The prime purpose of the paper is to present the case for the issue of longterm index-linked stocks by the government and by other borrowers, for the issue of index-linked life assurance and annuity contracts by life offices and for the index-linking of pension scheme benefits, all of which the author believes are possible and would be beneficial to all parties.

Part 1 of the paper uses the methods of statistical time-series analysis to study the way in which inflation has behaved in the U.K. over the long period 1661 to 1980 and over various shorter and more recent periods. While prices were far from static in the period up to 1914 the average change was nevertheless almost nil. However, during the 20th century prices have generally risen and in recent years this rise has accelerated. It is possible that the series has become unstable, and hyperinflation will result. It is certain that no one statistical model can satisfactorily “explain” the movements of prices. Future uncertainty is now very great.

The author concludes from this that index-linking of long-term contracts, i.e. adjusting for price changes after they have occurred, is more satisfactory to both parties to the contract than to guess at a single fixed inflation rate and build that into the contract.

Part 2 discusses the issue of long-term index-linked government stocks. It demonstrates the uncertainty attached to fixed interest borrowing and lending, and the harmful effect on the future PSBR of the government's present funding methods. The author discusses the Wilson Committee's view on index-linking, and supports their suggestions of tax changes to make practicable the issue by companies of index-linked loan stocks. Index-linked house purchase loans are also advocated.

In Part 3 the author presents the advantages to life offices and their policyholders of policies with index-linked premiums and benefits, and discusses some of the complications of such policies, in particular the tax obstructions for certain types of policy.

In Part 4 the author suggests that index-linked pensions are both desirable and possible for all pension schemes, not only those in the public sector, though possibly they should start at a reduced level. Evidence is presented to show that “negative real returns” on ordinary share investment were a temporary aberration of the mid 1970s, and that in more recent years ordinary shares have shown very satisfactory real returns, which may very well continue. Ordinary shares have nothing to fear from index-linked stocks, and pension funds should be able to earn satisfactory real returns on any assets other than long-term fixed interest stocks.

The following notes are intended as an introduction to the Faculty discussion on actuarial education. They are presented by the authors separately and personally, but solely as introductory notes, rather than as actuarial papers which might represent their considered judgement about the nature and purpose of what actuarial education should be. Instead it is hoped that they will stimulate a wide-ranging discussion about all aspects of actuarial education, particularly of course in the context of what the Faculty does or might do in this respect.

The formula suggested almost 50 years ago by Stoodley (cf. Reference 1) to allow for a reduction in rates of interest with the passage of time does not seem to have achieved the recognition which one might have expected, particularly in view of its easy application in practice. In his remarks summarising the discussion following his paper Stoodley conceded that the problem of choosing the parameters of the formula led to somewhat intractable equations, which could be solved only approximately by trial and error techniques. However, with modern calculation methods it is a trivial matter to solve this problem accurately and in §3 below we indicate one possible approach. On the other hand, the use of modern calculators considerably reduces the specific advantage of the original formula. Accordingly in §4 we consider the more general logistic curve (of which Stoodley's formula is a special case), which permits somewhat greater flexibility in modelling future trends.

Recently the C.M.I. Committee has given serious consideration to the construction of a table reflecting the mortality of female assured lives. The crude data underlying the proposed table relate to the quadrennium 1975-78. At this stage the work is not entirely complete, since there has not yet been time to extrapolate to childhood the mortality rates resulting from the graduations, which necessarily relate to adult ages. However the Committee is of the view that the present state of the work is sufficiently advanced to be of some general interest. This paper reports on progress to date and the Committee wishes to obtain the reaction of the profession to the work so far carried out. The final results of the investigation will appear in due course in a C.M.I. Report.

1.1. Part VI of The Insurance Companies Regulations 1981 comprises regulations governing the valuation of liabilities of insurance companies for various purposes under the Insurance Companies Acts 1974 and 1981. In particular these regulations govern the valuations of long-term liabilities for the purposes of an investigation to which Section 14 or Section 34 of the 1974 Act applies. Such an investigation would normally be for determining:

(a) whether the statutory certificate in respect of long-term business required by Regulation 18 of The Insurance Companies (Accounts and Statements) Regulations 1980 could be given;

(b) the extent to which assets could be transferred out of the fund in accordance with Section 24(2) of the 1974 Act, having regard to Section 25, as amended by Section 20 of the 1981 Act; or

(c) whether a dividend may be declared by the company or a parent, having regard to Section 24(6) of the 1974 Act.

Let θx, denote the number of deaths (from all causes or a certain cause) at age x last birthday arising from the central exposed to risk Ecx. We show that, under certain conditions, θx, has approximately a Poisson distribution with parameter

where μy denotes the force of mortality at age y. This result is applied to find confidence intervals for the true central death rate, to estimate the distribution of the cost of claims and the expected death strain.

The frequently-used actuarial formula

where A is the actual deaths and E the expected deaths, is found to hold in large investigations, as is the alternative (but generally less accurate) formula

1.1. This paper is written at a time when, I believe, the greatest challenge facing actuaries engaged in pension work is to communicate.

1.2. We must communicate with Trustees, with members, with employers, with Government, with accountants, with the O.P.B., with the S.F.O. and, through the media, with public opinion: we must also communicate with each other.

These guidelines:

(a) relate to the preparation of reports for trustees and/or employers on the periodic (including initial) actuarial valuations of retirement benefits schemes—they have been primarily designed for schemes where the benefits are defined by the rules and the cost to the employer depends on the actual experience but in other circumstances the guidelines will also apply except to the extent that they are incompatible with the nature of the scheme;

(b) are equally applicable whether advice is supplied directly by actuaries acting as individuals or in partnership or indirectly by employed actuaries—members have a responsibility to secure that their reports and recommendations are received by the trustees or employers to whom they are addressed and are not withheld or amended by third parties;

(c) have been prepared with U.K. requirements and conditions in mind—similar principles would apply elsewhere, subject to modification according to local conditions.

This is not so much a paper as a series of loosely-connected essays and it requires explanation.

For some years I have felt that my generation had an unusual duty to the history of the profession. The first 180 years of actuarial history no doubt seemed eventful enough at the time but they took place against a stable background when interest rates were seldom outside the range 3% to 5%. But since 1945, say, a turbulence undreamed of in those earlier days has become the commonplace of our activities.

If x1<x2<…<xn and the values of lx1, lx2,…, lxn are given, we may wish to estimate the value of the force of mortality at a particular age xi. Two alternative methods of estimation, each used in standard tables, are discussed in some detail.

The most general estimates for each method are given by equations (13) and (22) above, the coefficients {cij} in these equations being defined by equation (11).

In the particular case of consecutive ages, the relevant estimates are given by equations (14) and (23). In this case the values of {cij} for n = 3, 5, 7, and 9 are contained in Tables 1—4 above.