The subject I have chosen for my paper is one which needs no apology for its introduction to this Institute, closely connected as it is with one of the most pressing problems which those responsible for the management of a life assurance office have to deal with at the present time. It is, no doubt, difficult, in the face of the eager competition which has to be encountered, to increase the business of an office; but it is scarcely less difficult to satisfactorily invest the surplus arising from the premiums when they are obtained. One is reminded of the picture which appeared a few years ago in Punch, in which a Dean, importuned for alms by a beggar, exclaims, “Ah, my good “woman, it is not the poor only who have their troubles; you, “for instance, have probably never experienced the difficulty of “finding investments, combining adequate security with a “remunerative rate of interest”! It is probable that she had not, but it is equally probable that the actuary of every assurance company in this country has already experienced the difficulty, and is likely to experience it increasingly in the future. The investments which, in the past, have found favour with life assurance companies, have not increased in proportion to the increase of the funds to be invested.

Endowment assurance can boast of no great antiquity, though its constituent elements, the temporary assurance and the pure endowment, both date from early times. Traces of the latter are found as long ago as the 16th century; thus, in a pamphlet by one Thomas Wilson, published in 1572, and entitled “A Discourse upon Usurie, by waie of Dialogue and oracions, for “the better varietie and more delight of all those that shall read “this treatise”, it is stated that, “Whosoever lendeth such a summe “of money (£100), and hath a childe of one yeere, shall have for “his childe, if the same childe doe live till he be full fifteene years “of age, 500li (£) of money: but if the childe die before that “time, the father to lose his principal for ever.” It is evident that the rate of mortality in those days must have been alarmingly high, either among children or among the institutions granting these benefits. A form of assurance, similar in some respects to the above, called “Apprenticeship Assurance”, was introduced towards the beginning of the 18th century. In a prospectus dated 1710 it is stated that, “Anyone who now is, or that is to be an “apprentice, may by paying 1s. entrance and 2s. 6d. per quarter, “gain, probably from £40 to £50 up to £500 or £600.” After reading this astonishing statement, one cannot but admit that the tontine and other estimates of American Companies, about which we hear so much in the present day, pale their uneffectual fire before the similar extravagant statements made by our predecessors in the reign of Queen Anne.

Although a great deal of what might be fairly comprised under the heading to this paper came under discussion last year at the International Congress of Actuaries, I yet venture to submit that, upon so important and comprehensive a subject as the one I have chosen, there is a considerable amount of information, statistical and actuarial, which at that great gathering was not even touched upon. In the first place, the contributions to the Congress, valuable though they were, dealt only with the experience of individual Colonies or groups of Colonies, and the observations of the contributors were limited to particular branches of their subject. Secondly, some of the principal British Possessions, such as India, Canada, and the West Indies, appear to have been entirely unrepresented as regards life assurance among the subjects discussed. It is, therefore, with the object, partly of filling up a few of the gaps left vacant at the Congress, but chiefly of surveying the subject as affecting not merely individual Colonies or Dependencies, but the whole of the British Empire outside our own country, that I have collected and set down these notes.

The almost phenomenal advances that have recently been made in the business of industrial assurance have brought this branch of our provident system into a position of national importance. Ten years ago, the business of our industrial companies was, roughly speaking, as under:—

whereas to-day it is, approximately,

Beyond the business of these companies, a very large number of industrial assurance contracts exist in the societies, clubs, and various orders registered under the Friendly Societies Act of 1875.

The Annual Reports of the Registrar-General for England contain each year, tables giving information as to the mortality in the Navy and Army for a long series of years. My object in undertaking this paper was to compare the actual death-rates, as shown in these tables, with the rates prevailing among assured lives, with a view to ascertaining the extra mortality to which persons serving in the Navy and Army are subject. I subsequently found it desirable to extend the scope of the paper so as to include an examination of the recent mortality of the Navy, as shown by the Statistical Reports of the Health of the Navy, and of the Army, as shown by the Reports of the Army Medical Department.

“The rate of interest has fallen.” “The rate of interest is falling.” “The rate of interest will probably continue to fall.” These sentences, and others of a similar nature, we have read so often, that I fear it is quite possible “familiarity” may, to some extent, have had its usual effect. The fact remains, however, that any further fall in the interest yield is of vital importance to insurance companies with large funds to invest, and bound by contracts, the fulfilment of which depends, to a large extent, on the rate of interest obtainable.

In considering a subject on which to address you to-night, it occurred to me that I might invite your attention to some practical matters of office work, especially in connection with valuation books and forms.

Allow me, however, at the outset to express my thanks for the honour you have conferred on me by my election to the office of President. As a duty of my office an address is expected from me, and I must ask your indulgence in attempting to fulfil this obligation towards the close of what is to me the busiest season of the year.

I do not think that any apology, is necessary for asking the members of the Institute of Actuaries to devote a meeting to a consideration of the subject of Sinking Fund Assurances. My paper—if paper it can be legitimately called—contains, I am afraid, little, if anything, that will be new to those actuaries who have had to consider the subject, and doubtless in itself demands a very ample apology for the temerity of its author in submitting it to the criticism of the Institute. I am not, however, without hope that the ensuing discussion may bring out some points of practical interest, and if this should be so, and more particularly if fuller consideration of the subject should lead to an arrangement on the lines indicated in the concluding paragraphs of my remarks, I think I may fairly ask that these results may be considered as to some extent a mitigation of my offence.

One of the most striking features in the history of Life Assurance business during the past few years is the marked increase—both absolute and proportional—which has been shown in the number and amount of policies effected under the Endowment Assurance plan. There is every reason to expect that this increase will continue, and that ere long Endowment Assurances will divide honours with whole life policies as regards importance in the periodical valuations. It is consequently very desirable so to improve the methods of valuing such policies as to minimize the amount of labour involved, and it will become more and more necessary to abandon methods which answered very well so long as Endowment Assurances were looked upon as “Special Policies”, but which are extremely cumbersome when applied to a large mass of contracts. The shorter methods that have hitherto been suggested, though admirably adapted for use in test or check valuations, involve an error which many actuaries will consider too appreciable to be neglected, more especially as the approximate methods nearly always bring out a reserve which is smaller than the true reserve, and it accordingly becomes desirable to seek some process that will be free from this objection.

In assessing the risks to be provided against in the case of professional military and naval lives, consideration has to be given to the following distinct elements:

(1) The risk of death at home stations, or the normal mortality.
(2) The risk of death at foreign stations in time of peace, or the climate risk.
(3) The risk of death in active military service in the constantly recurring “small wars.”
(4) The risk of death in active military operations in “national wars.”
(5) The liability, in time of peace, to foreign service.
(6) The liability to active service in the field in “small wars.”
(7) The liability to active service in the field in “national wars.”

In a paper by the present writer, entitled Some Remarks on the Valuation of Endowment Assurances in Groups, which appears in the current volume of the Journal, pp. 61–84, a new method of valuing Endowment Assurances, based on Makeham's formula for μx and lx, was described, and it was shewn that very good results were obtained by the use of the method in the case of a fairly large Endowment Assurance business, particulars of which were summarized in the paper.

The following is a method of obtaining an approximate value of the annuity , based on the assumption that the mortality follows Makeham's formula. The numerical results will be found sufficiently close for practical purposes.

There appears to be a very general belief that every life may be accepted under the Double Endowment Assurance Table at the same rate, provided the term is fixed. One office, at least, grants such assurances without medical examination; another has accepted publicans under this table without the usual trade extra; and medical officers have been known to recommend acceptance at tabular rates for a Double Endowment after having declined the life out-right for an ordinary Endowment Assurance. It may be useful, perhaps, to ascertain how far this practice is justified by theory; and it is hoped, therefore, that a short note on the subject may not be without interest.