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Early Thought on Defined Benefit Pension Funds (1905-1921)

Early actuarial thought on defined benefit pension funds focused on the development of the algebra and substantial mechanical computation necessary for the valuation of a scheme’s liabilities and the assessment of a required contribution rate under a given set of deterministic assumptions for the scheme’s future development. In these early years, there was considerable discussion of how to set the decrement bases for the liability projection, but relatively little focus at this time on how to set the valuation interest rate. Asset valuation was rarely, if ever, addressed. Investment was predominantly in long-term government bonds, and in the late Victorian and Edwardian eras, long-term interest rates were remarkably stable by later standards: between 1875 and 1910 the long-term government bond yield moved within the range of 2.0-3.2 %. Valuing assets at the lower of book value and market value seemed simple, prudent and adequate.

This actuarial work was fundamentally similar in spirit to the reserving calculations made in life offices, but the calculations were even more convoluted and computationally intensive. Ralph Hardy developed the first defined benefit pension fund valuations around 1875. In doing so, he originated the commutation factor as a vital computational aid for this task.[1] Hardy’s work, however, was never formally published. The earliest British actuarial professional papers on funded pension schemes were published during the Edwardian era by disciples of Hardy such as George King (in 1905) and Henry Manly (in 1911).[2] Actuarial papers on funded pension schemes were nonetheless sparse—prior to the conclusion of Second World War, only a handful of notable papers on pension schemes were published in the British professional actuarial journals.

King’s paper presented the actuarial calculations that were required for pension fund valuations and the assessment of the contribution rate that would fund the ultimate benefits—that is, to find a contribution rate expressed as a constant proportion of salary that had a present value equal to the present value of the liabilities. It was the first paper to set out the detailed calculations that were necessary to allow for treatment of the various decrements (death, pre-retirement withdrawals and retirement) and assumptions (mortality rates, interest rate, withdrawal rates, salary growth) in the valuation of the liabilities (pensions, death benefits, withdrawal benefits) and the setting of the contribution rate required to fund the projected liabilities.

King suggested that the withdrawal, mortality and retirement rates should be estimated by each scheme based on their own recorded experience. These could be suitably graduated using methods such as those developed by Woolhouse for life office mortality experience tables. He emphasised how these assumptions should vary across pension funds and railed against the use of assumptions based on pooled pension fund data. He recognised, however, that scheme- specific data would seldom be available for pensioner mortality at the older ages and he advocated the use of one of the published population mortality tables such as English Life Table, No. 3 for this purpose. He suggested a salary scale should be specified (i.e. how salaries vary by age) again based on the actual experience of the scheme membership. Inflation was a relatively subdued economic phenomenon in this era—the UK inflation index was at the same level in 1904 as it had been in 1860; so the salary scale was intended to represent the growth in salary due to promotion and experience. In the examples he gave, he assumed that salaries would increase by about 80 % between the ages of 20 and 30, but by only 12 % between 50 and 60.

In considering the setting of the contribution rate, King only considered the calculation at the inception of the scheme, and hence avoided addressing the valuation of any pre-existing scheme assets. Nor did he discuss how the valuation interest rate should be set. It was simply a parameter that was subsumed into Hardy’s commutation functions.

Manly’s 1911 paper further discussed the estimation of the member decrement assumptions, and he also provided some analysis of the sensitivity of the valuation to those assumptions. Manly was more sanguine about pooling the experience of different pension funds for the purpose of estimating decrement rates, providing the pension funds reflected a similar profile of member. The paper included a ‘Life and Service Table’—the withdrawal, mortality and retirement rates and salary scale based on scheme experience—for the aggregated experience of several large railway schemes. He noted that selection effects would produce pension scheme mortality that would typically be lighter than that observed on assured lives. Members who were seriously ill at pre-retirement ages would tend to withdraw from the scheme as they would no longer be able to work. The surrender of a life assurance policy, on the other hand, would tend to be made by a person in good health.

Manly highlighted the sensitivity of the projection of the pension scheme, and the contributions required to fund the liabilities, to these assumptions by comparing the results obtained with those produced by assumptions published in other early studies. He showed that his life and service table implied that a 5 % salary contribution would fund a pension of 1.55 % of average salary for every year of membership whereas alternative previously published assumptions would support 2.38 % of average salary for every year of membership.[3] Manly also provided detailed year-by-year projections of the pension scheme asset values, contributions and benefit cashflows that would be generated over a 90-year projection using his assumptions and the alternative. This highlighted how the solvency of the pension scheme could go awry if experience deviated significantly from the basis assumed in setting the contribution rate, thus highlighting the need for careful and regular monitoring of the pension fund’s experience by the actuary.

The Staple Inn discussion of Manly’s paper generated some interesting debate on the purpose of advance funding of pension liabilities that illuminated the actuarial views of the time. One speaker, Thomas Tinner, noted that a primary reason for advanced funding was to provide security to the pension fund member:

Without a fund, or a guarantee from the employer, there was no security that when a man who had been paying all his period of service for the pensions of others came to retire his own pension would be provided by a younger generation. This was especially the case if the employer was a private firm.[4]

He also argued that the interest earned on advance funding of the pension benefits would reduce its cost:

The effect of accumulating a fund was to reduce the cost of the pensions, because the interest earned would help to pay the outgoings.[4]

Meanwhile, W.O. Nash argued that the main aim of the pension scheme was to recognise a smooth accrual of the cost of the pension provision:

What they were aiming at in starting a Pension Funds was an equalization of the annual expense for the pension.[6]

As we shall see below, these three reasons for advanced funding would be revisited and debated numerous times by actuaries, accountants and economists over the remainder of the twentieth century. The relative importance attached to each of these reasons would influence the choice and development of actuarial methods used in pension fund valuation.

The economic consequences of the First World War represented the first great economic shock to test British defined benefit pension schemes. It created considerable stress for the financial health and solvency of the pension funds. It also created new challenges for pension actuaries, particularly with respect to the treatment and management of inflation. Over the Pax Britannica period—the 100 years between the end of the Napoleonic War and the start of the First World War—inflation rates had at times fluctuated markedly both up and down but there was no discernible consistent upward trend in UK consumer prices. Indeed, the UK Consumer Price Index stood some 20 % lower at the outbreak of the First World War in 1914 than it had been at the end of the Napoleonic Wars in 1815. Thus, the risks associated with future price inflation did not feature prominently in actuarial thought on final salary pension schemes prior to 1914. No explicit assumptions for price inflation or real salary growth featured in the work of King or Manly. Their age-dependent salary scales were intended to capture the typical path of career progressions, not economic inflation.

In the years 1915-1920 inclusive, the UK CPI index more than doubled. Salaries and wages increased at a similar rate. This substantially increased the value of pension liabilities without generating an offsetting increase in the value of pension fund assets (which, as noted above, were predominantly invested in long-term government bonds at this time). This scenario was radically different to anything within living memory of actuaries. The possibility of such a scenario and its consequences for pension funds had, naturally enough, not been seriously considered by pension actuaries prior to the war.

In 1921, G.S.W. Epps wrote an important, and at the time controversial, paper[7] on the implications of this experience for pension fund valuation, noting in his introduction that ‘[due to] enhanced scales of salaries or wages which have resulted from the change in the value of money ... it is to be feared that in many funds a very serious position has to be faced’.[8] Epps used case studies to highlight that, for older, established pension schemes, the impact on the valuation of accrued service benefits and the resulting solvency levels was very substantial. Furthermore, at this time pension funds were not required to inflation-link pensions in payment, and Epps’s valuations made no allowance for such increases. But significant pressure bore on the schemes to provide some increases to pensions in payment in order to mitigate the significant reduction in real value of pensions which had been inflicted on pensioners over the previous decade.

This exceptional economic environment also naturally had an impact on the asset side of the pension fund balance sheet. Between 1900 and 1920, long-term government bond yields more than doubled from 2.5 % to 5.3 %. The implications of this interest rate rise for the valuation of the assets and liabilities of pension funds was a topic of considerable controversy within the actuarial profession at the time. Epps recognised that the net impact of such interest rate rises may not necessarily be adverse for a pension fund:

It is, of course, true that materially higher rates than those assumed in past valuations can be looked for in the case of the accruing funds to be invested for many years to come; but the question as to how far it is prudent to meet past depreciation by raising the valuation rate of interest is one of extreme difficulty, the solution of which throws a great responsibility on the actuary concerned.[9]

The topics of asset valuation and depreciation and the related treatment of the liability discount rate received much attention at the Staple Inn discussion of Epps’s paper. Some actuaries were reluctant to recognise the market value impact on bond prices, even if not to do so was evidently imprudent. For example, R.G. Maudling commented:

As to the general treatment of depreciation, he might be accused of heresy, inasmuch as he could not bring himself to write securities down to their present market value ... He preferred to make a reserve for possible loss on realization, and to give considerable weight to the fact that securities might ultimately recover. He was not inclined to give much credit to present market values because they were more or less fictitious, being the values which a man who was compelled to realize was prepared to take, and he thought it would be extremely unwise to write everything down to that level.[10]

J. Bacon expressed a quite similar view to Maudling:

He would certainly not write down investments to their present market price, but would simply set aside an investment reserve and write ofl2 any deficiency there might be by means of an annuity, believing as he did that in five or ten years’ time, when they got to a state of equilibrium, the annuity set apart would probably not be required, and by that means he would have succeeded in giving a degree of safety to the fund without unduly crippling the employer.[11]

So, the above actuaries advocated valuing assets above market value, though with perhaps a partial write-down from their book value. A reserve would be included on the liability for future realisation of investment losses, but this would be smaller than the difference between the assets’ actuarial valuation and their market value, reflecting the actuary’s confidence that the assets would subsequently increase in value as rates reverted back to historical norms. No change in the liability discount rate would be made using this approach. The current market yield was treated as an aberration that could be largely assumed away. However, S.G. Warner, an influential actuary who was Institute President during the years 1916-1918, suggested a quite different approach where assets were fully marked down to their current market values whilst the liability discount rate was increased consistently to reflect those market yields:

Depreciation should be severely dealt with, but that there should be little hesitation about using something nearly approaching the rate of interest which that depreciation revealed as having been secured.[12]

This is perhaps the earliest actuarial advocacy of a market-based pension fund valuation. As we shall see below, the topic of consistent pension fund asset and liability valuation in the presence of significant changes in market interest rates would occupy pension actuaries’ thoughts for much of the remainder of the twentieth century.

  • [1] See King (1905), pp. 129 and 175.
  • [2] King (1905), Manly (1911).
  • [3] Manly (1911), p. 157.
  • [4] Tinner, in Discussion, Manly (1911), p. 219.
  • [5] Tinner, in Discussion, Manly (1911), p. 219.
  • [6] Nash, in Discussion, Manly (1911), p. 222.
  • [7] Epps (1921).
  • [8] Epps (1921), p. 405.
  • [9] Epps (1921), p. 410.
  • [10] Maudling, in Discussion, Epps (1921), p. 444.
  • [11] Bacon, in Discussion, Epps (1921), p. 448.
  • [12] Warner, in Discussion, Epps (1921), p. 449.
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