L.ppt 29
Some Discrete Evergreen Bond Math
1050145L.ppt 30
Evergreen Bond Math (2)
1050145L.ppt 31
Evergreen Bond Math (2)
1050145L.ppt 32
Evergreen Portfolio Math
NotationM : Number of bonds in the portfolio;
iw : weight of bond i in the portfolio, with 10 iw ;
ir : constant repayment rate of bond i, with 10 ir ;
na : value of the repayment of the portfolio in year n;
nz : value of a zero-coupon bond with n years to maturity;P : price of the portfolio of M bonds.
a) The price of a portfolio, at an internal rate of return y, is
.
1
11
1
11
1
11
1
1
1
11
1
1
1
11 01 11
1
1 1
1
1 1
1
1
M
i i
ii
M
i i
iiM
i n
n
iiiM
i nn
niii
M
i nn
niii
n
M
i
niiin
nnn
ry
rw
y
ry
rw
y
r
y
rw
y
r
y
rw
y
rrwrrw
yazP
b) The modified duration of the portfolio is
.
11
112
*
M
i i
iiM
i i
ii
ry
rw
ry
rw
dy
dP
PD
1050145L.ppt 33
Evergreens and Annuities
Evergreens provide particularly long-dated cash flows, ideal for and greatly simplifying long-dated annuities
It makes as much sense to look at the economics of annuities from a single annuity as it does to look at the medical implications of a given treatment from the case history of one patient!
If a population of same-age annuity takers is analysed, two things become apparent:
— 1] it is backward-sloping— 2] it is largely predictable
Furthermore living annuity holders might benefit from the pool of Evergreens left behind by dead ones raising the total rate of return for all - Tontines
1050145L.ppt 34
Using the Survivor Curve to Enhance Returns: The Tontine
In a tontine, those who have contributed but die before payment forgo their investment
The same effectively happens in public pension funds
Those investment contributions are eventually shared by the survivors
The effect is to enhance returns to the survivors
Combining the advantages of Evergreens with a tontine form of pension contribution
And doing so throughout the contribution life of a cohort
Greatly enhances returns
1050145L.ppt 35
Creating the Tontine Assume that we are ensuring the pensions of a cohort
— Originally aged 20— Who will contribute annually until retirement at 65
Of the original 100,000 members of the cohort (say)— Only 83,936 members make it to retirement age— So over 16,000 members (or just <20% of the survivors)
– Never draw a pension– And subsidise those who do
Contribution rate 2% of salary — No salary inflation— A 3% flat yield curve— A sole twenty year Evergreen
Contributions are invested in the Evergreen at the forward first pension payment date.
1050145L.ppt 36
Tontine payments
Pension % Final Salary
0.1
1
10
100
0 5 10 15 20 25 30 35
Time (Years)
Pensi
on (
Pro
port
ion F
inal Sala
ry)
2% Contribution, No Wage Inflation, 3% interest rates, Retirement at 65
Pension never less than 78% of final salary.
1050145L.ppt 37
Another Tontine
2% Wage inflation, 5% Contributions, Retirement 65, 4% Interest rates
Minimum Pension 1.56 times final salary
Just 15.8% of enhancement at retirement is due to pre-retirement deaths
1050145L.ppt 38
Evergreen Maturity and Tontine Cohort
Twenty Cohort is unequivocally better off using the shorter maturitiy Evergreens
But the forty cohort isn’t
Does this imply that there is a natural shape to the yield curve ?
1050145L.ppt 39
Other issues : Longevity
In the context of the current debate on longevity it is interesting to note the behaviour of a portfolio consisting of two different life Evergreens
Imagine a portfolio with equal amounts today of a 2-year Evergreen and a 50-year Evergreen: today its weighted average life is 26 years.
In one year’s time (annual) 50% of the 2-year is redeemed; but only 2% of the 50-year, leading to an average life of 33.784 years
This is an extreme example, but it is relatively simple to construct a minimally dynamic portfolio that would keep up with observed longevity
1050145L.ppt 40
Solving the Longevity Problem with Evergreens
15
16
17
18
0 2 4 6 8 10 12 14 16 18 20 22 24
Av Lifein Yrs
Evolution of Average Life of (originally) Equal Holdings ofa 10- yr and a 20- yr Evergreen
Holding Period in Years
1050145L.ppt 41
Pension Fund Cash-Flows and Evergreen Match
Pension Fund data supplied by HewittYield Curve supplied by Hewitt
Portfolio of Five Evergreens£1,250,000 additional contribution leaves residual cash everywhere
positivePortfolio present value £107 million.
1050145L.ppt 42
Inflation Sensitivities
Perhaps the greater concern is inflation sensitivity
The modified duration of this Pension Fund is 17.86 years with today’s implied inflation curve.Shocking this implied inflation curve by +/- 1% results in modified durations of 19.17 and 16.70 years.(Given no change in real yield term structure)
But inflation-linked Evergreens are also perfectly feasible.
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