Evergreens: Pensions and Tontines

Chris Golden & Con KeatingNewton InstituteApril 2005

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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

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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

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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

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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

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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

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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!

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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

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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)

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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

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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

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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

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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.

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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

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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

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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

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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

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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

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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

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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

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The Other General Advantages of Evergreens

Benchmarking

Liquidity

Yield-curve Exposure

ALM

Long-dated Cashflows

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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 !

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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

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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

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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

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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

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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

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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

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Some Discrete Evergreen Bond Math

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Evergreen Bond Math (2)

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Evergreen Bond Math (2)

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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

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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

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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

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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.

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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.

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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

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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 ?

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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

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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

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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.

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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.