Extended warranty insurance for consumer durables was introduced into the United Kingdom as recently as 1981. Since then there has been a major expansion of this class of business, much of which has still to reach the later periods of exposure with, as yet, unknown levels of claims experience. Considerable future liabilities could therefore be involved, with implications both for reserving and rate-setting. The business has already caused problems for certain insurers and agencies, and has attracted an amount of adverse publicity amongst the public.

Many people would argue that this should be relatively simple business; in point of fact it is surprisingly complex and poses a number of problems of particular interest to actuaries and statisticians. This paper therefore aims to describe the basic features of this type of business, which will probably be unfamiliar to the majority of readers, and to highlight the principal problems and dangers involved for the insurers. It does not set out to solve all these problems. At this stage, as a learned judge has recently suggested, this may be better left to the astrologers!

In November 1983 I gave a talk to the General Applications Section of the Royal Statistical Society jointly with the Institute of Actuaries Students' Society, entitled “Time-Series Analysis in Investment Models: Inflation and Share Prices”, in which I outlined the statistical derivation of a stochastic investment model. This model was presented to the actuarial profession in a paper “A Stochastic Investment Model for Actuarial Use” discussed at the Faculty of Actuaries in November 1984. The statistical background, and other information, is discussed in Occasional Actuarial Research Discussion Paper No. 36, “Steps Towards a Stochastic Investment Model”, which is a sort of Appendix to the Faculty paper. It contains most of the material presented to the Students' Society in 1983.

The Faculty paper described a number of possible applications of stochastic investment models. I stated there that a “stochastic model for investments … can be used by actuaries in almost any circumstance where a rate of interest enters their calculations at present”. That is a pretty wide field. But I suggested that it opened up “wider possibilities for investigation too”. I intend in this paper to describe a number of simple applications of my stochastic investment model, in order to show the flavour of how such a model can be used. None of the topics has been comprehensively investigated, and I am sure that the reader will soon ask questions which I have not answered. I hope that he will be able to think of ways of answering them himself.

This paper takes its title from the recent judgment of the Court of Appeal in Auty and Others v National Coal Board (1984). Lord Justice Oliver stated that, “as a method of providing a reliable guide to individual behaviour patterns or to future economic and political events, the predictions of an actuary could be only a little more likely to be accurate (and would almost certainly be less entertaining) than those of an astrologer”.

The above statement was referred to by Stewart Lyon, immediate past President of the Institute of Actuaries, in his review of the Session 1983–84 at the Institute's Annual General Meeting in June 1984. Although the quoted passage had received all the publicity, he was more concerned with the judgment in the same case given by Lord Justice Waller who erroneously stated that the expectation of life was an average and assumed that everybody lived to that age and then died. Mr Lyon concluded his remarks on the subject by stating that the Appeal Court's handling of the Auty case raised the general question of whether the actuarial profession needs to adopt a more active approach to public relations.

This paper was born over a year ago in Autumn 1983 when I proposed a thorough discussion of the whole current image of the actuarial profession.

The reasons I gave then were:

(a) There were a number of current debates affecting our livelihood into which there had been little official input from the profession, the pensions debate at the time being an example.

(b) There had been no effective response to specific attacks on us by other professions; judges for example, or by the financial media.

(c) A number of actuaries in major positions reported a disturbing lack of knowledge of the profession among prospective new recruits, combined with a view that the profession is becoming a less attractive career option.

(d) We live in a changing world where the role of all the professions is being brought under public scrutiny, with the need to justify the quality and relevance of the services available. Other professions are taking very positive action to communicate an image and a role, this affects us directly as well as indirectly.

(e) There has been no comprehensive paper or related discussion within the profession before, arising not least from a feeling that it was not needed, as we are small and safe, secure within the wider financial and professional system.

The Guinness Book of Records once claimed that the number π to a million decimal places, printed in full and bound in book form, was the Most Boring Book in the World. To the uninitiated, the Department of Trade Returns of U.K. life offices must seem to be in the same class, and when I chose the topic I wondered if this might affect the welcome which this paper would receive. For anyone with a professional interest in life offices, however, the Returns are too important to ignore. They contain the greatest amount of published data on the U.K. life assurance industry, they form an essential prop of our liberal supervisory system and they ought to be a line of defence against tighter controls.

Life assurance has always been unusual in attracting long term contractual savings in large amounts. This was even more true a century ago than it is today, as there were no great pension funds or unit trusts. Human nature being what it is, this led some to view life assurance with more enthusiasm than sense. The mid-nineteenth century saw numerous small life offices set up, many of which were soon in trouble and it became common for such offices to be taken over by others. This was not so bad when the business was transferred to a larger, sounder office but quite often the new proprietor was an office in no better state than that taken over.

Many years ago the question of equitable distributions of surplus would have attracted much discussion. The subject received a full philosophical, financial and mathematical treatment, with the aim of getting it just right.

As time passed this subject became less precise. Wider variations in investment conditions and different investment strategies meant that the constraints of the usual bonus methods could only achieve rough justice. Premium rates and valuation bases remained fairly static (often quite rightly so), and the declared results seemed slightly arbitrary and perhaps a little conservative. The work of the traditional actuary seemed a little ‘stodgy’ and the challenge and activity turned to the field of unit linking.

Today the picture is different. Just as the introduction of banks to the personal mortgage market seems to have improved the service from Building Societies, so the advent of unit-linking seems to have spurred on the traditional actuary. The expectations of what can be achieved have increased. So, over the period that the methods for valuation, pricing and projection for unit linked contracts have achieved some measure of standardization, the traditional actuary has been pushed more into the role of the pioneer.