Perhaps this paper should be entitled A Description of Methods Being Used in Connexion With a Contract of the Grant and Kingsnorth Category ‘A’ Type, For Want of Any Better Ideas. (The reference is to Unit Trusts and Equitylinked Endowment Assurances by A. T. Grant and G. A. Kingsnorth, J.I.A. 93, 387.) It has been written because the publication of the Scott Report and the passing of the Insurance Companies Act make it desirable that the Institute should discuss unit-linked assurance again at this time, and because certain aspects, in particular maturity guarantees and reserves for tax on capital gains, have not been dealt with adequately in the past. Propositions in respect of these are made in the paper, and it is hoped that, as a result of discussion, ‘generally accepted actuarial principles‘category B’ type contracts, for example considerations affecting pricing units net of tax on capital gains, but the paper does not attempt to deal with this type of contract more generally, as fundamentally different considerations are involved. It does deal with ‘category A’ policies linked to unitized internal funds as well as those linked to units of Authorized Unit Trusts.

Electronic computers have been available commercially for about 20 years. Actuarial interest was soon shown, but although a number of papers have appeared over the years there has been little recent discussion of how computers can best serve the profession.

Many actuaries have little computing experience. To them it may appear a daunting task to learn to use a computer, because many instruction manuals seem, at first sight, extensive and complex. Our principal aim is to demonstrate to them that given suitable permanent facilities it is quite easy to use a computer for actuarial calculations, however complex these may be. We suggest that the complexity of most existing actuarial programming systems is unnecessary, and may have impeded the understanding of the computer's potential by actuaries.

A time-honoured convention in accounting has been that accounts should be based on the principle of historic cost, namely that all items should be recorded in terms of the purchasing power of the pound at the date of each transaction. This convention has the virtue that the accounts are based largely on factual monetary transactions and fewer items need be determined subjectively. It is a valid convention so long as the value of money remains constant, but in a period of inflation, accounts drawn up on this basis become distorted, and the higher the rate of inflation the greater the distortion. For example, amounts based on historic cost which are set aside for depreciation of plant and machinery will, in a period of rapid inflation, be totally inadequate either to provide funds for the eventual replacement of those assets or to maintain the real value of the shareholders' original capital investment. Similarly profits are overstated by the inclusion of profits on stock which arise solely from a general increase in price levels. Again, no account is taken of the real cost of holding cash or other monetary assets when money is losing its purchasing power. Conversely, no credit is taken for the gain derived from having borrowed money, when the liability for repayment of the loan is in real terms reduced.

This paper arose from a report prepared by a working party set up under the auspices of the Research Committee. The views in the paper are my own but they are, to a considerable extent, based upon work done by Messrs J. K. W. Davies and P. N. S. Clark. I am also indebted to Mr R. T. Foster of the Government Actuary's Department for clarifying points arising from the current Regulations.

2. The paper is concerned with the Returns made by Life Offices to the Department of Trade and Industry in accordance with The Insurance Companies (Accounts and Forms) Regulations 1968. The aims of this paper are:

(i) to discuss the objectives of the Returns,

(ii) to discuss whether the questions asked by the present Regulations and the answers currently being given in the Returns achieve these objectives,

(iii) to discuss possible changes in the Regulations, and

(iv) to discuss the role of the actuary in relation to the Returns and also in relation to the auditor.

The results of the investigation from 1945 to 1959 were presented in a paper to the Institute by R. E. Hayward and B. C. Lucena (J.I.A. 91, 286) and readers are referred to this for further detail on practical aspects of the investigation. This further report owes its existence to all those originally involved as well as those specifically involved in the follow-up. Professor J. M. Malins and Dr M. G. FitzGerald have continued to give us the help needed to obtain the required data from the hospital records. Those of our Society particularly involved in producing this follow-up report include B. C. Lucena, R. Betteridge, A. Roberts and M. Willett.

Supervision of Insurance Companies in the United Kingdom is based on the principle of ‘freedom with publicity’. For general insurance, publicity is provided through the returns required by the Insurance Companies (Accounts and Forms) Regulations 1968 (S.I. No. 1408) which was issued under the terms of the Companies Act 1967. If the principle is to operate successfully the returns must be scrutinized carefully if not by prospective and existing policyholders and stockholders then by those representing their interests, be they government departments, insurance brokers, stockbrokers, statisticians, accountants or actuaries. The nature of the information to be collected, as well as its presentation and interpretation requires special skills and experience. An actuarial training provides these skills and it is appropriate, therefore, that the returns should be discussed at a meeting of the Institute.

One of the most powerful devices in the theory of compound interest is Makeham's formula. The essence of the formula may be stated as follows:

Consider an admitted loan of C bearing interest at rate g per annum (payable pthly in arrear) per unit of admitted capital. The loan is to be repaid by a series of payments each of which contains a capital portion and an interest portion. Let K be the value at rate i per annum effective of all the capital portions.

Some 20 to 30 years ago considerable progress was made in understanding the variance of mortality rates and, for assured lives data, the effect on it of the presence of duplicate policies, e.g. Redington and Michaelson (1940), Seal (1941, 1947, 1948 and 1949), Daw (1945 and 1951), Vajda (1945), Solomon (1948), Beard (1951), Jager (1953) and Continuous Mortality Investigation (C.M.I.) (1957). I have the impression that since that time this understanding has tended to regress. For example it is disappointing to find that the whole course of reading on the analysis of mortality data makes practically no mention of the effect of duplicate policies in increasing the variance of mortality rates. Yet this is a matter which can have a substantial effect on the results of testing a mortality table graduation as is recognized in C.M.I. (1974). It is salutory to find that G. H. Hardy (1882) was aware that the presence of duplicates increased the variance although he did not express it in quite that way.

Staple Inn and the Patent Office are only separated by the width of a garden, and it might be wondered why none of the many ingenious schemes of insurance has ever been protected by patenting it. Such protection of an idea should be impossible, as will be explained later, but in 1778 one John Knox ‘Of Richmond in the County of Surry, Gentleman’ took the first step towards such a patent by petitioning King George III ‘that with great assiduity, art and pains and after many laborious calculations and at a considerable expence’ he had invented ‘A Plan, Different to any before that Time Discovered, for Assurance on Lives from Ten to Eighty Years of Age, upon a Twofold Beneficial Principle, Making a certain provision as well for Subscribers or their Representatives upon the Death of the Person on whose Life Assurance should be made within the Term Assured for, as also by Means of a Reserved Capital for the Surviving Subscribers whose Nominees should be Living at the Expiration of such Term….’

It is quite common for stocks (usually loan stocks) to be issued by companies and purchased by investors, which include among their terms an option to convert at some future date into other stocks (usually ordinary shares) on specific terms. Such options obviously have value, but I am unaware of any simple published method for estimating the value of such options in practical cases. The purpose of this note is to suggest a formula, based upon easily understood estimates of the future market prices of the stocks in question, which may be applied readily in practice to estimate the value of such options.

Pollard and Pollard have considered a stochastic approach to certain actuarial problems. In their notation ãx denotes the random variable whose expected value is ax. The random variable ãx depends on the random variable, time until death and the (assumed constant) rate of interest. The authors show how to calculate the second and higher-order moments of some common actuarial random variables such as ãx and Ãx. The second moments, in particular, are useful in estimating confidence limits for the total liability in respect of a group of contracts.

Classification of Stock Exchange Securities by Industry

As a result of quarterly meetings of the Index Constituents & Industrial Classification Committee, the classifications of 60 companies were changed either because the original classification was found to be wrong, or because the company had clearly changed its business. These changes were only made after notification to the company concerned and in most cases after discussions with the company; apart from those with whom negotiations had begun in 1972, a further 65 companies were approached in 1973. Classifications of newly floated companies were made by the Stock Exchange Quotations Department but the published lists were scrutinized and occasional changes were recommended.

The original classifications were set out in the 1970 note in this series (J.I.A., 97, 111–12). During 1973, Group 52 was renamed ‘Newspapers & Periodicals’, and five minor amendments to the definitions of other Groups were made.

ASTIN—the section of the International Actuarial Association whose main interest is in the actuarial study of non-life insurance—held its 10th Colloquium at the University of Essex from 4–8 September 1973.

In all 161 members, representatives of corporate members, and accompanying persons attended, including 20 members of the Institute of Actuaries and 4 Fellows of the Faculty of Actuaries. 21 countries were represented and for the first time Great Britain provided the largest delegation.

The subject for the Colloquium was ‘Mathematical and Statistical Models underlying nonlife insurance’ and 24 papers or written contributions were presented. The Colloquium was opened by R. E. Beard, O.B.E., F.I.A., in his dual capacity as co-ordinator of the Scientific Programme and Professor at Essex University. The Chairman of ASTIN, Professor Bühlmann from Switzerland, expressed the gratitude of all to the University of Essex for the facilities given and his pleasure at the 10th Colloquium being held in the United Kingdom, a country recognized as the Father of Insurance.