Both the Royal Statistical Society and the Institute of Actuaries are interested in the collection and analysis of data and the use of the results for forecasting possible future trends. This paper deals with future traffic estimates of the number of passengers likely to use new underground railway facilities and the likely effect on the existing underground railway networks and other methods of transport, both public and private. It does not deal with the future planning of main line railway suburban services; nor does it deal with the civil engineering and operational problems of construction, although, of course, the capital cost of construction for a new tube and the capital cost of rolling stock have to be taken into account in considering the financial prospect of any new schemes.

In the United Kingdom the customary approach to non-life insurance has been to rely more on the practical experience and flair of the underwriter than on a statistical examination of the experience. In some branches of non-life insurance an office is able to make adequate adjustments to its rates on the basis of claim ratios (i.e. the amounts of claims divided by the premiums) for fairly broad groups. In the more competitive branches such as motor insurance the experience needs to be examined in much greater detail, not merely to satisfy the minimum requirement of guarding against selection of the better risks by other insurers, but more positively in order to find out the extent to which the risk varies with each of the existing rating factors and any possible alternatives. Also, because of the rapidity with which conditions are liable to change, the experience studied must be as up to date as possible if reasonably reliable estimates of the future are to be made.

It has been said that everybody believes in the Law of Errors (i.e. the Normal distribution), the experimenters because they think it is a mathematical theorem and the mathematicians because they think it is an experimental fact. Text-books on statistics often seem to produce the Normal distribution as the conjurer produces a rabbit from a hat and the actuarial student, who should be something of both mathematician and experimenter, is frequently somewhat mystified as to why such an apparently complicated distribution function as

Fig. 1. The Normal distribution

(see Fig. 1) is suddenly introduced and given such prominence.

The object of this paper is to look at some of the practical problems which have to be faced in an analysis of motor insurance statistics and to point towards some of the solutions. In order to cover the ground, it has not been possible to examine any of the issues in any great depth and only private car insurance is considered. Much of the theoretical background to the subject has already been very ably put to this Society—in particular in papers by R. E. Beard and P. D. Johnson—with the result that a certain element of repetition has been inevitable, but this paper is in no way intended to be a complete theoretical treatise. The intention has been to consider various problems, discuss some actual statistics and their implications and then to continue. It is hoped that this may lead to a better understanding of the practical issues involved and at the same time may encourage others to delve into a quite entrancing subject which offers considerable scope for useful research.

These notes are concerned with the related subjects of expenses and their control, and forward planning in a life office. Little attention has been paid to the subject of expenses in the proceedings of either the Institute or the Students' Society in recent years, with the notable exception of the paper by Dyson and Elphinstone (1959), although expenses formed Subject 1 of the 17th International Congress. Forward planning of a life assurance company as a whole has received even less attention in our proceedings. This is in some ways not surprising since the problems are in the main managerial rather than strictly actuarial, but even if this is accepted they are nevertheless problems with which many actuaries have to deal, and this neglect is regrettable.

I use the expression ‘money market’ to describe those institutions in the City of London who are active in borrowing and lending money for short periods, from a single day to perhaps 5 years at the most. From being a tight circle centred on the Bank of England, the discount houses, and the clearing banks the money market has now grown to include, as active investors, public corporations, local authorities, merchant banks, overseas banks, hire-purchase companies, building societies, trustee savings banks and Lloyd's syndicates. In addition, institutions with long-term liabilities, such as insurance companies and pension funds, will occasionally have business to transact in short-dated securities, an example being the profitable employment of funds earmarked for the purchase of real property in a few months' time. In any event, it is worth while to remember that the long term consists of a series of short terms.

This paper covers a field in which few actuaries have been actively engaged in the past, namely the appraisal of proposed capital projects to determine their likely profitability. In recent years this subject has received increasing attention from the accountancy profession and from operational research practitioners. Various methods of tackling the problems have been proposed, including ‘discounted cash flow’ techniques. Most of the methods used employ compound interest and some involve probability concepts; it is surprising, therefore, that actuaries have not given the subject more attention. Furthermore, actuaries concerned with the investment of funds should also be interested in the matter from another angle: the shares which will yield the greatest return to investors may well tend to be those of the companies which carry out proper financial appraisals of the ventures in which they propose to engage.

I have chosen the word ‘Education’ rather than ‘Training’ so that discussion can wander as far afield as possible; for example: school, university, Actuarial Tuition Service, office, post-qualification education and training of various kinds. The experienced actuary is seldom a narrow specialist; the ambition of most young actuaries is to become a manager of some kind or another and this work involves basic disciplines and skills other than those covered by the examination syllabus.

Menzler's book The First Fifty Years will give the reader a good idea of the plight of the actuarial student during the 1920s. There was only one good text-book, that on life contingencies. There were other books that were helpful but they could hardly be classed as very suitable for the beginner. The only official classes were the oral classes in London. A provincial student had either to persuade an official tutor to correct test papers for him, or obtain the services of some other actuary; for example, classes were organized at the Prudential Assurance Company and the tutors were prepared to let other students have the test papers and any notes that were issued.

Last year the Manchester Actuarial Society asked me to speak to it on my experience before I entered the profession, with particular reference to investments. This invitation caused me to review my experience over about twenty years in the Trustee Department of a Bank in supervising a large number of miscellaneous portfolios ranging from quite small ones to substantial pensions funds. The general conclusion which I reached was that investment theories generally were surprisingly little help. This was a conclusion which was rather depressing and I invited the Society to do their best to prove me wrong, adding that for once in a way the speaker would be only too pleased if someone did just that.

Before committing myself to writing the present paper, I awaited that by Messrs Weaver and Hall given to the Institute earlier this year, and the discussion on it, as I hoped that I would find in either one or the other some of the answers to the fundamental questions which were troubling me. I regret to say that whilst I am not in any way criticizing the computer method, I find that these fundamental difficulties still persist.

This paper is not intended to be a fully comprehensive survey of the taxation of insurance business. Rather it is meant to highlight some of the aspects of the taxation of this business which have been affected by the 1965 Finance Act and which should now, I think, be influencing our thinking as regards the transacting of insurance from both the shareholders' and the policyholders' point of view. Despite the splendid efforts of both the Life Offices' and British Insurance Associations during the past year, not all these changes have had the publicity which might have been expected after a normal Finance Act. I have dealt with general insurance and ordinary life assurance separately and, although the paper is written from a proprietary office's point of view, most of it is equally applicable to a mutual office. Neither have I dealt specifically with industrial life business, but I believe that most of the paper applies to this as well.

During the 1930s there were allegations that London bus drivers and conductors had an undue amount of sickness, especially gastric disorders. Dr Bradford Hill (1937) was asked to investigate this allegation, but found that the data were limited. The London Passenger Transport Board determined that in the future adequate data for such investigations should be available. This was not possible until after the war. In 1948 the Central Record of Staff Statistics was set up to compile sickness-absence statistics and for other purposes. This lecture is mainly an account of the uses made of the statistics produced: how they can be used to study the effect of sick pay provisions, the secular trend of sickness absence in occupational groups, and the differences in sickness-absence experience between groups of various kinds. If the experience of these groups is related to the employees' work and the conditions under which it is done, the results are valuable in answering questions on health from management and unions. The data collected can also be used in medical administration and for research into the causation of disease.

H. O. Worger gave a simple rule (J.S.S., 5, 15 and J.S.S., 7, 116) for using tables of Bond Values for finding the equivalent gross redemption yield on a redeemable security where the dividend is subject to income tax but the capital gain is tax-free. He showed that it was unnecessary to go through the process of first finding the net yield by entering the tables at a dividend rate from which tax had been deducted. All that was needed was to reduce the unexpired term in proportion to the rate of tax payable, and enter the table for the full nominal rate of dividend. The purpose of this note is to show that a somewhat similar rule is available if both dividend and capital gain on redemption are subject to the same rate of tax.

Let P be the purchase price of a loan of 1 redeemable at par in n years time and bearing annual dividends at the rate g, and let t be the rate of tax.