By courtesy of the Government Actuary, the preliminary crude data relating to the proposed English Life Tables (No. 13) were made available to the authors. In this paper various graduations derived from these data “are described and an outline is given of the salient features of each.

The investigation covered the calendar years 1970, 1971, and 1972. For each integer x ≥ 2 the values of θx, the number of deaths during the investigation period aged x last birthday at the time of death, and Exc, the corresponding central exposure to risk, were available for both sexes. The central exposures to risk were obtained using population totals from the 1971 national census, by a method similar to that described in Appendix I of reference 4.

In the paper I shall have the honour of reading to you this evening, upon some points connected with the education of an actuary, I shall endeavour to describe some of the more important duties and responsibilities of that office—to offer some observations to the student, as to his preparation for the profession of an actuary—and to suggest to the Council of the Institute some reasons for enlarging the sphere of the examinations that they may think proper to prescribe.

I shall not detain you with any account of the ordinary duties of an actuary, which are of course well understood in this room, but shall at once proceed to the consideration of the foundation of all actuarial knowledge—mathematics.

The move from defined benefit to defined contribution (DC) has transferred the longevity and investment risks from the plan sponsor to the individual plan member. Without the actuarial cross-subsidies implied by pooling these risks, the danger of outliving one’s savings is significant. Much attention has been focussed on pre-retirement investment design but less on post-retirement. In most countries, the post-retirement systems in place are insufficient to solve this challenge for small asset sizes or small proportions of individuals’ retirement accounts. However, a number of DC markets are mature, such as Australia and Chile, and the principles of a solution that works for all must be identified. This paper researches a number of post-retirement systems around the world and identifies ten key factors that contribute to post-retirement solution design. These factors can result in an inconsistency between countries regarding the most appropriate post-retirement solution. Additionally, a disconnect is apparent between what retirees need and want in post-retirement. Successful post-retirement solutions will inevitably blend investment and insurance components in a balanced manner. With lengthening life expectancies, research supports strategies that blend a growth and income account-based approach for the first 15–20 years after retirement with longevity protection in later life.

The object of this paper is to continue the discussion on the valuation and bonus problems of a life office that was recommenced in the recent papers by A. T. Haynes and R. J. Kirton (T.F.A. xxi, 141) and by F. M. Redington (J.I.A. lxxviii, 286). Both of these papers were concerned, inter alia, with the principle of matching assets to liabilities or, in Redington's graphic phrase, of immunizing the life fund against the effects of a change in the general level of interest rates. Immunization of a life fund containing with-profits policies was shown by Redington to have far-reaching implications, and it was clear from the discussion on his paper that different opinions were held about the exact character of the immunization that might be most appropriate. For a non-profits fund total immunization may or may not be a suitable ideal with which to compare the practical position, and this would depend, in particular, upon the relative size of the capital and other free resources available and upon the level of the surrender and paid-up-policy options granted. But it is the purpose of this paper to argue that, for a with-profits fund, far from being a suitable ideal to be either aimed at or departed from, total immunization (including absolute matching) represents a dividing line between a zone of rational departure from another and more natural ideal and a zone in which a change in the level of interest rates would produce indefensible results.

There will, I venture to think, be no difference of opinion among the members of this Institute as to the advisability of an early and adequate discussion of the many points of difficulty presented by the new Assurance Companies Act. Neither will there be any doubt as to this Institute being the proper place for such a discussion, consisting as it does of an unrivalled body of experts on the subject of life assurance. In these circumstances I have ventured to undertake the task of bringing the matter before the Institute, confident in the fact that however inadequate my treatment of the subject may be, those before whom the paper is to be read are fully competent to make good any shortcomings on my part, and will be both able and willing to correct any errors into which I may have fallen.

The prime purpose of the paper is to present the case for the issue of longterm index-linked stocks by the government and by other borrowers, for the issue of index-linked life assurance and annuity contracts by life offices and for the index-linking of pension scheme benefits, all of which the author believes are possible and would be beneficial to all parties.

Part 1 of the paper uses the methods of statistical time-series analysis to study the way in which inflation has behaved in the U.K. over the long period 1661 to 1980 and over various shorter and more recent periods. While prices were far from static in the period up to 1914 the average change was nevertheless almost nil. However, during the 20th century prices have generally risen and in recent years this rise has accelerated. It is possible that the series has become unstable, and hyperinflation will result. It is certain that no one statistical model can satisfactorily “explain” the movements of prices. Future uncertainty is now very great.

The author concludes from this that index-linking of long-term contracts, i.e. adjusting for price changes after they have occurred, is more satisfactory to both parties to the contract than to guess at a single fixed inflation rate and build that into the contract.

Part 2 discusses the issue of long-term index-linked government stocks. It demonstrates the uncertainty attached to fixed interest borrowing and lending, and the harmful effect on the future PSBR of the government's present funding methods. The author discusses the Wilson Committee's view on index-linking, and supports their suggestions of tax changes to make practicable the issue by companies of index-linked loan stocks. Index-linked house purchase loans are also advocated.

In Part 3 the author presents the advantages to life offices and their policyholders of policies with index-linked premiums and benefits, and discusses some of the complications of such policies, in particular the tax obstructions for certain types of policy.

In Part 4 the author suggests that index-linked pensions are both desirable and possible for all pension schemes, not only those in the public sector, though possibly they should start at a reduced level. Evidence is presented to show that “negative real returns” on ordinary share investment were a temporary aberration of the mid 1970s, and that in more recent years ordinary shares have shown very satisfactory real returns, which may very well continue. Ordinary shares have nothing to fear from index-linked stocks, and pension funds should be able to earn satisfactory real returns on any assets other than long-term fixed interest stocks.

Health expectancy (HE) was only recently estimated for the Scottish population (Clark et al., 2004). The estimates were based on Sullivan's method, applying the morbidity prevalence in each age group to the expected number of years lived, to obtain the expected number of years lived in good health. First, we compare these estimates with a wide range of estimates in respect of the rest of the United Kingdom and the (pre-accession) countries of the European Union. We find that Scotland's HE is relatively low, especially for men. Second, we examine data comprising the responses to the 1998 Scottish Health Survey, linked to the hospital records of the respondents from 1981 to 2004, and death records from 1998 to 2004, with HE measurement in mind. Although time spent in hospital does not give a satisfactory measure of HE, the linkage presents a rare opportunity for statistical analysis of survey respondents' mortality and morbidity. We show the results of survival analyses, quantifying the effectiveness of various definitions of ‘unhealthy’ as predictors of future mortality and morbidity. The results suggest that enumerating recent serious hospital episodes might help to predict future patterns of demand for acute services.

The arithmetical method adopted in these notes is to assume that the level premium to cover a certain under-average life is known; to work out some of the different rates of mortality that might lead to it and then see what consequences follow. The numerical work, in connection with which I have to thank Mr. Sidney J. Perry, F.I.A., for help, will be confined to an unloaded level premium on a 4 per-cent basis of ·01914 for a life entering at age 30. This premium might result from the rates of mortality set out in Table I.

The rule which was given by Thomas Simpson for finding the value of an annuity on three lives is as follows:—let A, B, and C be the three lives, and let K be a single life, the annuity on which is equal to an annuity on the joint lives of B and C; then the value of an annuity on the joint lives of A and K is the required annuity on the joint lives of A, B, and C. The life A should be the youngest of the three.

Those with responsibility for the assets of institutional investors have a fiduciary duty to attempt to earn the best possible risk adjusted returns and to comply with ethical standards. A satisfactory resolution of these, and other, conflicting demands requires a coherent intellectual framework. Such a framework can be based on a traditional scheme that analyses the various components of profit in terms of the requirements of justice. The framework provides a basis for discussing the major challenges facing the institutional investors. These relate to their role in rational asset selection, effective corporate governance, job creation and the minimisation of environmental impact.

By this I do not mean what is usually called Newton's Table, but something which has a better right. First, however, I will speak of the table which, having Newton's certificate of accuracy, is (or was) usually called by his name.

Mr. Edleston, Fellow of Trinity College, in making researches for his biography of Newton, found out the author of the old table. His name was Mabbot, and he was manciple (mancipium) or caterer of King's College. Mabbot published his table in 1686, with the well-known attestation of Newton opposite to the titlepage. There seems to have been a special reason for procuring this certificate. The church lessors were beginning to open their eyes to the leniency of their terms, and Mabbot's tables were certainly intended both to urge them to raise their fines, &c., and to point out the proper way of doing it. Subsequent editions of these tables had attached to them the well-known letter which pointed out the advantage under which the tenant was living. As it was natural that the lessees should oppose the new scheme, and they would probably question its accuracy, it seems that Newton was applied to for the testimonial which, as is well known, he gave.

It has frequently been remarked, that however varied and uncertain may be the occurrence of the events to which the life of a single individual is exposed, the average return in a large mass of persons is so regular, as to be predicted with confidence within very small limits of error. On the uniform happening of these events under similar circumstances, or the discovery of the laws by which they are governed, the actuary depends for the application of the theories of probabilities to the many useful purposes for which they may be rendered available.

‘Suppose a man becomes ill, gets worse and dies. His death is instantaneous but the cause of his death—deterioration of health—may have been progressing for some time. Death takes place because his health has deteriorated beyond a certain limit.’ So wrote C. D. Rich (1940) in introducing his ‘General theory of mortality’ which can also be regarded as a theory of sickness, although Rich does not develop this aspect of it. The point in the gradual deterioration of health at which death takes place is unmistakable but the point at which sickness begins is hazy and ill defined, as also is the point at which recovery from sickness takes place when health is improving. As Stocks (1949) says ‘The distinction between the living and the dead is clear cut, but no such frontier line between sickness and health can be said to exist except in the case of acute illness caused immediately and directly by an external agent. There is a zone between the two states in which the decision whether the subject is sick or not depends on definitions or standards of good health and also on who decides.’