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Evergreens: Pensions and Tontines Chris Golden & Con Keating Newton Institute April 2005

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L.ppt 1 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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L.ppt 2 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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L.ppt 3 The Ratio Problem Birth Rates in OECD countries are declining People are living longer So the population is ageing Source : OECD & GAD

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L.ppt 4 The Ratio Problem With an ageing population There are not enough workers to pay the pensions of retirees Source : GAD

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L.ppt 5 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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L.ppt 6 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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L.ppt 7 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 Source: Dept for Work and Pensions

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L.ppt 8 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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L.ppt 9 Pensions: Intergenerational vs Self-funded Paying for todays pensioners from the pockets of todays 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 workers 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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L.ppt 10 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 funds 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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L.ppt 11 Population Survival is ALWAYS downward sloping

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L.ppt 12 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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L.ppt 13 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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L.ppt 14 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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L.ppt 15 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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L.ppt 16 The Cashflows of an Evergreen… Are downward-sloping

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L.ppt 17 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, 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 years

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L.ppt 18 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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L.ppt 19 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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L.ppt 20 The Other General Advantages of Evergreens Benchmarking Liquidity Yield-curve Exposure ALM Long-dated Cashflows

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L.ppt 21 Evergreens allow investors to match typical benchmarks easily (1) Dont try this with a conventional bond !

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L.ppt 22 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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L.ppt 23 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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L.ppt 24 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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L.ppt 25 Evergreens Smooth Exposure to Curve

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L.ppt 26 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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L.ppt 27 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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L.ppt 28 Some Discrete Evergreen Bond Math

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L.ppt 29 Evergreen Bond Math (2)

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L.ppt 30 Evergreen Bond Math (2)

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L.ppt 31 Evergreen Portfolio Math

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L.ppt 32 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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L.ppt 33 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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L.ppt 34 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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L.ppt 35 Tontine payments 2% Contribution, No Wage Inflation, 3% interest rates, Retirement at 65 Pension never less than 78% of final salary.

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L.ppt 36 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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L.ppt 37 Evergreen Maturity and Tontine Cohort Twenty Cohort is unequivocally better off using the shorter maturitiy Evergreens But the forty cohort isnt Does this imply that there is a natural shape to the yield curve ?

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L.ppt 38 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 years time (annual) 50% of the 2-year is redeemed; but only 2% of the 50-year, leading to an average life of 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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L.ppt 39 Solving the Longevity Problem with Evergreens

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L.ppt 40 Pension Fund Cash-Flows and Evergreen Match Pension Fund data supplied by Hewitt Yield Curve supplied by Hewitt Portfolio of Five Evergreens £1,250,000 additional contribution leaves residual cash everywhere positive Portfolio present value £107 million.

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L.ppt 41 Inflation Sensitivities Perhaps the greater concern is inflation sensitivity The modified duration of this Pension Fund is years with todays implied inflation curve. Shocking this implied inflation curve by +/- 1% results in modified durations of and years.(Given no change in real yield term structure) But inflation-linked Evergreens are also perfectly feasible.

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