Consistent Asset and Liability Valuation (1948-1963)

The exceptional inflation experience of the years immediately following the First World War proved to be a transitory phenomenon. Indeed, over the course of the 1920s, a significant portion of the price increases of the postwar years were reversed by a decade of deflation. By 1933, the UK CPI stood at a lower level than at the end of the First World War. The Second World War inevitably generated a further bout of inflation, but in its immediate aftermath the political stance—in particular, that of Hugh Dalton, the then Chancellor of the Exchequer—was to seek very low long-term interest rates. In 1946, long-term government bond yields stood at 2.6 % (they were 4.6 % 20 years earlier). The position pension actuaries faced was therefore reversed from the time of Epps’s 1921 paper: pension funds’ bond assets now showed a considerable market value appreciation, whilst the prospective future available yield on new money was considerably lower than had been assumed in pension valuations.

C.E. Puckridge published a paper in the Journal of Institute of Actuaries in 1948 which analysed these circumstances and their actuarial consequences.[1]

In the late 1940s, as 40 years earlier, standard actuarial practice was to value assets at book value or, if lower, market value (or perhaps somewhere in between), with liabilities valued using a broadly static valuation interest rate assumption. The liability valuation rate could be set with reference to the investment yield implied by the book value of assets, with some allowance made for how that yield was expected to evolve in the future. Puckridge, however, argued for an alternative approach that entailed a more systematic, consistent approach to the valuation of pension fund assets alongside liabilities:

Value assets (including existing investments) and liabilities at the rate of interest which it is anticipated can be earned on future investments.[2]

Puckridge did not provide much specific guidance on how to estimate this interest rate, but he did note that the rate will be

‘determined by considering the average rate at which investments could be made at the present time, taking into account the range of investments authorized for the particular fund and the proportion likely to be invested in the various classes; adjustments will have been made to allow for any interest margin that it is desired to incorporate and for the view taken on the probable trend of interest rates over a long period’.[3]

Puckridge’s future investment rate was an inherently long-term and subjective parameter. He likely envisaged that it would result in more stable asset and liability values than the market-based approach suggested by Warner back in the discussion of Epps’s paper in 1921. But the vital point of Puckridge’s method was that the actuarial assessment of the financial health of pension funds required greater and more transparent consistency between the valuation of assets and liabilities than was found in the then standard actuarial practice. Whilst this may appear obvious in hindsight, it was not a particular point of emphasis in the previous half-century of actuarial thinking on defined benefit pension funds. Though Puckridge preferred to reject the direct use of market prices, he did recognise the difficulty in placing a value on assets that exceeded their current market value:

It would in practice be difficult to adopt any value in excess of the total market value, and the balance would therefore be retained as a margin which would fall into surplus in the future as the excess interest is received.[3]

Puckridge’s idea of valuing assets by discounting their future income at an interest rate that is consistent with the rate applied to the liabilities gained considerable ground within the actuarial profession over the following 15 or so years. Eventually, a form of this ‘discounted income’ approach to the valuation of all assets in a defined benefit pension fund would become standard actuarial practice. Of course, S.G. Warner’s advocacy back in 1921 of using market values of assets along with a market-based liability discount rate could be viewed as one example of consistent asset and liability discounting. But pension actuaries were generally reluctant to shift their long-term liability valuation assumptions by the degree that could be implied by market movements. After all, in the context of open, expanding defined benefit pension funds, there would never be a need to sell assets, and actuarial judgement could apparently form a better view of yields available for future investments than current market prices. Puckridge’s embryonic notion of setting a stable long-term liability discount rate and valuing the projected cashflows of both assets and liabilities at that rate emerged as the pension actuary’s solution to consistent asset and liability valuation that would provide valuation stability through time.

Three actuarial papers published between the years of 1958 and 1963 were particularly important in further developing Puckridge’s idea and establishing its practice in British pension scheme valuation. Once again, economic conditions provided a spur to this progress. Following the post-war Dalton era of politically induced low interest rates, economic reality had reasserted itself. Long-term bond yields reverted from 2.6 % in 1946 to 5.0 % in 1958. Pension actuaries were once again wrestling with the consequences of substantial bond asset depreciation.

The first of these three papers was written by D.F. Gilley and D. Funnell.[5] Gilley and Funnell, like Puckridge a decade before them, argued that both asset and liability cashflows should be discounted at the ‘average yield on future investments’. However, in doing so, they also noted some of the perverse consequences that this may have. In particular, if this approach resulted in a deficit being identified in the scheme, the amount of money required to extinguish this deficit would not necessarily be equal to the assessed size of the deficit. Under the discounted income approach, actuaries were essentially operating in a parallel currency—actuarial valuation pounds had a different value to ‘real-life’ pounds. But they argued that their approach of valuing both sides of the balance sheet with a single discount rate was preferable to attempting to find consistency between liability valuation and book asset valuation by creating a discount rate that was an ill-defined blend of the current book yield and the assumed average yield on future investments.

Gilley and Funnell moved beyond Puckridge’s work when they considered the valuation of equity assets within their discounted cashflow approach. As we will discuss further below, equities became an increasingly important asset class for pension schemes during the 1950s. Any asset valuation method for British pension funds therefore needed to be directly applicable to equities. The simultaneous valuation of equities and bonds immediately gave rise to the question of whether and how the asset mix of the pension fund should impact on the actuarial valuation of assets and liabilities. Should a portfolio of equities and a portfolio of bonds, each with the same market value, command the same actuarial asset value? Should a change in the asset mix result in a different valuation of liabilities through a different choice of liability discount rate? In a nutshell, should the higher expected return of equities be capitalised in the current assessment of the pension fund surplus/deficit?

Gilley and Funnell were unambiguous in their view: ‘it would not be prudent for the actuary to reduce the contribution rate or weaken the basis of valuation by assuming a higher valuation rate of interest than the expected, long-term, gilt-edged rate’.[6]

So Gilley and Funnell were clear that the asset allocation choices of the pension scheme should not impact on the valuation discount rate applied to its projected asset and liability cashflows. However, that did not mean that they advocated the use of the market value of the equity holdings. They suggested that the market value of the equity portfolio be scaled by the ratio of the actuarial valuation of irredeemable consols (as implied by the valuation interest rate) to the market value of those consols. Or, equivalently, the equity market value should be scaled by the ratio of the market consol yield to the valuation interest rate, i. In this approach, the actuarial value of total assets would be the same for any split of assets between equities and consols. Thus, the asset allocation choice would not impact on the overall actuarial valuation of assets or liabilities. However, they added a caveat: the equity valuation may be reduced by a ‘margin of arbitrary amount’ if the actuary held a strong view that they were ‘over-valued in the market’.[7]

These asset valuation ideas were quite controversial at the time. Traditionally, actuaries viewed the writing-up of asset values above their book values as a dubious and imprudent practice. Gilley and Funnell’s approach could see assets valued significantly in excess of not just book values but market values.

The minutes of the discussion of their paper highlights the suspicion and hesitancy with which conventional actuarial thought welcomed these ideas. Gilley and Funnell’s essential point, however, was that subjective assumptions about future investment conditions must arise in pension fund valuations, and their method provided a more coherent and transparent approach to setting those assumptions.

Heywood and Lander’s 1961 paper, ‘Pension Fund Valuations in Modern Conditions’,[8] was the next significant contribution to British actuarial thought on the consistent valuation of pension fund assets and liabilities. Like Puckridge and Gilley and Funnell before them, Heywood and Lander again argued that the valuation discount rate should be set as the long-term interest rate that is expected to be earned on new money; and that assets should be valued consistently with that rate. However, Heywood and Lander differed from Gilley and Funnell in two fundamental respects. Firstly, whereas Gilley and Funnell had argued that the discount rate should reflect the expected future long-term gilt yield irrespective of the actual asset allocation of the pension scheme, Heywood and Lander believed that the expected return on the actual asset allocation of the pension scheme should be used. This meant that the liability valuation would be reduced by increasing the fund’s allocation to equities. They suggested that a 100 % gilts allocation would merit a 3.5 % discount rate, whilst a 50/50 equity/gilts allocation would justify a discount rate of ‘4 % or possibly even higher’.[9]

The second, and related, point on which Heywood and Lander diverged from Gilley and Funnell was on the valuation of equity assets. Equity investment was becoming ever more material for UK pension schemes. Heywood and Lander noted that a typical approach at the time of writing was to invest 50 % of assets in equities and 50 % in fixed income. Equities had proved attractive to pension funds both as an inflation hedge and as a high-yielding asset class (though the reverse yield gap was just starting to emerge at this time). Like Gilley and Funnell, they noted that the practice of valuing assets at the lower of book value and market value was still prevalent. And they expressed strong unease with the use of market values in general on the grounds of their volatility:

It seems very difficult to justify a method of valuing assets which places a value

upon the fund which may alter substantially if the valuation date were varied by

only some two or three months.[10]

They also noted that there was no reason to expect book values to provide an asset valuation that was consistent with the liability valuation basis. Like Gilley and Funnell, they concluded that a discounted income approach to asset valuation, using a discount rate consistent with that applied to the liability outgo, was the only way to obtain a consistent asset and liability valuation. For bond valuation, Heywood and Lander concurred with Gilley and Funnell: the projected cashflows of the bond could simply be discounted at the liability discount rate. For equities, they argued that equity dividends should be explicitly projected using a dividend growth assumption before discounting at the valuation rate. Thus, equities could be valued as a perpetuity discounted at the rate (i - 0’) where i was the liability discount rate, and 0’ was the assumed dividend growth. The dash was used because 0 was defined as the assumed rate of salary inflation that should be applied in the liability valuation. Salary inflation was typically not explicitly allowed for in liability valuation at this time, but Heywood and Lander argued that credit for inflationary dividend growth on the asset side of the balance sheet should only be taken if consistent treatment of inflation was applied on the liability side of the balance sheet. Moreover, they specified that 0’ should be less than 0 (though they did not provide any specific rationale for this).

So, under Heywood and Lander’s approach, the relationship between the actuarial valuations of equity and bond holdings were not directly constrained by their relation to their respective market values. This meant that a change in the equity/bond mix could change the actuarial valuation of assets as well as the actuarial valuation of liabilities. Shifting from bonds to equities would typically improve their assessment of the pension fund solvency position. However, their stipulation that, for reasons of consistency, this improvement should only be permitted if the liability valuation recognised a level of salary growth consistent (and not less than) the assumed equity dividend growth, meant that their approach would also be accompanied by a general strengthening of the liability valuation basis.

Finally, perhaps to hedge their bets, Heywood and Lander permitted a scalar parameter X to be applied to the equity valuation as an ‘arbitrary multiplier’. This was intended to allow the actuary to make any special adjustments that he deemed appropriate in the context of the valuation exercise. Whilst this might appear as something of a fudge, it prevented their methods from being cast as mechanical rules to be mindlessly applied by the actuary. It emphasised the application of actuarial judgement that was valued by the profession. In the Staple Inn discussion of the paper, Gilley suggested:

Truly, the actuary valuing the fund was in a better position to assess the relative values to the fund of ordinary shares and irredeemable gilt-edged securities than was the market.[11]

Not all participants in the discussion held to the view however that actuaries were better equipped to value equities than the market. J.G. Day, whose writings we shall discuss below, commented:

I am disturbed by the idea expressed in the paper that an actuary should be prepared to value ordinary shares in a way quite independent of market value, and that it should be presumed that his value would be superior to that of the market.[12]

The 1963 paper,[13] ‘The Treatment of Assets in the Actuarial Valuation of a Pension Fund’, by Day and McKelvey represented the final instalment of this period’s trilogy on consistent valuation of pension fund assets and liabilities. They once again started from the basis that the assumed value for the valuation rate of interest should be ‘the average rate of interest that is assumed for future investment over a long future term’.[14]

We saw above that Gilley and Funnell suggested that equities should be valued as their market value scaled by the ratio of the market consol yield to the valuation interest rate. Day and McKelvey suggested a variation on this theme: they argued equities should be valued as their market value scaled by the ratio of the equity dividend yield to the valuation interest rate. As the product of the market value and the dividend yield is the current dividend payable, it can be seen that this formula simply values the current dividends as a perpetuity at the valuation interest rate i. In what was now becoming an established actuarial asset valuation tradition, they also allowed an additional scalar parameter as ‘an arbitrary factor’.

Clearly, this approach to equity valuation ignored future dividend growth and they suggested this valuation formula should only be used when inflation is ignored in the liability valuation. They then suggested that the discount rate could explicitly be set as a real rate that could be applied to both sides of the balance sheet, and suggested a real rate of 3.5-4 % would be appropriate. This was fundamentally the same result as Heywood and Lander: it was, in essence, a dividend discount method where the market’s required return on equities had been replaced by the pension fund’s valuation interest rate (which, in turn, was to be set to reflect the long-term expectation for the pension fund’s asset return). Under these approaches, changes in equity market values that arose from changes in the dividend yield rather than changes in dividend payouts would have no impact on pension fund valuations of equity assets.

There was a broad consistency in the thinking of this collection of papers. They all eschewed market asset values on the grounds of consistency with a liability valuation that was to be made using stable assumptions. But some, like S.G. Warner many decades earlier, felt like this was tackling the consistent valuation problem from the wrong end. In the Staple Inn discussion of Day and McKelvey’s paper, Plymen commented:

They were assuming a certain figure for the rate of interest for valuing the liabilities, and twisting the valuation of the assets round to be consistent with that basis. Why not start off with the market value of the assets and try to deduce from that basis a consistent system for valuing the liabilities?[15]

Speaking at a Staple Inn meeting over 30 years after the publication of the paper, McKelvey’s son, K.J. KcKelvey, also an actuary, commented on the explanation his father had given him for tackling the consistency problem this way round:

The sole objective of that 1964 paper was to find a consistent basis for valuing assets, given an existing methodology for valuing liabilities. The liability valuation basis was off-market, by convention at that time. Therefore the asset valuation inevitably became off-market. The main aim of the authors was to move away from the valuation of assets by book value, which was still common. They simply did not think about market values since ... there were no formal discontinuance tests.[16]

We will see below how funding objectives such as discontinuance testing influenced valuation thinking in the latter decades of the twentieth century. But first, we will review how actuarial thinking on investment strategy for pension funds developed alongside the above ideas on asset and liability valuation.

  • [1] Puckridge (1948).
  • [2] Puckridge (1948), p. 2.
  • [3] Puckridge (1948), p. 12.
  • [4] Puckridge (1948), p. 12.
  • [5] Gilley and Funnell (1958).
  • [6] Gilley and Funnell (1958), p. 50.
  • [7] Gilley and Funnell (1958), p. 53.
  • [8] Heywood and Lander (1961).
  • [9] Heywood and Lander (1961), p. 323.
  • [10] Heywood and Lander (1961), p. 327.
  • [11] Gilley, in Discussion, Heywood and Lander (1961), p. 342.
  • [12] Day, in Discussion, Heywood and Lander (1961), p. 364.
  • [13] Day and McKelvey (1963).
  • [14] Day and McKelvey (1963), p. 108.
  • [15] Plymen, in Discussion, Day and McKelvey (1963), p. 134.
  • [16] K.J. McKelvey, in Discussion, Exley, Mehta and Smith (1997), p. 950.
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