In 1907 I had the honour of reading before the Institute a paper dealing with the Comparative Bonuses under Whole-Life and Endowment Assurances, and therein I pointed out that the method of apportioning the expenses between the two classes had a considerable effect upon the rates of bonus, and in the discussion more than one speaker referred to the relative premiums as vitally affecting the conclusions to be drawn from any investigation. The solution of the first problem will, mortality apart, also give us the key to the rates of premium which an office should charge for Whole-Life and Endowment Assurances respectively. As the premiums are the foundation of our business it is of the utmost importance that an analysis of the expenses should be made periodically in order to ascertain the adequacy of the remuneration the office receives for the risks it undertakes. The question of the office premiums has been frequently discussed, but I do not think any paper has been submitted to this Institute in which an agreement has been shown between the loadings adopted in obtaining the office premiums and the actual expenses of the office. The object of the paper is to elicit the views of the profession upon this subject.

The commission paid by the majority of offices is, for the principal classes of Assurance, usually a percentage of the sum assured on payment of the first annual premium and a percentage of the office renewal premiums. The loading required to provide for the commissions is therefore easily ascertained and requires no discussion.

The Mortality of Female Assured Lives has not been, so far as I am aware, the main subject under discussion at a sessional meeting of this Institute since February 1875, when the late Mr. Cornelius Walford read extracts from his exhaustive article on “Female Life”, which was subsequently published in the Insurance Cyclopedia. It is hoped, therefore, that in bringing forward this subject as the main theme for consideration, a useful purpose may be served by eliciting the current views of the profession in regard to assurances on Female Lives, and that the tables now submitted may prove of value in practice.

A secondary object of the paper is to bring under notice a new summation formula of graduation, and it is hoped that some part of the discussion may centre round the method adopted in graduating the tables.

Although the subject of Female Mortality has not received exclusive consideration at a sessional meeting of the Institute for nearly 35 years, it has incidently been mentioned in papers read in this Hall, and has been the topic of valuable contributions to the Journal.

The paper by Mr. G. F. Hardy on the mortality of assured lives and annuitants in France (J.I.A., vol. xxxiii, p. 485), and Mr. Ackland's paper on “The British Offices' Life Tables, 1893” (J.I.A., vol. xxxvii, p. 113), both deal at some length with the subject. Mr. G. H. Ryan's editorial remarks on the practice of Life Offices in regard to Female Assurances (J.I.A., vol. xxix, p. 75), with tables showing the experience of four French and twenty-three German Companies, and Dr. T. B. Sprague's observations on the Mortality of Healthy Female Lives insured with the Scottish Equitable Life Assurance Society (J.I.A., vol. xxxi, p. 2213) are also valuable contributions.

In writing upon the subject of this paper, I met at the outset with a difficulty which, I am afraid, will tend to make the paper less interesting to some of you than I would like it to be. The difficulty I refer to is this—that a considerable proportion of such information as I have upon the subject, and that which occurs most readily to me, is what I may perhaps call “particular” information, that is information relating to particular investments; whereas the information which appears to me to be most suitable to give here is that of a more general character, relating, primarily, to the principles which should guide us in selecting investments.

The first point to consider in connection with any railway the securities of which are under consideration for investment, is the value of the undertaking itself in relation to the amount of the issue of bonds or other security charged upon it. There are various ways of considering the value, the principal of which are:

1. The cost of the undertaking.

2. The probable cost of building another similar railway.

3. The actual present value as evidenced by the revenue derived from it.

As regards the first of these, it may be noted that this criterion of value is the least reliable of the three, but it is interesting not to overlook it, as it is in this respect that we find the greatest contrast between English and American railways. Whilst English, railways were built at very great expense, large sums being paid for land both in the country and in towns, and the actual work of construction being done upon the most expensive scale, American railways were, in early days, built very cheaply, the land being obtained without payment, and the railway construction being on an economical scale.

In bringing these Notes under the consideration of the members I feel some apology is needed for the reason that the subject may he said to be somewhat outside the scope of the ordinary proceedings of the Institute.

In addition, however, to its legal aspects, which will doubtless appeal to a profession which demands from its members a not inconsiderable knowledge of law, I venture to think there are other grounds on which the subject may be considered suitable for discussion.

The Public Trustee Act brings into being a Department, which, from its intimate connection with the affairs of the people and the large financial interests involved, may in course of time rank only second to some of the great Departments of the State, and, from this point of view alone, the subject is of interest.

Moreover, it has a close connection with the work of many Actuaries owing to the large investments made by Life Offices in reversionary securities, this kind of investment being peculiarly affected by questions concerning the trusteeship.

When, further, it is remembered that Insurance Companies form one of the classes of Corporate Bodies which may be authorized by the Treasury and Public Trustee to undertake the duties of Custodian Trustees, I think it will be admitted that the subject is one with which we are practically concerned.

Nearly twenty-two years have elapsed since the masterly essay of our President gave to the institute an opportunity for comprehensive examination of the British friendly society system. During the intervening period, phases of the subject have been occasionally before the Institute, but the period has been one of great activity amongst the friendly societies, and developments of interest to actuaries culminating, it may be suggested, in the co-operation of the State and the societies proposed by the Chancellor of the Exchequer, have emerged. In the circumstances it has seemed to me that the Institute might again survey this wide field of provident effort with interest to its members and profit to the community.

I propose accordingly to examine the more important groups of societies, paying particular regard in respect of the leading affiliated orders to the machinery by which it is sought to equip the constituent parts for the effective recognition of their duties; thence passing to some questions of special interest to ourselves. For the purpose of connected description it will be necessary to mention particular organizations, but I trust that nothing of what I have written may seem to depart from the excellent custom of neutrality which governs our debates. I venture indeed to say that so far from being unduly sensitive, all the societies which are striving for improvement (and I think this may be said of most of them) are receptive towards the stimulus of informed criticism.

In many staff pension funds there is a provision that if a pensioner dies before his pension payments amount to the oaccumulation of his contributions (with or without compound interest) to the date of retirement, the difference shall be paid to his representatives.

Although Mr. H. W. Manly and Mr. George King have dealt with the problèm of valuing this benefit, and Mr. Manly has shown how to calculate the rate of contribution to provide for it, the formulas presently to be deduced may be thought of sufficient interest to warrant their publication.

In considering the benefit mentioned above, it will be seen that if—

(i) the contributions amount to n times the yearly pension,

(ii) the annuity used in valuing the pension be continuous,

(iii) the benefit be valued on the assumption that the funds earn no interest—

the value of the benefit at the date of retirement, for each unit of annual pension, will be as follows, assuming the deaths to be equally distributed over the year:

Of lx persons retiring at age x, dx will die in the year of age x to x + 1, and as they will, on the average, die in the middle of the year, there will be payable in respect of them (n − ½)dx, being the amount of their contributions less ½dx which they will have received as pension.