Lord Kelvin many years ago expounded his oft-quoted dictum, ‘When you can measure what you are speaking of, and express it in numbers, you know that on which you are discoursing. But when you cannot measure it or express it in numbers, your knowledge is of a meagre and unsatisfactory kind.’ Operational Research is primarily concerned with measurement in management.

In many respects, this paper may be regarded as a logical sequel to an earlier one presented to the Institute nearly seven years ago. In that paper the assessment of industrial ordinary shares was discussed in considerable detail and methods were suggested which could be used both to make projections of future dividends and earnings for different companies and to utilize these estimates in making investment decisions. Much of the discussion on the earlier paper centred on the latter problem and the present paper is concerned entirely with this aspect of share assessment. The making of future projections will not be considered again; suffice it to say that our methods have remained largely unchanged. The principle on which the technique that we have now developed rests is closely linked with the previous concept of a ‘capitalization rate’ but in passing we would mention that we have made a brief experiment with what we term ‘growth yields’, i.e. the compound interest return to be expected from a particular share at a given price on the basis of the forecast future dividends. Our results utilizing this method were in fact significantly better than those obtained using the more familiar concept of relative yields (see §8) but, as the figures presented later in this paper show, they were not as good as those obtained using the method which forms the basis of this paper.

Unit trusts originated in the United Kingdom in the second half of the nineteenth century, but an early court ruling that unit trusts were not legal resulted in all but one unit trust changing to the form of investment trusts. Although the court ruling was later reversed, little further headway was made by the unit trust movement until after the Great Crash of 1929.

When I was invited to read this paper I felt not only honoured but particularly pleased to be given the opportunity to set forth for your criticism the views I have come to hold concerning the complex of problems centred round the use of Bayes's theorem. For what body of people has for longer been engaged in the application of the mathematical doctrine of probabilities to the affairs of life? And so, what body could be better fitted to judge the merits and the faults of any attempt to clarify the principles of the subject? It is no accident that the original publication of Bayes's famous paper was brought about by the author of the Northampton Life Table; and in the modern period, in dealing with the criticisms of Bayes's postulate stemming from Boole, the credit for a major advance is shared between Sir Harold Jeffreys and Mr Wilfred Perks, independent originators of the theory of invariant prior distributions. And, to anticipate a point I shall develop in more detail later on, it appears to me that the experience of actuaries in the formation of categories as, for instance, by occupational group, as abstainers or non-abstainers, and so on, can be highly relevant to the effective use of Bayes's theorem in many wider contexts; and an examination of the principles underlying the formation of categories should improve our insight into problems of statistical inference in general.

The Finance Act, 1965 (which will be referred to in this paper as ‘the Act’) introduced two major changes into the United Kingdom system of taxation: firstly, it introduced a corporation tax applicable to company profits in place of the income tax and profits tax to which those profits were previously subject; and secondly, it imposed a charge to tax on all capital gains, with certain exceptions, whether these gains accrued to a company or to an individual. The objects of these changes and the various associated arrangements were:

(1) To make the tax system more equitable by bringing into charge certain capital gains, frequently speculative gains, which had previously escaped tax altogether.

(2) To make the tax system more simple in some respects by separating the taxation of companies from the taxation of individuals and by levying corporation tax on a current year basis.

(3) To encourage the retention of profits by companies.

(4) To improve the country's immediate balance of payments by rendering overseas investment less attractive.

The problem of solvency in insurance is at present under a good deal of discussion in various interested quarters, both national and international. It is principally a question of finding criteria for determining the size of the solvency margin which a private insurer must have in the form of free reserves to be considered solvent. A criterion must produce a margin which is both sufficient and suitable: it must be valid not only for a model portfolio but for any portfolio. Consequently, only insurers with the prescribed margin would be considered solvent and authorized to write insurance business. In recent years, particularly because of the directives promulgated by the Common Market authorities, it has largely been a question of the solvency of non-life insurers.

It would be ungracious not to admit in the first lines of this paper that the idea of writing it was generated by the Presidential Address to the Faculty of Actuaries, delivered by J. L. Anderson on 19th October 1964. That address was largely concerned with the problems of senior (but non-technical) management of a life office, and it was at once apparent that those problems differed substantially from the management problems of a partnership.