Since the 1939–45 war, successive Governments have attempted by various political and ideological processes to provide this country with built-in prosperity combined with almost complete security. The measure of their success has been the reduction in the risks that attend economic enterprises of every type and the concomitant increase in the security of the incomes arising from them. No doubt from the standpoint of the owners of these incomes this has been exceedingly beneficial, but the reverse of the coin shows a progressively increasing distaste for incomes which are limited or reduced by further provisions of security and priority.

The assessment of ordinary shares is at present the subject of intense activity. A full-scale professional analysis of a particular share can, however, be a most formidable document and one which does not produce the answer to the question ‘What long term return can I expect from my investment?’ On the other hand a simple statement of dividend cover and dividend yield at the current price is clearly insufficient to decide on the merits of a share.

This paper describes a method of assessing ordinary shares in terms of ‘expected yield’, i.e. the compound interest return which a long-term buyer would expect to obtain from his investment, and includes a note on a simple way of adjusting a company's published rates of dividend and earnings to produce a consistent growth record suitable for use in estimating the expected yield.

The question of bonus distributions has been much in the minds of actuaries during the post-war period. In October 1959 a paper was submitted by Benz to the Institute of Actuaries which he introduced with the following remarks: ‘Recent financial events have caused new problems to come before actuaries when advising on the finances of life offices and, in particular, on bonus distributions to with-profit policyholders. These problems may be said very briefly to centre around the question of what circumstances make it appropriate for an office to depart from the normal procedure for distributing bonuses.’

When one considers the variety of ‘options’ available to policyholders and the large number of lives assured who are in a position to exercise an option, one might be haunted by a vision of legions of operators speculating on the optimum moment at which to make a deliberate choice advantageous to themselves and detrimental to the financial stability of life offices. The fact that offices are prepared to encourage various types of options clearly indicates one of two things, either (a) that the skill of the operators is not held in high esteem, or (b) that the skill of the offices is high enough to overcome intelligent selection by the option-holders. If it were true that the value of any particular option could be accurately stated by a mathematical expression and if the incidence of the exercising of the option were established to universal satisfaction, (b) would be mercifully true. This condition, however, does not hold for many options, and it is this element of the unknown which gives spice to the subject and justification for further comments.

Can the National Pension Scheme as a whole now be expected to maintain solvency? On what lines may the Scheme be expected to develop in the future? Should contracting out not have been permitted?

The temptation to go into these and other fascinating questions will be resisted as far as possible; it is proposed instead to confine the subject matter of this paper reasonably closely within the area implied in the title. In order to establish the context in which the present situation has arisen, it is appropriate, however, to begin with a very brief survey of the more recent history of national and private pensions in Britain before the passing of the National Insurance Act 1959, which will be referred to henceforward simply as ‘the Act’; the situation before the Act comes into operation will similarly be referred to as ‘pre-Act’. When the Act comes into operation two new situations will arise; ‘Contracted-in’ and ‘Contracted-out’. There are thus three conditions to consider, and as far as possible when using expressions in connexion with contracting out such as saving, extra cost, etc., it will be stated whether these are by comparison with the contracted-in or pre-Act position, lack of clarity on this point having been a source of confusion in some of the literature on the subject.

Dynamic programming, a mathematical field that has grown up in the past few years, is recognized in the U.S.A. as an important new research tool. However, in other countries, little interest has as yet been taken in the subject, nor has much research been performed. The objective of this paper is to give an expository introduction to the field, and give an indication of the variety of actual and possible areas of application, including actuarial theory.

In the last decade a large amount of research has been performed by a small body of mathematicians, most of them members of the staff of the RAND Corporation, in the field of multi-stage decision processes, and during this time the theory and practice of the art have experienced great advances. The leading force in these advances has been Richard Bellman, whose contributions to the subject, which he has entitled Dynamic Programming [1], have had effects not only in immediate fields of application but also in general mathematical theory; for example, the calculus of variations (see chapter IX of [1]), and linear programming (chapter VI).

In 1944 the Royal Commission on Population was set up in order to determine the probable consequences of population trends then current. In order to do this they prepared a range of sixteen separate population projections for Great Britain based on various combinations of assumptions as to mortality, fertility (and marriage), and migration. The method used, in which each component of population change i.e. birth, death and migration receives separate treatment, is generally known as the component method. This distinguishes it from cruder methods based on the assumption that the total numbers in a population follow some mathematical formula.

Since the Royal Commission reported, this method has continued to be used in preparing what may perhaps be described as the ‘official’ projections of the population of England and Wales.

In a recent note (Bizley, 1960) the writer described a device which simplifies the solution of certain derangement problems. The present note explains and illustrates another device in combinatorial work (and hence in probability) having potentialities that do not seem to be well known. It is useful in tackling problems concerned with the choice of objects from an array when restrictions are placed upon the relative positions of those to be chosen, and it has applications to runs of consecutive events.

In this paper the taxation position is described as it applied in the fiscal year 1959–60. The detailed provisions of the various enactments which govern taxation in Great Britain are subject to revision from time to time and it must therefore be made clear that minor variations must be expected in the future. Major changes in the basis of taxation of retirement benefit schemes having been effected by the Finance Act 1956, it is not expected that the broad pattern will be greatly changed in the foreseeable future.

The census taken in this country last April will still be fresh in everybody's minds, so that the present time seems very suitable for a discussion on census-taking. The subject is of particular interest, as considerable developments have taken place throughout the world in the 16 years since the war ended, and more developments are likely in the years to come. In these notes, therefore, I have tried to set the British census against the background of census-taking as it is practised in the rest of the world at the present time.

1. Consider the question: Given the group life assurance premium for death benefits, what extra should be charged for a premium rebate on the basis that the cost of the rebate must be covered by the extra? Assume no additional administrative costs are involved.

2. Let the rebate be a proportion s of the excess of a fraction a of the total office premium P′ over the total claim C in a year. The rebate is then s(αP′– C). Usually the benefit is more complicated, but as explained in §8, the extra premium for the more complex benefit is related in a simple manner to the extras for the benefit described. In order to avoid scale constants the average sum assured per life is taken as unity.

When your invitation came I thought what better subject is there to discuss than the problems facing our own institutions and in particular the problems that are likely to be left to your generation to solve or to suffer under. I therefore intend to deal in this address with one or two of the more controversial issues of the present time—issues which I feel will leave their mark on our business and our profession.

At the end of the 1914–18 War, Life Offices pondered and considered how they could regain their strength. Not only had war claims been heavy but they had suffered severe depreciation on their investments, due to the increase in the market rate of interest. The solution that the great majority found to this problem of regaining strength was to pass their bonus.

An essential part of the work carried out by the actuarial profession is the valuation of reversionary interests or life interests for the purpose of calculating either estate duty or stamp duty. The number of actuaries who are engaged in this work regularly is very small, but most actuaries are probably asked to undertake such valuations at some time or other. The object of this paper is to discuss some of the principles upon which these valuations are based and to illustrate the application of these principles by means of examples drawn from the authors' own experiences.

Under the Finance Act 1894, Estate Duty is payable on the principal value of a property. This is defined in Section 7 (5) of the same Act as follows:

‘The principal value of any property shall be estimated to be the price which, in the opinion of the Commissioners, such property would fetch if sold in the open market at the time of the death of the deceased.’

The course of reading for the examination does no more than touch on the way in which the business of purchasing, or granting loans on, reversions is influenced by legislation. The object of this paper is to peel a second layer off the fruit of reversionary knowledge, rather than to bite too deeply at one point on its circumference. The standard work by Withers, running to 480 pages, gives evidence of the number of layers left undisturbed.

Whilst most of the matters mentioned on the following pages fall primarily within the province of the solicitor, the partnership between solicitor and actuary will be more efficient and beneficial to the client if each partner has a rudimentary grasp of the affairs of the other.

It has long been recognized by statute and by general consent that the main purpose of a pension scheme is the provision of annuities for employees on their retirement and for the dependants of employees who die either in service or after retirement. In recent years, however, the provision of lump-sum benefits in addition to annuities has become widespread; in national and local government service, and in some of the public boards, superannuation arrangements include the provision of lump sums on a substantial scale. In industry and commerce, the advantages of tax-free lump sums have been vigorously sold, with considerable success, by brokers specializing in pension-scheme business.

The objects of this paper are to place such claims in perspective and to explain in broad terms the various methods by which lump-sum benefits may be provided. Reference will be made to insured and to privately administered schemes, but the detailed provisions of trust deeds and insurance contracts are not within the scope of this paper.

It is first necessary to consider why with-profit pensions schemes have been introduced. Three reasons emerge. The first is protection for the office; the second is a desire to be equitable to the policyholder, and the third is competition—from other offices and from private funds.

These reasons are now amplified.

Pension schemes are the longest form of liability undertaken by the office; further, existing benefits can be purchased by level premiums guaranteed to pension age (as in individual contracts) with an underlying rate of interest of the order of 4¼%. It is therefore desirable to have protection against both improvements in mortality and against the office's not earning an average of 4¼% on the premiums and interest which it has to invest each year.

This paper is not intended either to be an exhaustive treatise on investment department practice, or to give the student any assistance in examinations on investment policy. It is hoped, however, that it might engender an interesting discussion of points which a newcomer to an investment department will find useful, and it may give some background to examination reading. The paper is concerned only with investment in securities dealt in on the Stock Exchange.

The prime purpose of the Stock Exchange is to bring together buyer and seller of stocks and shares. In most Exchanges, including the provincial ones in this country, this meeting is made directly by the broker of the buyer finding the broker of the seller, or vice versa. In London a shop-keeping system exists with a number of firms of jobbers making prices in specialized sections of the market. For instance, three firms of jobbers will buy or sell insurance shares, and those same firms operate in three or four other sections of the market—one of them operates in bank, shipping, tea and hire-purchase shares.

1. Kennedy & Howroyd (1956) have discussed the application of the Lagrangian multiplier technique to actuarial problems. This technique permits the analytical solution of constrained optimization problems, where both the function to be optimized and the constraints must satisfy stringent analytical conditions. In particular, the first derivatives of all functions must exist.

When constraints comprise inequality as well as equation restrictions, as is the case in linear and non-linear programming, then the conditions required for the Lagrangian multiplier technique do not hold. It was therefore found necessary to develop a new body of techniques, known as mathematical programming techniques, for the solution of constrained optimization problems involving inequality constraints.