The Contemplation of the Mortality of Mankind, has besides the Moral, its Physical and Political Uses, both which have been some years since most judiciously considered by the curious Sir William Petty, in his Natural and Political Observations on the Bills of Mortality of London, owned by Captain John Graunt. And since in a like Treatise on the Bills of Mortality of Dublin. But the Deduction from those Bills of Mortality seemed even to their Authors to be defective: First, In that the Number of the People was wanting. Secondly, That the Ages of the People dying was not to be had. And Lastly, That both London and Dublin by reason of the great and casual Accession of Strangers who die therein, (as appeared in both, by the great Excess of the Funerals above the Births) rendred them incapable of being Standards for this purpose; which requires, if it were possible, that the People we treat of should not at all be changed, but die where they were born, without any Adventitious Increase from Abroad, or Decay by Migration elsewhere.

In looking over some papers of the late Francis Baily, at the request of his sister, for the purpose of advising on their disposal, I found in one packet a number of letters addressed to him by the late George Barrett, the inventor (in this country) of the method for calculating life contingencies which now goes by his name. I also found the manuscripts of Baily’s three works—on leases, on interest, and on life assurances: these are now in their proper place, the library of the Institute of Actuaries.

From Baily’s methodical habit of arranging his papers, I feel confident that the letters alluded to are all which he received from Barrett: unless, indeed, some passed which he preferred not to preserve. The interest with which actuaries look upon the method published in these letters makes me think it desirable to give some account of them in a work which all actuaries consult.

Projections of future mortality typically used for funding pension scheme liabilities assume that future year-on-year decreases in mortality rates will slow rapidly, and that there is very limited potential for further decreases at the oldest ages. This paper considers the consistency of such projections with current trends in life expectancy. Particular focus is paid to whether future mortality should be subject to a minimum level of improvement to reflect general advances in medicine. Care is taken to exclude the additional increases in longevity arising from a concentration of positive health factors amongst the generation who are currently experiencing the ‘cohort effect’.

If historic trends continue into the future, then period life expectancy from age 65 in England & Wales will increase at 26 days p.a. for women and 41 days p.a. for men, with additional increases arising from the ‘cohort effect’. This is a faster rate of period increase in life expectancy than embedded in the interim cohort projections. One way to ensure that actuarial projections keep pace with the population trend is to subject projections to a minimum level of (geometric) improvement of at least 11/4% p.a. for men and 3/4% p.a. for women, at all older ages and in all future years.

Consideration is given to the possible impact of differences between the socio-economic profile of England & Wales and the membership of the pension schemes to whom the projections will be applied ultimately. This paper also highlights that the application of a single minimum value, independent of time and age, simplifies a more complex underlying pattern, but that minimum improvements of 11/4% p.a. for males and 3/4% p.a. for females represent an average of historic improvements in mortality seen in England & Wales.

The paper includes a survey of the history of the low levels of mortality seen currently. The survey includes some discussion on the potential for future improvements and considers topical issues, such as the potential impact of obesity on life expectancy projections (and, in turn, the minimum value applied to improvements).

The financial impact of subjecting projections of mortality improvement to a minimum value is quantified.

The International Accounting Standards Board is undertaking a project to develop an Accounting Standard for Insurance. The basis for these proposals is that assets and liabilities should be shown at fair values (market values for quoted instruments). This is an updated version of a paper, prepared by a Working Party established by the General Insurance Research Organisation (GIRO) of the General Insurance Board of the actuarial profession of the United Kingdom, which was first presented to the GIRO Conference in October 2002. This paper summarises and comments upon the principal features of the proposals as they have emerged up to February 2003. The paper considers the implications for general insurance companies of these proposals. In particular, it examines the concept of market value margins, and the practical issues that insurance companies are likely to encounter in implementing them. The emphasis of the paper is on reporting for general insurance business, although many of the principles apply equally to life assurance.

The discussion on Maturity Guarantees, as applied to unit linked life assurance policies, has followed two quite distinct paths—the conventional or mainstream approach, as exemplified by Benjamin (1976) and endorsed by the Maturity Guarantees Working Party (MGWP 1980) on the one hand, and those who seek to reduce the risks associated with maturity guarantees by using an immunization strategy on the other (Brennan & Schwartz, 1976).

This Working Party has considered the pensions implications of a prolonged period of low inflation. Experience in the United States of America suggests weaker correlation between equity and bond returns and greater overall volatility of returns. Without a further significant increase in the valuation of equities relative to their underlying economic activity, the cost of pensions will rise, possibly as much as doubling within the next 15 years. It follows that for defined contribution schemes and personal pensions, current contribution levels are likely to produce disappointing and generally inadequate results. Similarly, the costs of defined benefit promises will increase. Future defined benefit provision is also vulnerable to the mismatch of mainly equity assets with mainly fixed liabilities and is therefore difficult to control. Many practical issues of scheme design still reflect past inflation and need to be addressed.

A brief description is given of some problems encountered in designing a model office program. The key to an effective and flexible model lies in the structure which the model imposes on the data. An example of a model used for research is described.

The general pattern of mortality in England and Wales in the present century is well known. Mortality rates have fallen steadily, the proportionate improvement decreasing with increasing age, and being greater for females than males. The position at the oldest ages is less clear; the published figures are not conclusive as to whether mortality over age 90 is constant, increasing or decreasing.

The experiments described in this paper arose from some calculations made in connexion with the recent discussion on the mortality of life-office annuitants (J.I.A. lxxviii, 27) and are a natural development of the principles described in the paper submitted to the Centenary Assembly of the Institute (Proceedings, 11, 89). They fall into two groups. Those in the first, arising from an attempt to find an alternative method on which to base projections, have an affinity with those set out by Starke in his recent paper (J.I.A. lxxviii, 171), in that a formula for expressing mortality is derived essentially dependent on year of birth. There are, however, fundamental differences between the approaches, in that Starke is concerned mainly with an ad hoc expression for a derived function of qx without regard to the problem of computing functions, whereas the present experiments are concerned with (i) further developing actuarial technique based on the curve of deaths rather than on rates of mortality, and (ii) the calculation of actuarial functions without recourse to the usual methods of commutation columns. The second group of experiments is an extension of the gamma-function technique to the calculation of joint-life functions, including contingent assurances.

The question of the premiums which should be charged to meet the eases of lives proposed for assurance admittedly incurring, or about to incur, risks more hazardous than those of the ordinary assured life, has from time to time engaged the attention of the Institute.

More stress has, perhaps, been laid upon the mortality of persons living in tropical countries, where the conditions of life are very different from those to which we are here accustomed, and statistics, obtained either from official sources or from business experience, have been furnished; whilst the only occupations to which attention has been directed are the Naval, Military, and Mercantile Marine Services, and those connected with the sale of alcohol.

With the view of obtaining, if possible, information respecting the modern practice of Life Assurance in connection with extra risks, I ventured to address to all the larger offices a Schedule intended to elicit such replies as would enable me to present a general idea of the methods applied to these cases.

In this I hope I have partially succeeded, but I need not add that the information must be regarded in a very general light. Many offices were particular to point out that, in the absence of any ascertained experience, each case of this nature would be considered upon its individual merits, and rated accordingly.

Most of the activity of actuaries with computers to date has been concerned with putting actuarial work on to computers, or—at one stage further back—putting life office data on to a computer data-processing system. This paper attempts to contemplate the next stage, the effect of computer knowledge and familiarity on the profession and its techniques.

1.1. The aim of this paper is to initiate a discussion between actuaries, accountants, the Department of Trade and others working in insurance on our basic concepts, language, methods and aims. We need to discuss concepts and to agree on language in order to be able to discuss methods and aims. The concepts and language developed by actuaries in life business are very different from those used in non-life insurance and a synthesis of the two is long overdue.

An observer of the United Kingdom financial services scene over the last few years will have noticed the rising numbers of closed with-profits funds and final salary schemes closed to new entrants. Closed funds were not previously unheard of, but until recently most life insurance and pensions actuaries would not have come across them in their daily work.

There can be no doubt that, when compared to open funds, the closed variety have different characteristics and their financial management requires different approaches. Life and pensions actuaries tend to operate in their own separate fields, largely oblivious to what their fellow actuaries in other practice areas are doing. The growth of closed funds gives the two major branches of the U.K. actuarial profession an ideal opportunity to explore what we can learn from each other.

I am very grateful to the authors for tackling this subject on behalf of the profession and hope that it will be the first of many examples of useful cross-fertilisation of ideas.

Compound interest was known to ancient civilisations, but as far as we know it was not until medieval times that mathematicians started to analyse it in order to show how invested sums could mount up and how much should be paid for annuities. Starting with Fibonacci in 1202 A.D., techniques were developed which could produce accurate solutions to practical problems but involved a great deal of laborious arithmetic. Compound interest tables could simplify the work but few have come down to us from that period. Soon after 1500, the availability of printed books enabled knowledge of the mathematical techniques to spread, and legal restrictions on charging interest were relaxed. Later that century, two mathematicians, Trenchant and Stevin, published compound interest tables for the first time. In 1613, Witt published more tables and demonstrated how they could be used to solve many practical problems quite easily. Towards the end of the 17th century, interest calculations were combined with age-dependent survival rates to evaluate life annuities, and actuarial science was created.

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.

1.1 In recent years, the United Kingdom members of the actuarial profession have become increasingly involved in the general insurance industry and therefore the Institute decided that the subject of general insurance should be included in its syllabus from 1977.

1.2 Prior to 1977 there were a number of papers and articles, written for either the General Insurance Study Group or the Research Committee, on various subjects related to general insurance. These papers and articles have not always had a wide circulation, although they have been deposited in the library at Staple Inn.

1.3 Most of these papers were of an explanatory or technical nature. In the authors' opinion, the actuary has a much wider rôle in general insurance than the technical one of estimating the liabilities of claims. In fact, the actuary should be able to provide a blue-print or framework for the financial management of a general insurance company.

1.4 A general insurance company is a financial concern; therefore the actuarial profession should have a rôle to play. In describing the financial concern, the actuary is required to chart the waters linking profitability, solvency, growth, reserving basis, dividend policy and capital requirements. As the second half of this paper will show, these items are inter-linked and decisions on one should not be taken in isolation as they will have repercussions on one or more of the other items.

1.1 The actuarial profession has for decades, indeed centuries, used age-related tables, particularly (although not exclusively) of mortality, which in preparation have been subjected to the process known as graduation. Five purposes of such graduation have recently been set out by Vallin, Pollard and Heligman and these may be summarized as follows:

(1) to smooth the data, make them easier to handle, remove irregularities and inconsistencies;

(2) to make the result more precise on the reasonable assumption that the real mortality underlying the observations is a smooth curve, i.e. to remove sampling and other errors;

(3) to aid inferences from incomplete data;

(4) to facilitate comparisons of mortality;

(5) to aid forecasting.

Of these purposes, (1), (2) and (3) may all be paraphrazed as implying that the purposes are to make the table smooth, and (4) and (5) as indicating uses to which a table may better be put if smoothed. So the purposes of what the profession has come to term ‘graduation’ all boil down to the production of a smooth table, and for the rest of this paper until the last section I shall use the word ‘smoothing’ rather than ‘graduation’. But what is smooth?

The paper compares and contrasts the theories and methodologies of financial economics with generalisations drawn from practical experience of institutional investment management. A Dynamic Equilibrium Model is put forward as a much more realistic theoretical framework than the Sharpe Diagonal Model, a downside theory of risk is developed from sports analogies, and a detailed model of human behaviour, incorporating benchmark levels of ‘unintelligent’, ‘intelligent’, ‘optimal’ and ‘rational’ behaviour, is suggested as a replacement for the very restrictive simplifying assumptions of existing theories. On the basis of a classification system derived from parallels with the history of astronomy, it is concluded that, as a scientific framework, the current theories of financial economics are seriously incomplete, the two crucial areas of incompleteness being the absence of a downside theory of risk and the absence of a realistic model of human behaviour under conditions of risk and uncertainty.

This paper investigates the recalculation from its base date of the Financial Times Index of Industrial Ordinary Shares (hereafter called the FT Index) using the ordinary arithmetic mean of the values of its constituents, rather than the geometric mean that is actually used in its calculation. The value of this arithmetic version of the FT Index represents that of a portfolio invested equally in each of the original constituents at the base date. The behaviour of the recalculated index may therefore be described in portfolio terms.

The arithmeticized index has been calculated at each end-year since the base date of the FT Index (1 July 1935). By the end of 1970 its value was 38% higher than that of the (geometric) FT Index. The percentage by which the new index exceeded the original was found to have increased approximately linearly with time; a least-squares linear fit over the whole period indicated that the percentage excess of the arithmetic version over the original index had increased on average by 0·8% a year. A separate fit for the period from end-1960 onwards shows that this rate had increased to 2·7% per year, and even over the period since 1950, it has been 1·1% per year. Use of these relationships gives a rough adjustment of the FT Index for portfolio comparison purposes.

We also calculated a series of arithmetic indices with base dates at the end of each year since the original base date of the FT Index. In the majority of calendar years since its foundation, the FT Index has not fallen far behind the corresponding arithmetic version over the twelve month period. However, over periods of more than a year, the geometric and arithmetic indices can show dramatically different results, particularly if the percentage change in the index value is considered. It is clear that longer-term changes in the value of the FT Index cannot be interpreted as the changes that would have occurred in the value of a portfolio equally invested in the thirty constituent shares at the beginning of the period.

None of these findings affects the usefulness of the FT Index for its original purpose, as a sensitive daily indicator of changes in the industrial ordinary share market. It is purely its long-run use as a portfolio standard that is misleading. For this purpose the more recently instituted arithmetic indices are likely to be useful in the future. Meanwhile, our arithmeticized FT Index values may be useful to correct the downward drift imposed on the FT Index by its geometric construction.