This note continues a regular series on mortality rates in the United Kingdom. Mortality experienced in each of the years 1994 to 1998 is shown by five-year age groups, and comparisons are made for broad age groups, on a standardised basis, with mortality in earlier years.

Ever since as a student I noted the remarks of a reviewer in the Journal tracing the effects of the Boer War in one of the English Life Tables, I have regarded the population mortality tables of a country as reflecting its political and social life. It is from this viewpoint that the mortality tables of England and the United States of America are examined. The subject of international comparisons is one fraught with difficulty, and in the following paper I have ever held before me William Farr's dictum at the head of this paper.

This paper stems from a suggestion that it would be worth while to bring to the notice of the profession the progress which has been made and the statistical problems that have arisen in the study of epidemiology in its wider sense, viz. the study, not merely of the spread of communicable disease as was formerly implied by this term, but of the natural history of disease; its prevalence, causation, symptomology and prognosis. It would, however, require a series of papers to cover so wide a field and would demand medical as well as statistical competence. It therefore seemed advisable to use the more restrictive title chosen in order to emphasize the fact that, in the main, consideration is devoted to statistical rather than to clinical aspects.

Amongst the disadvantages of the net premium method of valuation are the following: (1) In its application to policies participating under the uniform reversionary bonus plan, the reserve for future bonuses is, in part, secured by the use of a rate of interest remote from the experienced rate.

During the last few years the minds of medical men and of the general public have been exercised over the rapid and striking increase in the mortality from cancer, as shown by the statistics contained in the Registrar-General's Annual Reports. The following table, taken from these reports, shows how great this increase in registered mortality has been. The registered death-rate of males from this disease was 2·7 times, for females 2·0 times, and for both sexes together 2·2 times, as high in 1891 as in the average for the decade 1851-60.

The burden of legislation upon authorized insurers in the U.K. continues to grow and this is particularly true for the statutory valuation. In recent years regulations have been introduced to cover such matters as the valuation rates of interest, the provision for changes in investment conditions and the setting up of solvency margins.

The purpose of this paper is to summarize some of the more important aspects of the Regulations and comment upon their interpretation with reference to current practice. A substantial part of the paper is concerned with the provision for changes in investment conditions. Some implications for financial control and product pricing are also mentioned.

The paper will concentrate on the valuation of liabilities and is written in the context of assets taken in accordance with the asset valuation regulations, that is to say broadly at market value. Most of the paper is addressed to conventional business but a few comments on linked business are included. The material is discussed under various headings but is so interdependent that it is difficult to concentrate on one aspect without impinging on several others.

By courtesy of the Government Actuary, the preliminary data relating to the proposed English Life Tables (No. 14) were made available to the author. In this paper we describe briefly the graduation of the underlying crude mortality rates by cubic splines and give an outline of the salient features of the graduations finally adopted. Complete details of the English Life Tables are given in reference 1, which also includes historical comparisons.

1.1 The traditional approach to examining the financial status of a company is to look at the balance sheet and the profit and loss account. Such information is usually publicly available, it is certified by the auditors as having been drawn up according to relevant accounting standards and it is generally presumed to communicate reliable information.

1.2 In the case of a manufacturing or trading company the profit and loss account records purchases and sales and the balance sheet will include a valuation of stock in hand, since it is anticipated that this will give rise to future sales income. Working capital is required because products have to be manufactured or purchased before they can be sold. Profit is realized when the product is sold for more than it cost to buy it or to make it.

At so striking an epoch in the history of our times as the Jubilee of our Most Gracious Queen, it seems natural that those who are engaged in any special branch of trade, or commerce, or science, should look back with interest at the records of the progress of that branch during the period then completed; and I therefore venture to hope that the particulars which I have collected regarding the progress of Life Assurance Business in the United Kingdom during the last half-century, and which I propose to lay before you this evening, may prove in some degree interesting to you.

Before submitting to you these particulars, I think it may be useful if I refer for a few minutes to the condition of the United Kingdom in 1837, and to the changes which have occurred since then in matters which have had an important, though indirect, bearing on Life Assurance Business.

The study of methods of measurement of the rate of population growth is one of the most fundamental aspects of demographic science and one which, from its nature, should be of particular interest to the actuarial profession. It is therefore fitting that this paper should be devoted to a discussion of this side of the subject, particularly in view of the importance which the analysis of population trends has assumed in modern times as the result of the decline in birth-rates experienced by this country in common with most of the leading civilized nations.

Leaving out of account losses and gains by migration, the future development of a given population is determined by the numbers of children that people have, the proportions of these who survive and the sizes of the families which they have in their turn, the cycle continuing indefinitely. Whilst the consequences of changes in mortality must not be underestimated it is clearly the wide possible range of variation in birth-rates which plays by far the more important part in shaping future population trends. The measurement of population growth therefore rests largely on the analysis of fertility, a subject of considerable complexity.

As the reasonings of the actuary, when extended beyond the mere official routine of a Life Assurance Office, depend upon the proper collection of data relating to population, and the other important elements of the condition and progress of a country, we need make no apology to our readers for presenting to them the following very interesting supplement to the valuable Report of Dr. Farr on the Statistical Congress at Paris in 1855:—

“There are seven great powers in the world.

“England, France, Turkey, and Austria, have existed as great powers for several centuries. Prussia, Russia, and the United States of America, have entered this class within the last hundred years.

I. Equity-linked contracts have been the subject of discussions at the Faculty of Actuaries (J. B. Maclean, T.F.A.23, 327), the Institute of Actuaries Students' Society (R. H. Blunt and L. H. Lane, J.S.S.14, 259) and the Institute of Actuaries (J.I.A.84, 37). The papers delivered and the discussions devoted considerable space to the question of the desirability, from the point of view of both the industry and the public, of the issue of such contracts.

Since these discussions, several offices have entered the market both for assurances and for ‘self-employed’ annuity contracts, and this paper, recognizing the de facto position, is concerned with practical points arising from the issue of the contracts.

The combination of circumstances, which for generations past has impelled large numbers of our countrymen to establish homes in distant lands, has wrought vast changes on the surface of the globe. The progress and welfare of Englishmen call, from every continent, for our interest and sympathy; and, while there is, probably, no portion of “Great Britain” which usually attracts more lively interest than Australasia, special attention is just now directed to that important member of the British Empire. The richness of its soil, its varying and salubrious climate, embracing those degrees of temperature most conducive to health, and, above all, its immense possibilities for the future, combine to fascinate the mind, and inspire a wish for further knowledge.

A comparison of the population returns of Australia with those of the United Kingdom, presents a contrast as striking as can be found in any department of social science. The area of the continent,—which is estimated to be somewhat under three million square miles,—contained at the end of the year 1882 about 2,296,000 inhabitants. The average number of persons to the square mile in each colony was as follows:—

The paper highlights the role of risk budgeting — how risk is ‘spent’ — in the investment management process and some of the practical issues encountered. Risk budgeting has received a great deal of interest from the investment management community recently, but no clear consensus has emerged on how it should be implemented. In this paper we outline a pragmatic risk budgeting method that can be applied at the portfolio level, and show that it can produce superior results when used in conjunction with cluster analysis techniques. There are practical implications for chief investment officers and chief executive officers on how they allocate human resources and capital in the investment management process.

A statistical factor model for stock returns is used to build a risk model of the market that separates the factor components (representing the market, investment themes and styles) and the stock specific component. Then cluster analysis techniques provide a visualisation of the changing risk structure of the market. Natural groupings of stocks emerge within the market often different to the classical industrial classification systems widely used today. These natural groupings clearly change over time reflecting the changing nature of equity markets, e.g. these techniques show very clearly the emergence of the telecommunications, media, technology phenomenon in the late 1990s and its subsequent demise in early 2001.

Using the framework of a statistical factor model, risk budgets can be aggregated or dis-aggregated. Aggregation can be to country, sector or any other group. Dis-aggregation will be to common factors (e.g. the market, growth, value and other styles) and stock specific factors, derived from a multi-factor model.

1.1 On coming into pensions consultancy after many years in a life office I looked for an indication of current thinking on the valuation of funded pension schemes. Official guidance by the profession is confined to the 1969 booklet from the Institute and Faculty; the memorandum on professional conduct concerns itself with independence and how we present ourselves. The Institute's examination textbooks pass over the main objectives lightly and concentrate on detail. While there have been papers on many aspects of pensions, they all seem to skirt the fundamental principles of valuing final salary schemes.

1.2 This paper attempts to go some way to filling the gap. It provides an opportunity to review and discuss current practice. I have found it particularly illuminating to compare the way in which practice between the United Kingdom and North America diverges.

In the light of recent judgments by the courts, there are areas where the interpretation of Policyholders' Reasonable Expectations (PRE) by actuaries may need to be reassessed. Furthermore, the discussion paper on the exercise of discretion expected from the Financial Services Authority (FSA), as part of its review of with-profits business, is likely to raise wider issues.

The time is therefore right for actuaries to have the opportunity to debate how PRE should be interpreted in the future. This paper is presented as a catalyst to enable that debate to happen, and the authors have set out their own views on some of the key issues.

The paper discusses certain areas where the interpretation of PRE adopted by Appointed Actuaries in the past may no longer be consistent with recent court judgments. Following that discussion, the actuarial profession should attempt to establish a revised interpretation of PRE, in order to provide greater assistance to Appointed Actuaries currently advising on with-profits business.

Mr. George King's recent investigation of the magnitude of the error introduced into certain functions of a mortality table following Makeham's law when these are re-graduated by summation formulas (J.I.A., xli, 54), has again attracted attention to the subject of the graduation of mortality tables, and has recalled the lively controversy which took place some years ago between Dr. Sprague and the late Mr. Woolhouse over the merits and demerits of the methods championed by those distinguished authorities. Not the least interesting contribution to the discussion which followed the reading of Mr. King's paper was furnished by Dr. Sprague himself, who wrote in defence of certain criticisms expressed by him with regard to methods of summation generally and Mr. Woolhouse's formula in particular. Dr. Sprague remarked that he had “objected to Mr. Woolhouse's “formula of graduation,on two grounds, which it has in common “with all other summation formulas; that is to say, (1) because “it does not remove the irregularities of the original series of “facts, but only reduces them, and (2) because it distorts the “law of the facts to a greater or less extent.” He went on to say that the results of his re-graduation of the HM (Text-Book) Table by Woolhouse's formula had led him to the conclusion that the second objection might be disregarded in practice, but that there still remained objection (1), which he considered by far the more important.