In his paper of 1941, Seal included details of some experiments he performed in an attempt to estimate the appropriate number of degrees of freedom for the chi-square goodness-of-fit test of a summation formula graduation. These results are referred to by Tetley and by Benjamin and Haycocks in their textbooks when they mention the difficulty of determining the number of degrees of freedom or mean chi-square value.

Prior to the commencement of the present century, no direct method had been adopted to ascertain the number of the population in England. Various estimates, founded upon Domesday Books, Subsidy Rolls, and payments of Hearth and Poll taxes furnish, with more or less exactness, the numbers at previous periods. Three such calculations relating to the population towards the close of the 17th century are mentioned by Macaulay as being entitled to peculiar attention. “Of these computations one was made in the year 1696 by Gregory King, Lancaster Herald, a political arithmetician of great acuteness and judgment. The basis of his calculations was the number of houses returned in 1690 by the officers who made the last collection of hearth money. The conclusion at which he arrived was that the population of England was nearly five millions and a half. About the same time, King William the Third was desirous to ascertain the comparative strength of the religious sects into which the community was divided. According to the reports laid before him from all the dioceses of the realm, the number of his English subjects must have been about 5,200,000. Lastly, in our own days, Mr. Finlaison, an actuary of eminent still, subjected the parochial registers to all the tests which the modern improvements in statistical science enabled him to apply. His opinion was, that, at the close of the seventeenth century, the population of England was a little under 5,200,000 souls. … We may, therefore, with confidence pronounce that, when James the Second reigned, England contained between five million and five million five hundred thousand inhabitants.”

Towards the end of Mr. Brown's term of office as President I submitted to him the Table which appears in the appendix to this paper asking whether he thought it of sufficient interest for publication in our Transactions. Mr. Brown replied by inviting me to go further and write a paper for the Faculty on the subject of Investments using the Table as an illustration of past history. Later our present President supported this idea and the notes which I now have the honour to submit are the outcome. Apart from the fact that I dealt with the history of Life Offices' Investments at some length when addressing the Students' Society a few years ago, it seemed to me that something more than a historical survey was desirable. There are few papers in our Transactions dealing with Investment Policy and this was the subject on which I decided. I think that the correct prelude to a discussion of Investment Policy is its own history, and so I give in Part I of this paper a very short general survey of the years from 1871 to 1935. The Table in the appendix will give information additional to what is contained in my remarks to those who wish to go further.

The focus of this paper is the identification, and more importantly, sustainable management, of risks embedded in guarantees attaching to unit linked savings and retirement contracts (as commonly referred to as GMxBs). In developing customer centric guarantees that are not readily transferrable to the capital markets, insurance undertakings require the skills and resources to hedge the guarantees within their own balance sheet (or with a temporary use of packaged solutions such as reinsurance). In taking on the guarantee manufacture task insurers are departing from areas of historic competence and need to develop a comprehensive understanding of all elements of market risk replication. These include both first order market exposures as well as the material second order risks associated with market micro structure. The paper seeks to integrate this comprehensive analysis within a practitioner focused framework and concludes with a senior executive summary of “Seven key considerations in successful guarantee manufacture”.

This paper considers equity, or fairness, as being based on with-profits life insurers acting in accordance with their contracts. It uses the principles of with-profits business in conjunction with a legal approach to derive implied terms in with-profits contracts. The author examines certain situations of conflict between with-profits policyholders and shareholders. The paper does not regard all concerns put forward on behalf of policyholders’ interests as justified in practice: actuaries and regulators have been alert to issues and in many cases have taken appropriate action. However, it does suggest a number of practices that may be unfair. The paper also suggests that the current process for the reattribution of an inherited estate may favour shareholder interests over policyholder interests.

This paper considers the variety of social security and complementary pension scheme arrangements which have developed in different countries, and examines some recent trends in pension reforms, designed to address the problem of the ageing population and other structural shortcomings in existing structures.

Mr. President and gentlemen, I should like to express my pleasure at being back in the Faculty Hall, where I was privileged to listen to your interesting discussion last year on “The Growth of Pension Rights”. I am glad to find that the number of occasions on which economists and actuaries are not only on speaking terms but able to take counsel of one another is increasing, for I am sure that there are many problems, of which the future of pensions is only one, that can only be satisfactorily resolved through our joint efforts and deliberations. This conviction rests partly on my experience as a member of the Phillips Committee, which was heavily dependent both on the actuaries who served on it and on the members of the profession who, in one way or another, helped it along; but it is a conviction that is just as forcibly brought home to me when I look across the Atlantic to the inquiry that has been in progress since 1950 into the long-term trends in savings and investment in the United States—an inquiry carried out by economists but sponsored and largely financed by the Life Assurance Association of America.

In the Introduction to his famous Théorie Analytique des Probabilités, Laplace, after an eloquent summary of the progress of Astronomy from the days when every rare celestial phenomenon was regarded as a portent of human misery, to the verification in April 1759 of the perihelion passage of Halley's Comet, proceeds to say :—

“The regularity which Astronomy shows us in the movement of Comets exists, beyond doubt, in every phenomenon of nature. The curve described by a simple molecule of air or of vapour is regulated in a manner as certain as the planetary orbits: there is no difference between the two cases save our ignorance.

In the course of some recent work (cf. reference 2) it proved necessary to construct a life table from a set of graduated values of mx, the central death rate at exact age x. This meant that values of qx had to be derived in order to produce the life table from a given radix. Since the values of mx were known only for integer values of x, it was necessary to use an approximate method to derive the corresponding values of qx at each age. In this note we discuss briefly the approximations which we adopted. Our results are necessarily of an elementary nature and the principal reason for setting them down is to provide a reference for possible future use. It is perhaps worth pointing out that in a situation where the values of mx are given by an explicit mathematical formula values of qx may be obtained exactly using the results of reference 1.

The Paper discusses the general problem of appreciation and depreciation, with special reference to the relation between maturing assets and maturing liabilities, and describes a method of calculating the bonus-earning power of different classes of policy. This method is used to test the effect on bonus-earning power of two types of changes in interest rates:–

1. (a) a change, such as that caused by the War Loan conversion of 1932, which takes effect gradually; and

2. (b) a subsequent change, due to a rise in the rate of income tax, which has an immediate effect on the income from existing as well as investments.

Written concurrently with the first item in C.M.I.R.3, the Faculty of Actuaries Mortality Research Group's paper determines a range within which mortality rates of Life Office Pensioners may be expected to change in the foreseeable future. Comparisons are made between the observed changes in pensioner mortality rates and those observed for the population of England and Wales, and reference is also made to the trends of mortality rates assumed in recent British population projections. From these considerations two forecasts are made, based upon “optimistic” and “pessimistic” future mortality assumptions, between which it is expected the actual future rates of mortality change will lie.

In the second part of the paper the financial effects of the range of forecasts are set out, when used to project the graduated pensioner Mortality Experience 1967-70 (C.M.I.R., 2, 57). The implications are illustrated in the context of two model funds, one based upon life offices' data, and the other based upon a non-insured pension scheme for which the contribution rates vary in accordance with the levels of future expected pensioner mortality.