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.

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.

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.

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.

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 .