The purpose of this paper is to discuss briefly the implications for investors of the commoner forms of alterations in a company's capital structure, in the rights of its shareholders, or in the amount of its loan or issued capital, which may occur in practice. The object is to consider general principles only, and no attempt will be made to deal with all possible situations or with the many exceptions which may arise as a result of special rights or provisions in the articles or deeds governing the issues concerned.

Before discussing the implications of particular cases the main features of different types of stock-exchange investment and some broad considerations which govern their value to investors will be briefly reviewed.

During the course of a discussion on Mr R. C. B. Lane's paper, ‘The Dissolution of a Superannuation Society’, presented to the Institute on 24 January 1949, Mr V. A. Burrows enunciated the dictum that a consulting actuary's function, in connexion with friendly societies and pension funds, was primarily an educative one. In his view, it was the actuary's duty to explain and expound the mysteries of his craft so that the laymen who formed committees of management, trustees, local authority finance committees—whoever his clients were—should obtain some grasp of the actuarial principles of their particular funds.

Most consulting actuaries would probably agree with this definition of their task. Their clients can generally give only superficial and spasmodic thought to their own funds, since their primary attention will be devoted to their own trades or businesses. The consulting actuary, on the other hand, meets a succession of technical and administrative problems bearing on friendly societies and pension funds, and in course of time he should be able to exercise wide judgment in these matters. Trustees and committees of management of pension funds should come to feel that they can turn to their actuary for guidance on all points of difficulty whether these are of principle, policy or administration.

In Pension Fund work there arises the problem of determining the cost of a pension dependent upon salary and length of service, and it is often required to ascertain how this cost would be affected if a different salary scale were substituted for that upon the basis of which calculations have already been made. Attention will be confined in this Note to the type of scale most common in practice, namely, the ‘ratio’ scale wherein the successive values form a series of proportional numbers showing the average ratios by which present salaries may be expected to increase from age to age in the future.

We will suppose that the contribution, expressed as ą percentage of salary, is required on one scale when it has been calculated on another scale, or that the various effects of using several possible scales are to be determined. It may happen that the nature of the scales, or to be more precise their relative nature, is such that in order to find a solution to this problem we must consider the effect of the change separately upon the value of the pension benefit and upon the value of a contribution of 1 % of salary; or it may even be necessary to recalculate the required figure on each of the different bases.

At a time when attention is focused upon our foreign trade and when there is widespread recognition of the need to pay with goods and with services for the food and raw materials we are compelled to obtain abroad, there is much to be said for an appraisal of the overseas activities of British life assurance companies and for a discussion of the major problems calling for immediate attention. The subject was last dealt with in a paper read before the Institute by Mr W. F. Gardner in 1935, but the intervening years have been not uneventful, and today the accent is somewhat changed, although it will be found that the previous paper deals with many of the problems confronting us now.

The work of the actuary is largely made up of the four elements of Mortality, Interest, Taxation and Expense. These form what I shall term the actuary's ‘MITE’, and it is noteworthy that of the four, expense comes both last and least in actuarial literature.

There are many possible reasons for this. Expense is a grim subject and lacks the appeal of the other three. Mortality has its theoretical speculations, its mathematical adventures and sometimes, perhaps, its statistical stumblings. Interest is exciting enough, particularly in our attempts to forecast the yield which a life assurance fund may be expected to earn in the future. Taxation is not very exciting; but it is an intricate subject and all our actuarial ingenuity is sometimes needed to grapple with its problems. Expense, on the other hand, appears simple—at least on the surface; and perhaps its very simplicity is the reason why so little has been written about it. However, it seems to me that the objective analysis of expense is a necessary part of actuarial practice, and I think that it might well figure a little more frequently in our proceedings.

These notes are intended to elucidate the treatment of income tax and expenses in the analysis of surplus of a commission-paying office transacting ordinary life assurance and annuity business in the United Kingdom only. The Office is assumed to make an annual valuation for internal purposes, but not necessarily to distribute surplus yearly.

It may first be remarked that the analysis of surplus forms both a check on the accuracy of the valuation and a guide to the amounts and relative importance of the various sources of profit and loss. We are here not concerned directly with the first of these functions and only with two items of the second. It must be realized, however, that the analysis is related to the valuation bases, which may depart materially from the bases underlying the office premiums, particularly at a time when conditions are changing rapidly, or if there is a substantial proportion of very old business on the books.

The study of methods of measurement of the rate of population growth is one of the most fundamental aspects of demographic science and one which, from its nature, should be of particular interest to the actuarial profession. It is therefore fitting that this paper should be devoted to a discussion of this side of the subject, particularly in view of the importance which the analysis of population trends has assumed in modern times as the result of the decline in birth-rates experienced by this country in common with most of the leading civilized nations.

Leaving out of account losses and gains by migration, the future development of a given population is determined by the numbers of children that people have, the proportions of these who survive and the sizes of the families which they have in their turn, the cycle continuing indefinitely. Whilst the consequences of changes in mortality must not be underestimated it is clearly the wide possible range of variation in birth-rates which plays by far the more important part in shaping future population trends. The measurement of population growth therefore rests largely on the analysis of fertility, a subject of considerable complexity.

Although ordinary shares have for many years now been accepted by the actuarial profession as suitable investments for a portion of the assets of insurance companies and pension funds there is very little in the journals of the Institute or of the Society that will help students to discover the methods by which the merits of individual shares are judged. There are indeed papers dealing generally with ordinary shares [e.g. H. E. Raynes: ‘The place of ordinary stocks and shares (as distinct from fixed interest-bearing securities) in the investment of life assurance funds’, J.I.A. Vol. LIX]; but apart from these the only one dealing with methods is that by the late R. B. Gough in J.S.S. Vol. v, No. 1. This has become a little out of date especially since the new Companies Act which followed the report of the Cohen Committee. I therefore propose to set out the methods which I believe are now generally accepted for the preliminary examination of the record of a company, and then to indicate lines upon which further investigations might be made.

1. The analysis of the surplus of a life office disclosed by a bonus reserve valuation does not differ in principle from the analysis of the results of a valuation on a net premium basis, but the treatment of bonus requires special consideration. A method of analysis appropriate to a uniform compound reversionary bonus is discussed in the following paragraphs, and a numerical example is given by way of illustration.

2. It is assumed that the valuation formula is

where (S + B) represents the sum assured and existing bonuses,

P is the office premium,

k is the proportion of premium reserved for expenses,

x is the present age nearest birthday,

n is the curtate duration to maturity,

b is the rate of bonus for which a specific reserve is made.

This paper is submitted in the hope that it will assist members who are not actively concerned with investment matters to obtain a reasonably clear picture of the Stock Exchange and how it works.

The main object of the Stock Exchange, as an institution, is simply to provide a market for stocks and shares, i.e. rights to interest or dividends. Such a market has been in existence in one form and another since the latter part of the seventeenth century, and is virtually a necessity in the modern capital structure. Without it the investor would be loth to lock up his money in a joint-stock undertaking, and, if he did, would have difficulty in assessing the value of his holding at any time. Moreover, he would have little to guide him in making the best use of his capital and, on the other hand, companies requiring funds (to say nothing of the Government) would find it hard to guess the best terms for a new issue.

The object of this paper is to attempt to evolve a theoretically correct method of valuing life policies in an office having a ‘level’ Compound Reversionary Bonus system. This method can then be used to examine the existing methods of valuation in detail, and also to trace the connexion between the existing methods. The theoretical method of valuation can be approached by a mathematical analysis on strictly theoretical lines. A Compound Reversionary Bonus method has been used in this paper, but similar principles can be applied in the case of a simple reversionary bonus method.

It is emphasized at this early stage that I am only concerned with the theory of valuations, and the practical points, such as legal requirements, presentation of valuation results and simplicity of valuation machinery, are not considered.

Priority percentages are generally calculated when considering an investment in a joint-stock company with the intention of finding two limits, which may be defined as follows:

The lower limit is the percentage of net profits (after all expenses other than British taxation) which would just suffice to pay all prior charges and dividends on stock ranking prior to the stock under consideration.

The upper limit is the percentage of net profits which would just suffice to pay the dividend on the stock under consideration and all prior charges and dividends.

Now that profits tax is as much as 30% with a rebate of 20% on profits not distributed, it is important to consider to what extent profits tax should be treated as a prior charge.

An example of what may be described as the ‘normal’ method of calculating priority percentages is given on p. 186 of the new textbook, Principles of Finance and Investment, by L. G. Whyte, F.F.A. The whole of the profits tax, allowing for the rebate on profits not distributed is shown as a prior charge to all dividends. This appears to be the method used by the two principal statistical services.

In advising on the apportionment of a fund, an actuary is faced with practical problems of admitted difficulty. The following notes are an attempt to discover exactly what these problems are, and to determine the methods of approach most likely to lead to a satisfactory solution.

Trustees looking after a settled fund have a different attitude to investment from that of persons controlling the investments of a life assurance fund. The funds of a life office are normally increasing; in such a case it is easy to see that the object of investment policy is to secure accumulation at as rapid a rate as is consistent with safety. Changes in the portfolio can be considered which do not necessarily result in an immediate increase in current income. The securing of a capital profit or the avoidance of a prospective capital loss by a sale and reinvestment may be a valuable source of strength. Trustees, on the other hand, cannot ignore the importance of a high level of current income, for a trust fund is normally invested to produce income for disbursement, and there is a vital distinction between trust ‘capital’ and ‘income’.

The subject of making an allowance for initial expenses in a net premium valuation is one which has long interested actuaries, and it is usually associated with the name of Zillmer who first wrote an article on it in 1863. The following note, based on practical experience of valuing a young and rapidly growing life fund, may be of interest to students.

The normal method of making such an allowance is, in effect, to adjust the net premium used in the valuation by the equivalent of the initial expense allowance spread over the whole duration of the policy.

The student is familiar with the Z formulae for the expression of certain multiple-life contingencies in terms of symmetrical combinations of the component joint-life statuses. The present note develops an analogous method based upon last survivor statuses. In certain circumstances this latter type of expression may be the more convenient for practical use.

Consider a set of m lives. Then in the notation followed by E. F. Spurgeon, in his book, Life Contingencies, Zr represents the sum of the probabilities of r lives surviving a given period for all combinations of r lives that can be made out of the set of m lives. The number of combinations of r lives that can be formed out of the set of m lives is .

One of the principal problems of demography is that of comparing the mortality and fertility of different populations or of one population at different periods of time. This note defines and discusses briefly some of the measures which have been used for this purpose.

Notation

aPx number of persons in age group x in the population being considered (the ‘actual’ population).

amx death-rate in age group x in the actual population.

sPx,8mx the corresponding number of persons and death-rate in a population chosen as standard (the ‘standard’ population).

aM crude death-rate in the actual population.

sM crude death-rate in the standard population.

tx number of ages included in age group x.

The standard population may, and in fact usually will, be an actual population in the sense that it is a population which existed at some particular time.