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.

The problem of finding the rate of interest corresponding to a given annuity-value, has engaged considerable attention at various times; and many formulas have been proposed for obtaining approximate solutions by the aid of existing tables of annuities. Most of these will be found in Mr. Sutton's paper on the Rate of Interest yielded by Foreign Loans (J.I.A., xix, 77). Of the 5 formulas there given, (2) is probably the most generally useful, (3), (4), and especially (5) (Prof. De Morgan's formula), involving a good deal of calculation. The object of the present short paper is to suggest 2 new formulas, which give very accurate results, and at the same time require but little work in their practical application.

Let a be the value of an annuity for n years certain, at a rate of interest i, (which it is required to find), and let a1, a2, a3, be the tabulated annuity-values for the same term at the rates i1, i1 + h, i1 + 2h, where a lies between a1 and a2, and consequently i between i1 and i1 + h.

This is the preamble to the petition presented to the Secretary of State's office of the British Parliament in April 1757 by the promoters of ‘The Corporation for Equitable Assurances on Lives’, the seed from which modern life insurance has sprung. It is undoubtedly the clearest statement made as to the purpose and justification of the life insurance industry and stands as a challenge to those engaged in it.

The influence that occupation has upon health is a subject that has hitherto attracted but little attention, for though in the works of one or two writers on vital statistics it has been slightly alluded to, no work has yet appeared which, while founded on direct observation, has been devoted to the treatment of this subject.

Until within a very recent period the doctrines of probability have been applied to scarcely any great public purpose except the Assurance of human life. In that particular department of knowledge, a number of labourers have been for many years busily occupied in gathering the facts, endeavouring to classify events, and trace some general laws. In later years, researches have been extended into the effects of different classes of diseases upon health and longevity. Still more recently, the calculations of fidelity risks, of railway and other accidents, of bankruptcy, and of other circumstances affecting the person of an individual, or his commercial dealings, have been made with a view of proving their capability of being estimated for Insurance.

It has been remarked on many occasions that whilst there is a plethora of material which has been contributed to the Institute and the Students' Society on the actuarial valuation of liabilities, the subject of valuation of assets seems to have been consistently overlooked by all save one or two authors. We believe that a compelling reason for this apparent indifference to the subject may be found in the trend of interest rates within the experience of the actuaries who introduced the valuation techniques which a student may now tend to take for granted.

Consider Table 1, compiled from information given in a paper by C. M. Douglas, F.F.A., on ‘The Statistical Groundwork of Investment Policy’. During the period 1833–1912 the average annual rate neither exceeded £3. 11s. od.% nor fell below £2. 9s od.%, and in general the yield drifted slowly downwards.

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.

The third Lecturer to the Faculty of Actuaries is Mr Karel Van Hulle. He is a lawyer by training, and is Head of Unit at the European Commission (Directorate-General ‘Internal Market and Services’), which he joined in 1984, after having served for eight years with the Belgian Banking Commission.

He was subsequently Head of Unit for Accounting Standards, Head of Unit for Financial Reporting and Company Law and Head of Unit for Accounting and Auditing. In that capacity he was closely involved with harmonisation in the fields of accounting, auditing and company law, both at European Union level and internationally, and served as the Commission's observer with the International Accounting Standards Committee. He was Secretary of the High Level Group of Experts on Company Law, which prepared the Commission's 2003 Action Plan on Company Law.

Since November 2004 he has been Head of the Insurance and Pensions Unit. In this function, his main responsibility is the preparation of the new solvency regime for insurance and reinsurance companies (Solvency II).

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.

In October 1900, on the morning of the first day of the autumnal meeting of the Actuarial Society of America, Mr. Emory McClintock, Actuary of the Mutual Life Insurance Company of New York, read a paper entitled “The Objects to be attained in Future Investigations of Mortality and Death Loss”, in which he stated that probably four-fifths of the publications of companies' general experience possessed only a “casual interest”, and that the same amount of effort might much better have been devoted to investigating special classes of business, adding that “it is “more important to the future interests of life insurance to learn “how fishermen compare with farmers, how physicians compare “with clergymen, and the like, than it is to gather all these “heterogeneous materials into one grand average in the form of “a new life table.”

1.1. The concept of matching assets and liabilities has for many years been recognized as a crucial aspect of our professional work. Its importance is emphasized in the Institute's guidance notes entitled “Actuaries and Long-Term Insurance Business” and in many papers published in the Journal.

1.2. A particular form of matching, namely immunization, was developed by F. M. Redington in his paper “Review of the Principles of Life-Office Valuations” (J.I.A. 78, 286). Immunization signifies the investment of assets in such a way that the existing business is immune to a change in the rate of interest. One of the consequences of immunization is that the mean term of the asset-maturity dates is appreciably longer than the mean term of the value of the asset-proceeds and of the liability-outgo; and, at other than low rates of interest, a perpetuity can be too short to immunize a long-term contractual liability.