“The nastiest hardest problem…” Con Keating on pension drawdown

Con 8

Con Keating

Con Keating is currently in hospital with a poorly foot. He is a caged tiger on the ward, but the surfeit of energy has been dispelled by his putting his mind to what Bill Sharpe called the nastiest hardest problem in finance.

This is the result of Con Keating’s cogitations in hospital – drawdown is not for the faint hearted

The nastiest hardest problem.

It is a recurrent theme of many blogs that the conversion of a pension “pot” to an income in retirement is a very hard problem. The nature of the problem is simple to illustrate. It is that our life expectation does not decline linearly with elapsed time.


In this note, for simplicity, we will work with a unit fixed nominal pension, payable annually in arrears, with interest rates of zero. We use the ONS 2014-2016 life tables.
Suppose we have a fund equal to the sum of the expected annual pension payments, £22.73. In the first year of retirement, we pay £1 of pension and the fund is now worth £21.73. However, we find that our life expectation is now 21.9 years, and we will not have sufficient funds to pay pensions to this average age of death. The problem repeats and grows as every year passes. After 23 years we have exhausted all of the funds available to us, but still have a life expectation of a further 6.8 years.
The cumulative effect of this conditional cost is illustrated below.cdraw2

It is worth considering the position when this problem is collectivised, as is the case with insured annuities, or as proposed in CDC. The diagram below shows the annual payments under these collective arrangements; pension payments now follow the survival curve.cdraw3

One of the great attractions of drawdown is the fact that that if death occurs prior to the average life expectation, there will be funds remaining which form part of the deceased’s estate. Unlike annuities these sums are not lost. Of course, there would also be a corresponding shortfall if death does not occur until some age after the expectation. This is illustrated below.


The total cost of a drawdown pension is the member survives to age 100 years is £40, 166% of the cost of collective annuitisation. This would require an excess return from the investment of the fund of 1.28% pa to offset this shortfall. If survival is to age 90, the cost is 132% and the excess return required would be 93 basis point per annum. This is a very considerable hurdle for drawdown management to achieve.
If we alter the basic set up to reflect pensions in reality, adding indexation and other real-world features, the hurdle illustrated grows in magnitude and significance. This is illustrated below for pension indexation of 2.5% pa. The capital deficit at year 40 has increased from 17.7 to 46.36.
Drawdown really is not for the faint-hearted, or those without other resources from which to replace the pension income.cdraw5

This note has not considered the problem of realising asset values to pay pensions. That brings with it a further set of problems. Among these are the sensitivity of the fund to the stochastic variation of market prices and the dependence of the pension upon early realisations. Glide paths and similar de-risking strategies are one attempt to minimise these issues, though they usually come at the expense of returns.

con-keatingguestAbout the author

Con Keating is an adviser to AgeWage and on the board of Warwick Business School. He lives in Leamington Spa and is currently recovering from a foot infection in a local hospital- we wish him a  speedy recovery!

About henry tapper

Founder of the Pension PlayPen, Director of First Actuarial, partner of Stella, father of Olly . I am the Pension Plowman
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4 Responses to “The nastiest hardest problem…” Con Keating on pension drawdown

  1. Sandy Trust says:

    Agreed – this is a very nasty hard problem. We did some research on this a few years ago and I reckon its essentially impossible for most individuals without quite an advanced understanding of the problem to understand the risks, let along manage them.

  2. Con Keating says:

    The article linkedabove is worth reading. And on that note, it is probably worth revisiting the four blogs I wrote a few years ago for Henry’s blog.

  3. Con’s argument works by isolating a single factor. If you ignore the uncertainty about sustainable real income in the presence of both investment return uncertainty and inflation uncertainty, longevity risk will, by default, dominate the risk of drawdown. This is what the theoretical example here does.

    When the problem is defined as one of setting a sustainable real draw rate that matches the preferred spending profile (or time preferences) of the individual and the required certainty of avoiding both unplanned cuts to spending and running out, it is then investment uncertainty that dominates. It dominates to the extent that only in the late stages is it useful to separate the longevity risk from the investment risk. By that stage, in the absence of a bequest motive, and with an asset allocation that is dependent (because risk is) on the time horizon, the choice becomes one between annuitising (at which late stage it may be less important to buy an indexed linked annuity) and holding broadly the same assets as the annuity provider but with enough to fund to a very late age to cover the longevity tail risk.

    It is also pointless to speculate on the theoretical challenge without comparing the cost of avoiding drawdown, which Con’s example ignores. To start with, avoiding drawdown requires the inflation risk to be confronted in a way that the default of a nominal annuity, often with a glide path pre retirement through matching gilts, does not. In the typical arrangement, equity risk is removed only to be replaced by inflation risk. Were equities replaced by a glide path using index linked gilts to hedge an expected index linked annuity, the true cost of gradually avoiding all risk would be revealed (as either more resource or less income) and the probable drawdown outcomes could then be properly compared. It is this comparison that Freedom and Choice arguably envisaged, because policy makers had evidently come to realise that the default to nominal annuities was suboptimal, both because retiring capital when we retire is extravagant and because the cost of manufacturing and providing annuities is inefficiently high. The reason for the second, considering it is a product that relies on the same benefits of collectivisation and scale that Con advocates, is something worth investigating.

  4. henry tapper says:

    I think Con’s piece points towards a collective solution for the drawdown of pension savings. I agree with you that the only way individuals can really deal with the longevity problem by themselves is using annuities, but that is not what people want to do! Even if interest rates went back to 2% or so, I don’t think we’d see a big rebound in individual annuity take up. The cost of manufacturing annuities is quite low (Orzag and Murtha studies) , similarly the cost of providing them, the real difficulty with annuities is the opportunity cost of not being in growth assets for the remaining years of your life!

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