JIA 90 (1964) 104-147 104 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] INTRODUCTION 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 only. 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interest at which it will be possible, on the average over the long period until all existing members of the fund have withdrawn, died, or retired, to invest the future net increments in the Valuation of a Pension Fund 105 fund or carry out disinvestment after the fund has reached its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 another. 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 concerned. 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. II. ECONOMIC GROWTH, INFLATION AND EQUITIES 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 prices. 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 growth. One has to remember, however, that expansion does not automatically lead to higher profits; there is a danger of profitless expansion as has been D 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 investor. 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. III. THE VALUATION RATE OF INTEREST 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 conditions. 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 investment.) 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 liabilities. 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 included. IV. VALUATION IGNORING INFLATION 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 side. 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 value. 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 × i 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 i 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 R×T× 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 R×T × (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 strain. 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 R×T× j–ƒ dividend yield on share which simplifies for a portfolio of equities to R×T × (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 R×T× j × dividend yield on share which simplifies for a portfolio of equities to R×T × (market value of equities) × (yield on 2½% Consols). . . . . .(2) j 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 growth. 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. VI. A PRACTICAL ILLUSTRATION OF THE METHODS 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 dividends. 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 ignored. (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 which: (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 shunned. 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. E 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, value 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 investment? 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 right. 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 RxTx 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 provision. 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 designed. 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 F 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. THE FOLLOWING WRITTEN CONTRIBUTIONS WERE SUBSEQUENTLY RECEIVED: 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 respect. 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 context. 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 arms. 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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