I have limited this paper to the consideration of appreciation or depreciation in fixed interest-bearing securities resulting from a fall or rise in the general level of interest rates and not from any alteration in the intrinsic value of the securities, i.e. there is assumed to be no change in the probabilities that the terms of the contracts will be fulfilled. My object is to discuss how this appreciation or depreciation should be treated in order to obtain the maximum practicable degree of equity between the different generations of policyholders in an office which distributes its surplus by means of a uniform reversionary bonus.

The problem can be most easily discussed by showing the effect on a model office of adopting various methods of treating this appreciation or depreciation. I propose to limit the discussion in the first place to the question of depreciation in an office employing a bonus reserve valuation.

Pollard and Pollard pointed out that, while it has been conventional to refer to Ax, as ‘the present value of an assurance of one on a life aged x’, this value is a random variable (denoted by Ãx) with mean Ax.

In a discussion I had with Professor J. J. McCutcheon and Dr W. F. Scott, the authors of the new book on compound interest, An Introduction to the Mathematics of Finance (Heinemann 1986) it was suggested that a chapter describing the theoretical economic background to the determination of interest rates might be of interest to actuarial students. I therefore drafted the substance of this note as such a chapter. In the event it was felt that the subject fitted uneasily with the mainly technical and numerical approach to compound interest appropriate for students at that particular stage of the examinations, and that the more theoretical approach in this note would in any case be of wider actuarial interest. It is therefore presented as this note in the Journal. I am grateful to Professor McCutcheon and Dr Scott for agreeing to this, and to the discussions I had with them while the note was being drafted.

In every branch of business, even in the very rudest stage of barter, men have to count. A skin is exchanged for so many cowries, a rifle for so many skins. Do what we will, go where we will, the necessity for counting meets us. Yet, though numbers be essential to all our operations, we do not easily form an idea of large numbers. Thus in no language do the separate names for numbers reach to twenty. In one, I believe, the numeration goes as far as fifteen; in the northern languages of Europe it reaches to twelve, but in most languages it stops short at ten.

In the year 1885 the New York Life Insurance Company commenced to do business in India and continued actively there until the outbreak of the World War. A reinsurance arrangement was made in 1922 with the Sun Life Assurance Company of Canada. Before disposing of the statistical records mortality investigations have been made, the results of which are now published in the hope that they may be of value to actuaries.

In the early years a goodly proportion of our policies were issued to British residents of India, but this condition gradually changed so that since 1900 the great majority of policies were granted on natives of India. The change was partly due to the British companies granting the former more liberal treatment than we did. In determining the rates of premium our Company did not distinguish between natives of India and others. Until the end of the year 1913 the Company charged the tropical scale of premium and then changed to the semi-tropical rates, with a restriction, however, to 10, 15 and 20-Year Endowment Insurances maturing not later than age 65.

The mortality, according to age, of the general population of England in all localities, was first satisfactorily determined for the period of seven years, ending with the year 1844. The observations and results were published by the Registrar-General in the year 1849; and in the following year I was allowed the opportunity of exhibiting in The Lancet (vol. i. 1850, pp. 297–330) the principal results in new combinations, with my conclusions therefrom. The knowledge thus obtained of the mortality of the general population (with distinction of town from country districts) is valuable for testing the correctness of independent observations made on the mortality of classes of the labouring population, such as are contained in “Friendly Societies,” whose mortality and sickness it is now proposed to discuss.

The last paper presented to the Institute on the general subject of investments was that by J. G. Day (J.I.A. 85, 123) in October 1958. He summarized and commented upon the actuarial approach as disclosed in the major post-war papers and the subsequent discussions on this subject and set forth succinctly the position that had been reached, so that there is no necessity for doing so again. However, a major development in the investment policies of life offices since then has been the increased interest in overseas investment, and it is the purpose of this paper to set forth some of the considerations affecting investment in this field.

The importance of this subject may be indicated by the fact that more than half a million a year is paid by the British Life Offices to their assured, as surrender values on the discontinuance of their policies. Competition also, and the increasing interest which is being taken in the subject by the insuring public, have a tendency to induce companies to make these surrender values a prominent feature in their prospectuses; perhaps also it may be an inducement to some companies to offer large values in order to bid for larger patronage.

The liability of the employer to compensate his employees, as well as other persons, for injuries sustained through his fault, may be traced from an early period in the world's history in the Common Law of various countries.

For example, by the Jewish Law, said to have been promulgated about the year 1500 B.C., if a master were the means of causing the loss, either intentionally or unintentionally, of the eye or of the tooth of his slave, he was bound to let him go free for his eye or his tooth's sake. Again, according to the same law, if an employer allowed his ox to gore either his servant or a stranger, he was required to pay various compensations to the injured if he survived, or to his relatives in the event of the injury being followed by death.

During the 1930s there were allegations that London bus drivers and conductors had an undue amount of sickness, especially gastric disorders. Dr Bradford Hill (1937) was asked to investigate this allegation, but found that the data were limited. The London Passenger Transport Board determined that in the future adequate data for such investigations should be available. This was not possible until after the war. In 1948 the Central Record of Staff Statistics was set up to compile sickness-absence statistics and for other purposes. This lecture is mainly an account of the uses made of the statistics produced: how they can be used to study the effect of sick pay provisions, the secular trend of sickness absence in occupational groups, and the differences in sickness-absence experience between groups of various kinds. If the experience of these groups is related to the employees' work and the conditions under which it is done, the results are valuable in answering questions on health from management and unions. The data collected can also be used in medical administration and for research into the causation of disease.

The paper investigates the level and incidence of saving required in order to maintain the standard of living that a household experiences whilst of working age into retirement. In order to do this, a model has been constructed that follows the income and expenditure of a household, allowing for tax and social security, as well as changing family circumstances. The model can be used to explain how a household should save in order to achieve a given standard of living in retirement.

The author concludes that the usual message, to save a fixed proportion of income throughout a working lifetime, is at best not helpful and at worst could lead to a lower standard of living over the household's lifetime. People can and should manage the timing of their saving and borrowing in order to achieve optimum incomes.

The education of actuarial students has been a problem for the profession almost since its inception. Despite considerable efforts to seek improvements, difficulties have repeatedly arisen in the examinations, the syllabus and the teaching.

Over the past five years the profession has identified four major areas of concern:

—The average time to qualification of those who complete the exams is too long.

—The proportion of entrants who never qualify is too high.

—It is becoming difficult to recruit enough students to produce the required number of qualified actuaries 4–10 years later.

—There are insufficient actuaries available to fulfil the tutoring and examining duties required by the education service.

The first three of these points can be illustrated by considering a single cohort. In 1980, 289 students enrolled in the Institute. Only 5% of these had completed the exams within 4 years, and only 14% within 5 years. It is unlikely that more than about 30% of this cohort will ever qualify. Incidentally, much of the careers literature available to these students indicated that a diligent (but not extraordinary) student could expect to qualify in 3 or 4 years.