1. After the discussion on Sir George (then Mr) Epps's paper on ‘Superannuation Funds’, the President in proposing a vote of thanks said: ‘It is 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 inconsistency in the advice which we respectively give to those who consult us.’ In 1921, when Epps's paper was presented, actuaries were faced with the position that current yields on new investments were very much higher than had been anticipated in earlier valuations, while most of the older funds had suffered very heavy depreciation in values of existing investments. Today the circumstances are reversed. The rate of interest which can be earned on new investments is very low, but there has been substantial appreciation in values of existing investments. It is in the hope of provoking an exchange of views on the best method of dealing with this present situation that this paper has been written.

(1) The proper method of taxation of annuities has been a subject of contention for many years, and it seems a suitable time to discuss what are the correct principles to be applied.

(2) It seems illogical that life annuities should be taxed on a different principle from annuities payable for a fixed period not dependent on life. It also seems wrong that, whereas a person who has saved capital on which to live in old age may draw on the capital from time to time without being taxed on it, the same person if he buys an annuity so as to equalize the payments throughout the remainder of life has to pay tax on the capital content of the annuity.

(3) Various methods(1) have been devised in other countries as practical measures giving some allowance for the capital content of annuity payments, but those methods that I have seen suffer to my mind from being founded on arbitrary rules rather than on principle. It should be noted that the practice of each country is bound up with the definition of taxable income and the treatment of wasting assets in that country. In Great Britain it is possible so to word an annuity contract that part of the annuity is not taxable, but personally I think the question of principle should be faced, and not avoided by rewriting the contracts in some other form.

The purpose of this paper is to discuss the actuarial principles on which the investment policy of life assurance offices should be founded. The policy considered relates, firstly, to the principles on which the selection of investments should be made and secondly, to the basis of their subsequent valuation.

Mortality statistics have now been available for the population of Great Britain for just over a hundred years and during this period there has been a steady and sustained decrease in mortality at all ages and in both sexes, though the extent of the decrease has been progressively less with increasing age.

The main part of the improvement in mortality during the latter half of the nineteenth century was due to improvements in sanitation and hygiene and above all the provision, at any rate in cities, of a reasonably safe water supply. Cholera which occurred in severe epidemic form in London between 1832 and 1866 had disappeared completely well before the beginning of the twentieth century. The widespread epidemics of typhoid fever which occurred as a result of water supplies becoming contaminated with sewage ceased when adequate precautions were taken to safeguard the sources and transmission of water in cities. It is true that small and localized epidemics of typhoid still occur, but these are all found to be due to contamination of food or water by ‘typhoid carriers’. A recent epidemic in Wales, in which some 150 cases of typhoid occurred, was shown to have been caused by the eating of ice-cream which was handled and sold by a man in perfect health but who, following an attack of typhoid many years previously, had continued to pass virulent typhoid organisms in the stools. Fortunately the notification of cases of the disease enables the public health authorities rapidly to track down carriers in this type of epidemic.

Twice in the past forty years war has abruptly changed economic conditions in the country and the new economic conditions have in their turn affected the circumstances of all pension funds. Before the war of 1914–18, the great majority of pension funds provided pensions based on the average salary through the period of service for a low contribution rate, The inflation of salaries and wages between 1914 and 1919 disclosed the weakness of the system since the pensions provided proved to be small in comparison with the new level of remuneration and to be inadequate to support the member during retirement. The experiences of this period led to the adoption of the system of basing the pension on the remuneration of the final year of service or of the average remuneration of the years immediately prior to retirement, The financing of the additional pensions to members for whom pensions on the pre-1914 basis had been provided and the establishment of the new system for members currently contributing was materially assisted by the high yield obtainable on investments. It should be added that for a scheme with funds invested before 1914 the depreciation of assets due to the high interest rates which had been obtaining immediately after the war increased the cost of reorganization of the scheme.

The actuary employed in life office work is very closely concerned with the methods by which the valuation and other records of a life office are built up. It is surprising, therefore, that there are very few references in the pages of the Journal of the Institute to the use of punched-card equipment for life office work. The use of the equipment for calculations of interest to the actuary, such as the construction of tables, has also been largely ignored. Actuaries employed in work outside life oflices so often rely on punched-card equipment for their statistical data that the authors feel that no apology is needed to either class of actuary for presenting a paper on the subject. Punchedcard equipment has received much more attention in the Transactions of the Actuarial Society of America, most recent volumes containing a paper or note on its application.

The measurement of the rate of population growth has attracted considerable attention in scientific literature of recent years. This is, no doubt, a result of the continual decline in the birth-rate which has formed the topic of innumerable articles in the popular press and elsewhere. Several attempts have been made to obtain a simple statistical measure of the reproductivity of a population at a particular time—that is, a measure of the extent to which a population will be replacing itself if current fertility and mortality continue indefinitely. It is the aim of this paper,

• in section 1, to discuss the simple approximate formulae that have been suggested;

• in section 2, to discuss some more elaborate and more efficient formulae;

• in section 3, to analyse the effect on the formulae of section 2 of a change in the proportions married at a given age;

• in section 4, to outline the male versus female rate anomaly;

• in section 5, to suggest a formula which avoids the anomaly; and finally,

• in section 6, to discuss the application of these formulae to Australian population statistics.

In this paper, everyday actuarial data have been examined by means of standard statistical techniques. The data in question have been drawn from the publications of the Continuous Mortality Investigation Committee, and the methods of statistical analysis have been applied to investigate the nature and extent of the heterogeneity which may exist in those data.