1.1 The background to the production of this paper is somewhat involved, but is necessary for an understanding of why it contains what it does. Readers who are familiar with recent developments in the valuation field may proceed straight to Section 2.

1.2 Statutory valuations of long-term insurance business under the Insurance Companies Act 1982 (‘the Act’, which superseded the 1974 and 1981 Acts) and the Insurance Companies Regulations 1981 (‘the current Regulations’) have now been prepared by actuaries for some years. Similarly the guidance issued by the profession to Appointed Actuaries, specifically GN1 and GN8, has also remained substantially unchanged over that period. The time was opportune for valuation practice to be reviewed in the light of recent experience.

The President (Mr M.H. Field, C.B.E.): Tonight we have a double event and so commemorate the names of two distinguished actuaries: John Finlaison, our first President from 1848 to 1860; and Sir Alfred Watson, the first Government Actuary and our President from 1920 to 1922.

In 1985 the Council reviewed the procedures for awarding medals and decided to widen the eligibility of the old Silver Medal and to change its designation to a renamed Finlaison Medal. The Finlaison Medal may be awarded “in recognition of service to the Actuarial Profession in furtherance of one or more of the various objects as set out in the Royal Charter”.

In the course of work undertaken as members of the Executive Committee of the Continuous Mortality Investigation Bureau in the preparation of graduated tables of mortality for the experiences of 1979–82, we have had occasion to make use of and develop a number of statistical techniques with which actuaries may not be familiar, and which are not fully discussed in the current textbook by Benjamin & Pollard (1980), though some of them have been referred to in previous papers by the CMI Committee (1974, 1976). We therefore felt that it would be useful to the profession if we were to present these methods comprehensively in one paper. We do this with the permission of the other members of the CMI Committee, who do not, however, take responsibility for what follows, whether good or bad.

1.1 There are three starting points for this paper. The first is Marshall Field's challenging Presidential Address to the Institute of Actuaries in 1986 on the subject of ‘Risk and Expectation’. The second is the example, still fresh in our minds, of a medium-sized mutual life office which overstretched itself and found it necessary to merge with a competitor. The third is the impending requirement, stemming from the Financial Services Act 1986, to give an investment client, including the holder or prospective holder of an insurance savings contract, what is described as ‘best advice’.

1.1 In recent years insurance companies have begun to employ marketing techniques in search of greater success in an increasingly competitive market place. Several companies have Marketing Departments. However, those who have used marketing techniques most efficiently are not necessarily those with the largest departments.

It is a privilege, Mr President, to be invited to lecture to your Institute, especially in commemoration of Alfred Watson who did so much to establish the firm foundations of your profession. These are of such detail and intricacy that you remain elite and hardly subject to the kind of challenges which more and more affect other professions. Perhaps your time will come as mutterings are heard about your valuations of pension funds and to whom they belong.

The subject of this lecture tonight is the way in which risk has forced itself to the front of public discussion and finds the expression in comment almost every day, whether on the issue of vaccine damage to children, medical negligence, the Chernobyl disaster, landslides in Colombia or floods in Bangladesh.

This paper has the strictly practical objective of devising procedures for managing Equity portfolios to the best advantage.

First, Modern Portfolio Theory, (MPT) which has been developed over the last 35 years with just this objective, is critically examined; from a study of the history of MPT and of its philosophy, principles and practices, the authors conclude that this discipline makes no contribution whatever to improving the performance.

The Index Fund step-up is a sterile concept. Surely a professional investment manager, using modern techniques of data banks, investment analysis, etc. should improve on the Index performance. This objective is in conflict with the Perfect Market Principle. For the less erudite investors, who are, of course, in the majority, the Perfect Market Principle may well apply, at any rate, to the well researched leading shares. However, the Perfect Market Principle should not apply to the erudite, professional investor, well equipped and well advised, who should be able to find many opportunities for situations with undervalued and overvalued shares, both among the leading issues and particularly within the smaller companies that get less research attention.

The Decennial Supplement on Occupational Mortality published in 1978 commented on mortality differences between the social classes (Chapter 8) using data from the 1971 Census and the deaths in the period 1970–72. The analysis was based on life tables prepared for the individual social classes from which derived indices, for example expectations of life, were calculated. It is proposed here to repeat this exercise using the data for males recently published in microfiche form by the Office of Population Censuses and Surveys—OPCS. This time, the Decennial Supplement has omitted to provide an analysis and commentary and we propose to make some attempt to remedy this deficiency. In our analysis, the Decennial Supplement data have been supplemented by data from the OPCS Longitudinal Study.

1.1 Medical expenses insurance, as we know it today, has been available in the United Kingdom since the late 1940s. In recent years the market has increased significantly to a point where we estimate approximately 6m people are now covered by medical expenses insurance, which represents over 10% of the population. Furthermore, there is evidence that the market is continuing to expand.

By courtesy of Robin Michaelson, data derived from a United States of America life insurance experience (1970–75) for individually insured lives was made available. The data consisted of the proportions of smokers in the population and the ratio of smokers' mortality to that of non-smokers. In both cases separate data was collected for males and females and at integral ages from 15 to 84. From these data it was possible to construct separate life tables for smokers and non-smokers, which were subdivided for males and females. These tables are shown as Tables A–D at the end of this note.

A common method of measuring relative mortality experience in actuarial, demographic and epidemiological studies is by way of comparison of the actual number of deaths and the number expected if a given standard experience were applicable. The properties of this method are discussed. Further ways of making such a comparison are described, one of which (the widely used Cumulative Mortality Ratio) has a serious bias in application to follow-up mortality studies. The properties of an alternative approach, the Ratio of Geometric Average Death Rates (RAD), are also discussed. This extends the analysis published in 1982 by the author, although attention is focused here on ratios that measure relative mortality experience.

1. With reference to the Actuarial Note by Messrs Hathaway, Rickard & Woods (HR&W) J.I.A.113, 509–520 there is a simpler way, which is much easier to calculate, of approximating from the gross yield to redemption to the net yield, with taxation on the basis assumed by HR&W.

It is now some sixteen years since Sir David Cox (1972) published his epoch making paper in which he incorporated regression type arguments into life-table analysis. Central to the method was the introduction of the multiplicative hazard

with vector of covariates z, unknown regression parameters β, and so-called base-line hazard λ*(t) = λ (t, 0). Applications of the method, based on the conditional likelihood argument expounded by Cox in which the base-line hazard λ* is unknown, have proliferated in the intervening years, largely in the field of medical statistics. There have been relatively few applications in which the base-line hazard is assumed known at the outset. Specific cases include Breslow et al. (1983), Berry (1983) and Hill et al. (1985).

This paper proposes a simple model for studying the variability of contribution rates and fund levels, when rates of return are random. The funding methods considered are those which (1) produce an actuarial liability (AL) and a normal cost (NC), and which (2) adjust the latter by a constant fraction ‘k’ of the difference between AL and the actual fund (this discrepancy is known as the ‘unfunded liability’; for a description of actuarial cost methods the reader is referred to Trowbridge (1952), Winklevoss (1977) or Turner et al. (1984)). Thus at every valuation date

total contribution = normal cost + k × (unfunded liability).

In 1953 together with a colleague (Benjamin and Logan) the author called attention to a paper by Haenzel (1950) describing a new index of mortality years of life lost.

The argument was that many people were living for more than the three score and ten years and that every earlier death represented a loss of potential further years of life; that adding up the total years of life lost might be a significant measure of the toll of largely preventable disease; that changes in this total year by year would maximize the improvement gained by curative and especially preventative medicine.

When two or more independent or component loans are consolidated to form a single composite loan the result is often referred to as a cocktail loan. In this paper we analyse properties of a composite loan induced by properties of the component loans. Of particular interest are the properties of the composite yield in terms of the yields and other characteristics of the component loans. Some upper and lower bounds are also established for the composite yield in terms of the component yields. Of some importance is a sensitivity analysis of the composite yield with respect to various parameters of the component loans.

1.1 The publication last year of the English Life Table No. 14 enables my earlier paper (Daw, 1982) to be extended to include the latest table. This paper applied Redington and Michaelson's rx test to E.L.T. Nos. 8 to 13 and the corresponding figures for E.L.T. No. 14 have now been calculated. The Government Actuary's Department kindly supplied me with the unpublished exposed to risk figures which were used.