The proper functioning of a present-day economic system is dependent upon money and prices. This is particularly the case when a large part of the economy is based on private enterprise.

For many years economic text-books have stated the three functions of money to be (1) a means of payment, (2) a store of value and (3) a unit of account. The third function will not be considered in this paper, although a study of the controversy that has occurred recently about the correct principles of accountancy at times when prices change substantially will convince the reader that this function is important.

Whilst all three functions of money have been recognized for many years, the emphasis given to each has changed radically from time to time. Prior to 1930 almost all the emphasis was given to money as a means of payment. This led to an approach to the subject which has been called the transactions-velocity approach.

It was originally proposed that this paper should be entitled ‘Property Investment’, but it was found to be quite impossible to condense such a subject satisfactorily. Also, a paper was presented to the Society some eight years ago entitled ‘An Introduction to Property Investment’, by Lane and Leach (J.S.S. 5, 166). It is thought that the two papers can be read together with advantage. What has been done in this paper is to provide a series of statements and opinions with a view to provoking thought and discussion. Many points may be raised which have been left out. Much, no doubt, has been put in which is obvious and elementary.

We are concerned with Property Investment on a long-term basis, i.e. we are not concerned with speculation, namely, the quick purchase and re-sale of property to make a profit; furthermore, we are not concerned with House Purchase schemes. It must also be emphasized that this paper relates to England and Wales and not to Scotland. In the authors' view, basically sound property investment as distinct from owner occupation is very difficult indeed to achieve in Scotland, owing to rating complications, low yields, horizontal ownerships and other legal difficulties.

The transaction by British offices of life assurance business outside the United Kingdom brings with it problems which have been discussed by W. F. Gardner in his paper to the Institute on ‘Some considerations affecting the transaction of overseas life business’ (J.I.A.66, 198) and by C. D. Sharp in his paper on ‘British life assurance overseas’ (J.S.S.9, 2). These papers dealt with the principles to be observed and the practice to be followed in writing life business overseas having regard, inter alia, to local insurance laws. My intention is to consider the laws themselves, to point out some of the differences between them, and to consider to what extent they are consistent with actuarial principles.

To keep the subject within practical limits I shall confine myself to Ordinary branch business in the Commonwealth and Egypt. Furthermore, I shall not consider laws which directly control the relationship between insurer and insured, and between insurer and field staff.

It will be appreciated that inflation is not a purely war-time or post-war phenomenon. The last two wars have considerably increased the rate of inflation, but the process has been more or less continuous for a very long time. Any appreciable degree of inflation can have very far-reaching effects on the accounts of a trading company. It is the intention of this paper to consider the effects of inflation on the Balance Sheet and the Profit and Loss Account and on the interpretation of the figures in these accounts after inflation has done its work, and to consider the extent to which such accounts give a true picture to the Company's Board of Directors and Shareholders.

The preparation of accounts has as its purpose the provision of information to shareholders and to those whose duty it is to control the policy and to undertake the day-to-day management. The needs of the two groups vary to some extent, particularly as regards volume and detail of information. In both cases, however, the immediate aim of accountancy is the provision of a summary record of financial progress during (usually) a year's operations and of financial standing at the end of the period. The standard method of preparing this record uses only actual past figures of income and expenditure, expressed in units of currency.

How are the Friendlies faring? This catch-phrase was born soon after the take-over of Approved Societies in 1948 and was bandied about in Friendly Society circles for the next two or three years. It is perhaps a pity that the question had not been asked 10 or 15 years earlier. Be that as it may, the answer to-day is fairly clear.

That the Friendly Society movement as a social institution of the country is fast declining is, I think, undeniable. The Registrar's Statistical Summaries show that the total number of Registered Branches and Societies, excluding collecting societies, declined from 19,429 in 1939 to 15,226 in 1950. This apparently alarming fall, 20 % in 11 years, is not, however, quite so bad as it looks—of the total wastage of 4203 Societies, 2590 relates to Branches of the Affiliated Orders and reflects various policies of centralization, amalgamation and reorganization; actually many of the Branches which have been deleted from the Register still exist as agencies instead of autonomous units. In the same way, of the balance of 1613 wastages among Societies without Branches, a fair number will have been due to the amalgamation or absorption of different Societies.

This paper is an attempt to give an account of the various considerations which must be borne in mind in fixing the terms which can be quoted for the alteration of a policy. It is divided into various sections as follows:

A. The formulae which are theoretically suitable.

B. The modifications which can be made to the formulae for use in practice.

C. The points to be considered in choosing the actual basis used.

D. The various types of policies and of alterations not dealt with in the preceding sections.

E. Points of procedure and the method of dealing with altered policies for valuation, etc.

Only ordinary life business will be considered: Industrial Assurance is outside the scope of the paper.

For the purpose of sections A and B only non-profit policies are considered, and the formulae apply to an alteration from a whole of life policy to an endowment policy. With suitable changes they can be used for other alterations.

The reassurance of life assurance policies is readily accepted by us all as an essential, though a minor, part of Life Assurance. Each office tends to have its own traditional approach to this problem, coloured very often by its attitude to the general problem of underwriting. I think that a discussion on reassurance falls naturally into two parts. First, what amount should be retained for an office's own account? Secondly, having determined the retention, how should the reassurance be effected?

The scientific transaction of Life Assurance began in 1762 with the ‘Equitable’, but, until other Life Offices began to issue permanent policies, there was no scope for reassurance; nor, probably, was there much demand for very large policies. It must be remembered, of course, that in those days £100 was a considerable sum of money. As Life Offices grew and multiplied, reassurance became more common as will be learned by the references to it in the early numbers of J.I.A. Reference should be made to G. T. Foster's paper in J.I.A. 72, 337, where it is pointed out that, one hundred years ago, reassurances were looked at with considerable suspicion; this attitude still exists to some extent.

‘Extending the scope of the profession’ is such a well-worn cliché that one could define the wider field effectively, if ungrammatically, as the place professional scope extends or can extend into.

F. A. A. Menzler raised the matter to the level of public importance at the Annual General Meeting of the Institute in 1924, exercising the Fellow's democratic right of intervention. At the invitation of the Council, he developed his ideas in a paper submitted to a Special General Meeting of members on 26 October 1925. He drew attention to the growing importance and recognition of statistics as a tool of government and of management. He claimed that the actuary was ipso facto a trained statistician, and that actuaries might reasonably expect to fill the increasing number of statistical posts then becoming available. Menzler also showed that the membership of the Institute had grown substantially in numbers during the preceding twenty years.

When it comes to cricket we are all statisticians. Indeed, a daily paper has only to use the heading ‘The Averages’ for every (male) reader to understand that he will find below the batting and bowling averages of first-class cricketers. Most schoolboys take a keen interest in these figures and many soon begin to realize that they are not an altogether satisfactory means of comparing the prowess of individual players. It is noted, for instance, that an opening batsman has, on the whole, more dangerous bowling to cope with than one who goes in fifth or sixth wicket down; and that a bowler who secures cheap wickets among ‘tail-enders’ is flattered as compared with an opening bowler who has very different opposition.

The sales of Wisden bear ample evidence of the fascination of cricket records. Sir William Elderton (1945) and George H. Wood (1945) have published enlightening analyses of batsmen's performances, which are but samples of the delights to be found in browsing among these records. Not only does such work throw new light on the published figures, but it often leads to clearer ideas on statistical analysis and interpretation in general. Understanding of the effects of statistical analysis is much facilitated by the relatively clear-cut nature of the data, which, despite ambiguities and unrecorded factors such as pitch, weather and tactics, are less subject to confusing factors than most statistical data.

By the courtesy of the editors, I submit some remarks which time did not permit me to utter during the discussion on Mr Spratling's, ‘paper.

At the meeting a member asked why should an actuary engaged in exercising his profession in a Life Office seek employment in the wide open spaces? The answer is, of course, that if his employment provides full contentment—as well as reasonable prospects—there is no earthly reason why he should be adventurous unless, of course, he is inclined that way. For it is an adventure to take on a job in an entirely new and unfamiliar environment, especially in industry, where the tendency is not to bother much about your academic or professional diplomas, and the test is rather what you can contribute to the work and prosperity of the firm.

Now what is it that we can contribute? It takes a good man to stand up to our training and examinations and come through unscathed.

Much of the demographic research undertaken in this country is naturally concerned with statistics relating to the British nation. It is very desirable, however, that attention should also be directed abroad. As Prof. J. B. S. Haldane has recently said, ‘any branch of knowledge is improved by a background’; it follows that our understanding of the affairs of our own population can be increased by a study of the numbers and movements of people elsewhere. Theories formed in order to account for occurrences in one country may appear unreasonable when tested in the light of other population data. Alternatively, they may find useful confirmation; a good example is to be seen in W. S. Hocking's article in J.I.A. on the mortality of males in later middle life. By making international comparisons, not only did the author find valuable supporting evidence for his observations based on British data, but he was enabled to carry his analysis a stage further and examine the effects of differing degrees of industrialization upon the relative levels of male and female mortality.

Given an ordered sequence consisting of fixed numbers of A's and B's, it is sometimes necessary to test whether these letters occur in a random order. In particular situations A and B may represent positive and negative signs, heads and tails of a coin, defective and effective parts, wet and dry years, and so on. Many tests of randomness are available, but this note only deals with two of the possible tests. One of these tests is described by Johnson & Tetley in their Statistics text-book (vol. 2, p. 238), where the sequence of positive and negative signs of the deviations between actual and expected deaths in a mortality table graduation is investigated for randomness. However, it is not made plain in the official text-book exactly what aspect of randomness is being tested; it is hoped that this note will make the matter clear.

The situation to which both the tests described below are to be applied is as follows. Given fixed numbers n1 of A's and n2 of B's arranged in an ordered sequence, it is found that the particular sequence observed contains g1 groups of consecutive A's and g2 groups of consecutive B's.

In a previous paper (J.S.S.9, 105) the present writer investigated the effect upon pension fund contribution rates of a change in the salary scale. A further note (J.S.S.10, 47) discussed the effect of a change in the rate of interest. The present note is concerned with the variation in contribution rates with varying entry age, the actuarial bases remaining constant. The note takes account only of the contribution in respect of the pension benefit and disregards any additional contribution required to provide a benefit payable on death or withdrawal.

As before, we suppose that a single pension age, M, independent of entry age, sufficiently allows for normal, late and early retirements (if any) and that the pension is 100 k% of pensionable salary for each year of service.

Some three years ago a note in this Journal (J.S.S.10, 24) called attention to the rapid decline that was taking place in the numbers of unmarried women in this country, due to the fact that the number of marriages was exceeding the number of young women reaching the marriageable ages. During the past three years statistics of a further three or four years' marriages have been issued and a sample analysis of the total population enumerated at the 1951 Census has been published. It may be of interest, therefore, to examine these data to see whether the trends exhibited in the years up to 1947–48 have continued and whether the 1951 Census results confirm the estimates given by the Registrar General for the inter-war years.

The first assertion made in the note referred to is that ‘a considerable fall in the number of marriages, to be followed by a consequential fall in the number of births, is almost inevitable during the next few years’. As the number of marriages in England and Wales in the years 1950–52 averaged only 356,000, whereas during the period 1939–47 the average level was 385,000 a year, the first part of the assertion is being substantiated.

In this note, we consider a problem and its implication. The problem is the control of the flow of new business in a portfolio in a certain type of policy. Supposing we know in advance what the investment implications of a certain trend of reserves will be so that we can decide a programme of development of the fund purely from investment consideration. If the flow of new business is ‘controllable’, e.g. by the amount of advertising, commission, and reward to the selling staff allowed from time to time, what volume of new business is required in order to build up to a predetermined reserve pattern? In solving this problem, we will use a mathematical integral employed in electricity, physics, chemistry and other fields. This is so fundamental in other fields that perhaps it will solve many more of our problems.

In this note, emphasis is given to the amount of insurance in force because that is customarily done in the United States.