The purpose of this paper is to consider some of the practical problems arising from the application of punched cards to one particular aspect of Life Office work, namely the work connected with bonus distribution in Ordinary Branch business.

No attempt has been made to describe the punched-card equipment itself, since this was fully dealt with in the paper submitted to the Institute in 1948 by N. E. Coe, K. J. Hedley andL. H. Longley-Cook; this paper also contained a comprehensive survey of the application of punched cards to Life Office work, including brief references to their use in connexion with bonus distribution.

This paper attempts to give a sketch of the history and present practice of life assurance in Australia. It is not unnatural that its earliest beginnings should have been based on principles and methods which had already been developed and proved in this country. There are still many similarities, but differences have arisen in the new environment, and an examination of these differences may be of interest to members of the Society.

Little more than 100 years ago the population of the colony of New South Wales, which then included the present territories of Queensland and Victoria, was only about 250,000, yet a few provident pioneers had already formed a Mutual Society to transact life assurance. They had been appalled by the plight of the families of the early settlers who died before they had time, by other means, to make provision for their dependants.

The development of this Society was at first very slow, but it had the good fortune to have no death claims during its first three years, nor did they exceed £2500 in any of the first ten years. It was not until the introduction of the canvassing system, with the appointment of the first full-time agent in 1860, that there was any appreciable expansion. To-day that Society is the largest mutual life office in the British Commonwealth with assets of £300 millions.

The idea of a census goes back into the mists of antiquity. It is reported that the Romans under Servius Tullius, the sixth King of Rome about the sixth century B.C., took a census every fifth year and the right of citizenship depended on the making of a complete return. The main objects of the census seem to have been the raising of men and money for further conquests. But the concept of sampling which is often thought to be of more modern origin must have been there even if dormant, for the process of taking a small quantity of material for tasting or testing in order to determine the quality of the bulk has gone on for centuries. However, the big impetus for ideas and practical applications of sampling methods seems not to have come until just after the immense strides taken around 1600 in the field of probability by such men as Cardano, Galileo and later Pascal and Fermat. There is direct evidence that Pascal's work inspired De Witt, the Dutchman who calculated the first life annuities, and no doubt others were similarly inspired.

In the course of the discussion at the meeting at Staple Inn last October one speaker regretted the absence of any reserve figures from the notes then under discussion. This comparison of reserves under a new table with those under a table to which we have become accustomed is something of a habit which we tend to do perhaps without asking ourselves why we do it. What does a comparison between A1924–29 and A1949–52 reserve values tell us? Does it really tell us what change to expect in our liability as a result of a change of valuation basis or are these figures merely calculated as a matter of interest, serving in practice no useful purpose?

The answer to that must depend, at least as far as reserves under the main classes are concerned, on the extent to which we use a true net premium valuation. Interesting information is to be found in the paper recently given to the Faculty by J. M. Beattie.

The object of this paper is to discuss the main principles underlying the pattern of interest rates on government securities in this country. It does not attempt to examine the place in the yield structure of those stocks which may possess special characteristics of term or provision for repayment, etc.; and because of its concentration on general principles the complex effects of taxation have been relegated to the background. The subject is approached by the following stages:

(1) The pattern in the hypothetical case of complete certainty.

(2) The idea of a ‘normal’ pattern, i.e. in conditions of complete uncertainty.

(3) The changing pattern in conditions of varied and fluid expectations.

Members of this Society and of the parent Institute have considered, from time to time, questions affecting the investment of life insurance funds. In the early days ‘Bailey's Canons’ were propounded, and comparatively recently J. B. H. Pegler's ‘Actuarial Principles of Investment’ and H. G. Clarke's ‘Broad Analysis of the Problem’ have been discussed. Also, the more practical aspects of the subject have received due consideration: notably Stock Exchange Investments by A. S. Holness, Loans and Mortgages by W. Murray Simpson and Real Property by G. B. Lane, F.S.I., and W. A. Leach, F.S.I., in 1944, and further by A. C. Wheeler and K. A. C. Wheeler in 1953.

My purpose is to present certain legal points affecting these investments. I hope my remarks may to some extent be supplementary to these previous contributions on the subject of investments, and I shall try to avoid covering the same ground.

This paper sets out those considerations which appear to the author to be of major importance in the formulation of economic policy and some of the history of the development of thought on these matters. It should be emphasized at once that it represents the knowledge acquired by an actuary, with no formal training in economics, in the course of attempting to appraise the policies actually adopted in recent years, and that it is addressed primarily to those setting out with the same equipment on the same path.

The only other introductory remark necessary is that, inter alia, considerations of space prevent any lengthy discussion of non-economic factors which influence economic policy. This does not imply that technological, moral or social problems may be ignored, but that, for this purpose, they are regarded as parameters in the economic equation.

The history of the actuarial profession in South Africa starts, as far as is known, during the last decade of the nineteenth century when three actuaries arrived in the Cape Colony from the United Kingdom. Two of these took up positions with the two South African life offices which were then in existence and the third became Government Actuary to the Cape Colony. By the time the Union of South Africa was established in 1910, four more actuaries had arrived from the United Kingdom, and a further four had arrived by 1920. Some of these gentlemen established permanent homes in this country, while others returned overseas after varying periods of time. It was no doubt due to these early beginnings that the actuarial homes of South African actuaries are today London and Edinburgh.

The first South African-born actuary qualified as a Fellow of the Faculty in 1921, and since that time increasing numbers of South Africans have become qualified, mostly as Fellows of the Faculty.

It is a matter of some regret to me that a member of the Actuarial Society of South Africa cannot be here this evening to provide an introduction to the paper before you. While I feel I am honoured by my South African friends in being asked, as an ex member of the Society, to undertake this duty, I must confess that I am wondering whether my personal experience is sufficient to qualify me for this task.

For much of his work the actuary is concerned with the people living around him and I think therefore that I should say something about the people living in the Union of South Africa.

South Africa was first discovered around the end of the fifteenth century, but it was not until 1652 that the first settlement was made by the Dutch East India Company. The settlers were under the control of Jan van Riebeeck who was charged with the duty of providing fresh vegetables, etc., for replenishing the stores of ships rounding the Cape.

In recent years there have been a number of papers read to statistical societies and much written on the place of the statistician in business. In the fields of quality control and operational research the position of the mathematical statistician is unchallenged. That of the statistician employed in the day-to-day running of a business is, however, very different. He may have had a mathematical training but is more likely to be an accountant or an economist. This has tempted the author to analyse the extent to which he, as a statistician in business, makes use of his mathematical and actuarial training and employs the mathematical techniques of the statistical textbook. Most of the energies of such a statistician are employed in the collection and tabulation of data; in the main his especial skills are based on an intimate knowledge of the sources of his information (which range from the firm's accounting system for internal statistics to the almost newspaper reporter tactics needed by the market intelligence statistician) and on a familiarity with the needs of the users of the figures (psychology can play its part too in their presentation).

This is a subject which may seem a little remote from the normal run of discussions at these meetings. But with the increasing tendency for actuaries to take up posts in Government service, in industry and in commerce, in which official statistics are an everyday need, I hope that some of you, at least, will find it interesting to have this brief account of the work of a Government statistics division.

The Statistics Division forms part of the Secretaries' Office of the Board of Inland Revenue. Its primary function is to supply the Board with the figures which the Chancellor of the Exchequer needs for Budget purposes, i.e. estimates of the future yield of taxation at current levels and of the cost or yield of possible changes in rates and allowances. The whole of the year's work centres on those requirements, but in the course of it many figures useful for other purposes emerge or can be collected with little additional effort.

Social insurance is becoming increasingly important in the economic and social life of many countries. In several the expenditure on insurance benefits has been estimated to be over 10% of the national income. About forty-five nations now have insurance schemes in which the state plays a part, and about seventy have compulsory private or state ‘workmen's compensation’ insurance. Others have assistance schemes. There is continual expansion in the number of countries operating schemes and in the scope of these schemes.

In this paper a summary is given of the types of benefit commonly found, and the methods used to assess contributions, and financial systems in use, are then discussed. Although Great Britain was one of the pioneers of social insurance, very few schemes have been modelled on ours and it is instructive to examine the differences.

1. The subject of analysis of surplus has been given much study by actuaries both for the intellectual satisfaction it affords and for the practical value of the results of such inquiry. One of the earliest papers in our literature is that of G. H. Ryan in 1892 (J.I.A. 30), the first half of which was entitled ‘On a Method for determining the Gain or Loss from Mortality in an Annuity Company’. Since that date, however, attention has been devoted almost entirely to the analysis of surplus of a life fund, in view of the problems involved in its distribution, and Ryan's restricted treatment remains the only reference for students with regard to the analysis of surplus of an annuity fund. The purpose of the following notes, therefore, is to illustrate symbolically a full analysis of such a fund comprising immediate, deferred and contingent annuities, obtaining a complete reconciliation, and at the same time to indicate briefly the practical difficulties and the consequent steps in the analysis at which curtailment would be necessary in practice. Discussion of the relative importance of sources of surplus is outside the scope of these notes.

The object of this paper is to provide a basis for a discussion on the advisability or otherwise of life offices issuing ‘variable annuities’ in this country on a commercial basis.

As this is a relatively new subject it is, perhaps, as well to define our terms at the outset. The form of contract which has come to be referred to under the name of ‘variable annuity’ is one under which the annual amount payable is not a fixed sum in terms of money, but a fixed number of annuity units the cash equivalent of which varies from time to time in accordance with the variations in the market value of the assets in which the fund is invested.

The substance of the paper was originally written about a year ago as an internal office memorandum summarizing reports and notices appearing in the financial and insurance press both here and in the U.S.A. about this new American idea, and the authors were of the opinion that as the subject had received little other attention in this country it would form a suitable topic for discussion at one of the Students' Society meetings.

Following upon the growth in the number of pension funds which has occurred in recent years, employers have become increasingly concerned with the preservation of the pension rights of employees leaving their service to enter that of other employers who may even be competitors. Having accepted the obligation to provide pension benefits for his staff as a whole, an employer must decide to what extent, if any, he wishes to preserve the pension rights of transferring employees. Before reaching his decision, however, he will, if he is wise, seek the guidance of the actuary to the fund, who should be prepared to present the alternative fundamental principles and attitudes open to him. From these should follow his decision as to whether he has an obligation to preserve the pension rights of transferring members of his staff and, if they are to be preserved, how the actuary should make the relevant calculations. Whilst decisions must ultimately rest with the employer, the actuary must be fully conversant with the subject as a whole so that he can give sound advice and be able to make the necessary calculations. It is the actuary's duty to present all sides of any problems which arise in connexion with the scheme and to indicate the consequences which may result from the employer's decisions.

During the past decade ‘electronic brain’ and ‘automation’ have become part of the vocabulary of most inhabitants of this country and of many others. Some users of these expressions, however, have at the most only the vaguest impression of the equipment and techniques involved, of their capabilities, and, which is perhaps most important, of their limitations.

The Institute has been fortunate. The paper by R. L. Michaelson which was presented in April 1953 explained, in considerable detail, the logical operation of an electronic digital computer, while A. C. Baker's paper two years later demonstrated how an installation based on this type of equipment might be used for life office work. Moreover, the Institute has set up several study groups concerned with different aspects of the subject, while from the Society of Actuaries in America emanates a steady flow of reports, for the most part based on practical experience within the insurance companies of the U.S.A.

The Friendly Societies Act 1896 provides for two methods of combining the membership, the assets and the liabilities of separate registered friendly societies. Following the procedure of §70 (1) of the Act the societies may amalgamate as one society. For this, the written assent of five-sixths, in value, of the members of each society must be obtained; the value of the members is defined by giving one vote to every member, with an additional vote for each 5 years of membership up to 20 years.

Alternatively, under §70 (2) of the Act, one society may transfer its assets, engagements and liabilities to another. If this procedure is followed, the written assent of five-sixths, in value, of the members of the society transferring its engagements is necessary, but the society receiving those engagements can do so on the resolution of the Managing Committee alone, provided that the Committee has the requisite powers under the rules of the society. For this reason, if one of the societies is large or if it is difficult to contact the members, a transfer of the engagements of the smaller society to the larger is more practicable than an amalgamation.

In 1952 the Statutes relating to income tax were gathered together into one consolidating Statute, the Income Tax Act, 1952 and the whole system of taxation of a life office is laid down in a few sections of this Act. The position has been modified by the passing of the Finance Act, 1956, but the effect of this will be considered in the latter part of these notes. A proper understanding of the relevant sections of the 1952 Act necessitates some knowledge of the fundamental principles of income tax in general as laid down in the Act. As it is the object of these notes to try to deduce as clearly and logically as possible from the Act how a life office is taxed with special reference to its annuity fund, it will therefore be desirable to refer briefly to some of these general principles.

Income is charged to tax in one of two ways, viz. by deduction of tax at the source by the payer of the income or by direct assessment on the recipient under one or other of the five Schedules A, B, C, D and E, enumerated in Section 1 of the Act.

Two conditions have been proposed (Anderson & Dow, 1948) for the census method of constructing a mortality table to be ‘strictly correct’: (1) that at the beginning and end of the investigation, ages of lives are evenly spread over the year of age x to x + 1, or (2) that numbers and distributions of ages are the same at beginning and end.

In effect, these alternative conditions are proposed to insure that the approximate formula for the total period of exposure to risk, derived from annual census,

shall be reasonably correct. It is, however, of interest to examine the method more closely, under the hypothesis that the total period of exposure to risk can be determined with negligible error, as would theoretically be possible by holding censuses with sufficient frequency.

In recent years the statistical technique known as ‘sequential analysis’ has been developed to a considerable degree of refinement and applied in many varied fields. The technique may, however, be new to some readers, and some examples and illustrations of the application of sequential methods to data of the type encountered in actuarial work should therefore prove of interest.

The raison d'être of sequential analysis is the reduction of the average number of observations required to reach conclusions from observed data without altering the degree of reliability specified in the usual fixed sample size technique. If such a result can be achieved a saving in both time and money may be effected.

In the usual fixed-sample size techniques the size of sample necessary to achieve a given degree of reliability in the conclusions reached can be computed. However, in the course of the selection and examination of the sample it often becomes apparent, at quite an early stage, what form of conclusion is likely to be reached.