The following notes are for the most part based upon the actual valuation of a registered friendly society and an attempt is made to describe the various operations involved and the points which arise for consideration, from the time the actuary (or valuer as he is commonly known in friendly society circles) is approached, to the time he signs his report and presents it to the society. I have, however, digressed occasionally from the main subject of these notes in order to express my views on certain general points which frequently arise in the valuations of friendly societies. It should be understood that these notes do not necessarily embody official opinion.

The specimen society is a typical “centralised” rural society (i.e. without branches) of about 1,000 members, their occupations being described as domestic, horticultural and agricultural.

It may be well to recapitulate briefly the questions asked at the recent Census, and the statistics which were published, showing the results of the previous Census. The questions asked on the 1931 householder's schedule comprised name, relationship to head of household, usual residence, sex, age, marital condition, birthplace, nationality, occupation, industry, and size of house. The volumes based on the 1921 Census dealt with occupations, industries, workplaces, dependency and orphanhood, ages and marital conditions, education, birthplace, nationality and housing, and general, sectional and occupational mortality, the subjects being dealt with both nationally and, in a condensed form, for each administrative county. For simplicity, attention is confined in this paper to the Census in England and Wales.

In considering the question as to whether an assurance can be granted to a particular proposer, the Chief Medical Officer and the Actuary of the Company have available the Medical and other reports of the life proposed. From the information given in those reports they have to form an opinion as to the present state of health and likelihood of longevity, taking into account all the factors before them. In some cases it does not require a doctor nor yet an actuary to decide that the policy can be issued at ordinary rates, but in other cases there will be some degree of impairment, varying from the case where a spin of the coin might be as fair a method as any, to the case which is obviously uninsurable at any rate. It is the border line cases which cause the most inconvenience. A certain proposer is slightly overweight, so we do not like the look of him, but this may be counterbalanced by favourable chest and abdominal measurements. Then, again, there may be a lack of longevity in the family history, but on the other hand he may only require a short term endowment assurance.

The title to this paper covers a very wide field and unless each of the subjects was dealt with somewhat briefly, the paper would be of inordinate length.

The general principles on which a valuation should be made are the same for Industrial as for Ordinary Assurance business. The methods adopted differ, however, one of the main differences being the system of grouping the policies in “select” form, either by calendar year of issue, sub-grouped by age at entry, or by age at entry sub-grouped by year of issue, the former being possibly the more popular and the one described in these notes. One of the original reasons for this form of grouping was the system of increasing the sums assured after a policy had been five years in force and again after it had been ten years in force, and in consequence the duration of the policies had to be taken into account in the valuation.

In America distributions of bonus are made on a “contribution” method, but in Great Britain most of the offices use a bonus system of the compound reversionary or the simple reversionary type. To an actuary practising in England a contribution method seems to entail a great amount of work and may not reach exactitude in the end; while an actuary practising in America must, I think, feel inclined to ask English actuaries how they reach fairness between different classes and different ages at entry.

If we define “fairness” for our present purpose as such a distribution as leads to an equation at the outset between the present values, on an experience basis, of benefits on the one hand and of premiums (less expenses) on the other, then a complete contribution method will provide “fair” bonuses whatever the basis of valuation; and this is true though the valuation basis may be far removed from actual facts and though the “profits” in the valuation sense, from interest, loading, withdrawals and mortality, bear no relation to the premiums or the facts assumed in calculating those premiums.