The Actuarial Profession by alicejenny


									JIA 90 (1964) 104-147


           THE   TREATMENT         OF ASSETS       IN THE     ACTUARIAL
                    VALUATION          OF A PENSION         FUND
           BY J. G. DAY,     M.A. F.I.A. AND K. M. MCKELVEY,             F.I.A.
                    [Submitted to the Institute, 25 November 1963]

     THIS paper has its origins in the authors’ thoughts on the paper pre-
     sented to the Institute by G. Heywood and M. Lander in 1961 under the
     title Pension Fund Valuations in Modern Conditions (J.I.A. 87, 314). Little
     claim for originality is made for the present paper: rather is it an attempt
     to consider in greater detail some of the problems raised by Heywood and
     Lander. We would also refer to the paper by C. E. Puckridge (J.I.A. 74,1)
     which, although we would not agree with some of its details, set out for
     the first time, in our opinion, some of the basic principles.

                         I. FUNDAMENTAL        BACKGROUND
        1.1 The basic aim of a pension fund is to produce sufficient income in
     future years to meet the benefits as they arise. The object of the valuation
     is therefore to enable the actuary to form an opinion whether the future
     investment income and redemption        proceeds from the assets now held,
     together with future contributions,       will meet future outgo. For this
     purpose contributions    consist of all payments at current rates from both
     employees and employer, and benefits are as provided by the rules; both
     contributions   and benefits are considered in respect of present members
        In practice a valuation      balance sheet is produced      by discounting
     estimates of all future income and outgo back to the valuation date; how-
     ever, the actuary is essentially concerned with future income and outgo
     with the object of advising the client whether appropriate         provision is
     being made for future liabilities. It is not difficult to imagine that, as
     techniques change and with the aid of computers, the form of presenting
     valuations may change.
         1.2 In discounting future income and outgo back to a single point of
     time we believe it is essential to aim at consistency of treatment on both
     sides of the balance sheet. For example, £10 of expected income due in
      1980 should be discounted by the same factor as £10 of expected outgo in
      1980. To achieve this consistency both assets and liabilities must be valued
     in the same way and the key is the long-term rate of interest assumed. This
     is the actuary’s estimate of the rate of interest at which it will be possible,
     on the average over the long period until all existing members of the fund
     have withdrawn, died, or retired, to invest the future net increments in the
                        Valuation   of a Pension     Fund                     105

fund or carry out disinvestment after the fund has reached its maximum
and started to decrease. It is the rate to be earned on future investment
in respect of existing members that matters, for even with existing invest-
ments one will value income, and what was paid for them is of no concern
except indirectly as a guide to the investment ability of the trustees. The
treatment of a pension fund valuation should also take account of the
basic characteristics   of pension funds.
    1.3 The problems facing a pension fund are basically different from
those of a life office whose valuations have the object, apart from ful-
filling certain statutory obligations,      of producing an orderly release of
surplus for bonus declarations.        A pension fund valuation is in some
respects akin to a solvency valuation.
    It would be only coincidental if the average rate of interest one expects
to earn on new investment in future, or at which one expects to effect sales
if one is dealing with a decreasing fund invested too long, were the same
as the yield the fund is now receiving on either book value or market value.
The approach suggested is fundamentally         different from the use of market
values or book values and it is perhaps worthwhile to set out the particular
advantages or disadvantages       of these.
    Book values are, of course, easy to produce, do not fluctuate, tie in with
the accounts and are easy for the layman to understand. But equal amounts
 of one stock purchased at different prices at two different times will be
brought in at different values, so that the relative values ascribed to the
investments will normally be quite illogical if one looks forwards instead
 of backwards.
    Market values are also easy to understand and easy to use. They relate
 assets to the current market rate of interest (or rather structure of interest
 rates); market rates can vary quite sharply over a short interval when there
 has been no change in one’s estimate of the average long-term rate of
 interest and no change in the future receipts that one expects to receive
 from a given asset. The great advantages of market values are that they
 are independent, they reflect the views of many investors and they should
 be consistent one with another. Quite apart from the question of con-
 sistency between the two sides of the valuation there are three objections
 to market value for a pension fund valuation, namely:
   (a)   The market produces prices which          balance   marginal   buyers and
         marginal sellers.
   (b)   Ordinary share prices are mainly      determined by tax-paying in-
         vestors to whom capital profits are    more valuable than dividends
         whereas to a pension fund the two     are of equal value.
   (c)   The net U.K. rate of tax applicable   to a dividend affects the value
         of a share to a pension fund.
   Using market values (or book values) causes little difficulty when market
rates of interest (or rates on book value) are close to our estimate of the
106             The Treatment    of Assets   in the Actuarial
long-term average, but when this is not so the valuation results are dis-
torted because liabilities are valued at one rate of interest and assets at
   1.4 The main problems of carrying out a valuation in the consistent
way suggested are concerned with the valuation of future income from
equities, and with inflation; and it is with these that this paper is mainly
   Many pension schemes are tied to final salary or average salary so that
anything that affects salaries affects the value of the fund’s liabilities.
However, even if pensions are not so tied most present-day employers would
probably agree that, to achieve their object in instituting a pension fund, it
must provide a pension on which (together with the state retirement
pension) a man can live. Anything that causes higher wages and salaries
is therefore likely to lead, directly or indirectly, to higher pensions.
   The cloud on the horizon which may alter a fund’s liabilities, and the
public attitude towards pensions, is the state’s growing share of super-
annuation liabilities. Increases in the level of state pensions may lead to
reductions in pension fund benefits which may offset the effect of salary
inflation. The extent to which this may apply depends not only upon
Government     social insurance policy but also upon the Inland Revenue’s
attitude to decreases in occupational      pensions when there are increases
in state pensions.

   2.1 This is the age of invention, new techniques and (one hopes)
increasing productivity.  The NEDC is assuming a 4% growth rate—
although a lower rate seems more likely. Such growth leads to higher
earnings in real terms either (1) by falling prices and unchanged money
earnings or, more likely, (2) by higher money earnings and unchanged
   These two alternatives  would seem likely to have the following re-
spective effects:
(1)   Pension fund liabilities would be unaffected; gilt-edged investments
      would produce a fixed income of increasing real value. Falling prices
      could be due to technical advances, lower profit margins, greater
      productivity or a combination of all three. Profits would probably be
      stationary or only slightly increased in money terms but would cer-
      tainly increase in real terms.
(2)   Pension fund liabilities would be markedly increased;       gilt-edged
      investments would produce a fixed income of static or reducing real
      value; if not squeezed by higher labour costs, company profits and
      dividends should increase in money terms.
  There are of course many variations     between the two alternatives
which also omit the more subtle changes that could occur (i) in the shape
                        Valuation   of a Pension   Fund                      107

of the salary scale (ii) in the differentials and relative earnings (much upset
by recent inflation) between office staff and manual workers and (iii) in
pension levels and pension age.
    2.2 We have seen recurrent inflation since 1945 accompanied by higher
salaries and wages, higher prices and a steadily depreciating currency.
    In this changing period the ravages of war have been made good and
there is now over-capacity in many industries (an alternative, one hopes,
to unemployment).
    However, deflation is painful (and politically dangerous) and govern-
ments are always likely to err on the side of overspending.             The trade
unions are now strongly entrenched and even in times of deflation basic
wage rates and salaries scarcely fall (though earnings may); indeed public
opinion would regard lower wages as political failure and a social sin.
    2.3 In future one expects to see economic growth and higher produc-
tivity with occasional slight inflation. One anticipates an age of rising
wages and salaries and also rising pension liabilities, although one should
distinguish between the very different possible causes for this.
    2.4 It has been widely and authoritatively        suggested that, to meet the
dangers of inflation, pension funds should invest in equities. (property
should be considered as a particular form of ‘equity’ and is not discussed
separately in this paper). It has been argued that with inflation a business’s
real assets increase in money terms; one can also argue, no less logically,
that the value of ‘know-how’, goodwill, etc., should also increase in money
terms proportionately       so that, although     inflation may initially cause
difficulties and distortions,    an equity investment will eventually have in-
creased in earning power in rough proportion to the effect of inflation (or
very often rather more, as prior charges lose in value).
    It can similarly be argued that if the United Kingdom achieved economic
 growth without inflation, equity profits would increase because earnings
 and consumption would rise.
    One must recognize, however, that the potential gain in value on equities
 will not in either instance necessarily be equal or proportionate         to the
 increase in value of liabilities.
     2.5 There is another factor which may cause equity earnings and divi-
 dends to increase. Many British companies retain a substantial proportion
 of earnings. Part may be required to make up depreciation to a true figure
 based on replacement cost, but some earnings are quite frankly retained
 to finance expansion. Many companies would claim that retained earnings
 were required to maintain their competitive position, but even this often
 implies expansion because industry is developing into larger units or
 using bigger machines because of growing markets. Often expansion
 financed by retained profits is a reflection of the country’s economic
     One has to remember, however, that expansion does not automatically
 lead to higher profits; there is a danger of profitless expansion as has been
108              The Treatment     of Assets   in the Actuarial
seen in recent years in North America, where severe competition has caused
the effect of increased sales to be offset by lower profit margins. It is also
apparent in some industries in this country where competition               to use
increased capacity leads to price cutting.
     2.6 In considering equities we wish to distinguish between the effects
of inflation and what we would term a company’s ‘growth’ prospects,
which could reasonably be expected, in the absence of inflation, due to
retention of earnings to finance expansion, to new inventions and tech-
niques and also to the ability of the company’s management.              ‘Growth
rates vary from company to company depending on management                  quality
and the industry engaged in, but mainly on the former since the latter
can usually be modified or extended if the management is good.
     2.7 The market’s assessment of equity shares includes the benefit one
would expect in the event of inflation in addition to the other factors
 mentioned      above. Market values are also affected by the prospect of
 capital gain, whatever the cause. Certainly the expected yield is the expecta-
tion of all possible future benefits, and for many private investors this
 certainly includes an expectation of a capital profit, whether taken or not.
 There are rational arguments behind this, for increasing dividends and
 profits should usually imply increasing prices. Income and capital profit
 are of equal value to a tax-free pension fund but not to the private taxed
     Yields based on last year’s dividend are misleading, and investment
 sophistry to explain a ‘reverse yield gap’ is largely a waste of time because
 investors think, even if unconsciously, in terms of some sort of expected
 yield which is greate than the yield on Consols.
     In assessing equity prices, earnings yields certainly have some appli-
 cation, because they allow for the shareholders’ share of the earnings that
 are ploughed back. Unfortunately         earnings fluctuate, and also one cannot
 be certain how much should be required for true depreciation.            Whereas
 earnings are quoted gross and would often be worth the gross amount
 to a pension fund if paid out, only a net amount after tax is actually
 retained. In fact the pension fund investor would do better if earnings were
 paid out by way of dividends up to the hilt and companies made ‘rights’
 issues to raise some capital each year. In theory one could say that the
 earnings yield to a pension fund should be based on the gross dividend
  and net earnings retained after tax.
      Subject though it is to the qualifications set out in the earlier sections of
 this part of the paper, it is our firm conclusion that increased pension
  liabilities due to inflation or to economic growth may be offset to some
  extent by an increase in the future income from well-selected equities.

    3.1 As stated in § 1.2, the key to the valuation is the average rate of
 interest that is assumed for future investment over a long future term; this
                        Valuation   of a Pension   Fund                   109

is normally unrelated to market conditions at the valuation date and is
only indirectly anything to do with the recent rate of interest earned on
the fund. Being the best estimate of the average rate which the trustees will
earn on future new investment, it is therefore a function of:

  (1)   the trustees’ investment powers, i.e., how widely they may invest;
  (2)   their ability in using them;
  (3)   the tax exemptions which one expects the fund to enjoy;
  (4)   the general expectation for future interest rates and investment

Of the first three factors   we would say:

  (1)   this is factual and can be ascertained by reference to the trust deed;
  (2)   this is indicated by the quality of the existing portfolio and the
        trustees’ future intentions which are most important        and should
        be discussed with them;
  (3)   tax exemptions and net U.K. rates of tax have an effect on the
        rate of interest earned which is easily ascertainable         now, but
        which could vary in the future.

   3.2 It is a basic concept of actuarial work that reasonable estimates
can be made of the future from experience of the past course of similar
events. When one comes to item (4) mentioned in the previous paragraph,
the general expectation for future interest rates and investment conditions,
it may not be sound to be guided by past experience. It is common for
those who deal with investment matters to consider that there is no such
time as one in which conditions are normal. With regard to the long-term
rate of interest one may not go as far as saying that conditions are ab-
normal but one would say that there are valid reasons for suggesting that
they are different from those in the past. For example, many investors
are concerned with yields after tax and if net yields are likely to vary be-
tween certain limits, then, in times of high taxation as we have now and
foresee for some time, gross yields ate likely to be higher than those re-
garded as ‘normal’ in the past.
   3.3    Since the 1939-45 war the yield on undated Government securities
has varied between 2½% and 7%. Clearly investors’ views on the long-
term outlook have fluctuated widely while the post-war problems have
proved different from the pre-war difficulties. Unemployment     has not been
heavy, but we have suffered from inflation and capital shortage; looking
ahead, severe inflation is unlikely to be a problem but technical change,
over-capacity and capital shortage seem likely to be major factors. Invest-
ment is more than ever dominated by political decisions, and, as the invest-
ment world becomes more international,         rates of interest overseas are
likely to have a greater effect on U.K. interest rates than they have had in
the past.
l10             The Treatment     of Assets   in the Actuarial
   3.4 At the time of writing, 2½% Consols yield 5·41% and the F.T.-
Actuaries 500-Share index gives a yield on dividends of 4·44% and on earn-
ings of 7·84% (before allowing for net U.K. rates of tax). Nevertheless the
level of interest rates still appears to be historically        high; one might
expect the rate of interest for future new investment to average at least
3½% in the long term if the trustees confined themselves to fixed-interest
stocks and a higher rate, by some ½% say, if the investment                policy
included equities to any considerable extent. (When referring to the rate
of interest on equities we mean the expected yield at the time of
   In existing circumstances we would expect the valuation rate of interest,
when ignoring inflation and the secular growth, to be about 3½% to 4%,
but one could envisage conditions in which a varying rate, or a different
rate for a certain period, was assumed (e.g. special taxation or political
conditions which were believed to be for a limited period only).
   3.5 As already stated, the valuation rate of interest is used (or a variant
is used) to value both liabilities and the income including redemption
proceeds from existing assets. This gives a value to existing assets. The
current return being earned on existing assets at book or market value
does not, therefore, come directly into our consideration when determining
the valuation rate of interest.
   3.6 It can scarcely be a coincidence that, in recent years, as the con-
sciousness of inflation has sunk in, one has also seen long-term rates of
interest rise to a historical ‘peak’.
   These considerations     suggest that if one is going to postulate continuing
inflation one must also postulate consciousness of it on the part of investors.
One has then no ‘past course of similar events’ to study; it seems probable
that so long as fear of inflation persists, fixed interest rates of over 5% will
be demanded      and available. It is also likely that the fund will hold a
substantial proportion     in equities (and equities as we know them today
are scarcely comparable with those of the years before 1939). The ultimate
yield on the cost of those equities will probably be well over 5% but we
would be unlikely to take a rate as high as that except in some special
circumstances    when we allow for the effects of inflation on the value of
   In fact an assumption      of inflation would affect not only the liabilities
of the fund, but also the valuation rate of interest to be chosen. In our
opinion, if one postulates inflation at a rate off per annum then one’s valua-
tion rate should be higher and might well be pitched at 3½% + ƒ if assets
are confined to fixed-interest      stocks, or ½% or so higher if equities are

   4.1 There are advantages in ignoring inflation, if the circumstances of
the fund make it possible. The degree of inflation probable is so uncertain
                        Valuation   of a Pension    Fund                      111
and is dependent       on so many unknown          factors that individual   esti-
mates fluctuate widely. This argument           often leads to the conclusion
that the commonsense          thing to do is to ignore inflation          on the
liabilities side, relying on its being offset by holding equities on the assets
   In this part of the paper therefore inflation is ignored; but in Part V we
consider methods of allowing for it if one feared that it might prove over-
optimistic to expect that the rise in the value of the equities would neces-
sarily offset the increased liability of the fund and felt it proper to provide
in advance for this potential liability.
   4.2 If i denotes the rate of interest used for valuing liabilities, fixed-
interest investments should be valued by discounting future interest income
and, if redeemable, redemption proceeds at rate i. This process is algebrai-
cally identical with taking fixed-interest investments at book value plus
the discounted     value at rate i of (i) future investment income in excess
of i times book value and (ii) excess of redemption            value over book
   Theoretically,   preference share dividends and debenture interest (and
associated redemption proceeds where relevant) should be multiplied by a
factor to allow for the risk of default. This could easily be calculated by
an index of preference or debenture yields relative to gilt-edged. (This would
over-estimate the risk, because in part the lower yield on gilt-edged is due
to marketability.)     However, this theoretical adjustment is rarely worth-
while in practice as debentures and, more particularly,        preference shares
usually form so small a proportion of most pension fund portfolios. If the
holdings were large, adjustment would be necessary.
   4.3 One finds in practice that the alternative exposition of the method
in §4.2 is, although longer, more readily appreciated by the client. It also
leads to a modification which is appropriate          for the closed fund. This
is to value the excess interest for only a limited period, fixed after making
an approximate      estimate of emerging costs, and to assume that, if not
redeemable before the end of the limited period, the assets will then be
sold. A sale price must be assumed. In recent years when fixed-interest
securities have, historically, been depressed it has been prudent as well as
convenient to assume that these forced sales, if any, would command a
price equal to the market price at the valuation date.
   We would add, regarding the valuation of a closed fund, that under our
view as to what is implied by the valuation rate of interest, the higher the
rate used the more stringent is the valuation unless the mean term of the
assets is shorter than that of the liabilities.
   4.4 When it comes to valuing equities the problem is more difficult and
two approaches have been made.
    D. F. Gilley and D. Funnell, in an outstanding        paper to the Students’
Society (J.S.S. 15, 43) on the valuation of pension fund assets, suggest
for equity shares:
112                The Treatment     of Assets   in the Actuarial
Aggregate    market value of these investments
                                                × Value placed on £100 of
  Market     value of £100 of 2½% Consols      2½% Consols by the Actuary;

but they do qualify this formula with possible arbitrary adjustments on two
grounds. Firstly Gilley and Funnell state that the yield on all equity shares,
grouped together, and based on market value, should be compared with
the yield on 2½% Consols; if the ratio of the two yields seems within the
range of short-term fluctuations from the mean and no long-term change
is expected, then the value can be taken unadjusted;       but if the equity
shares held were, on the whole, overvalued a margin might be taken.
Secondly Gilley and Funnell point out that equity yields may be depressed
by being bought as a hedge against inflation and they state ‘If the
valuation of the liabilities makes no allowance for future inflation it seems
unreasonable    that the full market value of the equities should be taken
into account in the valuation balance sheet. We see no way of assessing
the amount by which the market value of equities is increased as a result
of such buying and we can only suggest that an arbitrary deduction from
the value calculated by the proposed method should be made.’
    Gilley and Funnell’s formula can alternatively be expressed as
                                                  yield on 2½% Consols
       market     value of equity holdings ×

It is a formula based on current market value, but suitably             adjusted   for
the current level of long-term interest rates.
   Heywood and Lander (J.I.A. 87, 314) suggest
              λ × current annual dividends       from equity holdings
where λ is an arbitrary multiplier, which would be chosen bearing in mind
the actual portfolio-the      possible risks, the proportion of low-yielding
equities etc.-and   is intended to represent
            expected   average future dividend if there is no inflation
                              current annual dividend

with a safety factor for the degree of risk associated with the expectation.
   This is essentially an approach based on income. Its obvious defects are
that it is based on last year’s or current dividend rates and that it involves
the need for an arbitrary multiplier.
   4.5 For the type of valuation which we are discussing, we consider
that the formula used to value equities should value income and must
ignore inflation (which market value does not). Perhaps more contentiously
we would also wish to eliminate the effect of the general secular trend
because this will, in our opinion, increase the fund’s liabilities.
                         Valuation    of a Pension   Fund                     113

   The income we wish to value would seem to lie between                  current
dividend and current earnings and we suggest a formula like
            current annual dividend ×     dividend yield on ordinary share index
                        i                      dividend yield on share
where R is an arbitrary factor and T allows for tax not reclaimable.
   This formula does attempt to allow for low-yielding shares, where we
and the market expect genuine ‘growth’, due to able management            and
retention of earnings, to emerge even with stable prices. By using the factor
                    dividend     yield on ordinary share index
                               dividend yield on share
one is allowing for low-yielding shares where one expects the dividend to
increase and for high-yielding shares where the dividend may not be main-
tained; and one is suggesting that in each instance the long-term dividend
yield on present market valuation will approximate to the current yield on
the index.
   Now that it is available, one would use the F.T.-Actuaries       All-Share
index. Because last year’s or current dividends can be so unsatisfactory
the arbitrary and subjective factor R is there. This could be used (at a
value less than 1) to allow for risks when the general level of dividends
appeared unlikely to be maintained    or (at a value greater than 1) when
they appeared to have abnormally high cover due to artificial limitations
of dividends. To allow for the effect of the net U.K. rate of tax one must
add a factor T, which is net dividends plus tax reclaimed divided by
gross dividends.
   4.6 The formula we would suggest is therefore in line with that of
Heywood and Lander but with some added elaboration;        it simplifies to
           × (market value of equities) ×     (dividend yield on ordinary
    i                                                           share index).

   4.7 It will be seen that        the general   reasoning   approach   to the ex-
pression set out above is:

       ‘Present value at rate i of a perpetuity of the income which would
       result from selling all the equities in the fund (and thus realizing all
       the capital appreciation   in them due to the market’s expectation of
       their future) and reinvesting the proceeds in a representative     cross-
       section of the equity market; allowing by R for last year’s dividends
       being misleading and by T for the effect, on the income from shares
       held, of their net U.K. rates of tax.’

This approach is close to the rationale for the formula devised by Gilley
and Funnell. We differ from them only in having ‘dividend yield on a cross-
section of ordinary shares’ where they have ‘yield on 2½% Consols’. We
114             The Treatment       of Assets   in the Actuarial
prefer our formula because it does not, under this rationale, require, as
theirs does, the assumption that one is going to realize all equities and
reinvest in stocks of an entirely different character.
   In current conditions the value by Gilley and Funnell’s formula is larger
than that given by our formula. This is because 2½% Consols yield more
than the F.T.-Actuaries   index, reflecting to a large extent the general view
of the secular trend and expectation       of possible inflation. We wish to
eliminate these two factors.
   We would claim to have succeeded in excluding both these factors
because they occur equally in the numerator and denominator         of

                   dividend     yield on ordinary share index
                              dividend yield on share

   4.8 It might be said that our formula is conservative in that our valua-
tion of future income should use a figure nearer current earnings than
last year’s dividend. Apart from the obvious snags over earnings we
wish, as pointed out in §4.7, to eliminate the secular trend and, in very
rough terms, by taking the dividend yield we seem likely to achieve this.
   4.9 To many actuaries it may appear arbitrary to take a value for
equities above market value. However, one should remember that market
prices are merely the values placed on future income by tax-paying
investors using a gross rate of interest which is usually greater than that
employed to value pension fund liabilities.

              V. VALUATION         ALLOWING       FOR INFLATION
    5.1 An allowance for inflation on the liability side can be rigorously
justified only if benefits are linked to salary levels. The most typical
example of this, of course, is the ‘final salary’ scheme which is very
common among privately invested staff funds.
    5.2 If there is to be such an allowance, should it ignore inflation after
 retirement? Valuation in strict accordance with the rules will nearly always
 mean ignoring such inflation. In practice, however, one suspects that, if
 inflation is going to be allowed for at all, realism may require us to re-
 cognize the effect of inflation after retirement age, so as to build up the fund
to the state where it could make increases in existing pensions without
    5.3 Arguments      similar to those advanced in § 5.2 can be adduced in
 favour of an inflation allowance even in a fixed benefit scheme since ‘2s.0d.
 per week pension per year of service’ may be eroded by inflation more
 quickly than is compensated        for by changes in National Insurance and
 require to be increased if it is to be effective. On the other hand a change in
 the attitude of the state may make this unnecessary.
     5.4 If we define the annual rate of inflation to be allowed for as ƒ and the
                           Valuation      of a Pension     Fund                                              115

valuation rate of interest as j, then in the paragraphs below we discuss how
allowance for inflation could be made.
   We have already discussed in § 3.6 the view that if one postulates
inflation one should assume a higher return in money terms from both
fixed-interest stocks and equities and therefore a higher valuation rate of
interest. In our opinion j could be as high as 3½% to 4% plus ƒ, depending
on the investment policy; put a different way, we would expect j—ƒ to be
in the range 3½% to 4%.
   5.5 Liabilities are valued by the normal methods using a rate of interest
of j–f up to retirement and j or j–ƒ(see §       5.2) thereafter. In combination
with the asset valuation bases set out in the following paragraphs,            this
ensures consistency between the two sides of the valuation balance sheet
in the allowance made for inflation.
   5.6 Fixed-interest    investments are valued by the same methods as set
out in § 4.2 but using j in place of i.
   5.7 In valuing equities we are aiming to include the increase in income
that we expect from inflation and also any increase that we may expect from
the secular economic trend, as well as the increase resulting from an
individual company’s natural growth. One obvious approach is to adopt a
formula very similar to that in § 4.5 but to use j-f         as a denominator    in
place of i; that is for a particular share

                  dividends          dividend     yield on ordinary share index
                     j–ƒ                        dividend yield on share
which simplifies for a portfolio       of equities to
            × (market value of equities) × (dividend yield on ordinary                                     share
  j–ƒ                                                      index). . . . . . . . . . . . . . . . . . . . . . . .(1).
   It could be argued that in these circumstances the dividend yield is too
low, although probably few would go so far as to substitute ‘earnings
yield’ for ‘dividend yield’ in the numerator. In any event we have allowed
for inflation by taking j–ƒ rather   than j in the denominator.
   As an alternative approach, one could for an individual share advance
a formula such as

                              dividends              yield on 2½% Consols
                                 j              ×   dividend yield on share

which simplifies for a portfolio       of equities to
             × (market value of equities) ×              (yield on 2½% Consols). . . . . .(2)
This uses the factor
             (yield on 2½% Consols) /(dividend                yield on share)
116             The Treatment     of Assets   in the Actuarial
in an attempt to assess the market’s valuation of inflation and of a par-
ticular share’s growth prospects. Also, having established an estimated
level of ‘certain future income’, it values this income, as a perpetuity, at a
rate of j, not j–ƒ.
    There is no particular reason why the value of equity dividends (includ-
ing inflation at rateƒ) should equal the value of the fixed income that would
result if all equities were sold and reinvested in 2½% Consols; if one thought
that inflation would occur one would not sell equities and buy 2½% Consols.
    Of the formulae, we incline towards the first, because it does lead to a
consistent approach as to the degree of inflation and secular improvement
being anticipated on both sides of the valuation balance sheet. Inflation and
the secular economic trend are both so indeterminate       that any approach is
open to criticism; a valuation is, at best, very approximate          and with a
series of valuations one is merely aiming to regulate the pace of funding
 of the liabilities.
    5.8 We would be uncertain of the effect on a valuation of allowing for
 inflation if the funds were wholly in equities; from general reasoning we
 would hope that the result would not be significantly altered.
    However, where a fund is invested partially or wholly in fixed-interest
 stocks, a valuation allowing for inflation will produce a less favourable
 result than one which ignores inflation. The outcome of a less favourable
 valuation result emerging, due to the inclusion of an inflation allowance in
 the basis, is likely to be a recommendation      of an increase in the level of
 employer’s contribution     by the actuary. The question which must then be
 answered is: In the face of inflation, as prognosticated       in the valuation
 basis, would these additional contributions      not do more good in the em-
 ployer’s business (or, in the case of a local authority fund, in the rate-
 payers’ pockets) than in the pension fund? We think the answer to this
 question is almost certainly ‘yes’. At the risk of opening up a new line of
 thought-which        we do not propose to pursue very far-the       argument of
 the last sentence can lead one to an argument against funding pension
 liabilities at all, namely the argument that the employer can make money
 fructify better in his own business than anywhere else and that this is
 therefore the best place to keep it. It is only necessary, to dismiss this
 argument as a general proposition,      to mention:

   (1)   the interest earned on accumulations    on an approved pension fund
         is gross while that earned on normal company reserves suffers tax;
   (2)   orderly financing of pension liabilities during employees’ working
         lifetime demands funding;
   (3)   it is only right and fair to employees that moneys should be put
         aside, out of reach of the company and so independent          of its
         fortunes, to meet the cost of the promised pensions: this is even
         more strongly true of a contributory        than of a non-contribu-
          tory scheme.
                         Valuation   of a Pension   Fund                   117

    5.9 We accept these arguments against the retention in the employer’s
business of funds to cover the main pension liability even though, as part
of a formal pension fund, they will be invested to a considerable extent in
fixed-interest securities at a time when one expects inflation and secular
   We would put forward the view, however, that any additional liability
resulting from an allowance for inflation in the valuation basis is better
left ‘unfunded’. This strengthens     other arguments against an allowance
for inflation in the valuation basis.

   6.1 The results quoted in this section are based upon those of a recently
completed valuation of a ‘final salary’ pension fund.
   The index referred to is the F.T.-Actuaries      500-Share index. We used
this consistently in our illustrative figures because we include results based
on the use of an earnings yield which is not available for the F.T.-Actuaries
All-Share index.
   6.2 The values of the assets on various bases were as shown in Table
A. The bases of valuation were;

  (i)     All assets taken at book value.
  (ii)    Fixed-interest  stocks by the method of § 4.2 and ordinary stocks
          by the method of § 4.6 using ‘dividend yield on index’ (valuation
          rate 4% throughout).
  (iii)   Fixed-interest stocks by the method of § 4.2 and ordinary stocks by
          the method of § 4.6 using ‘earnings yield on index’ (valuation rate
          4% throughout).
  (iv)    Fixed-interest  stocks by the method of § 4.2 (valuation rate 6%)
          and ordinary stocks by formula (1) of § 5.7 (valuation rate 4%).
  (v)     Fixed-interest  stocks by the method of § 4.2 (valuation rate 6%)
          and ordinary stocks by formula (1) of § 5.7 (valuation rate 4%)
          but with ‘earnings yield on the index’ in place of ‘dividend yield
           on the index’.
  (vi)    Fixed-interest  stocks by the method of § 4.2 (valuation rate 6%)
          and ordinary stocks by formula (2) of § 5.7 (valuation rate 6%).

The first three bases are those consistent with ignoring inflation. One of
the second three would be used if one wished to assume that the average
rate of interest for future investment would be 6% but at the same time
wished to allow for 2%, per annum inflationary        increase in ordinary
   Because debentures and preference shares formed as much as 12% and
9% respectively of the book value of the fund, we made adjustments as
suggested in § 4.2. 5% was deducted in the case of debentures and 12½%
in the case of preference shares. In valuing equities T was allowed for on
118               The Treatment      of Assets in the Actuarial
each holding where applicable and R was taken at unity throughout    since
we did not feel that at the valuation date any of the arguments set out in
§4.5 for a greater or lesser value were applicable.

                              Table A. Value of assets
      Valuation     Fixed-interest     Ordinary       Loans ‘at call’       Total assets
        basis        investments        shares         & debtors
          (1)              (2)             (3)             (4)                  (5)
                           £                £               £                    £
           (i)         1,041,000          674,000        151,000             1,866,000
          (ii)         1,204,000        1,275,000        151,000             2,630,000
         (iii)         1,204,000       2,517,000         151,000             3,872,000
         (iv)            940,000       1,275,000         151,000             2,366,000
          (v)            940,000       2,517,000         151,000             3,608,000
         (vi)            940,000       1,126,000         151,000             2,217,000

  6.3 The values of the net liabilities on two bases were as shown in
Table B. The bases of valuation were similar throughout        in all respects
except for the valuation rate of interest. The latter varied as follows:
           (a) 4% throughout
           (b) 4% before retirement,       6% thereafter.

   The first basis would be used if one were ignoring inflation, or if one
were valuing at a 6% rate of interest but allowing for 2% per annum
inflation of salaries before and pensions after retirement.
   The second basis would be used if one were valuing at a 6% rate of
interest but allowing for 2% per annum inflation of salaries before retire-
ment only.

                       Table B. Value of net liabilities
      Valuation    Current       Prospective    Prospective Contributions                Net
        basis      pensions      retirement      widows’        less                  liability
                                  pensions       pensions     returns
         (1)        (2)               (3)          (4)           (5)                    (6)
                     £                £               £                 £                £
         (a)       346,000       2,760,000          954,000      2,417,000           1,643,000
         (b)       290,000       2,410,000          856,000      2,419,000           1,137,000

   The small difference in column (5) is not one about which one would
bother in practice. On basis (a) the present value of future returns of
contribution,   a negative component   of column (5), is computed at 4%.
On basis (b) it is computed at 6% in respect of past contributions    and,
effectively, at somewhere between 4% and 6% in respect of future contri-
butions. The value of future contributions   themselves is computed at 4%
                           Valuation   of a Pension     Fund                     119
on both bases. There should be the same difference between the two
interpretations  of basis (a).
   6.4 The result of any actuarial valuation is marginal, being the com-
paratively small difference between two large figures. Bringing together
the results set out in Tables A and B we see this fact strikingly illustrated
in Table C. Nine methods are illustrated:
Method (i) is what might be termed the traditional one.
Method (ii) is the one which we favour for the reasons set out in §§ 4.5
and 4.7.
Method (iii) is a variant of method (ii), substituting in the valuation of
equities the ‘index earnings yield’ for the ‘index dividend yield’. It gives,
in our view, an extreme valuation result which could not be justified.
Method (iv) shows the effect of modifying method (ii) so as to assume a
higher gross rate of interest but to allow for inflation throughout    life. In
this fund, with 36% of book values in equities, it gives a result of the same
order as method (ii). It would show a far smaller surplus were the fund
confined to fixed-interest investments.
Method (v) varies method (iv) as method (iii) varies method (ii).
Method (vi) is somewhat severe and is open to our objection to incorporat-
ing the yield on Consols.
Methods (vii) to (ix) correspond to methods (iv) to (vi) but allow only for
inflation before retirement. We can accept little logic in this and regard
methods (vii) and (viii) as insufficiently    stringent.  In this particular
instance method (ix) gives a result close to that of method (ii) which we
favour but this is coincidence rather than being rested upon a rationale in
which we have confidence.

                            Table C. Valuation Results
             Basis of valuation            Basis of valuation        Valuation
                 of assets                   of liabilities           surplus
      (i)    Book value                       4%. Inflation           223,000
     (ii)    4% compound interest value       4%. Inflation           987,000
             of fixed-interest assets;          ignored.
             ordinary shares valued as
             per §4.6 using ‘dividend
             yield on index’
     (iii)   as (ii) but using ‘earnings      4%. Inflation          2,229,000
             yield on index’                     ignored.
     (iv)    6% compound interest value       6%. 2% inflation        723,000
             of fixed-interest assets;        allowed for through-
             ordinary shares valued by        out life.
             formula (1) of § 5.7
      (v)    as (iv) but using index          as (iv)                1,965,000
             earnings yield in place of
             index dividend yield
120                      The Treatment         of Assets   in the Actuarial
            (vi)   as (iv) but using formula          as (iv)                    574,000
                   (2) of § 5.7
        (vii)      as (iv)                            6%. 2% inflation          1,229,000
                                                       allowed for before
                                                       retirement only.
       (viii)      as (v)                             as (vii)                  2,471,000
        (ix)       as (vi)                            as (vii)                  1,080,000

                               VII. GENERAL OBSERVATIONS
Presentation of valuation results
   7.1 Having thus shown in Part VI the many alternative results which
could emerge on the various assumptions discussed in Parts IV and V of
the paper and having briefly commented on them, we must add a most
important reservation.
   7.2 It is impossible to say that any of the results set out in Table C
is the ‘right’ one. Even within the limitations of purpose suggested in
§ 1.1 there are many variations in the circumstances surrounding a pension
fund valuation which will influence the actuary, well within the limits of
professional standards, as to the form of his final report. Two examples
might be:
(i)         The client company wishes to make some reduction in the normal
            pension age and accepts an increase in normal contributions        for the
            future, but hopes that there will be sufficient surplus in the fund to
            meet the resulting increase in back service liability. Then, in the
            context of the wide range of justifiable results shown in Part VI, if
            the increase were not more than £900,000 or £1,000,000 we would
            regard it as the most desirable course for the actuary to present a
            report indicating    that the object could be achieved without any
            deficiency contribution    being called for. We would be reluctant to
            present such a report if the increase in liability were appreciably
            greater than £1,000,000.
(ii)        The same client company wishes at this valuation to make no
            change in benefits or contributions,   but would be reluctant to see an
            excessive surplus disclosed, having plans for the use of a surplus at the
            following valuation but not yet. In these circumstances the actuary
            would be justified in strengthening the position of the fund by adopt-
            ing valuation method (1) of Table C and recommending             that the
            £223,000 surplus be carried forward.

Between these two extremes there are many intermediate                        circumstances
and we suggest strongly that:
      (a)      A valuation report completed and submitted after consultation
               with the client at every stage will give him the greatest benefit and
               understanding    of the actuary’s advice and will be in the best
                       Valuation   of a Pension   Fund                     121
        interests of the beneficiaries. Without consultation    our profession
        and the advice we give are liable to be misunderstood   and underesti-
        mated by commerce and industry.
  (b)   When the calculations      are complete, technique must yield to a
        certain flexibility applied in the knowledge that there is no right
        answer but only a range within which the right answer almost
        certainly lies.

The actuary and investment policy
   7.3 It is pleasing to observe that, although perhaps more slowly than
one could wish, actuaries are gaining acceptance as one of the natural
sources of expert advice on pension fund investment policy. To continue
to enjoy and deserve this we suggest that the actuary must resist all tempta-
tion to let the basis and technique of valuation determine the investment
policy. The actuary who as investment adviser advocates a determined and
appreciable entry into equity investment must when he comes to prepare
his actuarial valuations (unless of course there has been a fundamental
change in the long-term outlook) present a valuation result which is no less
favourable than that which would have emerged had the trustees adhered
to fixed-interest investments. It takes a particular combination  of circum-
stances to make this point of practical importance;     such a combination
has materialized over the last two years or so in the case of pension funds
  (a)   are confined to trustee investments and so only acquired the power
        to buy equities in 1961;
  (b)   have been using that power appreciably since, so buying equities
        on a 3% or 4% dividend yield basis during a period for much of
        which they could have purchased long-dated gilt-edged stocks and
        debentures to show a redemption yield of 6% or more.
   Such funds, mainly Local Authority superannuation          ‘funds, in many
cases embarked on equities near the May 1961 peak. Though they have
been buying steadily through the lower equity markets of 1962 and 1963,
it could well be that without thought on the actuary’s part the valuation
results of 1964, 1965 or 1966 could look worse than if equities had been
   Similarly if a fund invested heavily in debentures, the actuary should
make some adjustment in valuing these debentures (as stated in             4.2),
so that the value is not substantially more than the value that would have
been attributed to gilt-edged stocks of similar dates.
   7.4 If (i) a differential of ½% or even ¼% in the valuation rate of interest
for liabilities, as mentioned in 3.4, and (ii) the methods of asset valuation
advocated in this paper, are incorporated      in the actuary’s approach, we
believe that he will successfully avoid the pitfall described in 7.3.
122             The Treatment     of Assets   in the Actuarial
The pace of funding
   7.5 Our final reason for (a) not accepting of over-stringent       methods
of fixing the valuation rate of interest and of valuing assets and for (b) our
plea for consultation   with the client throughout    the valuation process, is
that the operating conditions of a pension fund are so full of imponder-
ables, notably the future of state pensions. This is more so even than for
most life office funds.
   7.6 There is therefore much to be said for the slowest pace of funding
consistent with (i) non-prejudice of emerging benefits and (ii) the employer’s
wishes in the matter within the limits of Inland Revenue approval. By
these standards    one could, but for inflation, justify a valuation      basis
which aimed only at retrospective (‘paid-up’) solvency.
   This, however, represents an absolute minimal level of funding. We
would regard it as inadequate in face of the likelihood of some inflation
and secular growth, even though we are against a full and specific allow-
ance for these factors in the valuation basis.
   Except for the kind of temporary reason set out in (ii) of 7.2, we would
nevertheless be most reluctant to recommend a rate of funding as high as
that implicit in taking the assets at book value in valuing a fund such as
that discussed in Part VI.
                             Valuation        of a Pension   Fund                          123

                  ABSTRACT               OF     THE     DISCUSSION

The President (Mr K. A. Usherwood, M.A.), in welcoming the guests, mentioned par-
ticularly Professor Dr Kracke, President of the German Institute of Actuaries, who sent
the following message:
     May I tell you that I felt very honoured indeed to have been invited by your old and
  honourable    Institute, in the country of origin of life assurance and of actuaries. The
  German actuaries are very happy to send you their greetings and are looking forward
  to the 17th Congress next year in Britain.
     My English is bad and for that reason I should like to close this message in Latin:
    Utinam  benignitas     benevolentiaque     deorum immortalium       actuarios britannicos
  approbet ac fortunet     et concilium    internationalem nostrum      proximum    septimum
  decimum bene vertat!
Mr J. G. Day, in introducing the paper, said that since the paper had been written, some
months earlier, the economic and investment         background   had altered, but not to an
extent sufficient to change the authors’ views. They had not gone out of their way to
answer potential criticisms of their views but were aware that they existed. Some people
thought the authors went too far; others that they did not go far enough. Those who
felt the paper did not go far enough were usually those who, when they came to the
formula in 4.5, asked, ‘Why did you lose your nerve and use an arbitrary factor?’ The
reason was that any assessment of an income from ordinary shares brought in individual
judgment, and if the last year’s dividends were used (as the authors thought they should
be) then it was felt to be essential to use an arbitrary factor; it could not be accepted
without it. After all, an arbitrary factor of that kind was very much a characteristic        of
actuarial work.
    Then there were those who complained        that the authors seemed to have departed
from what might be called apparent reality, and said that they accepted market values
or adjusted market values but found it very difficult to accept any method which pro-
duced a value which could be greater than market value. Usually they cited an easy
example: suppose there was a fund of £10,000 in cash and the valuation rate of interest
to be used was 4¼%, if the fund were invested in War Loan yielding 5¾% then instead
of the £10,000 in cash there would be an investment in War Loan valued by the authors’
methods at £13,500. There was an immediate profit of 35% which was regarded by those
people as a dreadful anomaly. The answer was, of course, that if a fund were valued at
4¼% when War Loan was yielding 5¾%, it was very advantageous            to invest in War Loan,
and the profit was a measure of that advantage. It would seem to the authors much more
 worrying to be in the position of not wanting to invest in War Loan; that would call for
considerable    explanation  for it would mean that the investment policy took account of
inflation which might not have been allowed for in calculating liabilities. The alternative
 was that the valuation rate of interest might be wrong, but that was a different problem.
    The authors had tried very hard to explain the disadvantages      of those very ephemeral
 things, market values; they had also tried to explain the benefit of consistency, because
 it seemed to them that the most important     feature was that a deficiency or surplus was
the difference between two very large and rather approximate         figures. The interest rate
at which liabilities were valued did not vary from day to day or even from month to
 month, so it was felt that using market values only produced an apparent realism, which
 was not as real as might be thought, and produced distorted results.
    Much closer to the authors’ views were those who preferred some form of adjusted
 book value. Those were used quite commonly,          the argument being that if the actual
income from a fund was greatly in excess of that obtained by applying the valuation rate
 to the book value, then the excess income was capitalized and added to the book value.
 That produced a very similar result to the authors’ method, depending on the techniques
 used and what was done about redemption          profits and losses, but the authors much
 preferred their method of valuing the income ab initio as accurately as possible.

124                   The Treatment            of Assets      in the Actuarial
The President, in calling on Miss Merriman to open the discussion, drew attention to the
fact that it was some 27 years since a discussion at the Institute was opened by one of the
lady Fellows, and expressed the hope that there would not be so long an interval before
another similar occasion.

Miss P. E. Merriman, in opening the discussion, said that a valuable feature of the paper
was its clear re-statement      of a number of basic actuarial principles which sometimes
tended to get submerged in the pressure of day-to-day work. For example,                    7.2 stressed
the need for consultation      with the client at every stage, and for flexibility in interpreting
the results produced by the actuary’s techniques,           and    7.3 warned against the dangers
of allowing actuarial techniques to dictate investment policy. If the trustees of a pension
fund had followed a wise investment policy, and had put a substantial              amount of money
into equities, that should not be nullified by a valuation result which was less favourable
than if the trustees had confined themselves to fixed-interest            investments.     In     1.1 the
authors pointed out that the actuary’s essential concern in a pension fund valuation
was with future income and outgo, and whether appropriate                provision was being made
for expected future liabilities, while         1.2 emphasized    the need for consistency of treat-
 ment on both sides of a valuation balance sheet. She admitted to some disappointment,
however, that in the following paragraphs            there was comparatively       little reference to
 the valuation of the liabilities.
     In   7.2 it was implied that the actuary’s task was to recommend            what seemed to him
 the most reasonable      answer, lying within a range of possible answers, having regard to
 any special circumstances       in a particular case. In       7.5 and 7.6 the authors gave some
 indication of their own views as to what was a ‘reasonable answer’. They considered that
 in view of the imponderables       which overshadowed       the operating conditions of a pension
 fund, in particular     the future of state pensions, there was ‘much to be said for the
 slowest pace of funding consistent with (i) non-prejudice            of emerging benefits, (ii) the
 employer’s wishes in the matter within the limits of Inland Revenue approval’. There
 she did not entirely agree with the authors; if she were a client she would take full ad-
 vantage of the consultative       sessions in order to argue the point with them! It was true
 that at the time there were many imponderables,             but people had been saying that ever
 since she entered the profession,         and, human nature being what it was, they would
 probably go on saying it in the future. Indeed, she felt that the imponderability              of future
 political activity in the pension field was in itself an excellent reason for disregarding              it.
  In deciding the extent to which liabilities should be funded, surely an important consider-
  ation was the rate of interest obtainable        on investments.    The authors would no doubt
  agree that currently interest rates were high as compared with the expected long-term
  future rate. In view of that she would revise the authors’ dictum in              7.6. and advocate
  the most rapid pace of funding consistent with (i) the employer’s wishes in the matter,
  and (ii) the limits of Inland Revenue approval. That difference in basic outlook coloured
  her approach     to the new methods of valuing equities suggested by the authors. Their
  formula, set out in 4.6,

                 R x T/i x (market   of equities)   x (dividend   yield on ordinary     share   index)

 would give a value greater than the current market value if the dividend yield on the
 ordinary share index, adjusted by the factors R and T, exceeded the long-term rate of
 interest, and that would tend to occur whenever rates of interest were above the long-
 term average. She, on the other hand, would normally regard the greater of book and
 market value as the upper limit of the value to be placed on equity investments           in a
 pension fund valuation-a         view which, incidentally,   might well be shared by some
 clients, especially those with an accountancy     background!    In other words, if an invest-
 ment had depreciated      since purchase she would not care to value it above its purchase
 price; if it had appreciated   she would not care to value it above its market value.
     Part II of the paper dealt with two distinct factors which could lead to increases in
                                   Valuation       of a Pension          Fund                                125
the level of wages and salaries: growth (in                  2.1) and inflation (in           2.2). In     2.6 the
authors emphasized         that they wished to distinguish             between the effects of those two
factors. It was therefore a little disappointing            that elsewhere in the paper the distinction
was not so carefully maintained,              and there were a number of places where the term
‘inflation’ was used loosely to cover both factors, e.g. in the first sentence of 1.4 and in
    5.1. In    5.4 f was defined as the ‘annual rate of inflation’, but                      5.7 implied that f
included both inflation and growth. There were some places where she had been unable
to decide in which sense the term ‘inflation’ was used, and in particular                          she wished to
ask the authors in what sense it had been used in the second half of 5.9 (that was where
the authors expressed the view that ‘any additional liability resulting from an allowance
for inflation in the valuation basis is better left unfunded’) and at the end of 4.1 (where
the authors suggested that it was only necessary to allow for inflation if it was feared that
it would increase the liabilities by more than it would increase the value of the equities).
The same difficulty was met in the practical example in Part VI, where bases (iv), (v) and
(vi) included an allowance of 2% per annum for inflation, but the question of growth
was not mentioned at all.
     Her view was that, since both major political parties were committed to an expanding
economy, and to the maximum                 rate of growth which could be achieved without in-
flationary pressures, it was prudent to take growth into account in a valuation basis but
reasonable     to ignore inflation, as the extent to which it would occur was so much less
predictable.     She also considered         that, where pensions were geared to retiring salary,
particular    attention should be paid to the matching of assets and liabilities, not only as
regards term but also as regards type of investment.                  The extent to which that had been
done should be taken into account in deciding how much growth should be allowed for
specifically in valuing the liabilities,          and how much could be regarded as covered by
equity investment.       The authors wisely pointed out at the end of                    2.4 that the potential
 gain in the value of equities, whether due to growth or inflation, would not necessarily
 be equal or proportionate            to the increase in valuation          liabilities.    She was not clear
 whether the authors had in mind there the point she had just made. (For example, if a
final salary scheme had invested only 10% of its assets in equities it would be most un-
likely that the appreciation           on those equities would be sufficient to match the entire
 growth in valuation liabilities.) She wondered if the authors were saying that the rate of
 increase in equity values might not correspond               to the rate of increase in wage and salary
 levels. That was indeed true, but in the case of growth increases she would have thought
 it a not unreasonable         assumption.      So far as inflationary        increases were concerned,           if
 such were expected, ‘matching’ as defined earlier became even more important.
     Thus she suggested that an important            first step in a pension fund valuation was to see
 what proportion        of the assets was invested in equities, and to compare that with the
 estimated proportion         of the net liabilities which would increase in direct proportion                   to
 future increases in salary levels, which she proposed to call the variable liabilities. (In the
 case of a final-salary scheme financed by a percentage contribution,                       the variable liabili-
 ties would usually approximate             to the net liabilities for active members.)               It was also
 necessary to consider possible changes in those proportions                        in the future, especially
 with a growing fund. Quite apart from its usefulness as a valuation preliminary,                         such an
 exercise would be a useful guide to investment policy. She wished to make it clear that
 she was not advocating           an automatic      investment      in equities of k%, where k was the
 ratio of variable to total net liabilities. What she was suggesting was that if the propor-
 tion in equities amounted          to less than k% then there should be some direct or indirect
 provision for future growth in valuing the fund’s liabilities. For that reason she was a
 little concerned      at the consequences         of the proposed       method of valuation            for fixed-
 interest investments,      since it automatically        capitalized   future interest earnings in excess
  of the valuation rate. Similarly, the method of valuing equities proposed in 4.6 auto-
  matically capitalized      the excess of the adjusted yield on the ordinary share index over
  the valuation rate. She had normally found that one of the chief sources of profit in a
  pension fund valuation,         available to offset the effects of increases in salary levels, was
126                The Treatment        of Assets in the Actuarial
interest earned in excess of the valuation rate, and that would disappear to the extent
that it was capitalized in advance.
    In conclusion she wished to consider the application of the principles she had outlined
to the practical example given by the authors. From Table B in Part VI it could be seen
that on the 4% valuation basis the value of current pensions amounted to just over 20%
of the net liability. That suggested a value of k of approximately 80%, but in fact only
36% of the assets (at book values) consisted of equities. Even if the entire equity holding
were set off against the variable liability (that gave £674,000 of equities compared with a
net liability of £1,297,000) it was found that nearly half of the additional liabilities in-
curred by future increases in the level of salaries would have to be met by sources other
than future increases in equity dividends. Assuming an annual rate of growth of 3%-
4% per annum that would correspond to an annual rate of increase of 1½/-2% per
annum. That could be allowed for directly, by incorporation in the salary scale, or
indirectly, by leaving a margin between the valuation rate of interest and the rate ex-
pected to be earned in future by the fund, or, indeed, by a combination of direct and
indirect allowances. She had estimated from the figures supplied by the authors that the
current yield on book values for the fund in question was in the region of 5¾%-6%.
Bearing in mind that it might not be possible to invest new money so advantageously as
the existing portfolio, and that no provision for future increases in salary levels had been
made in valuations (i)-(iii), she would have said that in that particular case there was
little scope for taking credit for capital appreciation. If, however, a bigger proportion of
the fund had been invested in equities, that might well have been possible.

Mr H. A. R. Barnett would have liked the authors to have considered the possibility of
winding up. Small concerns were in danger of being swallowed up by large concerns;
large concerns were in danger of being nationalized; the future of even a nationalized
industry was not absolutely guaranteed. When a fund was being valued, it could never
be said with absolute certainty: ‘This fund will not be wound up during the next 5 years.’
It was a pity that more funds did not contain a provision which would preserve the fund
in a closed form on the closing down of the employing concern. The advantages of
keeping a fund in being in that way would outweigh the disadvantages, but the fact
remained that it did not happen, and there was, therefore, in any fund a real possibility
that the assets might have to be realized in the foreseeable future.
   He agreed completely with the authors’ treatment of fixed-interest securities. The
price of those varied inversely with current interest rates; if interest rates rose, then at
the time of winding up the market value would have dropped, but so would the market
price of the annuities which would have to be purchased to replace the benefits in the
fund. He was glad that the opener had drawn the analogy to the matching of assets and
liabilities in a life office, and it should always be remembered that if a portfolio consist-
ing entirely of fixed-interest securities was matched perfectly to the liabilities, then it did
not matter what rate of interest was used for valuation. He could not, however, go along
with the authors in their treatment of ordinary shares, but neither did he agree with the
opener. He would hate to have to explain to a client what he had done in valuing the
assets by the authors’ formula in § 4.6. and if he tried to do so he did not really think he
would any longer be able to command his client’s confidence. In view of the winding-up
possibility he did not think that the client would like the actuary to take a value of
 ordinary shares materially above their market price. Admittedly it was consistent with
 the treatment of fixed-interest securities to value the income in perpetuity; the use of
current income, of course, took account of growth only up to the current date.
    The market value of an ordinary share, unlike the market value of a fixed-interest
 security, was affected by the current rate of interest, but that was not the most important
factor-the     question was: how much future growth was it permissible to take into
 account? He would have thought that if only the current income was taken and it was
 valued at a relatively high rate of interest there was a danger of going too far below the
 market value, and if that occurred there was a danger that the people making the
                               Valuation      of a Pension       Fund                             127
investments  would be instructed   by the employer not to buy any equity shares during
the year before the valuation date, because if the actuary was going to value them below
book value it would throw a strain on the fund. He had, after long consideration,    come
to the conclusion   that, because it was not possible to go either appreciably   above or
below the market value, the right figure for ordinary shares was something close to the
market value. The market value on a particular date could be affected by chance factors,
and it might therefore be better to use the average market value over a recent period.

Mr T. M. Springbett had been considering              the question from the point of view of a life
office and had incorporated        his views in a paper which was to be read to the Faculty, he
hoped, in January 1964.* There was a statement                in  1.2 of the paper to the effect that
‘both assets and liabilities must be valued in the same way and the key is the long-term
rate of interest assumed’. In his opinion the key to a valuation of assets and liabilities at
a notional rate of interest was the extent to which the fund was fully immunized.              It had
to be made very clear what was to be the criterion for deciding whether the fund was
fully immunized        or not, or, in other words, what exactly should be left unchanged             if
there were a change in the rate of interest. For the current purpose he proposed merely
to assume that the criterion was that the values of the assets and liabilities were both
affected in the same proportion          for a given change in the rate of interest. If, therefore,
the values of assets and liabilities were equal at one rate of interest, and the fund was
fully immunized,        they would, broadly speaking, be so at any other rate of interest. It
was for that reason that he expressed doubt whether the future average rate of interest
was the key to the valuation.         He did not, however, say that that might not be the most
suitable rate of interest for other reasons such as the desirability             of adopting a rate
which might be left unchanged           over a long period, or perhaps the necessity for making
some provision for the strain of new entrants. In his view, the paper did not give suffi-
cient emphasis       to the protection      which full immunization       could give against future
changes in the rate of interest.
   The word ‘immunization’           did not appear in the paper; but it was relevant to the
question which Mr Day mentioned in his introductory                remarks concerning the £10,000
in cash invested in 3½% War Loan, which gave rise to a 35% appreciation                   apparently
from nowhere. A valuation of assets and liabilities at a notional rate of interest which
was different from the market rate of interest could give rise to spurious profits or losses
if the assets were not of the same mean term as the liabilities, and if no steps were taken
to make an appropriate         adjustment    for that. He could best clarify his point by taking a
much simplified illustration.         Suppose there were two identical funds with identical
assets and liabilities.     Normally the trustees      of both funds held investments    appropriate
for full immunization,         and the trustees of the first fund had adhered closely to that
principle. The actuary valued both the assets and the liabilities of the first fund at the
current market rate of interest, say 5½%, and found that the assets equalled the liabilities.
Having read the authors’ paper the actuary also made a valuation at 4½%. The values
placed on the assets and liabilities were both higher but as the fund was fully immunized
the actuary was not surprised           to find that the value of the assets was still equal to
that of the liabilities.     But the trustees of the second fund became convinced,            shortly
before the valuation        date, that rates of interest were going to fall and they therefore
switched the fund into investments          with as long a term as possible, in the full realization
that it would not then be fully immunized and that the mean term of the assets would be
longer than that of the liabilities.        The actuary valued the assets and liabilities of the
second fund at the valuation           date at the current market rate of interest, 5½%, and
found that again the assets equalled the liabilities. He also valued them at 4½% but the
value of the assets rose more than the value of the liabilities, because the assets had a
longer mean term, and the actuary therefore brought out a surplus. That was a spurious
surplus unless rates of interest had in fact moved almost overnight from 5½% to 4½%,

                                          * T.F.A.   28, 231.
128                  The Treatment          of Assets     in the Actuarial
and it seemed rather lame if the actuary did no more than say, as the authors said in
effect at the end of        4.3 of the paper, ‘I know that if the mean term of the assets is
longer than that of the liabilities, then the lower the rate of interest I use the weaker is the
valuation,   and so I am not surprised there is a surplus, but it does not mean anything.’
   There was no time for him to discuss the full implications            of that paradox but it was
possible to develop a rewarding and intellectually         satisfying theory which resolved the
apparent absurdity.       Two guiding principles emerged. The first was that in a valuation
of assets and liabilities at a rate of interest other than the current market rate the amount
of an item was not sufficient to specify its value completely:        it was necessary also to know
its mean term. Consequently         it was only appropriate      to add or subtract items which
had identical mean terms. The second principle followed from the first, and was that if
a valuation     of assets and liabilities was being made at a rate of interest other than the
current market rate, and if the fund were not fully immunized, then before any compari-
son was made of the values of the assets and the liabilities,              a hypothetical    switch of
the assets at the current market rate of interest should be made into assets which had
the same mean term as the liabilities;         in other words, what he called a mis-matching
adjustment     should first be made. In his illustration,        if the mis-matching      adjustment
were made in the valuation of the second fund at the notional rate of interest of 4½%,
the spurious surplus disappeared,        as it should do. If, however, rates of interest had in
fact moved from 5½% to 4½% almost overnight, no mis-matching                      adjustment     would
be necessary for the 4½% valuation,         as 4½% would then be the current market rate of
interest and the valuation       would bring out the true profit which had been made by the
trustees’ having taken a correct view about the future course of interest rates. A mis-
matching adjustment         would, however, then be necessary for the 5½% valuation of the
second fund, and that valuation would show a surplus too, as it should do. Unfortun-
ately, the information       the authors gave about the values of the assets and liabilities in
 Part VI was not sufficient for an estimate to be made of the extent to which the fund
 was fully immunized        and what the mis-matching       adjustment,      if any, should be, but
 the fixed-interest    stocks were certainly a good deal shorter than perpetuities.

Mr J. B. Lieberman         found it helpful in tackling an actuarial        problem first to define
a theoretical   model and then to consider how the model had to be modified to reach a
practical solution. The theoretical       model adopted by the authors for the valuation of a
pension fund was described in            1.1 and 1.2 of the paper, and was based on a prospec-
tive approach.    He did not think that their model was the best for a growing pension
fund which was open to new entrants, provided the usual types of benefit, and had a
widely-spread    portfolio of investments.
   He considered     that the authors’ model had three features which tended to make it
unsuitable for practical use, despite its clear academic attractions.            The model assumed
that the investments      held on the date of the valuation either would continue to be held
until they were redeemed or would be sold only on advantageous               terms. He felt that that
assumption     was somewhat unreal. The paper submitted by G. T. Pepper to the meeting
of the Institute held on 28 October 1963 had brought out clearly that modern investment
policy was dynamic, not static. Many pension funds pursued a highly active investment
policy, and continuously       rearranged the fixed-income and, to a lesser extent, the variable-
income contents of their portfolios.        Such funds were becoming more and more typical.
The application    of the authors’ methods to them would bring out significantly different
values for their assets according to the particular          date chosen for the valuation over a
relatively short period. The reason for that, of course, was that the methods used by the
authors to value both fixed-income           and variable-income     investments    were not directly
related to current market values, so that if one investment             was switched into another,
the authors’ value of the assets changed. The techniques used to value the benefits and
contributions    could not be applied to the investments:         whilst an attempt could be made
to estimate the contribution        income and benefit outgo in, say, 1980, it was not possible
to estimate the then investment income, because it was not possible to assess the proba-
                                Valuation      of a Pension        Fund                              129
bility of the fund holding at that time any particular security or property out of the in-
deed unknown population        of securities and properties which would then be available.
   The second disadvantage      of the authors’ approach was the arbitrary nature of their
method of valuing ordinary shares. That destroyed any advantage that might be claimed
for their method of valuing fixed-income            securities. He saw no powerful reason for
there being the direct relationship       which was implied by the model in                  4.6 between
(a) the current level of dividends, and (b) the discounted              value of the expected future
income and capital payments in respect of a portfolio of ordinary shares.
    His third and most important        comment on the paper was one that he appeared to
share with Mr Barnett. He also feared that the client was unlikely fully to understand
the authors’    methods.   He accepted       that the client might appreciate             the alternative
method of valuing fixed-income         securities described in 4.2 but he was not very san-
guine about the client’s ability to understand        the authors’ treatment        of ordinary shares.
He felt that, unless the client could see that the actuarial               calculations     were relevant
to his workaday      world, he would be unlikely to have full confidence in the advice
the actuary gave.
   The theoretical   model which he preferred to that of the authors for the type of grow-
ing pension fund he had described was more retrospective              than prospective in approach.
The aim of the pension fund was defined as the accumulation                of sufficient money during
the working lifetime of the members to provide their benefits as they arose. The valuation
rate of interest was defined as the average long-term rate of growth in the amount
invested out of the contributions     to the fund. This rate of accumulation            reflected the net
experience with regard to interest, dividends, rents, underwriting                commissions,     invest-
ment expenses, taxes, and capital profits and losses. He stressed that that rate of ‘interest’
was not necessarily equal either to the current income yield on current market value or
to the rate of interest achieved on the fund since the last valuation                  as shown by the
usual Hardy formula. On that approach,            the value placed in practice on the assets for
the actuarial valuation had regard both to the total cost price, which represented the net
amount that had accrued to the fund, and to the current market value, which was a bench-
mark for forming a view as to future capital profits and losses. The value could be
regarded as the cost price plus such adjustment          as seemed appropriate        for capital profits
and losses, both realized and unrealized, accrued and future, real and imaginary. Again
the value chosen did not necessarily equal either the book value or the market value; it
could well lie between them, but equally it could be greater or less than either.
    He did not consider that a formula could be proposed which could be applied by rote
to value the assets in all circumstances.        He wholeheartedly          agreed with the authors’
comments in        7.1 and 7.2 about a flexible approach            to valuation     policy. He shared
their views that the valuation result should be arrived at by the actuary after discussion
with the client and in the light of all relevant considerations,         both within and without the
pension fund. A useful approach for the type of fund where the company’s contributions
were expressed as the balance of the cost of the benefits was to calculate what value of
the assets was implied by a certain level of contribution             and then to consider whether
that value was reasonable.       For that purpose it was often helpful to consider what
changes from the current level of an index of ordinary share prices could reasonably
be contemplated;    and also to what extent the fund could be reinvested in such gilt-edged
securities as would match the investment income to the net liability outgo. In practical
day-to-day work he had found considerable            success in presenting that alternative model
to clients and pension fund investment           managers. The concept of accumulation                 was
much more readily grasped than that of discounting. The client saw a direct link between
the value placed on the fund by the actuary and that put on it by the trustees in their
annual accounts. Investment       managers saw a direct link between the approach and the
aim of their investment policy, namely, to maximize the expected yield of the fund over a
long period of years while minimizing fluctuations           of risk. The reverse of his model was
that he regarded the values of the liabilities more as reserves against future benefit pay-
ments than as the discounted      values of the expected amounts of those payments. That
130                   The Treatment           of Assets      in the Actuarial
recognized how inexact under modern conditions        were the concepts of an average rate
of accumulation   and the assumptions     made about salary rises and membership turnover.
He considered   the analysis of surplus and the subsequent examination       of the contribu-
tion rates to be more meaningful      than the figure brought out in the valuation balance
sheet as the surplus or shortfall. Pension fund valuations      had to be played by ear, not
from a printed score.

Mr K. Sandom believed that valuations              of assets should be prospective          and not retro-
spective. He was glad to see that the paper mentioned market values of equities at an
early stage. That seemed a natural starting-point             and he was pleased that market values
appeared in the formula. The formula ignoring inflation in 4.6 was: a perpetuity of the
income which would result from selling all the equities in the fund and re-investing the
proceeds in a representative         cross-section     of the equity market. The difficulty was:
should the actuary value the future income that the market expected at an unknown
expected yield or interest rate (in other words, market value), or should he, alternatively,
value the hypothetical      current income from a cross-section             of equities at a hypothetical
rate of interest-at      best a cautious estimate of the average rate of interest for future
    In      2.6 and 2.7 the authors rightly contended              that market prices discounted          in-
flation and growth. The formula in 4.6, excluding inflation, tended, however, to pro-
duce a value higher than market value; in other words, as he saw it, to ignore inflation a
value higher than that which took inflation into account was used-an                    assumption which
he believed played havoc with expected rates of growth, inflated or otherwise. Formulae
 (1) and (2) of 5.7 also seemed to suffer in that way. The general adjustments                      R and T
 seemed to be refinements.       T for lost tax affected the yield, he maintained,             rather than
 current value. The subjective factor R, to allow for risks and hopes, was usually dis-
 counted in market prices-perhaps            more than necessary in either direction.
    In    1.3 the authors clearly stated their objections to market values but those, he felt,
 tended to over-simplify the situation. Market prices certainly represented levels at which
 buyers and sellers exchanged marginal amounts of stock. The market comprised a wide
 range of investors with differing requirements,           but laws of supply and demand tended to
 ensure that price levels were continually            self-correcting     as company news, economic
 conditions    and political developments        emerged. The power of the market as a market
 place had to be remembered.            For equities, there were numerous              unknowns:      future
 dividends, successive rates of growth in dividend, the pattern of expansion, take-overs
 and so forth. The expected yield from existing investments and rates of interest likely to
 be earned on future investments were also unknown. In a world of unknowns it seemed
 unwise to discard a most useful and independent                assessment of the discounted value of
 future equity income. Rates of discount, or the expected yield, were different for each
 investor but the share price and subsequent rates of growth in dividend levels were the
 same for all investors. Theoretical         consistency      was implied by discounting          income at
 the same rate of interest as that employed in valuing liabilities. That was essential in
 valuing emerging costs, or the excess of outgo over income, but, as mentioned                        by Mr
 Lieberman,     the lack of knowledge about future equity income complicated                   it. The most
 erudite forecasting      techniques     hardly reached the precision             which actuaries      could
 rightly claim for calculations      of emerging liabilities.
     He suspected     that the reluctance       to employ market values might arise from an
 actuary’s distrust of ungraduated        data. Discontinuous         price movements were inevitable,
  being developed by a process of trial and error. Collectively, however, fluctuations                  were
 less marked for equity portfolios.           Variable      investment     reserves, both positive and
 negative, could be employed to minimize fluctuations                   in equity portfolio values over
 successive periods. As a part of the valuation process they could hardly hinder investment
 policy. Indeed, variations      in market valuations         of equity assets could form an integral
 part of the actuary’s analysis of surplus. Rigorous experience tests could be applied to
 the assets as well as to the liabilities.
                               Valuation        of a Pension         Fund                         131
Mr. D. F. Gilley said that the desire of four speakers to use market values as a basis of
valuation had moved him to say that when a valuation of a pension fund was made a
whole variety of results could be produced, including one which showed the minimum
degree of funding, and which certainly made use of the market value. In the ‘minimum
funding’ valuation    the liabilities were expressed as the cost of providing the accrued
benefits (whatever they might be, and perhaps only an employer could say what they
ought to be) by purchase in the market at that time, and were set against the market
value of the assets. A higher degree of funding could be used, of course, and the highest
degree was that which the Inland Revenue would permit. The valuation method to be
adopted was simply that method which would enable him to rationalize               or justify to
himself the result which, having regard to the surrounding      circumstances,   he knew to be
   In his opinion the authors had dismissed the considerations       affecting the choice of R
in their formula a little too easily. Suppose it was wished to make a valuation           on the
assumption    of no future inflation, the value of the future income from equities would be
                                                 current     dividend
                                           valuation       rate of interest
or, allowing    for the market’s   assessment    of the prospects       of individual   stocks,
                                                                   F.T.-Actuaries       yield
               Rx   T x (market     value of holdings)       x
                                                                 valuation    rate of interest
That was the authors’ formula of 4.6. If R were taken as unity, as suggested in 6.2, it
assumed implicitly that the dividends were as well secured as the dividends on Consols.
That was, to his mind, inconsistent         with the authors’ precautionary   deduction of 12½%
on preference      shares, which was tantamount          to valuing a perpetuity   of the present
income from preference shares as a perpetuity at a rate of interest of 4%, if 3½% were
the valuation rate of interest. If, as many actuaries might think, such a deduction were
thought to be appropriate        in the valuation of preference shares, it seemed inappropriate
not to make a deduction at least as large in the valuation of ordinary shares. If, therefore,
in non-inflationary     conditions equities yielded more than gilts, part of the excess should
perhaps be regarded as no more than a premium to cover risk of dividend diminution or
loss on realization,    and only the remainder as genuine gain. The factor R should then be,
he thought,
   normal long-term      average yield on gilts plus the true yield gain to the fund              from
   investing in equities, divided by the normal long-term average yield on equities.
The valuation rate of interest would be somewhere between the numerator and the long-
term fixed-interest rate, depending on the proportion        of the portfolio held in equities, as
the opener had suggested.
   If there were a general expectation       of inflation there was a presumption        that the
immediate yield on ordinary shares would fall below the yield on fixed-interest securities,
and that the yield on the latter would rise to an extent sufficient to compensate          for the
loss of purchasing power of fixed dividends. If inflation of salary levels were accompanied
by increased productivity,    the yield margin required by investors to compensate        for loss
of purchasing power would be less than the rate of escalation of salary and wage levels,
and it would require an expectation      of dividend increases on ordinary shares equal to the
rate of escalation    of salary and wage levels to cause the fixed-interest         yield to rise
sufficiently to bridge the gap. As the authors said, it should be recognized             that the
potential gain in value on equities would not necessarily be equal or proportionate              to
the increase in value of liabilities. If, therefore, it was wished to allow in the valuation of
a pension fund for a 2% per annum escalation of salary and wage levels, the valuation
rate of interest should, in all probability,   be rather less than 2% in excess of the valuation
rate which would otherwise have been chosen. The addition would in fact reflect the rate of
dividend increase consonant       with 2% per annum escalation of salary and wage levels.
Then, given R and T, the value of the increasing dividend as a perpetuity would be the
132                  The Treatment         of Assets     in the Actuarial
same whatever degree of inflation were assumed and would be the same as the value
assuming     no inflation and no dividend increases.         He could see no obvious case for
altering R just because a valuation        assumed future inflation, so that the re-valuation
result would be a reflection of the differing valuation rate of interest on the value brought
out for the liabilities.
    It was clear that if R were chosen on the lines he had suggested, then the factor by
which to assess the amount by which the market value of equities was increased as a
result of equities being bought as a hedge against inflation ought to be taken as
F.T.-Actuaries      yield
                            Then the second formula of 4.4, adjusted also for tax, Heywood
   yield on consols
and Lander’s formula with a consistent          value of , and the authors’ formula in           4.6
would all yield the same result.
    The first formula of       4.4 was by no means the same as the second one, in that the
first allowed for the possibility of a change in the level of interest rates on a realization
taking place; the second did not. If a conservative        estimate had been made of the valua-
tion rate of interest then allowance should be made for a higher rate of interest on a
realization    taking place, otherwise an undervaluation        might result.
    The authors suggested that, in assuming the value of an equity share, regard should be
paid not to the current dividend income but to the current rate of earnings, or possibly
a figure between the two. If, during an inflationary           era, a high level of profits was in
general being retained, it was presumably           with a view to increasing dividends in the
future, and the market recognized that in the value which it placed on equities relative to
that which it placed on fixed-interest       securities. In a valuation,      therefore, which took
account of future inflation, it was presumably          correct to take account of the dividend
yield on a high level of market values because the high level of market values did reflect
 the expectation     of increased dividends which should accrue from retained profits. For
 that reason he would reject bases (iii) and (iv) in 6.2.

Mr W. D. Scattergood      disagreed with the authors in their statement that the basic aim
of a pension fund was to produce sufficient income in future years to meet the benefits
as they arose. Surely it was necessary to go further than that. The real purpose of a
pension fund was to provide a standard of living in real terms for the pensioner. It might
be that a pension fund was so organized that the benefits were regularly provided over a
long period as they fell due, but if the value of those benefits in real terms reduced
steadily over the years he would have said that such a pension fund had failed. It was
true, in the limited context of the paper, to say that the actuary was essentially concerned
with advising the client as to the provision of resources for meeting future liabilities.
That was not, unfortunately,      the kind of advice required from, many actuaries engaged
in work on pension arrangements.       As he saw it, the profession was, like Gaul in ancient
times, divided into three parts. There were those actuaries employed by the Government
who advised the Government         on questions relating to the cost of state pensions;    there
were those who advised trustees as to the cost of pension provision by private funds, to
which the paper, of course, basically referred;         and there were also those actuaries
employed by life offices, one of whose important       duties was to advise their management
on questions affecting the provision of pensions by schemes whose funds were generally
invested as part of the life fund and whose security was backed by the life fund. Those
three bodies were not giving similar advice because they were advising different bodies
on different subjects.
   A paper by C. E. Puckridge in 1947 (J.I.A. 74, 1) referred to a remark made by Sir
Alfred Watson (then President) in 1921 that it was ‘of the highest importance           that we
should exchange views with one another and try to come to a common opinion on
matters of practice so that the world at large will bring against us no charge of incon-
sistency in the advice which we respectively give to those who consult us’. Whilst as a
profession    they advised different people on different aspects of pension provision, he
felt that there was a common ground for them all, which was that the basic purpose of a
                             Valuation      of a Pension      Fund                           133
pension scheme was to provide a standard of living in real terms for the pensioner after
he retired. All their advice should therefore be conditioned      by the consideration    of the
degree in which that purpose was satisfied or might be satisfied in the future. The
importance    of the paper was that the techniques explained tended to condition the rate
of funding and to emphasize the importance       of investment policy in a way likely to help
in achieving the purpose he had stated.
   The authors also referred to the growing share of the state in superannuation            pro-
vision. If as a profession their preoccupation    was to be with the liabilities for particular
benefits rather than for pensions as a standard of living, then he felt that that attitude
could only result in the acceleration  of the rate of increase in the state’s share of pension

Mr E. F. Rogers particularly          liked the emphasis laid by the authors on the need for
flexibility, but he wanted to comment on one aspect where it seemed to him that the
authors had not themselves shown quite the degree of flexibility they advocated.               The
authors said in       5.9, ‘We would put forward the view, however, that any additional
liability resulting from an allowance for inflation in the valuation basis is better left un-
funded.’ The justification      for that was contained in the previous paragraph,      where they
said, ‘In the face of inflation, as prognosticated        in the valuation     basis, would these
additional   contributions     not do more good in the employer’s business . . . than in the
pension fund? We think the answer to this question is almost certainly “yes”.’ The
implication    of that argument appeared to be that money retained in the business to cover
an expected pension liability arising from inflation or economic growth would earn
something     like the net return on capital employed in the business as a whole. That
argument was almost certainly justifiable for a young, rapidly expanding company where
lack of finance might be a serious obstacle to further expansion,            and in those circum-
stances it was to his mind simply one facet of the general argument that the interests
of the company and its employees were best served by a rate of funding as slow as was
consistent with the safety of accruing rights. The position of many large, well-established
companies was, however, very different in that they might have ample untapped borrow-
ing powers, or even ample liquid resources, and the pace of further expansion might be
determined by factors other than shortage of finance. One obvious possibility was short-
age of management       resources, and good managers might be in shorter supply than money.
   In those circumstances      it seemed to him that the effective return on money retained in
the business to cover expected pension liabilities was not the net return on capital
employed as a whole, but the net cost of borrowing.             If that view were accepted the
balance of advantage between funding pension provision or retaining it in the business
would clearly be shifted, and it seemed to him that there was much to be said for making
in the pension fund valuation a reasonable allowance for the growth in salary levels that
was generally expected and was implicit in the investment             policies followed by most
funds. He agreed with the authors that making such an allowance                 should have little
effect on the valuation result for a fund invested wholly in equities. Most funds would,
however, continue to hold a significant part of their assets in fixed-interest securities, and
in those circumstances      there might well be advantages in funding at the higher rate that
would be produced by a valuation that made reasonable allowance for expected growth
in salaries.

Mr B. H. Fison supported Mr Scattergood      in disagreeing with the authors’ statement at
the beginning of      1.1 that the basic aim of pension funds was to provide sufficient
income in future years to meet the benefits as they arose. Mr Scattergood     referred to the
need for a pension fund to provide a certain standard      of living, and that was the sort
of definition that he normally used. In 2.7 it was stated that the yield on an equity share
based on last year’s dividend was misleading.      He fully agreed that it was misleading
when it came to carrying out actuarial valuations,    and the nearest mention that evening
to what he and some of his colleagues would regard as a sensible approach was that
134                 The Treatment         of Assets     in the Actuarial
made by Mr Sandom. Considerable            work had been done on the assessment          of equity
shares, and he referred to the paper by D. Weaver and B. G. N. Fowler (J.I.A. 86, 243)
and that by J. R. Hemsted (J.S.S. 16, 401) trying to find out what was the expected
return on an equity investment. In his view a considerable        amount of nonsense had been
talked that evening about methods          of valuing equities relying purely on either the
current income on an equity or the current income on the index adjusted by some
arbitrary factor R.
   A previous speaker had referred to the fact that there had been very little discussion
about the factor R, and in the only numerical illustration       in the paper it had been taken
as unity, which struck him as not a very great advance on basing the valuation entirely
on current dividends. His own method would be to have amongst a number of trial
valuations   a best possible shot at seeing what he was really going for in an equity; to
value an equity giving a current income of 2% on the basis of the current market yield
on an index, and then to apply an arbitrary factor of R as unity was, to his mind, of no
use at all. Therefore     he stood with those to whom Mr Day referred in his opening
remarks who felt that the authors had not gone far enough. It was interesting that it was
those who were in fact engaged in carrying out valuations            of pension funds who felt
the authors had gone a little too far, whereas possibly the stockbroking         actuaries might
be quite prepared to push the theoretical       arguments   a bit further. Possibly the idea of
projecting equity dividends might be regarded as academic rather than practical,               but
among his trial valuations       the actuary could make an attempt to produce a realistic
estimate of future equity income.
    In   1.3 of the paper it was stated that prices in the equity market were largely made
by tax-paying investors. They were discussing a paper on gross pension funds, and he
submitted that there was a considerable      weight of new money affecting the equity market
from the investment       of gross funds. Nevertheless,    if it could be accepted as correct
that taxpayers determined      the prices, then the pension fund could secure above-average
gains by concentrating      on high yields, because if a high-yielding     equity (which gave a
7% current income) were ranked correctly by the tax-paying              investor with a growth
stock yielding 2% there was no doubt which of the two was the better bargain for the
pension fund, namely, the high yielder. Thus if the pension fund bought the high
yielder the advantage should be brought out somewhere in the valuation basis,               but in
the calculations    envisaged by the authors,      whether stocks yielding 2% or 6% were
bought, all were valued as giving the index yield of 4%. That seemed to him to be mis-
leading, and should be allowed for in the factor R. If the factor were applied to in-
dividual shares it might be possible to push R a little bit over unity when allowing only,
say, 4% yield to a 6% stock.

Mr J. Plymen felt that the impression was getting around that there was something quite
immoral in valuing assets at market values, whereas an elaborate valuation process using
R’s and T’s and indices and other assumptions       that produced a figure about 20% higher
than the market value was perfectly respectable! The authors’ theme suggested that fixed-
interest investments     were to be valued long-term       at about 25% above their market
value. He felt that that was tackling the problem from the wrong end. It was traditional
that with a life office valuation a decision was taken on the rate of interest for the valu-
ation of the liabilities and that was that. The authors were taking the same line with a
pension fund valuation.     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?      At that time the indices
suggested that the valuation rate for fixed-interest     stocks should be about 5¾% and for
equities about 4¼%. That suggested about a 1½% rate of growth in equity dividends.
Surely there would be nothing immoral or fanciful in saying, ‘Let us use something like
that basis for valuing the liabilities;  let us value the fixed part of the liabilities at, say,
5¾% and that part of the liabilities dependent on rising salary levels at, say, 4¼%’? If it
                              Valuation     of a Pension       Fund                            135

was wished to go a stage further, and import some inflation into the equation apart from
growth, the rate of interest on the variable part of the liabilities could be put even lower.

Mr H. P. Clay said that         7.3 seemed to him to suggest that after many years in the
pension field an actuary automatically       became a great investment man by stepping over
into the investment   field. In his view the two fields were different. A President of the
Institute had said: ‘All of us, senior as well as junior, should hesitate to embark without
leadership on professional     activities of a kind in which we have no experience.’ Possibly
that President might agree that in referring to ‘activities of a kind in which we have no
experience’ he might have gone on to say ‘without experience gained by full-time work
for some years’. He shuddered at the idea put forward by the authors that, having been
treated as entitled to pontificate on the pensions side, it should then be possible to move,
with anything less than 20 years’ experience, into the investment         field and appear to
carry a halo that was not earned by full-time experience in the investment field.

Mr P. N. Downing wished to comment briefly on one aspect of the problem to which Mr
Fison had already alluded. In general, the decision to value an ordinary share arose in
connexion     with a proposed    purchase    or sale. The value placed on the share by the
valuer was compared with the market value and a decision to buy or sell was based on
that comparison.      For such purposes it was unnecessary       to state precisely the dividend
payments postulated for valuation. Indeed, if several series were postulated,          all of which
had the same discounted value, it was unnecessary to specify which postulated series had
finally been accepted and discounted         to determine the capital value.’ As long as the
purpose of valuation did not require the expected dividends to be specified, an approach
which led directly to the required value was acceptable. The authors appeared to have
restricted themselves to such an approach, their solution being given in 4.6. However,
the authors had introduced      their paper by stating that the basic aim of a pension fund
was to produce sufficient income in future years to meet the benefits as they arose, and
that the actuary was essentially concerned with future income and outgo. The solution
to that problem surely required the series of dividends which was expected to arise
from each ordinary share to be postulated.           The mere discounting        of the postulated
series to produce the asset value for inclusion in a traditional         valuation balance sheet
was relatively easy.
    Although the actuary was essentially concerned with future income and outgo, the
traditional   method of valuation merely required the discounted value of future dividend
payments expected without postulating        them. The authors stated that it was not difficult
to imagine that the form of presenting valuations         could change. The particular         form
with which they were all becoming familiar was emerging costs. In his view, at least
when advising on a closed fund, especially if such a fund were still increasing, an emerg-
ing cost investigation    was virtually essential. Where the assets comprised a substantial
holding of ordinary shares it was therefore necessary to postulate future dividend income
—in total if not for individual shares.
    The approach to that problem would therefore seem to be the setting up of a mathe
 matical model in which the dividend at time 0 would be the last declared dividend, the
dividend at time 1 the next year’s expected dividend, etc. The method readily springing to
mind was a mathematical       curve controlled by parameters.     The authors inferred that they
did not accept the one-parameter       formula of Heywood and Lander on the grounds that
 a very arbitrary multiplier was involved. They therefore put forward a three-parameter
 formula in      4.6. Analysis of their parameters     was instructive.   The first parameter      R
 contained all the subjective factors under the control of the valuer. It was suggested
 that R should vary about unity, but little specific indication was given as to how far it
 might vary. It seemed that R was still a very arbitrary multiplier,          being less arbitrary
 than that used by Heywood and Lander only in that two specific factors had been trans-
 ferred to other parameters.    The second parameter      T was designed to allow for the un-
 reclaimable   tax which would appear to be determined          by reference to the current net
136                 The Treatment        of Assets     in the Actuarial
U.K. rate of tax. Allowance for variation in that rate was presumably       one of the factors
considered   in assessing R. It was not clear whether T was assessed for each individual
holding or on the portfolio as a whole—the form of the expression in 4.6 suggested the
latter. The third parameter was the dividend yield on the ordinary share index divided by
the dividend yield on the share. That parameter     was outside the control of the valuer;
it was a function of market values and the particular     composition     of the share index
chosen. He presumed that if the valuer did not accept the current market ‘view’ he would
merely adjust R! The authors therefore appeared to accept a three-parameter          formula.
He would have thought that a satisfactory three-parameter      mathematical    curve could be
found to postulate future dividends, especially when one of the parameters         was appar-
ently so open to the individual valuer’s choice.
Mr C. E. Puckridge said that, reference having been made to his own paper (J.I.A. 74, 1)
he might perhaps be forgiven for joining in the discussion,           although he had in recent
years had no practical experience of pension fund valuations.         If the authors were feeling
at all depressed at the somewhat           rough handling some of their ideas had received,
they could console themselves          with the thought that it was moderate compared with
the reception accorded to his ideas 16 years earlier! His purpose in writing a paper had
been to set out some of the basic principles for the benefit of elementary students in the
subject and to enable Institute examiners (of whom he was then one) to set questions
which mentioned        ‘valuation  of assets’ and ‘valuation rates of interest’, on which there
was no reading whatever in the Institute Journal. To his surprise the basic principles
were not generally accepted, and his purpose was defeated by the inclusion of the paper
in the reading as ‘optional and suitable for advanced students only’. His approach was
obviously regarded as rather dangerous and too controversial             to be read by the young
and inexperienced.      It could be imagined how relieved he was to read in 1961 in Heywood’s
and Lander’s paper (J.I.A. 87, 314) that in the light of their accumulated          experience of
some 14 years they had reached the conclusion that his approach was essentially a sound
one, and then to hear from the authors of that evening’s paper that in their opinion he
had succeeded in setting out some of the basic principles.
    He was not, however, in the least surprised that the authors did not agree with some
of the details in his paper. Since 1947 the approach to investment of pension funds had
entirely changed. In 1947 the yield on Consols was around 2½% and the Financial Times
Index showed a yield of 3½%. Obviously few investors were thinking of ordinary shares
either in terms of their growth potential or their virtues as a hedge against inflation; the
emphasis was on the potential risk incurred by accepting such attractive yields. He had
been mainly concerned to direct attention to the unduly pessimistic picture that would be
presented to an employer by valuing on the assumption            that the then current low rates
of interest would persist, and bringing in assets in the valuation at book values sub-
stantially below their values to earn the valuation rate of interest. The whole atmosphere
had changed since then and investors generally were prepared to accept current yields on
equities substantially     below gilt-edged yields because they regarded growth of profits and
and inflation as essential features of the economy.
    He hoped he would be forgiven if he introduced a note of slight scepticism by wonder-
 ing if the cult of the equity might not ultimately over-reach itself, if indeed it had not
 already done so. If for temporary        political or economic reasons equities should at some
 time in the future become less fashionable          he would warn the authors that they could
 expect someone else to disagree with some of the details in their paper. He none the less
congratulated    them on their thoughtful approach to a very difficult problem.
Mr G. H. Ross Goobey referred to       1.3 of the paper, where it was stated, ‘A pension fund
valuation is in some respects akin to a solvency valuation.’ That might have generally
been the case in the past, but owing to the more enlightened investment policy pursued
by many pension funds in recent years the picture for many of the funds had changed,
and in the pensions field as well as in the life offices, they were sometimes concerned with
an equitable release of surplus.
                              Valuation      of a Pension       Fund                             137

    Reference had been made in 5.7 to the income of a fund if all the equities were sold
and re-invested in 2½% Consols. In the case of the fund with which he was associated
that would result in the yield on book value becoming something of the order of 11%
or 12%, but it was not only the impracticability            of that exercise which prevented them
from carrying it out but the fact that they firmly believed that their equities would in the
long run produce over-all a higher yield than if they put the money into 2½% Consols.
One of the arguments,       no doubt, which a consulting actuary would put forward for not
using such astronomical        rates of interest would be that made by the opener, that
new money was currently           being invested at much lower yields than the figures he
had mentioned. That was because they had not reached that state of Utopia about which
they had read in the textbooks,        the state of equilibrium-which        he personally thought
was only a figment of textbook imagination              and would never happen because of the
effect of inflation. Nevertheless,      they were faced with a Gilbertian       situation:    the more
realistic and adventurous       a consulting actuary was with his valuations the larger would
 be the surpluses disclosed which could be distributed in the form of higher pensions and
 reduced contributions,      both of which would bring nearer that Utopian state of equili-
 brium and therefore justify the actuary in his apparent departure from the traditional.
 What, in effect, would be happening was that they would have a higher yield on smaller
 funds. Concern was already being expressed in some quarters that if funds were being
 accumulated     in excess of requirements     the Inland Revenue might be justified in restrict-
 ing the taxation allowances to that part of the fund sufficient to meet the liabilities.
     Another small point, which had been touched on by Mr Lieberman,                    concerned the
 first paragraph    of the paper, where it was stated that the valuation was              done by dis-
 counting all future income. Many pension funds indulged in such practices as ‘stagging’,
 underwriting     and switching, and no actuary (as far as he knew) would dare take into
 account in his valuation the estimated income of those. On a rather more controversial
 point,     1.1 also stated the well-known         principle that the valuation       related only to
 present members. There again, an actuary might well consider, if there were a well-
 established pattern, that the future entrants to the fund, if they were coming in at over-
 adequate rates of contribution,         would provide a surplus which might be taken into
 account in arriving at the surplus to be distributed.           He mentioned those points in the
 hope that commercial       employers would seek the advice of actuaries for their accurate
 assessment    of the future rather than actuaries acquiring a reputation           for always being
 well on the conservative      side.

Mr G. Heywood, in closing the discussion, said that the discussion would indicate to the
authors how timely their paper was, and how important were the problems of valuing
assets and allowing for inflation in a pension fund valuation. It      had always seemed to
him most surprising that in the history of the Institute and, indeed, the Faculty, when
there had been perhaps some forty or fifty papers on the subject of pension funds, it was
not until 1947 that Puckridge was bold enough to mention assets for the first time. The
remainder     concentrated   mainly on the special techniques     for valuing the liabilities
while implicitly assuming that the fund would be taken at book or market value, which-
ever was the less.
    The opener had called for further comment on the valuation          of liabilities, but he
would have thought that that field had been explored to the full and that the paper under
discussion had gone some way to redress the balance; indeed, as Gunlake had said in
his presidential address some three years earlier: ‘We have devoted too much of our atten-
tion to liabilities and too little to assets-though      in recent years we have begun to
remedy this defect.’
    The authors stated their fundamental   principle early in the paper, in 1.2, where they
 said that in discounting   future income and outgo back to a single point of time it was
essential to aim at consistency of treatment on both sides of the valuation balance sheet.
 He was in full agreement with that as a principle in valuing assets, although a number
 of speakers had indicated that they preferred other methods.         He was surprised     that
138                   The Treatment          of Assets      in the Actuarial
nobody had mentioned that the problem of asset valuation was also concerning actuaries
in the United States; in fact, the subject was extremely topical there and quite recently
he had received a transcript       of a discussion held at a meeting of the American Pension
Conference     in New York, some 18 months previously, where one speaker had said: ‘I
recently read an article in the Journal of the British Institute of Actuaries by a couple of
consultants    there called Heywood and Lander. They discussed this question of asset
valuation and came up with what seemed to me some rather radical ideas, particularly
coming from two Englishmen.’            Nevertheless,   in the United States the problem was one
which was confronting       actuaries,    but so far as he was aware all the methods they used
were related directly to book value or market value or some combination                      of the two.
Quite a popular basis was to write up the fund by a fixed percentage                   every year—the
percentage most usually adopted being 3%.
    In the second part of the paper, on the subject of economic growth, inflation and
equities, most speakers seemed to be in agreement with the views which the authors put
forward     but some criticized       them for not distinguishing         consistently    between real
growth and inflation. He supported           that criticism because he felt that the authors had
been inconsistent    in one or two places, although he would say in their defence that
whether the increase in salaries arose from growth or inflation made little difference to
the valuation results. He was interested in the opener’s argument in favour of funding
for growth but not for inflation. Mr Rogers appeared to want to go rather further and to
fund for both growth and inflation because he felt that the real test was not whether
the money could be put to better advantage in the fund compared with what it would
earn in the company but what was the marginal net cost of borrowing to the company.
He doubted whether he would be prepared to go so far with him in that respect. There
was another aspect to consider, for if continuous          inflation were assumed the profits of an
industrial company would be expressed in pounds of ever decreasing value. Was that not,
therefore,   a case for paying for inflation as late as possible when the cost to the em-
ployer in terms of real value might well be at a minimum?
    The section of the paper on the valuation rate of interest did not raise a great deal of
comment in the discussion. The authors gave their definition, namely, that the valuation
rate of interest was that rate at which new money could be invested over a long period in
the future. He was not so sure that that definition was as good as appeared at first sight,
and he was particularly      interested to hear the comments of Mr Springbett on immuniz-
ation, leading, as they did, to the theory that if there was complete immunization                 then it
mattered little whether a high or a low valuation rate was used. Those arguments,                      and
also the paradox      he indicated,      were impressive,      and led him to doubt whether the
authors’ definition of the rate of interest was really the correct one.
    The greatest part of the discussion,         as might be expected, was concerned with the
value to be placed upon the assets, and there was fairly general agreement on the treat-
ment of fixed-interest    investments.     In ordinary shares, as one speaker said, the authors
perhaps did have some rough handling, but he had tried to keep a record of those who
were in favour of using formulae of the type the authors had put forward and those who
were against, and they seemed to be just about evenly balanced. There were, of course,
a few who would be described by those who forecast election results as ‘don’t knows’.
He was personally—as       they would probably guess—in full support of the use of formulae
of that type.
    The authors criticized the formula put forward by Lander and himself in their paper
 of some three years earlier by saying that they had used the current dividend rates or the
 previous year’s dividend in the numerator;             and yet, although the authors made that
criticism, the same item appeared consistently throughout            all the authors’ own formulae!
The authors had also, as a number of speakers mentioned, criticized the use of Heywood
 and Lander’s arbitrary       factor , and then again, as had been indicated,               retained an
 arbitrary factor but called it R instead of ! George Orwell might have said that some
 constants   were more arbitrary than others! Perhaps the authors’ most important                     con-
 tribution was the use in the formulae of the ratio (dividend yield on the ordinary share
                                Valuation      of a Pension        Fund                              159
index) ÷ (dividend yield on the ordinary share) and the introduction                of that ratio was a
real attempt to try to allow for the market assessment of growth or lack of growth in
any particular       case. In his experience of using the old formula,         usually fell between ·85
and ·95, whereas under the authors’ modification             he would have expected R to be almost
invariably unity, or, if not unity, at least very close to it.
     He was surprised         that there was virtually no comment             at all on the practical
example which the authors were bold enough to set out in Part VI of their paper. They
set out the figures with considerable            frankness and they were at first sight perhaps a
little alarming, in that they ranged from one extreme, with a surplus of only £223,000,
 to the other, with a surplus of £2,471,000. He felt, however, that most of the nine results
 which were produced           could be ruled out as not giving an appropriate            picture of the
 valuation     position.   He would rule out method (i), taking book value, because it was
 contrary to the basic concept; he would also rule out methods (iii), (v) and (viii) because
 he felt that using an earnings yield on the index instead of a dividend yield was being far
 too liberal and putting too great a value on the future earnings of ordinary shares. He
 would also rule out methods (iv), (v) and (vi) because in his experience employers were
 not yet ready to recognize in advance inflation after retirement,               quite apart from the
 other objections to allowing for inflation in advance which he had already mentioned.
 That left methods (ii), (vii) and (ix) where the range of surplus was £987,000 to £1,229,000,
 and it was, he thought, within that area—and it was still an area—that                the best measure
 of the valuation position arose.
      On the final part, on general observations,        he was in the fullest agreement, particularly
  where the authors referred to consultation          between the actuary and the client at all times.
  He was sure from what had been said by many speakers that the picture of the actuary
  sitting remotely in an ivory tower surrounded               by esoteric and mystic symbols had
  vanished, he hoped for ever. If the valuation results were to be of the greatest value
  and if it were accepted that the answer lay within a range, then the importance                        of
  consultation     throughout     in the frankest terms could not be over-emphasized;            and there
  he disagreed with one or two speakers who said that they would find it difficult to con-
  vince the clients of certain courses of action put forward by the authors.
      He was also in full agreement with the authors’ suggestion of the actuary acting as
  investment     adviser, and he had to quarrel very strongly with Mr Clay in that respect.
  He thought the actuary, by his training in investment and by his understanding                     of the
  long-term emerging nature of the benefits of the fund, was very well qualified to advise
  in that subject, because it was against that background              that all investment policy was
       He concluded      by saying that although the authors had directed attention               to many
  problems, he was sure they would be the last to claim that they had given all the answers;
  nevertheless,     they had stimulated       thought on the subject, and he hoped that as a
  result others would come along with papers and take them all a little further along
   the road to a final solution.

 The President, in moving a vote of thanks to the authors, remarked that the discussion
 had been a long and lively one. He welcomed (as did nearly everybody) the continued
 emphasis on valuations     of assets and liabilities being closely connected in the pension
 fund world as well as in the life office world. He was bound to observe that life office
 actuaries might perhaps envy pension fund actuaries the absence of the constraint          of
 the publication   of statutory   balance sheets, but that did seem to him to require an
 appreciable   measure of education      of employers during the consultation   process which
 had been recommended        by the authors and which he heartily endorsed. His comments
 were on the basis that there would be no higher degree of regulation         or publicity for
 pension funds than was then the case, but that was a possibility which they were bound
 to envisage as a consequence     of political events.
     He had been going to say earlier that, whereas the life office actuary had the problem
  of the emergence of surplus, the pension fund actuary had the problem of the emergence

140                  The Treatment         of Assets      in the Actuarial
of the load on the employer, but he had been suitably reminded that even in the pension
fund world, though it might not be a problem, there could be an interesting exercise in
the emergence    of surplus. Nevertheless he thought the distinction he had made was
generally true.

Mr K. M. McKelvey, in reply, mentioned           that in Table A, Value of assets, the market
values in the particular     fund were, in column (2), fixed-interest    investments, £893,000;
in column (3), ordinary shares,    £1,140,000; and in column (4), £151,000; total, £2,184,000.
Those figures might be of interest and it was a pity they had been left out. It was inter-
esting to note also that the total value placed by the market on those assets on the
valuation   date (18 months earlier) was almost the same as the value on basis (vi). The
market thought slightly less highly of fixed-interest investments        and rather more highly
of ordinary shares but on balance there was not much in it.
    R had come in for a lot of attention.     Like most people present, he and his co-author
were actuaries and they liked to have an insurance. He thought that (not to be entirely
serious) one of the reasons, at least in his case, why R was in the paper was that there
would have been an even longer discussion if it had not been. The authors would have
been accused of being able to conjure figures out of the air which they claimed were fool-
proof and never needed adjusting.
   ‘There were two points in particular that arose out of what had been a most interesting
discussion;    both were mentioned       by several speakers. One was the definition of the
valuation rate of interest. The authors’ approach to that had been that, leaving aside the
traditional   actuarial interests of mortality rates, withdrawal    rates, retirement rates, and
salary scales, the one unknown, a purely investment factor, was the rate of interest at
 which it would be possible to invest the known future hump in the fund. In fact, it was
 not a hump but a perpetuity,      because future entrants to a pension fund operated by a
 continuing company could not really be wholly ignored. That was the one thing remain-
ing unknown;       an assumption    had to be made about it, and, once made, many other
 things followed.
    Market value had been defended. If there were a state of affairs such as in May 1962,
 when equity markets on both sides of the Atlantic took a rapid tumble, the market value
 of a fund could be affected by 25% in 24 hours; but, of course, nothing would have
 changed the expected income, and by reducing the market value of the fund by 25%
 those same events had put 25% on to the dividend yield on the index. When the two
 were multiplied     together the effect on the pension fund was nil—quite rightly in the
 authors’ view, because they were considering         what income would come in during the
 next half-century     and not what the assets could be sold for on Monday or Tuesday.

Mr F. W. Bacon: The authors rightly stress the need for consistency of treatment on both
sides of the balance sheet and this is particularly               necessary when considering        the
allowance to be made for inflation or secular growth, since the allowance can be made
on either the assets side or the liability side, or both. In their treatment         of this allow-
ance in Part V the authors appear to make the assumption that j—f is constant, in other
words that the rate of growth or inflation will be precisely offset by a corresponding             rise
in the rate of interest, even where the fund is invested solely in fixed-interest         securities.
It is true that this Part is headed ‘Valuation allowing for Inflation’, but as there is no
other reference to allowance for growth, it appears reasonable             to assume that the argu-
ment is intended to apply to both.
    I can see little justification,    either in theory or from experience, for assuming that j—f
will be constant. So far as secular growth is concerned, I would expect that over the long
term a higher rate of growth would tend to reduce the interest rate rather than increase
it. I agree that inflation tends to increase the preference of investors for equities as
against fixed-interest      securities, but within this framework higher interest rates are one
of the weapons used by the monetary authorities              to combat inflation; one would there-
                            Valuation     of a Pension     Fund                           141
fore expect higher interest rates to be accompanied by a lower rate of inflation and vice
versa. I would not think, therefore, that one can make the easy assumption that allow-
ance for growth and inflation can be precisely cancelled out by a corresponding increase
in the valuation rate of interest. Incidentally, I would find it very difficult to explain to a
client that a valuation which allows for growth and inflation before retirement will
produce a bigger surplus than one which ignores such allowance, which appears to be
the conclusion to be drawn from the results of methods (ii) and (vii) in Table C.
   I would also disagree with the authors’ view in 5.7 that ‘Inflation and the secular
economic trend are both so indeterminate that any approach is open to criticism.’ I agree
that inflation is indeterminate but I would have thought that secular economic growth
could be reasonably assessed at between 3% and 4% per annum, which is probably as close
an assessment as we can make of several other elements in the valuation, including the
rate of interest. It would therefore appear desirable to make an allowance of this order
for secular growth either directly in the salary scale, or indirectly by keeping the appro-
priate margin, after allowing for the portion of the fund which is invested in equities,
between the valuation rate of interest and the yield on the fixed-interest assets. By
combining the two methods, it is possible to use book values for the fixed-interest
securities and so to avoid the difficulties which arise, and which the authors ignore,
from capitalizing excess interest for the difference between the terms of the assets and
the liabilities.

Mr W. F. Marples, from the U.S.A.: I do not see why an actuary in the circumstances
referred to in the third sentence of 7.3 ‘must . . . present a valuation result which is no
less favourable’. I would suggest that if the original arguments which induced the client
to adopt the original idea of investment in equities fully covered the subject, the client
would be prepared for the possibility of initial recession in investment performance and
would appreciate that a longer period than three or five years is required for the effects
of the policy to be evident.
   My next point relates to the valuation results produced by the authors and their
discussion of the choice of method for presentation to the client. Before I would be
prepared to make a choice, I think I would wish to see the results of the methods applied
to a sequence of valuation results. In other words, I would like to see results for, say,
four consecutive valuations and to examine the fluctuations in emerged surplus before
committing myself to an asset valuation basis to which I might be held for many years
in the future. I really do not think a decision can be made on one set of figures.
   Now may I add some comments of my own. The unfolding of this subject has not gone
unnoticed in the United States and interest is awakening. However, there appears to be a
strong reluctance to move the asset valuation away from the twin rocks of book value
and the market value. In part, this is due to the fact that the banks who act as corporate
co-trustees have traditionally handled investment matters and there is not the same
emphasis on an actuarial valuation being a valuation of assets as well as liabilities. (It
may be noted that the Internal Revenue Service requires a statement of the asset valu-
ation basis as part of the information to be submitted with a request for approval and as
one of the items in which a change requires their re-affirmation of approval.) The other
factor relates to the mental discipline which has to be assumed if one of the authors’
more erudite methods of presentation is to be adopted. The proposed methods will have
to be discussed and examined for a long period before interested parties will be found
willing to assume this discipline. The subject could only be broached to the more
sophisticated clients now.
   The visible difference in the immediate yield as between fixed-interest securities and
equities has led thoughts along the line of developing a yield on equities consistent with
the growth expected at the time of purchase. The procedures under consideration involve
the writing up each year of the book value of the equities with the corresponding increase
in asset value and the enhancement of the investment performance either by increasing
the yield or by dealing with the increase as an asset gain.
142               The Treatment       of Assets    in the Actuarial
   There are a number of methods of achieving the desired result. A simple example is,
for instance, starting with the thought that the average growth in equities is 3 % per
annum and consequently writing up the book value equities by 3 % per annum with two
provisos. First, that no write-up occurs until, say, 15% unrealized market appreciation
is exhibited and, second, that no write-up shall raise the book value to more than 85 %
of market value. The 3 % write-up is then treated as a lump sum gain and applied to
reduce subsequent annual contributions. An alternative method is to apply it as an
addition to the interest income, thus increasing the yield and laying the ground for an
increase in the valuation rate of interest. I am not aware of this being done at present.
   The subject of this paper is part of the more general subject of the control of funding
of a pension plan. One of the related facets of this subject is the question of adequate
security of pensions—not only the incumbent pensions, but the pensions promised in the
future to today’s employees. This raises the whole question of the general application
of the adjusted asset valuation. To what pension funds should they be applied? Surely,
only to those funds set up by adequately-financed employers. Local authorities? Yes.
National Boards? Yes. Commerical companies? Possibly, with caution and with due
regard for the effect on pension security. I would welcome a comment from the authors
on this aspect.

Mr W. Perks: I would first like to say something about the early section of the paper
entitled ‘Fundamental background’. In this section there are references to such vague
concepts as ‘the average rate of interest one expects to earn on new investments in
future’ and ‘one’s estimate of the average long-term rate of interest’. I do not believe
that an actuary or anybody else can, or should pretend that he can, legitimately have any
such expectation or make any such estimate or indeed that such a subjective factor
should enter into the valuation of a pension fund or any other actuarial calculation. All
that an actuary can do is to make an assumption about future rates of interest with
all proper regard for the security of the organization to whom his advice is being given.
    It is odd that the authors seem to reject many of the relevant objective facts—the yield
on the fund, the current yield on new investments, the book value and the stock ex-
change prices of the securities included in the assets. Instead they prefer to think
of some future long-term rate of interest at which to value both the liabilities and the
investment proceeds after making certain adjustments corresponding to some notional
changes in the investment portfolio. And all this in the interest—misguided, I would
say—of valuing so-called expected income and expected outgo in a given future year
by the same factor (see 1.2) and avoiding the so-called illogicality of taking different
values for two identical securities bought at different times at different prices (see 1.3).
    All this worried me in reading the early part of the paper until I came to § 3.4 where
it appears that the valuation rate to be used is not really an estimated rate at all but a
pure assumption made with due reserve. Again, with regard to the emphasis placed—
 unduly placed, I would say—on the need to value assets and liabilities on the same basis,
 I began to see light again when I reached §§ 4.2 and 4.3 where the authors give the
 alternative explanation of their valuation method of taking fixed-interest securities at
 book values with an additional value placed on the excess income thereon over the valu-
 ation rate. I know that this begs the question of the treatment of equities but I think
 similar ideas apply.
     However, this helps me to reconcile the comparison between the surplus figures for
 items (i) and (ii) in Table C. Item (i) is the orthodox valuation method taking assets at
 book values. Item (ii) is the authors’ preferred method (see § 6.4). Their method produces
 about four times the’surplus that the orthodox method is purported to produce. But the
 comparison is not fair; I think that most actuaries who, in the circumstances of the ex-
 ample, had made a valuation at 4% with assets at book values, would be concerned
 about the large amount of excess income on existing investments that they had not taken
 credit for and which would fall into surplus in future years. They would either do as the
 authors suggest in §§ 4.2 and 4.3 and put some conservative value on part at least of
                            Valuation     of a Pension     Fund                          143
the future excess income or they would decide that 4 % was too low a rate of interest
to be used in an orthodox valuation of a fund with such features as are apparent even
from the limited facts given by the authors in 6.3. It is a pity that we are not told
what is the current yield on the book values of the assets. It is, however, apparent that
it is much higher than 4% and the opener’s estimate confirms this. I have little doubt
that an orthodox valuation could be justified at 4½% or possibly 5 % and that the sur-
plus this released would then compare reasonably with that produced by the authors
with method (ii) which they prefer.
   Summing up, I think that they have been a little unfair to the more orthodox method
(i) and to those of their colleagues who continue to have confidence in more orthodox
methods when properly understood and applied.

Mr P. T. Jenkins: If I understand them correctly, the authors are making a veiled
reference to matching technique in saying that to look at the discounted value of assets
and liabilities at the valuation date may not represent the ultimate in our attempt to
find out whether liabilities are being funded at the right pace. Clearly, if it were
possible to ensure by an appropriate distribution of the assets that the future progress
of the liabilities could be exactly met by investment income or capital sales, it would not
matter what the discounted values were at any particular time. However, this is seldom
the case in practice, even with a life fund, and I venture to think that the process of
matching, or even of immunization, may well be virtually impossible in the case of a
pension fund. This is particularly true if the fund is increasing, as are most pension funds.
If the liabilities are more volatile in relation to the long-term rate of interest than are
undated gilt-edged securities, that is, as it were, ‘longer’ than undated gilts, the discount-
ing approach inherent in traditional valuation practices may well be the only weapon in
our armoury. To this extent, the choice of the valuation rate of interest is of crucial
importance, and it becomes a question whether the assets should be valued at the same
rate. It may be, however, that I have read too much into the authors’ intentions in this
    Approaching the subject of immunization from the viewpoint of investment policy,
it is perhaps unfortunate that a pension fund which, since the war, had been invested in
 gilt-edged as long as possible, that is to say in undated, would have fared worse than
 one invested in almost any other way. Indeed, so far as capital values are concerned, it
 would have been better to leave the money in the bank. One might go so far as to say
 that, for all except two of the 18 years since 1945 (the last two) strict matching tech-
 nique has been a dismal failure in relation to pension fund investment.
    Considering now the question of inflation, with which the authors are much concerned,
 a minor point is that I do not personally set much store by the idea that increases in
 state pensions may offset the inflationary growth of liabilities in a pension fund because,
 presumably, the rate of contribution is likely to be amended correspondingly. That is
 to say, the employer may well wish his contributions, expressed as a percentage of
 salary, to be related to the level of pensions, also expressed as a percentage of salary.
 More generally, I believe that to ignore inflation in a valuation is quite unrealistic, at
 any rate if the past may be considered any guide to the future. Perhaps the only hope
 (if that is the right word) in this respect, is that economic conditions in this country may
 follow those in the U.S.A., wherein the growth of automated techniques may be tending
 towards a substantial body of under-employed, thus relieving the pressure towards
 ‘wage-push’ inflation. This factor apart, if we ignore inflation we are in effect consistently
 under-funding, with the result that the employer, by having to pay continually increasing
 deficiency instalments, fails to pay the constant percentage of salaries which, as I have
 suggested, is his aim. True, by such under-funding we leave money in the business, but
  wherein does inflation—surely as predictable a variable as interest rates—differ from
  the other factors of a valuation basis? Are we against actuarial funding?
     In considering equities as a prophylactic against inflation, it may not be going too far
  to suggest that equity income is likely to grow faster than inflation, because of retained
144                 The Treatment         of Assets    in the Actuarial
earnings—a thought which must be tempered by the realization that periods may occur
when industry, or certain sections of it, is over-extended, leading to relatively profitless
trading. This is a long-term problem, which I do not believe is with us in this country
as yet.
   In regard to their remarks on the long-term rate of interest, it is difficult to see how
the authors arrive at the figure of 3½%, if, as they suggest, they are abstracting from
inflation. In this country, and indeed throughout the world, there is little or no historical
basis for judging interest rates on a non-inflationary basis—all we can judge by is a range
of interest rates in an inflationary historical context. There was, of course, the inter-war
period, but what is 20 years in the life of a pension fund? Again, immediately after this
period, interest rates fell to a lower level, despite a high degree of inflation. I am not against
the authors’ contention that inflation tends towards higher interest rates in a sophisticated
society, but merely wish to emphasize the irrelevance of the inter-war period to a judg-
ment of what interest rates might be at the present day in the absence of inflation.
   If we may make the assumption that, on the basis of post-war experience, the rate of
inflation is between 2½% and 3 % per annum, the authors evidently estimate long-term
fixed-interest rates at over 6 %, which does not seem particularly conservative used as a
valuation rate, even in an inflationary context. Again, is the ½% margin for equities well
founded—surely this must depend on the proportion of equities in the fund, allowing,
say, a 2 % margin above gilt-edged on the equity proportion? In suggesting this I have
in mind that the long-term yield on equities, over a long period in the past, has been be-
tween 7½ %   and 8 % per annum, taking dividend increases into account in an inflationary
context. Naturally, I cannot say what the yield on equities may be in a non-inflationary
   My last point concerns the formula used for valuing equities, in regard to the sub-
jective factor R. Admitted this is put in to allow the actuary an element of judgment, but
what are we supposed to be judging? The authors’ explanation is that R allows for last
year’s dividends being misleading—but would not this be reflected in the market value
and in the dividend yield on the ordinary share index?
   To sum up, while I believe that the authors have taken a step in the right direction,
their paper leaves the profession very far from a satisfactory theory of pension fund
valuations, and there remains scope for further research into this important subject.

Mr M. Lander: I agree very substantially with the theme of the paper. Indeed it would be
rather surprising if I did not, following as closely as it does the general principles which
Heywood and I attempted to put forward in our paper in 1961. I would, however, like
to make three specific points. Firstly, in 4.3, talking within the limited context of a
closed fund, I think that the assumption of present market prices for the eventual sale
price needs to be modified when the asset under consideration is a redeemable fixed-
interest asset. If the expected date of realization is anywhere near the redemption date, a
price of par would be more appropriate than the market price at the valuation date.
Secondly, and this is I think quite important, the authors in 4.4 mention two obvious
defects of the formula suggested by Heywood and myself for valuing equities. The factor
T which they rightly introduce into their own apparently more sophisticated formula
would, of course, be taken into account in arriving at a value for the factor λ in our own
formula. The trouble is that their final formula seems to me to suffer precisely the same
defects as the one we originally put forward, and I cannot see therefore that it marks any
particular step forward. Thirdly, in discussing briefly the arguments for and against fund-
ing pension liabilities in 5.8, I would myself add a rather important fourth argument to
the three enumerated at the end of the paragraph, to the effect that it is usually a con-
siderable advantage to be able to spread pension costs over the working lifetime of an
employee with considerable flexibility rather than over the much shorter period of his
expectation of life at his date of retirement with much less flexibility. Finally, I must take
issue with Mr Clay on the remarks he made during the discussion in connexion with
the function of the actuary as an investment adviser. While I would admit at once, and
                             Valuation     of a Pension     Fund                            145
indeed insist, that any actuary holding himself out to be an investment adviser must
ensure that he has the necessary technical equipment and experience to carry out this
task successfully, it is strongly my opinion that no one is better fitted than the actuary
to step into this important role. Far from eschewing the investment side of pension fund
work, an actuary advising a pension fund should in my opinion embrace it with open

Mr D. F. Gilley: A valuation deficiency is in the nature of a debt owed by the company
to the Fund, and if met by a cash payment, the company may need more capital to the
same extent. In this case the shareholders would in future years gain the benefit of the
extra capital’s fructification but they would, at the same time, deprive themselves of the net
dividends which they could get elsewhere on the capital they subscribe. The deficiency
being met, the pension fund would be in a position to acquire the shares which the
shareholders had sold in order to raise the additional capital, so that the pension fund
would then receive the gross dividends which the shareholders had given up. If, on the
other hand, the deficiency were not liquidated, the shareholders would find it necessary,
if the fund were to be in precisely the same position as it would have been in had the
deficiency been liquidated, to forgo income equal to the net equivalent of the gross
dividends which the pension fund would not then get; the shareholders would receive
the benefit in future years of the fructification of the cash sum not paid into the pension
fund. Now the net equivalent of the additional contributions which the pension fund
needs to put it into the same position as it would have been in had the deficiency been
liquidated by cash payment is precisely the same as the amount of the net dividends of
which the shareholders would have deprived themselves had the deficiency been liqui-
dated by a capital payment—which shows that to the shareholders it does not matter
when the deficiency is liquidated. If a shareholder feels that he would be better off, in
view of imminent inflation, to spend as much money as he can, he can do this whether
the deficiency is liquidated or not. I do not agree with the authors, therefore, that
additional liabilities resulting from an allowance for inflation are better left unfunded.
If, however, a valuation allowing for inflation is made, the actuary should invite the
client company to consider what the effect on its operations would be of inflation to the
same extent; otherwise the reasoning on which action is taken is likely to be incomplete.

The authors subsequently wrote as follows:
   A detailed and comprehensive reply to the discussion and the later written contribu-
tions would be almost as long as the paper itself and so cannot be attempted. Several
speakers trespassed on the adjoining subjects of pace of funding on the one side and
investment policy on the other; this was perhaps inevitable as the paper was restricted
to a narrow field. However, we, like the closer, were surprised at the lack of comment on
the wide range of results produced by the alternative valuation bases as set out in
Part VI of the paper; especially as we are not aware that such results from an actual
fund have been published before. We were also surprised at the number of speakers who
supported market values without any constructive or practical suggestions for sur-
mounting the difficulties involved in the valuation as a whole.
   A further general point which is relevant to several contributions, including the
opener’s, is that behind our thinking is the concept of a real yield such as that analysed
in the December 1963 edition of District Bank Review by Merrett and Sykes. While,
therefore, we agree that, historically, current interest rates look high we do not expect
that the redemption yield obtainable on new investment in long-dated fixed-interest
securities will decline very much so long as investors retain their current consciousness
and fear of inflation. We-still would not, however, except where one is allowing for in-
flation as in Part V. wish to value assets and liabilities at anything like as high a rate as 5 %
to 5½%. By keeping the valuation rate down to around the 3½%to 4 % level, by investing
50 % to 60 % of new money in equities and by treating assets as indicated in Part IV, one is
146                The Treatment        of Assets    in the Actuarial
really making a partial provision for future inflation. This course is method (ii) of 6.4
and we would refute any suggestion that, in that part of the paper, we failed to indicate
our own preference.
    It must be admitted that in some places the paper does not distinguish sufficiently
clearly between ‘secular growth’ and ‘inflation’. This is partly because in many of the
ways in which they affect our arguments, such as the level of equity profits or the level of
pension fund liabilities, they will both have the same effect or they are likely to be
intertwined. The equity investor does not necessarily distinguish between them. Our
fraction ‘dividend yield on index ÷ dividend yield on share’ is intended to eliminate both
and to leave only the individual ‘growth’ prospect of a particular share above the
average. We naturally have sympathy with the criticism that using the dividend yield on
 the index may give a poor estimate of the growth of dividends from a particular share;
 in defence we would point out that it is determined by the market and should be on the
 conservative side, whilst any other more detailed estimate by a computer or otherwise
 cannot command any certainty and may involve a prohibitive amount of work on the
 part of the actuary valuing the fund. The answer to Mr Downing’s question is that T is
 applied to each separate investment.
     Mr Springbett’s comments on immunization are .most relevant and interesting. The
 reason for the spurious surplus in the apparent paradox he puts forward is that the
 hypothetical actuary involved, having done part of his sums assuming a 5½% world in
 future, then assumes that in such a world he will be able to realize assets (needed before
 redemption) on a 4½% basis. If there is a fall in interest rates, as the trustees think prob-
 able, then a real surplus will be achieved; if the trustees are wrong then the surplus will be
 spurious. We wonder, however, where the ‘over-long’ assets were found because we see
  no reason (with only one equity holder in the fund, namely the employer, and thus little
  of the life office’sconcern for ‘generation equity’) to ignore future entrants to the fund in
  choosing investments or, partially even if not wholly, in valuing future ‘excess interest’.
  Thus we cannot envisage an open pension fund invested ‘over-long’. Furthermore,
  during the discussion, speakers seemed to use immunization, or matching, in two
  different senses; as in Redington’s definition and in the sense of the increase in the value
  of equities matching the increase in the value of liabilities occurring due to inflation.
  While both concepts are helpful theoretically, we would agree with Mr Jenkins that,
  with the type of fund we had in mind, neither can be achieved in practice.
     It may be useful to mention that, in so far as they occur below about age 40, future
  inflationary salary increments are likely to be self-supporting if the normal contribution
  rates are a percentage of salary and are based on about 4% interest (as we think they
  should be); in fact we agree with Mr Goobey rather than Mr Springbett on this subject.
  We also share the view of Messrs. Heywood and Lander (J.I.A. 87,324) on.‘the mumbo
  jumbo of negative values’ so that, collectively, increments up to about age 50 may well
  involve no ‘initial strain’.
      We agree that spurious valuation profits could result from switching as Mr Lieber-
  man suggests, which is a reason why the actuary should be involved in investment policy.
  If he knows the switching is short term and agrees that it is advantageous he should
  insulate his valuation result against any effect until the switch is closed.
      We found Mr Gilley’s remarks most interesting and we are, of course, fundamentally
   in the same camp. His ‘true yield gain from equities’ would be hard to ascertain. Our
   reply to his comment on the 12½% deduction from preference shares but none from a
   spread of equities is that, even in times of stable values, equity dividends are not, like
  preference dividends, subject to a ceiling though as regards lack of a floor they and
   preference shares are similar.
      We agree with Mr Marples’s comments about the early effects of going into equities on
   a low dividend/price ratio. As he may well recall, however, many pension fund officials
   are responsible to finance committees less moved by long-term advantage than by short-
   term political expediency. Mr Marples’s wish to see four valuations before committing
   himself is easier achieved in the U.S.A. than the U.K. where funds are rarely valued
                            Variation    of Pension    Fund                           147
more often than triennially and very often quinquennially. We regard our methods as
relevant to all funds for the reasons set out in 1.2. The variable factor is not the method
but the valuation rate of interest, as explained in Part III of the paper.
   To those who dislike our reference to average future rates of interest we would put
the question ‘how do you fix the valuation rate of interest for the initial valuation of a
pension fund?’ We see no reason, as Mr Perks implies he would, why with a fund even
only 2 or 3 years old set up on a 4% basis one should change the valuation basis for
liabilities because          (with A and B at book value) during the period had been
more than ·04. It might (though not of recent years) have been because one bought high
coupon stocks at a premium. If it was because we had bought stocks (whether high or low
coupon) on a better redemption yield than 4 %, our method would reflect this fact with-
out going on to make the assumption that the same investment terms would, on average,
be available for the ensuing half-century. In answer to the question asked by Mr Perks
and others, the running yield on the fund discussed in Part VI was £5 9s. % per annum
at the valuation date with no account taken of redemption profits or losses.
   We cannot agree with the opener that excess interest ‘disappears’ when it is capitalized.
It is always there and by not showing it as an asset one is merely creating a hidden
reserve and speeding up the pace of funding (and misleading the client?).
   Also in answer to several actual and implied comments we should point out that most
of the paper, and all of Part VI, has for its context a ‘final salary’ scheme. Preserving
the real value of pensions up to retirement, as far as members are concerned, is thus
built into the rules: the main task of the advisors is to invest accruing monies in the
manner which will most economically enable the employer to fulfil the objective im-
posed by the rule. Our reference to National pensions, in specific reply to Mr Jenkins,
therefore relates primarily to inflation after retirement. Recent investigations we have
made show that for existing pensioners in many of the more modest cases ‘Fund pension
plus basic state pension at retirement’ can be increased in accordance with the change in
cost-of-living indices since retirement without exceeding ‘Fund pension plus basic
state pension at valuation date’. Most schemes are set up on the basis of a ‘normal con-
tribution rate’ sufficient to support the average new entrant either with no inflation or
with an investment policy which combats inflation; there is often also a special contri-
bution by the employer for a fixed period to meet the balance of liabilities over assets in
the initial valuation balance sheet. Mr Jenkins’s wish for a constant ratio of employer’s
cost to salaries leaves scope for some increase in this special contribution. We would
also refer Mr Jenkins again to 3.6. Another way of putting that paragraph is to suggest
that there has never been much variation, outside the 3 %–4% range, in the ‘real’ yield in-
vestors demand after allowing for the rate of inflation they consciously expect at the
time of investment. This conscious expectation only dates from the 1950s.
   No practical difficulties have been found in putting to clients the methods outlined in
the paper. From the financially less sophisticated one finds acceptance and, from the
more sophisticated, relief that actuaries should now distinguish clearly between the
known yield terms upon which past money has been invested and the estimated average
yield terms upon which new money in the future will be invested.
   Finally, although we do not think that it comes within the scope of the paper, we
would like to comment on Mr Fison’s conclusion that, if our approach is accepted,
pension funds ought to invest in high-yielding equities. This view is not new, having been
advocated by some actuaries for many years. Whereas it used to be a very reasonable
policy, though one that was difficult to ‘put over’, it may no longer be valid as the market
is now more sophisticated and high yields do involve particular risks rather than in-
dicating lack of marketability and a small company. In so far as the high price of a ‘low
yielder’ derives from expectations by the tax-paying investor of tax-free capital gain,
then we agree that such a share could be too expensive for the gross fund.

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