Our Journal contains singularly little information on Vaccination—a brief remark by S. H. Ward, M.D., in 1860 (J.I.A., viii, 339); some paragraphs in a general paper by H. W. Porter, in the same year (J.I.A., ix, 151); and a paper by Dr. Sprague in 1877 (J.I.A., xx, 216), are the only references to the subject that I have been able to trace.

The present paper is a continuation of that in the Companion for 1840, on the application of Barrett's method of calculating Me contingencies. No tables were then published for contingencies involving two lives; but since that time Mr. Jones's tables have appeared, in his work on the subject in the Library of Useful Knowledge. It may therefore be worth while to collect and describe the formulæ relative to two lives which are most likely to be useful in practice; with some other matters, which may partly interest the actuary and partly the commencing; student.

Although a great deal of what might be fairly comprised under the heading to this paper came under discussion last year at the International Congress of Actuaries, I yet venture to submit that, upon so important and comprehensive a subject as the one I have chosen, there is a considerable amount of information, statistical and actuarial, which at that great gathering was not even touched upon. In the first place, the contributions to the Congress, valuable though they were, dealt only with the experience of individual Colonies or groups of Colonies, and the observations of the contributors were limited to particular branches of their subject. Secondly, some of the principal British Possessions, such as India, Canada, and the West Indies, appear to have been entirely unrepresented as regards life assurance among the subjects discussed. It is, therefore, with the object, partly of filling up a few of the gaps left vacant at the Congress, but chiefly of surveying the subject as affecting not merely individual Colonies or Dependencies, but the whole of the British Empire outside our own country, that I have collected and set down these notes.

1.1 On 21 December 1976 I received the following memorandum from Mr A. E. Tinckler, who was then the Actuary of my Company. It read:

1.2. “We have been discussing recently some of the effects on the Life Fund of a significant fall in interest rates, and I think we agree that the time has now come to set up a formal study to analyse the problem and to make recommendations.

1.3. “There is no doubt that interest rates in the United Kingdom are very much higher at the present time than in other comparable countries. There are good reasons for this state of affairs, but it is most unlikely to continue over more than a few years, unless the country is to descend to very low levels indeed in the international league. In spite of many pessimistic assertions to the contrary, there are good grounds for thinking that the present rates will come down very substantially indeed over the next few years.

The paper first discusses in a general way the methods hitherto devised for giving effect in actuarial calculations to a falling rate of interest, which methods it is suggested are cumbersome and inelastic and so of little practical value. A method is put forward which it is claimed facilitates the study of the many important and interesting problems involved in the assumption of a declining rate of interest.

Where it is the rate of interest in the tth year, the assumption is made that

where a, c and k are constants to be determined.

By making certain substitutions the following equation for the value of it is derived :–

It is demonstrated that under certain conditions this equation produces a decreasing series, and that by giving the constants suitable values a wide range of interest curves of the same general character may be obtained.

The formula is developed in combination with actuarial functions, and it is shown that where f′(x) represents the value of a function at a decreasing rate of interest determined by the above formula

where is calculated at rate k and at rate l.

The method is applied to the evaluation of annuities, reversions and other actuarial functions under four sets of interest conditions and the results are analysed and compared with values on a 4 per cent. basis.

The cognate question of an increasing rate is also touched upon.

Little space in the Journal has been devoted in the past specifically to graduation tests, and nowhere have the tests generally applied been concisely set out and fully discussed. The only papers during the last forty years on the subject have been by Seal and Daw; both these papers were submitted and discussed during the war years, with the result that many actuaries were unable to be present and state their views; indeed, many of us did not even know of them until the numbers of the Journal in question were published, and an opportunity to study them did not arise until after the war.

In this paper we investigate the effectiveness of the Minimum Funding Requirement (MFR) (pre-1999 version) under random future investment conditions. In particular, do the various liabilities calculated under the MFR deliver a suitable level of security to pension scheme members?

The paper considers active (and deferred) members and current pensioners separately.

For active members, Monte Carlo simulation is used to compare how the proceeds arising from investment of the pre-1999 MFR liability in an equity-backed personal pension would compare with the deferred pension promised by the scheme. It is found that, while there may be the intended 50% chance that the personal pension has a better outcome, there are very substantial downside risks for younger members. Investment strategies based upon index-linked gilts are shown to result, on average, in lower personal pensions, but they provide an extremely effective means of limiting the downside risks.

For pensioners, Monte Carlo simulation is used to find the distribution of the initial amount of assets required to pay off precisely the pension liabilities as they arise. This investigation considers the effectiveness of the 12-year rule and different investment strategies. The 12-year rule in combination with an equivalent investment strategy is shown to provide reasonable security for a typical group of pensioners. However, if investments are restricted to an appropriate mixture of gilts then the level of security for pensioners is much increased. In particular, we investigate the use of value-at-risk reserves. It is found that 95% value-at-risk reserves are lower for a mixed conventional/index-linked gilts strategy than a mixed gilts/equity strategy.

It is argued, because of the high degree of downside risk, that there is no place in MFR calculations for high, anticipated equity returns. Instead rates of interest should be based solely upon fixed-interest and index-linked gilt yields.

The historic barriers between the different companies which comprise the financial services industry are breaking down. In order that organisations may prosper in the new environment the relationships between products, distribution and clients need to be understood. A theory is developed to explain the historic position and the dynamics of the current environment and indicate future trends. The conclusion is that successful organisations will be those which fully understand and specialise in a limited number of sectors, and those who start with a clientbase and a distribution system which will not inhibit the introduction of other distribution methods so that they can become multi-product and multi-distribution organisations. Finally, the paper explores the relationships between pricing policy and distribution by means of distribution chains to determine the point and degree of price sensitivity.

A principal use of logarithms is to solve all the cases of compound interest which are not, without great difficulty, attainable by the rules of common arithmetic. But before we proceed to the practical part, it may, perhaps, not be improper to say something of the foundation or demonstration of the rules we are to give.

The paper is in the nature of a summary of the authors' book “Surplus in British Life Assurance—Actuarial Control over its Emergence and Distribution during 200 Years”. Copies may be purchased direct from the Institute of Actuaries (price 17s. 6d.). Members and Students of the Faculty may obtain a copy for personal use at the reduced price of 11s. post free. It begins with a survey of the principal factors that have influenced the development of theory and practice in regard to surplus throughout the years. It describes the manner in which surplus first arose in scientific life assurance, and traces how this and other historical developments have had an important effect both in the early days and later as a valid standard of equity was gradually evolved. At the same time the influence of long-dated contracts and of the expectations of the public has been a stabilising factor in spite of rapid changes in the economic and social scene.

The characteristics of the nineteenth-century image of equity are described, and the history of the twentieth century in regard to surplus is seen as one of attempts to preserve that image through sharp and contrasting vicissitudes. This idea is explored in some detail for both ordinary and industrial life business.

The problems of the present day are reviewed one by one and the paper touches on such matters as economic inflation, the public demand for pension schemes, the introduction of computers and data-processing devices and the prospect of Britain joining the Common Market. Against this background, various modern concepts of equity are contrasted and brief reference is made to matching, immunisation and gearing. Equity in with-profit pension schemes and systems of variable policies are also considered.

This general survey leads the authors in the end to ask some critical questions about the performance of the profession throughout its history. These questions relate to the success or otherwise of actuaries in foreseeing the future, in attaining equity and in progressing with the times. The authors attempt to answer them and are able to end on a cheerful note as regards past achievements and to express great hopes for the future, which may well bring a new era for the profession.

The UK has seen a significant transition from Defined Benefit (“DB”) to Defined Contribution (“DC”) for occupational pension saving. The planned automatic enrolment program starting in 2012 is expected to increase the use of DC. The main features of DC are that investment risk falls onto the individual during the pre-retirement phase and that there are no guarantees as to investment returns or the level of pension. In July 2012, Steve Webb, the Pensions Minister, challenged industry to think hard about meeting the need for more certainty about pension savings in DC plans and to consider providing an affordable ‘Money Safe’ guarantee where the member would get back at least the nominal value of their contributions (individual, employer and tax relief). This paper explores whether this is viable for the mass market.

When a series of quantities which depend on a fixed law, whether known or implied, follow each other in a due order of succession, the general accuracy of their numerical values may be satisfactorily tested by observing the regularity of the progression of a suitable order of differences. If the tabular quantities are the results of calculation from a given formula, with equidistant arguments, by differencing them up to a certain order the existence of an isolated error, if one should exist, is thus prominently exhibited and therefore speedily detected. Moreover the precise locality of the error and the fact of its individuality being indicated by a characteristic interruption of the law of progression, the proper correction is ascertained by carefully noting the central position of the disturbance, and revising the corresponding portion of the original computation. This work of revision may, however, be dispensed with, if necessary or desirable, as the magnitude as well as the locality of the indicated error can in general be readily deduced, with sufficient accuracy, directly from the differences, by the method of adjustment here given. The method, being so far independent of fundamental origin, is therefore equally applicable to the adjustment of a series of quantities derived from observation, or from statistical data; only in this latter case, as almost every quantity must be more or less affected by imperfections arising from defective information and other known or unknown incidental causes, the influence of which may sometimes be augmented by paucity of numbers, the progression of the differences is disturbed by a more complicated combination of the effects of an irregular series of errors, and it becomes more difficult to eliminate the value of each separate correction.

The subject of this Paper is Whole Life Non-Profit Assurances with uniform Premiums payable throughout life.

In choosing this subject for investigation, I have been influenced mainly by the following reasons :

(1) This type of policy represents life assurance in one of its simplest and earliest forms. The premium and the sum assured are both fixed throughout life, save for the very slight chance of insolvency of the office causing the contract to be reduced. Also nowadays it is not uncommon to find that the surrender values and equivalent paid-up policies are guaranteed from the outset.

(2) Other tables such as Whole Life by Limited Premiums, Half Premiums for first “n” years, &c., are as a rule founded on the basis of the simple whole life ordinary rates.

(3) A considerable body of data derived directly from the experience of British Offices under ordinary whole life non-profit policies is available as a result of the British Offices Mortality Investigation, 1863-93.

(4) In spite of the apparent simplicity of the contract, there are marked divergencies in the rates of premium charged by first-class offices and in the surrender values and equivalent paid-up policies offered by them.

1.1.1. In October 1980 the Council of the Faculty of Actuaries set up a Working Party with the following brief:—

• (1) To investigate the criteria by which the solvency of life assurance companies should be assessed and to determine the amount of the solvency margin which should be required in practice by supervisory authorities. The existing requirements of the E.E.C. Life Establishment Directive should be considered with a view to recommending any desirable alterations thereto to be made when those requirements are reviewed in due course by the E.E.C. Commission. In carrying out its work the Working Party should co-operate with Working Parties or Committees of other actuarial bodies.

• (2) To report the result of their investigations to Council.

Traditional and standard discounted cash flow valuation techniques are unable to deal with a variety of options contained in lease contracts. In the United Kingdom the most important embedded option is the upward-only rent review. This becomes more valuable to the landlord in an era of low demand and low inflation, as nominal market rents are more likely to fall. Lease contracts are freely negotiated between landlord and tenant, and alternative forms of rent review clause would fundamentally change the investment characteristics of property. Many other less common options also exist in lease contracts and these create further valuation difficulties. It is essential that property valuation techniques be developed that explicitly value the options in lease contracts.