Investment conditions have changed widely and rapidly in the post-war era; and since the publication of Mr Lewis G. Whyte's textbook, Principles of Finance and Investment, there has been a spate of papers on investment theory, each of them either covering a small part of the subject or setting forth a particular view.

The aims of this paper are:

I. To suggest a balanced and consistent approach to investment principles as they affect funds of actuarial interest.

II. To discuss the application of these principles to particular types of funds.

III. To discuss the characteristics of the securities that are available in present-day conditions to implement investment policy.

These aims may sound comprehensive, but within the limitations of a paper it is only possible to touch on them briefly.

Recent years have seen a material growth in the annuity business of British offices and in many instances what was a relatively insignificant part of the offices' activities has now assumed considerable importance. In fact in the case of some offices, the amount of the liability in respect of annuity business exceeds that in respect of assurances.

The theory of ‘temporary selection’ is concerned with the variation, for fixed x, of q[x–t]+t the observed rate of mortality at age x during the t+1th year after the issue of an assurance or annuity contract. The classical view is that—apart from chance variations—q[x–t]+t increases gradually with increasing t until the effects of selection have disappeared after which time q[xx–t]+t is a constant depending on x only.

Various reasons have been suggested for the persistence of temporary selection in an observed series of values of q[xx–t]+t. The chief of these are:

(1) The continuing effects of an initial selection on the part of the assurance company or by the annuitant (Morgan, 1834);

(2) The gradual withdrawal from assurance of healthy lives (Higham, 1851); and

(3) Secular improvements in medicals election or in the self-selection of annuitants (Karup, 1903).

In this paper the reader is asked to watch the heuristic development of an idea and its implications.

The subject is the way in which the working of a life office is unaffected by changes in the market rate of interest. For this purpose all other questions such as mortality, expenses, etc., will be ignored as far as possible. The idea is that actuarially a life office is qualitatively different from the sum of its individual policies; that many of the difficulties in discussing this subject occur because basic actuarial concepts and techniques, especially

(i) the idea of an average rate of interest, and

(ii) the method of discounting into a present value,

which have been designed primarily to deal with the problems of individual policies, are inappropriate to the large-scale problems of a life office, e.g. valuation, investment and bonus declarations.

The heuristic development is that of an alternative theory and technique; these do not, for instance, make use of (i) and (ii) above.

Of the three major elements in the formulae for office premiums, mortality has been subjected to refined investigation; interest has been considered closely, particularly since the war; expenses alone have hardly been considered. We have found only four papers on the subject in the whole of J.I.A., three (19, 153; 44, 415; 49, 111) many years ago, and the fourth (69, 50) before the war. There have been a few papers since in T.S.A., notably Mr Pedoe's (4, 485).

Our object is to analyse the expenses of a group of British life offices, so as to provide a reliable basis for comparison of offices, to enable managements to test the efficiencies of their own offices against others, and to provide means for getting standard costs as a tool of administration.

1. The field of biased and unbiased errors in recorded ages is vast, and there are many opportunities for research in it. This note is restricted to a consideration of a small part of the field. First, only errors from digital preference are considered, i.e. errors to move the age to one with a preferred end digit such as 0 or 5 or in general any even number. Secondly, concentrations at isolated ages which are a genuine feature of the population are not considered. Thirdly, the use of supplementary data (such as birth registrations) or supplementary calculations (such as graduation) is ignored.