It is impossible in these notes to attempt any comprehensive review of the system of compulsory Unemployment Insurance which has operated in this country since 1912. Moreover, the paper by Messrs Kyd & Maddex read before the Institute in January 1929 gives full information up to that date. But I want to start by outlining the original scheme, as I think the way in which it has been modified and extended may be found of interest.

The system began with the National Insurance Act, 1911, Part II. Contributions commenced in July 1912 and benefit in January 1913. Only a few industries which were considered to carry a specially heavy risk of unemployment were included, and the numbers insured at the outset were about 2¼ millions. Contributions were 2¼d. per week each from employer and worker, and 1⅔d. from the Exchequer. Benefit was 7s. per week, with a limitation of one week's benefit for every five contributions paid, and a maximum of fifteen weeks' benefit in a year.

I propose in this lecture to confine my attention for the most part to staff pension funds, i.e. funds set up and administered within firms. There are, of course, pension schemes the administration of which is entrusted to insurance companies and special legal points necessarily arise in that connexion as well, but I find on consideration that there is ample to occupy the time at my disposal if I apply myself particularly to those private or “house” schemes which find their expression in the setting up of a pension or superannuation fund. However, some of the points I raise and the views I express apply also to schemes carried on through insurance companies.

A Group Life and Pension Scheme is an employer's scheme instituted for the benefit of his employees. The real position of the life office, which is usually responsible for arranging the scheme, is that of underwriter. From the life office's point of view, with which this paper is solely concerned, the guaranteeing of these schemes on a group basis, as opposed to issuing an individual policy on the life of each employee, is a special class of business with certain definite characteristics which have not changed very much since N. C. Turner presented his paper to the Students' Society in 1930 on the subject of Group Insurance and Group Pension Schemes.

The object of this commentary is to indicate the fundamental principles underlying the selection of property investments from the point of view of an insurance company. It is, however, essential first to examine the phraseology of real property, with its legal background, before we can distinguish between the various types of property and the degree of security afforded by each type. In the time at our disposal, we must of necessity confine ourselves to the basic elements of the subject, and make no attempt to deal with war-time legislation or present prospects of changes in legislation.

By currency stabilization we can mean one of two things. We can mean either the stabilization of the internal value of a currency—the quantity of goods and services that a unit of it will purchase inside the country concerned—or the ‘stabilization’ of its external exchange value in terms of the quantities of the currencies of other countries that it will purchase.

The internal and external values of a currency are of course closely interconnected. There was a time, when the gold standard was working more or less smoothly, when the fixity of foreign exchanges was taken for granted, and discussion of currency stabilization was mainly concerned with the desirability and possibility of maintaining a stable internal price level. Now, however, as a result of the shrinking of international trade in the Great Depression and the consequent bedevilment of the exchanges in nearly every country, the focus of attention has shifted, as the Keynes and White plans clearly show, to the problem of achieving and maintaining equilibrium in the external balance of payments of the different countries while avoiding drastic exchange restrictions or, alternatively, wide and erratic fluctuations in their exchange rates.

1. Recent investigation has brought to light the fact that the usual formulae are not necessarily practicable for the calculation of the force of mortality at very young ages. The problem is not only of considerable theoretical interest, but is also of practical importance to the Industrial Assurance Companies, which transact a very considerable volume of business at these ages. These companies use continuous functions for their various calculations, and μ being large at these very young ages, variations in the method of calculation are of such importance as to justify a detailed examination of the matter.

The existing writings dealing with industrial assurance subjects in the Students' Society and Institute Journals are mainly confined to two narrow aspects of the business—processes involving actuarial technique, and details of legislation. These matters are dealt with comprehensively whilst the broader, and perhaps more vital, problems of the business are almost ignored. This imposes no hardship on those in contact with industrial assurance but it must hinder those students who are not in such contact and it would perhaps help them if some indication were given of the more important matters conditioning the business as it is in Great Britain and Ireland. The great difference between the conditions of the large industrial assurance companies and those of the small collecting societies makes it impossible to attempt completeness in a short note, and the present note is written, therefore, with the position of the industrial assurance companies mainly in view, although it will be realized that much of it is also applicable to the larger collecting societies.

Redemption yields on redeemable securities may conveniently be found with the aid of tables of Bond Values. These tables make no allowance for the fact that income tax is payable on the full dividend payments with no adjustment for profit or loss on redemption.

Those investors who are taxed on the full dividends require to know the net yield after allowing for tax, or, more usually, the gross equivalent of this net yield, commonly known as the “equivalent gross yield”. It is often inconvenient to deduct tax from the dividend rate and find the net yield direct, as the net dividend frequently does not coincide with the rates for which tables are available. There is, however, a very convenient and extremely accurate approximation to the required equivalent gross yield which is as follows:

To find the equivalent gross yield, reduce the unexpired term in proportion to the rate of tax payable and enter the table for the full nominal dividend rate.

The widespread practice of making bonus reserve valuations for publication or internal purposes has brought to light a number of points which do not arise when surplus is being analysed following a net premium valuation. The following notes have been prepared with a view to their elucidation and are based on a slightly different method of treatment of the problem from that usually employed. The revenue account and corresponding valuation account are brought side by side, and it is shown that in the main surplus is the difference between the corresponding items. The surplus is analysed symbolically, and finally the whole operation in symbols is shown to give a complete reconciliation. The symbols which are not defined by their context are explained in Appendix A.

A particular method of analysis has been followed but it is not claimed as the ideal; the individual may choose to vary the method, but so long as correct principles are maintained the surplus will be traced—which is the object sought.

The problem considered is that of Todhunter's Textbook (1936 edition), ch. VIII, para. 6, p. 176, but the method employed is suitable also for finding the yield on a loan issued at a price different from par, and redeemable through the operation of a cumulative sinking fund, applied in drawings at par or at a premium.

Let a′ be the value of an annuity of 1 payable annually for n years; it is required to find i′ the unknown rate of interest.

An examination of any published set of tables of annuity values, such as Oakes's Tables, will indicate that rate of interest i, to the nearest ⅛ %, at which is most nearly equal to a′.

Let dashed symbols refer to functions calculated at rate of interest i′.

In any discussion on recent trends in national finance the most important feature to note is that the State is being called upon more and more to redress the balance in the social and economic system. This tendency shows itself in the introduction of quotas, subsidies, Government-guaranteed loans to industry, health and unemployment policies, etc., and can, of course, be traced back to the nineteenth century. During the last few years, however, some of the changes have been so rapid that it is not yet possible to appraise their true value, and it seems likely that in the not too distant future private enterprise will cease to be the dominant force in the economic life of this country, whatever may be the party labels of successive Governments. Apart from forces at present operating, the coming task of adjusting the economic system to a falling or even stationary population will certainly require Government assistance on a large scale, especially in the labour market if much unemployment is to be avoided.

The actuary's ideas on statistics tend to be biased in the direction of Life Office statistics. It may therefore be useful to set down a simple use of statistical methods which has been adopted in industry and which was the subject of a lecture to the Students' Society some two years ago, viz. Statistical Quality Control. Where the mass production of articles is employed, various systems of inspection aim at watching the quality of the product to prevent unsatisfactory work being passed on to the consumer or to a later stage in the manufacturing process.

It should not be difficult to extend the work already performed by Mr Craig to devise a formula which will be accurate to seven places of decimals even in very unfavourable circumstances (e.g. very long or short terms for very high or low rates of interest). Mr Craig's formula gives the correct value of ρ for the example given in the Textbook, but is not so accurate for more unusual conditions.

Developing as in Mr Craig's note:

We have, as far as terms involving ρ2 in numerator and denominator,

or

and ρ1= t0/t1.

An examination of the form taken by the values of i/ρ — i/ρ1 for various values of n, i and ρ suggests that it is very nearly independent of ρ for intervals up to considerably more than 1/16%.

It would thus probably be possible to find the form of this function from calculated values.

These notes deal mainly with that part of the investigation of securities which involves the study of company accounts.

At the outset, it should be stressed that the figures of various companies are not computed on a common basis. In company accounts, as in an actuarial valuation, the same general principles can be modified to give varying results, with the important qualification that even the general basis does not have to be published. There is therefore plenty of scope for variations in accounting practice, and hard and fast conclusions cannot be drawn from figures alone. In this connexion, one cannot do better than quote the remarks made by Mr Arthur Chamberlain at a company meeting last year, when he said:

I do not suppose there are many of my audience who are simple enough to believe that a company's accounts, particularly those of a holding company, set forth the actual and exact profits earned in each year.… I do not think it would be too cynical to say that the ordinary shareholder is lucky if he can read from the figures of a balance sheet more than an idea of the general tendency forward or backward, unless the directors are themselves aware of it and wish him to.… It is possible within the law to present a more or less truthful but entirely misleading position of affairs.

In the present state of company law, therefore, it is of no use trying to produce complicated formulae or elaborate indices intended to indicate true share values at a glance.