Smoke and daggers (Con Keating on ”confusions and misunderstandings”)


The pension contract

This article was published in yesterday’s Professional Pensions and is published here in its entirety with the permission of Con Keating. A search on Con Keating will give up other articles on this topic to which this blog refers!

Given their basic, rudimentary and often personal nature, it is tempting to dwell upon the motivations of many of the very many who responded to my earlier articles on the subject of pension liability valuation and analysis. The theory of motivated reasoning, Veblen’s concept of trained incapacity and more recently Anant Admati’s invocation of wilful blindness all offer themselves as candidate methods, and there are many more. However, I shall apply the principle of charitable interpretation and treat all as if they are simply confusions and misunderstandings.

At its most elementary level, all that I have pointed out is that the contributions made together with the projected or expected pension benefits fully define the pension contract. It is unnecessary to invoke or introduce any external factor, and to do so is to expose the analysis and reporting to the near-certainty of error in quantification, and can induce perverse behaviour and management practice.

I am agnostic as to how those contributions were determined. By similar measure, I am agnostic as to the actuarial or econometric methods employed in the projections of benefits, including their calibration or parameterisation. The first, contribution amounts, are a matter of historic fact. The second are routinely calculated under existing approaches. I do not propose and there is no need for any change to those methods. While, for pedagogic simplicity, I describe the situation deterministically, these projections may be estimated in their full stochastic glory and complexity; this does not alter the fact that when taken together with contributions, the analytic problem is fully defined and determined.

The element absent from standard descriptions of pensions is their intrinsic (promised) investment attribute; this I have described as the accrual rate in recent articles and in earlier pieces as the investment growth rate. It is perhaps most easily understood in the context of a member’s voluntary contribution. Here the scheme member pays an amount of money, a proportion of his or her salary into the scheme and is promised a defined amount of pension. This is an investment contract in every sense. The accrual rate or investment growth rate is fully defined by what the member paid and what the member was promised by way of pension income. Technically, this is a deferred annuity.

The investment accrual rate is the primary measure of the generosity of the pension. This is the baseline around which such things as risk and security assessments should be based. It is the promised investment return.

It is unnecessary for such member contributions to entail similar benefit terms to those of employer contributions, though they may.

Employer contributions made together with benefits projections define the accrual rate; it is the cost of production of the pension promises made by the employer. It is analytically comparable to a zero-coupon bond issued by a company. The contribution corresponds to the principal advanced to the company and the repayments or pay-offs are a sequence or strip of amounts rather than a single payment – the accrual rate is also known as the internal rate of return of these cash flows.

The diagram below shows, for an illustrative scheme, the contributions made prior to, and the benefits projections prevailing at the time of valuation (2016). It also shows, using the accrual rate, the accumulated value of those contributions together with the discounted present value of the outstanding projected benefits. The accrual rate is that rate which equalises these cash-flow sequences. It is unique and time-consistent.

Contributions, Projected Benefits and Accumulated Amounts


As members die, their outstanding contribution records and their associated liability projections are excised. For pensioners in payment, as benefits are paid and those liabilities discharged, their contribution records are amortised in proportion to their residual life expectation.

Another way of describing the valuations arising under the proposed method is as the degree of progress expected towards the complete and timely discharge of the promised or projected benefits. This is the value expected by both sponsor and scheme member, under the terms and conditions of their award. Of course, this is a definition scheme liability value.

Several correspondents have raised the question of the contribution as part of the employer’s cost of provision of DB pensions. There are two parts to understanding this issue. First, that it is the contribution actually made that is one of the two determinants of the investment accrual rate. Second, that the question of the extent to which the contribution made is considered by employees in respect of their total employment compensation and in the employer’s overall labour costs is another quite distinct issue, but one which is irrelevant to the task in hand, the correct estimation of the liabilities incurred arising from pensions awarded.

In the case of the illustrative scheme, the accrual rate embedded in the stock of pensions promises is 6.07% and the capital value of the liabilities is £153.37 million. It happens that this rate is high relative to current gilt yields, but this rate is an accumulation of awards dating back as far as 1952, and includes periods in the 1970s and 1980s when the rate for new awards was in double digits. It is slowly moving. Currently-used methods produce a valuation of £260.28 million. Currently-used methods are shown to result in significant overvaluations of the liabilities. Had these currently-used methods been in use in the 1970s, the result would have been massive undervaluation of liabilities. Here, there would be the germ of an argument for the smoothing of discount rates if they must persist in being used.

The more important point is that the pension must be attractive as an investment proposition to scheme members. This is obscured and distorted by both over and undervaluation.

It may help to consider two pathological variants to the illustrative scheme. One in which contributions made were only half of those actually made (A) and a second (B) in which contributions were as made but benefits awarded were only half those promised in the illustrative scheme. The accrual rate in the first case (A) is 8.23%, and in the second (B) is 3.89%.

The valuation of the first pathological scheme (A) would be £123.46 million. Note that this has the same promised ultimate liabilities as the illustrative scheme, but has a value of those liabilities almost £30 million lower. Contrary to the beliefs and assertions of many, the same future cash flows do not need to have the same value today; the value today is determined by the detail of the promises made.

Accepting the more aggressive higher accrual rate (A), achieved through the lower contribution rate, is in this sense riskier to the scheme member. Suppose that it was possible to remove the scheme assets at the time of the valuation and that these schemes were fully funded, the illustrative scheme would need to achieve a new compound investment rate of 6.07% on assets of £153.37 million to achieve the benefits originally promised, while the aggressive scheme (A) would need to achieve a rate of 8.23% on assets of £123.46 million.

Scheme (B) is also interesting; its value today, £99.53 million. Note that although the benefits are half those promised in the illustrative case, this is 65% of the illustrative case valuation. The hypothetical challenge would be to find an investment return of 3.89% on assets of £99.53 million. While, clearly, this should be easier and less risky than finding an investment return of 6.07% on assets of £153.37 million, and much more so than finding 8.23% on assets of £123.46 million, it would be necessary to have two such entitlements to achieve the same retirement income as the other schemes.

This analysis also points to a problem at the heart of the now-popular belief that consolidation of schemes can be achieved and will bring benefits of scale. This may be true when pension contributions and benefits are commonly negotiated and applied, and are in this sense a homogenous class, as they are in the Netherlands, but in the UK, schemes are very far from this. Heterogeneity in scale, design and history are almost a defining characteristic here.

In order to keep this article to easily readable length, I shall defer discussion of further subjects and aspects to later articles. As for the epithets coming my way, such as crackpot, imbecile and moron, I must confess to having been inured to such things long ago. At the age of 13, I had an A-level maths teacher: Irish, often incomprehensible, dishevelled, permanently clouded by his aura of chalk dust, fag-ash and dandruff, and with the only discernible colour, the yellow-ochre nicotine stains on his fingers and teeth. At the least provocation, he would deliver diatribes to the beat of clips around my ears with his blackboard duster. Monologues that, without hesitation or repetition, would begin: “doss, dolt, dunderhead, …” and often continue far longer than a minute. Ducking the spittle and duster may be absent, but they bring back very fond memories of a brilliant teacher.

To end, it seems appropriate to quote another grand Irishman:

“I don’t think it helps people to start throwing white elephants and red herrings”

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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2 Responses to Smoke and daggers (Con Keating on ”confusions and misunderstandings”)

  1. George Kirrin says:


    Con needs to reconstruct a DB pension as they were and are, which means there are groups of members accruing service over years, with members’ contributions being set initially and then re-set triennially, with members’ pensionable “final salary” often changing annually, with so-called “non-contributory” schemes which should also include employers using “salary sacrifice” and paying sums in lieu of member payments, etc.

    That’s what payrolls and trusts have to contend with.

    Con’s also not clear on closed/frozen schemes where members pay nothing but employers pay so-called “deficit reduction contributions”.

    Nor does he seem to recognise the use by trustees, often on advice, of prudent margins for known unknowns.

    I feel the tone of these articles and letters is not helping “the debate” or helping to inform the DWP’s consultation or the PLSA’s taskforce.

    Liked by 1 person

  2. henry tapper says:

    I don’t agree with you George. Con’s positions are quite abstract and are drawn from first principals. But the obfuscation you refer to is not of his making, it was created by super complicated variations created by clever people like me (who don’t look so clever now!)

    Liked by 1 person

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