In treating of the above subject, it cannot be expected that any new principles will be put forward, or that any great amount of novelty will be found in the method of handling the question. All that I have aimed at is, to apply acknowledged principles to the discussion of a question of considerable practical interest at all times, and more peculiarly so at the present time.

A great deal of theoretical and empirical work has been carried out in recent years, particularly in the United States, on the use of mathematical models as an aid to the selection of investment portfolios containing equities. The present paper attempts to survey some of the more important advances that have been made, and to assess them in relation to the problems that managers face in the running of a portfolio.

The last paper submitted to the Institute on the special problems arising from the transaction of overseas life business was that submitted by W. F. Gardner in 1935 (J.I.A. 66, 198). The expansion since that date in overseas life business justifies a further review of these problems. In 1935 the revenue premium income (other than annuity purchase money) from the overseas business of British life offices as recorded in the Board of Trade Returns was some £6.4 million, representing 7.9% of the total ordinary branch premium income of British life offices; in 1954 the premium income from overseas business was £34.4 million and represented 12.3% of the total.

Sir,—In compliance with your instructions, we have the honour to submit to you the following observations upon the Accounts and Statements submitted to the Board of Trade in pursuance of the Life Assurance Companies Act, 1870.

A “company” is defined for the purposes of the Act to mean “any person or persons, corporate or unincorporate, not being registered under the Acts relating to Friendly Societies, who issue, or are liable under policies of assurance upon human life within the United Kingdom, or who grant annuities upon human life within the United Kingdom.”

The theory surrounding sickness rates has received little attention in the United Kingdom during the past two decades. This may be a consequence of the assumption by the British Government of the role of principal insurer against sickness, and the resulting reduction in numbers of those who otherwise might have turned to the traditional friendly society for sickness insurance. It is unfortunate that the decline in interest in sickness rates should have coincided with the burgeoning of the theory of stochastic processes, for sickness is a stochastic process.

The rapid growth of Accident Assurance, the passing of the Employers' Liability Act, and the periodically recurring discussions respecting schemes for a National Accident Fund, have created a demand for statistics on the subject of accidents, which cannot be said to have been satisfied.

The Tables given in this paper are believed to be unique as regards this country. The object of their compilation was to show the Rates of Fatal Accidents in various occupations. They are based upon a comparison of the male population in each occupation in England and Wales, as enumerated at the Census of 1871, with the average of the number of the violent deaths occurring to male persons following that occupation in England and Wales during the three years, 1870, 1871 and 1872. For the extraction of the particulars relating to these deaths from the records of the General Register Office, special permission was obtained by Dr. Farr; and it is with his cordial approval that the facts are now laid before the members of the Institute.

The Census of 1871 was taken on the 3rd April of that year. The population enumerated was therefore slightly in excess of the mean population to which the average of the deaths for the years 1870, 1871 and 1872 would have reference. The difference would, however, be slight; and for the present purpose it was thought that the population as enumerated might be considered suitable.

In pursuing the traditional practice of introducing myself officially by an Inaugural Address, I desire unaffectedly to state that any conventionality, which this course may have acquired from custom, is merged and lost in a deep feeling of grateful recognition of your generous confidence and goodwill.

Notwithstanding the very large amount of leasehold property, which in the course of every year is bought and sold in this country, and notwithstanding the extensive transactions—of almost hourly occurrence—in the public market, in Government and other temporary Annuities, the subject of the rate of interest which any given purchase will yield the buyer is very imperfectly understood, even by those most deeply interested in the inquiry, unless they happen to be at the same time well versed in actuarial computations.

The problem of solvency in insurance is at present under a good deal of discussion in various interested quarters, both national and international. It is principally a question of finding criteria for determining the size of the solvency margin which a private insurer must have in the form of free reserves to be considered solvent. A criterion must produce a margin which is both sufficient and suitable: it must be valid not only for a model portfolio but for any portfolio. Consequently, only insurers with the prescribed margin would be considered solvent and authorized to write insurance business. In recent years, particularly because of the directives promulgated by the Common Market authorities, it has largely been a question of the solvency of non-life insurers.

The various Pension Funds which have been established in the Presidencies of India in the Military, Medical, and Civil Services of the late Honourable East India Company have afforded the means of bringing together a great variety of interesting facts relating to the rates of mortality and marriage amongst Europeans in India. They were originally founded as mutual charitable schemes, giving assistance or pensions to the widows or children of such Members of the services as had not left sufficient pecuniary means for the support of their families or for putting them forward in life. The Company saw fit to encourage these laudable designs by allowing high rates of interest on their invested Funds, and making favourable arrangements in the exchanges for payments to be made in England.

We now pass to the traces of the early practice of LIFE INSURANCE, a subject which has in general been but very slightly noticed.

The estimation of the value of human life in its rudest approximation—that is, of the term of years which, on the average of a sufficient number of observations, would be observed to fall to the share of each of a given number of individuals born under certain circumstances, and continuing in certain climates or ranks—was to all appearance a subject the consideration of which, not only the speculations of the remoter ages had no impelling cause to enter upon, but one which, if pursued, would have led not only to scepticism, but even to persecution, for entering on a tacitly admitted forbidden ground.