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1.1.1 The Faculty of Actuaries' Marketing Research Group was set up in May 1988 to research areas of interest to that new breed of Fellow, the “Marketing Actuary”.In the initial meetings two general areas of interest were identified—namely the marketing of the actuarial profession, and the marketing of financial services products.Whilst the group has spent time on both subjects this first paper is concerned with the marketing of the actuarial profession.1.1.2 We felt that the starting point for a marketing audit of the profession was to conduct research amongst the members. In addition we have investigated the coverage achieved by the profession in the media, and looked into developments in North America, including a survey which ranked the actuarial profession against other forms of employment.

The paper firstly examines the way in which U.K. mutuals operate and the forces which are leading mutuals to consider demutualisation. Demutualisation is normally accomplished by a Scheme of Transfer under Section 49 of the Insurance Companies Act 1982. The role of the directors and actuaries is discussed, including the impact of the Institute's latest Guidance Note (GN15).The protection of policyholders' reasonable expectations, the value of membership rights and the basis of dealing with any orphan surplus are the central problems. The paper examines them in the context of both the open fund and closed fund situation and shows how they may be resolved.A simple model is used to project the financial position of both an open and closed fund in a demutualised company. The relative advantages and disadvantages of each indicate that different courses of action may be appropriate for mutuals in differing financial positions.

We both started working in Spain at the end of 1991: one of us in a joint venture life company between a Spanish health insurer and a U.K. life office, and the other in an international actuarial consultancy.At the time of writing this paper we can only claim in the region of “4 man years” of experience of Spain. Therefore we do not pretend to offer an authoritative view of Spanish insurance or pensions, or of its actuarial profession. Clearly such a text would be better prepared by Spanish actuaries, or other long-standing practitioners of the Spanish market.

1.1 The principal motivation for this paper is our involvement in the valuation of pension benefits under the Family Law (Scotland) Act 1985 and the review being undertaken by the Pensions Management Institute Working Group on pensions and divorce. As a consequence of the introduction of the Family Law (Scotland) Act 1985, there is an explicit provision that pension benefits should be included as part of the matrimonial property in a divorce settlement. It will be clear from this paper that we have considerable doubts as to whether the present law is satisfactory; nevertheless it is difficult to argue that such an important item as pension rights should be disregarded in divorce. This however, is often the position in England, Wales and Northern Ireland.

The aim of this paper is to use a model office to examine the potential impact of AIDS on non-linked life assurance business in the UK.The subject of AIDS continues to stimulate a large amount of research. The UK actuarial profession has been kept informed by the regular Bulletins [1-5] from the Institute of Actuaries AIDS Working Party (the “IAWP”). Using a model developed by A. D. Wilkie [6], the IAWP examined the possible spread of the infection amongst male homosexuals and produced tables of additional mortality. The most recent Bulletin (No. 4), published in March 1989, updated these projections in the light of new data, and we have based our investigations principally upon these more recent projections.

The paper describes the philosophy of with-profits business which has been developed in the authors' office, as a practical illustration of the running of such business in modern conditions. A description is given of how the philosophy is implemented in the main areas of actuarial management, including valuation methods, bonus distribution, product design and expense control. The discussion is extended to address a number of topics which are the subject of current debate including the financial strength of offices, future bonus prospects and disclosure of expenses.

In giving their advice, actuaries form part of a complex series of interlocking relationships – pensions advice must take account of the Trust Deed, the Faculty's and the Institute's Rules of Professional Conduct and the law.The law is paramount as interpreted by judges. Lawyers and judges have little difficulty in investigating transactions of many years ago – what was deemed normal and proper by actuaries then could well not be perceived by the court as reasonable – either then or now. The fact that everyone does it may be a defence against negligence – or it may not.

SynopsisThe paper discusses the implications of the Social Security Pensions Act 1975 and associated Regulations for occupational pension scheme design and finance. Firstly, a general preface deals with currently topical matters. Secondly, integration of State and Occupational Schemes as practised up to the present time is described. Next, integration in future, whether contracted in or contracted out, is considered from the scheme design point of view, and some problems are mentioned. Finally, the financial background to the contracting-out conditions is described and some evaluation made of the terms available.

SynopsisThe paper is the result of work carried out by the authors as members of the Bonus Research Group of the Faculty of Actuaries. The authors designed a computer model of a life office in order to examine the emergence of reversionary bonus under differing conditions. The use of a computer model enabled a dynamic study to be made over many years. The investigations quantified the extent to which the reversionary bonus emerging was affected by the valuation basis, the rate of expansion of the office, the rate of return on the fund, the extent of investment in equities and the office's experience in respect of expenses, withdrawals and mortality. The authors also examined in quantitative terms the extent to which policies would, on the assumptions made, receive more or less than the full share of surplus to which they were entitled as well as examining the size of the valuation estate under differing conditions.

SynopsisIn recent years, the insolvency of Life Assurance Companies has become a subject of practical importance to the actuarial profession. In April 1976 Mr. Peter Shore, then Secretary of State, stated in this connection that “prevention is better than cure”. The authors of this paper contend that prevention has been neglected because of the more immediate problems of recognition when insolvency is reached and the action required after the event.After some comments upon the legislation, the authors discuss the role of the Appointed Actuary. They then consider the main causes of insolvency, and suggest that the basic cause of the recent financial difficulties of certain Life Offices was rapid expansion based upon inadequate capital and free reserves. The paper argues the need for explicit solvency margins in preference to implicit ones and proposes a method for determining the capital base of a life office and the maximum growth rates which can be supported.

1.1. The purpose of this paper is to present to the actuarial profession a stochastic investment model which can be used for simulations of “possible futures” extending for many years ahead. The ideas were first developed for the Maturity Guarantees Working Party (MGWP) whose report was published in 1980. The ideas were further developed in my own paper “Indexing Long Term Financial Contracts” (1981). However, these two papers restricted themselves to a consideration of ordinary shares and of inflation respectively, whereas in this paper I shall present what seems to me to be the minimum model that might be used to describe the total investments of a life office or pension fund.

The guide to the profession on this subject first appeared in the Faculty Year Book for 1975-76 and it was discussed at our sessional meeting in February 1976 (and at the Institute's sessional meeting in January 1976). In the time since these meetings there have been changes in the guide and additions to it. No doubt future changes in business conditions in the years ahead will bring forth further amendments. The reasons for devoting another sessional meeting to it at this time are, firstly, to review the manner of its production and to consider what weight it carries, and, secondly, to give members the opportunity of considering the detailed wording of the guide, as distinct from its general intention. The analogy that comes to mind is with an Act of Parliament. The Bill is prepared in a department of government, is drawn up with care and professional skill by parliamentary draftsmen, and receives two readings before the House of Commons when its general aims and intentions are approved: it then moves into the committee stage where, if time permits, every clause is gone over individually to see that it expresses clearly and unambiguously the intention of parliament. It then has its third reading and, if approved, may be expected to go on to become law. The sessional meetings here and in London in 1976 correspond in this analogy to the first two readings of the Bill, and they showed that the intention of the guide and its general terms had the approval of the profession.

1.1. The concept of the matching of assets to liabilities is fundamental in matters of finance. In its broadest sense matching is relevant both to the investment of life office and pension funds and to actuarial calculations in relation to those funds.1.2. Matching is inherently connected with the uncertainty of future conditions, as measured by such indicators as rates of interest, inflation and currency exchange. It is when conditions do not work out as hoped for or expected that the risks associated with mis-matching can materialize. Whether considering investment policy or an actuarial calculation it is important that the nature of a portfolio which minimizes these risks be appreciated, and yet it is often difficult to specify such a portfolio with precision. This may not be a source of difficulty in practice when the judgement of the actuary is applied to the problem in hand, but there is evident scope for refinement of the concepts.

SynopsisThe Authors apply their experience, as former life assurance managers, to develop new methods of investment analysis of life assurance shares.Monitoring the profitability, per unit of with profit premiums, shows how improving investment performance mitigates the adverse effect on bonuses and shareholders' earnings of the heavy new business needed to maintain the business in times of inflation. Studies of likely investment performance are made, in an attempt to forecast bonuses and dividends over the next 3 years. These methods are demonstrated practically, using the figures from the published accounts of five U.K. life offices from 1976 to 1978.If more time and space had been available, the Authors would have liked to apply these methods to the analysis of Accounts and D.O.T. Returns of all significant U.K. life offices, proprietary, mutual and composite, that publish annual valuations. Life office managers would then be able to compare their own profitability, investment performance and bonus prospects with those of their principal competitors. In addition insurance brokers would be enabled to assess likely future results for prospective policyholders from competing life offices in a more reliable and rigorous way than is done at present, using merely historical bonus records.The Authors have to admit that application of their techniques, although achieving considerable success with these varied objectives, is handicapped by the poor quality of life assurance Accounts and Returns. At present offices with a large group pensions component cannot be analysed, because the format of the D.O.T. Returns for this class of business is out of date and inadequate. They would like to see life office accounting methods improved, and they make some specific suggestions to this effect. In addition, detailed comments on the standard of presentation of the D.O.T. Returns are given in the Appendix, together with suggestions for improving these Returns.

SynopsisThe main purpose of this paper is the determination of a basis for the calculation of “prudent” reserves for maturity guarantees in annual and single premium unit-linked life assurance policies, particularly those in which the investment medium is a broad range of U.K. equities. Estimates of the proceeds of equity investments required, and theories of stock market movements are discussed; it is concluded that yearly growth rates, including reinvested net income, may be represented approximately by the lognormal distribution and that yearly growth rates are not random, but negatively correlated. A mathematical model is then developed; the evaluation of the resulting distributions, which is a problem of some interest in its own right in the annual premium case, is discussed in the Appendix. There is a general discussion of certain valuation principles, and we give tables showing the level of reserves suggested by our methods. Various practical questions, such as the treatment of the assets and the effects on reserves of mortality, withdrawals, capital gains tax, policies with different terms and existing business, are also considered.

1.1. The paper “The F.T.-Actuaries Fixed Interest Indices” by G. M. Dobbie and A. D. Wilkie (J.I.A., 105, 15 and T.F.A., 36, 20.3) gave details of the purpose and construction of the F.T.-Actuaries fixed interest indices, and the note “The F.T.-Actuaries British Government Securities Indices 1976” (J.I.A., 105, 27 and T.F.A., 36, 2.1.4) gave details of the constituents, changes and values of the B.G.S. indices in 1976. The present note continues the history for a further year.1.2. In §8.2 of the paper it was observed that during 1977 the government had issued stocks where the issue price was payable in separate “calls” on a series of dates. The published indices, however, included these stocks only when they were fully paid. An alternative series of indices has also been constructed, allowing for the calls as and when they occurred. This note gives details for the alternative series, but refers also to the published series where the results differ.

SynopsisWritten concurrently with the first item in C.M.I.R.3, the Faculty of Actuaries Mortality Research Group's paper determines a range within which mortality rates of Life Office Pensioners may be expected to change in the foreseeable future. Comparisons are made between the observed changes in pensioner mortality rates and those observed for the population of England and Wales, and reference is also made to the trends of mortality rates assumed in recent British population projections. From these considerations two forecasts are made, based upon “optimistic” and “pessimistic” future mortality assumptions, between which it is expected the actual future rates of mortality change will lie.In the second part of the paper the financial effects of the range of forecasts are set out, when used to project the graduated pensioner Mortality Experience 1967-70 (C.M.I.R., 2, 57). The implications are illustrated in the context of two model funds, one based upon life offices' data, and the other based upon a non-insured pension scheme for which the contribution rates vary in accordance with the levels of future expected pensioner mortality.

1.1. This paper developed from an earlier paper given by the authors to the New Zealand Society of Actuaries. The authors were involved in acquisitions and mergers at a time when there was very little actuarial literature on the subject. Since then, the 1980 International Congress of Actuaries had as one of its subjects “Estimating the Value of Insurance Companies and Portfolios” and a wealth of papers appeared on the subject of pricing life funds. However, the aspect of merging life funds does not appear to have been covered to the same extent.

The following notes are intended as an introduction to the Faculty discussion on actuarial education. They are presented by the authors separately and personally, but solely as introductory notes, rather than as actuarial papers which might represent their considered judgement about the nature and purpose of what actuarial education should be. Instead it is hoped that they will stimulate a wide-ranging discussion about all aspects of actuarial education, particularly of course in the context of what the Faculty does or might do in this respect.

1.1 The background to the production of this paper is somewhat involved, but is necessary for an understanding of why it contains what it does. Readers who are familiar with recent developments in the valuation field may proceed straight to Section 2.1.2 Statutory valuations of long-term insurance business under the Insurance Companies Act 1982 (‘the Act’, which superseded the 1974 and 1981 Acts) and the Insurance Companies Regulations 1981 (‘the current Regulations’) have now been prepared by actuaries for some years. Similarly the guidance issued by the profession to Appointed Actuaries, specifically GN1 and GN8, has also remained substantially unchanged over that period. The time was opportune for valuation practice to be reviewed in the light of recent experience.

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.

The improvement in vitality is a subject of interest alike to the actuary and to the public statistician. It formed one of the topics for discussion at the Fourth International Congress of Actuaries held in New York in 1903, and papers were submitted by actuaries of different countries dealing with the subject mainly from the point of view of population statistics. The results of most direct interest to us were embodied in a paper by Mr. S. G. Warner On the Improvement in Longevity in the Nineteenth Century. They were based on the summarised returns of the Registrar-General's Reports for England and Wales for the years 1875 and 1900; and, while admitting the defects inherent in the data, Mr. Warner held that the statistics showed “a distinct decrease in the rate of “mortality as the century progresses; a decrease, on the whole, “so steady and symmetrical that it might fairly be looked on as a “settled and permanent tendency.

The method of calculating the values of prospective pensions which I am about to describe differs in some respects from those given in the standard papers on the subject, and will be found, I think, to possess advantages of its own. I shall deal with its application to the case of pensions based on salaries, when the amount of the pension is a uniform percentage of salary for each year of service taken account of.I have followed Mr. Manly in the use of the following symbols (see his paper of 1901—J.I.A. xxxvi, 209), namely, lx to denote the number living and remaining on the active list at age x as given in the Service Table, and Dx and Nx to correspond; rx to denote the number retiring from failure of health between ages x and x + 1, sx to denote the salary receivable between ages x and x + 1, and Dsx to denote Dx X sx. When however lx, Dx, Nx, or Dsx have a circumflex accent, these symbols have the ordinary meanings, and the functions are based respectively on the Pensioners Mortality Table. I have found it necessary to employ also a certain number of new symbols which are described in the Key to the Special Notation (see pp. 31, 32). I have also followed Mr. Manly in the assumptions made in the paper mentioned above, that the retirements or superannuations applicable to any year of age take place at the end of the year, and that the pension commences at the same time and is payable yearly thereafter.

SynopsisThe paper describes certain aspects of life insurance business in Canada under the following headings :—(a) Legislation and regulation, both federal and provincial(b) Taxation(c) Investment of funds(d) Agency system(e) Ordinary life insurance, including a description of some current developments(f) Group pension plans(g) Group life insurance(h) Actuarial and professional societies.In dealing with the above subjects emphasis has been placed on matters where the Canadian practice may differ somewhat from the British.

SynopsisThe Paper sets out to examine whether existing group pension business written on certain premium bases will prove to be profitable or not. In the first part of the Paper the trends and effects of mortality, interest, income tax and expenses are examined in turn and a table of annuity values is constructed embodying the conclusions drawn.In the second part of the Paper the working of a model group pension scheme for the year 1955 and the results of the year's working are analysed, firstly according to the assumed experience basis, and secondly according to the premium basis.

It is sometimes overlooked that any Makeham joint-life annuity value at any arbitrary interest rate may be calculated to any required degree of accuracy by using the first few terms of one of two alternative series expansions. Moreover, tables (Pagurova, 1961) are now available that eliminate the need for this series evaluation in a great number of cases. This observation is of much wider application than may appear at first sight. It is well known that almost any 30-year range of ages in an arbitrary mortality table can be successfully regraduated using a Makeham formula. Since a life annuity deferred for 30

SynopsisThe purpose of the paper is to stimulate a discussion among the members of the actuarial profession on the part the actuary can play in the assessment of compensation for loss of support, in order that some consistency of approach (which the authors regard as essential) can be evolved.The paper commences with a discussion on the unique ability of the actuary to determine the capital value of a given series of future payments, contingent upon human survival, and the significant part that this can play in the assessment of compensation for loss of support. The extent to which this ability is accepted by the Courts is discussed, and reference is made in this regard to the paper by J. H. Prevett in J.I.A., Vol. 94, pp. 293 et seq.The authors then proceed to consider the technical aspects of valuing the loss of future support, drawing particular attention to the need for the actuary not to be held responsible for the non-technical aspects.The paper concludes with a consideration of the general aspects of the subject, such as the professional conduct of the actuary at Court appear ances and other stages of a claim, the alternative of awarding compensation in the form of an income, and the use of actuarial assessors.

SynopsisThis paper describes a practical co-ordinated system of calculating financial terms for policy alterations and calculating surrender and paid-up values of policies which have been altered. The system is primarily designed to produce numerical results which are consistent, equitable and capable of evaluation without the need for special actuarial experience. The calculation formulae make use of the tabular rates of surrender values and paid-up values currently granted for unaltered policies and the current premium rates charged for new policies; the often difficult selection of suitable actuarial functions is thereby avoided automatically without departing from general actuarial principles. Since the actuarial bases inherent in these tabular rates are not used explicitly the rates can be changed independently at any time without affecting the use of the formulae. The system is equally suitable for operation by clerical staff or for computer application and should produce economies in the valuable time of skilled staff.At the end of the paper, examples are given comparing results with those calculated by conventional methods.

1. The theory of Integral Equations, which is an important branch of the wider theory of Functionals, has been developed by mathematicians during the past 60 years. Many valuable applications of these equations have been made in various branches of applied mathematics, including economics, biology, and especially physics. It is believed, too, that they may not be entirely void of interest to the actuary. In this paper, therefore, a brief discussion of integral equations is given, and various problems involving their use are considered. It may be that some of these problems will be thought artificial, or trivial, or both. The writer would request, however, that the examples be regarded as illustrative only. If any of them should suggest new and more important problems to actuaries, or if the methods developed herein should prove of value in the solution of present problems, the purpose of this paper will be achieved.

Joint life and survivorship annuities on two lives form a troublesome class to deal with in valuations. Since the reserves are functions of two variables the annuities fall naturally into so many groups that they are often valued individually. In an office which writes much annuity business this process is laborious.

The word “amortisation” is now being used in insurance circles in America to represent the operation of a sinking fund, whereby bonds or other fixed term securities, bought at a premium or at a discount, will be brought down, or up, to the par value at the date when repayment is promised. The scientific basis of the method is so well known to actuaries and is so fully explained in such standard works as King's Theory of Finance and the Institute of Actuaries Text-Book, that there is no need for me to enter upon a discussion of the principles. But of late years the system has assumed great practical importance, and the general method, with the suitability of its application to our business, are subjects worthy of consideration and discussion.

In submitting these remarks on Income Tax I need hardly say that they do not form an exhaustive article on the subject. The paper is intended rather to show in a general way the practical effect of the Income Tax law as regards Life Assurance Offices. The method of dealing with the subject would appear, perhaps, to be following the line of least resistance; but, as the more recent Income Tax legislation, so far as regards the assessment of such Institutions, is hardly yet out of its infancy, I think the purpose of the paper will be best served if it is confined to a review of the recent changes in the law and of the law as it at present stands.

SynopsisAlthough the average degree of solvency among friendly societies has been steadily rising in recent years, valuations in a considerable number of cases still disclose a deficiency. Some of the large affiliated orders have methods of their own for assisting branches in difficulties, but in the case of many societies no such help is available, and other means have to be found for improving the financial position. The object of the paper is to consider some of the methods by which the degree of solvency may be raised, more particularly with reference to such aspects of the problem as (1) negative values, (2) the relative shares of the extinguished deficiency borne by members of different ages, and (3) the effect of different age distributions.

SynopsisThe paper considers the role which the State should play in the provision of pensions to the retired population. The role of occupational schemes is also considered with particular reference to the restrictions placed on that role by the authorities through the requirements for approval for tax purposes and the cost and level of State pensions. The main features of various State pension schemes which have been proposed in successive White Papers are discussed together with their shortcomings and advantages. The White Paper “Better Pensions” and its implications for the pensions industry are then considered in greater detail.

SynopsisThe Paper deals with some of the problems which arise in the valuation of Widows' Funds with special reference to the Widows' Funds of certain professional bodies in Scotland.An analysis is made of data derived from the Scottish Bankers' Marriage and Mortality Experience 1923–1943 (T.F.A., 19, p. 149) with a view to determining the applicability of the Collective Method to a valuation of the “existing” at the close of that Experience.The various factors entering into a Widows' Fund valuation are examined in relation to a particular Fund and the importance of the valuation rate of interest illustrated.The Paper concludes with a discussion of the “reserve for loss on future entrants” often met with in the valuations of such Funds, and of the arguments for and against proposals which have been made for its elimination.

The methods adopted for collecting and tabulating the annuity experience for the five years 1921-1925 carry out the arrangement that was accepted by the Committee at the time when the permanent investigation was set up. Members of the Committee who were not Members of the Committee when the decision was reached will appreciate that the method adopted is a census method and not a policy year or calendar year method of the type ordinarily used in the past for investigating mortality experience, e.g., such as was used in the OM experience (see however Appendix).

SynopsisThe European Economic Community (Common Market) was established by the Treaty of Rome signed by six countries, namely, Belgium, France, Germany, Italy, Luxembourg and the Netherlands, in 1957.Many of the eleven basic aims of the Treaty have some bearing on insurance business. The free movement of persons, services and capital is of the greatest technical interest to insurers but the measures designed to promote the economic growth of the Community which will include the expansion and improvement of capital markets could be of even greater interest—particularly to life assurers. Another aim of the Treaty, viz. to ensure fair competition within the Community, could act as a constraint on the introduction of liberalizing measures.The general programme for the progressive establishment of the Common Market over a transitional period of 12 years (extended if necessary) included a specific timetable for the introduction of freedom of establishment and freedom of services in respect of insurance transactions. The implementation of this programme as it concerns insurance has fallen into arrears and only one of the five directives which were scheduled has so far been promulgated. Nevertheless, the achievement of the aims of the Treaty of Rome must eventually result in the gradual harmonization of legislation affecting insurance business within the member states. Chiefly because of the need to avoid any distortion of competition, the measures introduced are likely to apply to all insurers within the E.E.C. irrespective of whether they transact business in one or more member states.It is premature to consider in detail the likely terms and conditions of the E.E.C. legislation as this is still a long way off. Insofar as the present pattern of insurance control legislation of most E.E.C. countries is more restrictive—particularly for long-term business—than in the United Kingdom, any short-term solution for harmonizing legislation would seem likely to involve British companies in more stringent rules. It is hoped that the E.E.C. will take into account the outcome of the discussions on similar issues which have taken place over the last decade within international organizations such as the Organization for Economic Co-operation and Development and the Comité Européen des Assurances on which the United Kingdom is represented. E.E.C. thinking may also be influenced in the direction of the progressive liberalization of insurance control legislation by the record of life assurance business in the United Kingdom and by the need to encourage the development of capital markets to which life assurance is an important contributor as a source of long-term and regular savings. Thus the ultimate pattern of E.E.C. legislation may well reflect the British system of freedom, provided such a system is well presented within the E.E.C. negotiations. Generally, problems for the British actuary will arise from the imposition of new rules within the E.E.C. not only for insurance transactions but for the many other commercial transactions with which the actuary is professionally interested as advisor or participant.Special areas of long-term business such as pension schemes; life reassurance; equity-linked contracts and private sickness insurance are described. Last but not least, in connexion with the introduction of freedom of mobility of labour, it may be necessary to consider to what extent actuarial qualifications earned in another member country can be recognized as enabling an actuary to practise in the United Kingdom.

SynopsisThe paper records the growth in the number of apportionments of trust funds due to the passing of the “Trusts (Scotland) Act 1961”. It considers the problems, as they arise in Scotland, of allowing for the impact of taxation, both in determining the interests to be valued and in fixing the valuation rate of interest, and it is suggested that the same net rate of interest need not necessarily be appropriate for all the beneficiaries.Numerical examples are given of the effects on funds of varying size and investment content of various valuation assumptions, and the problem of disposing of the potential savings in taxation is discussed. The paper ends with a general section covering some practical points in the preparation of schemes to vary trust purposes.

SynopsisThe paper discusses developments resulting from (1) the recent passage by most of the state legislatures of the “Standard Valuation Law” and the “Standard Non-forfeiture Law,” and (2) the general adoption by the companies of a lower interest assumption in the calculation of premiums, reserves and non-forfeiture values.After a brief review of the system of regulation of life insurance in the United States and of the more important differences in practice as compared with practice in the United Kingdom, the paper proceeds to outline the background which led to the appointment of the “Guertin Committee” by the National Association of Insurance Commissioners to study and report on the need for a new mortality table and related matters and (subsequently) on non-forfeiture benefits. The main recommendations of the Committee and the subsequent modifications thereof as adopted by the Commissioners and later embodied in the Standard Laws are detailed.The effects on life insurance operations of the new Standard Laws in conjunction with lower interest assumptions and the marked upward trend in expenses are discussed. The paper concludes with a brief reference to two important changes being made by some companies in their policy conditions.

It is demonstrated, with particular reference to the OM, OM(5) and A1924–29 Tables, that over the range age 20 to age 65 of a normal mortality table, μx can, with a close degree of approximation to the tabular values, be expressed in the formleading to the following analogous expressions:—Generally, all functions involving mortality within the stipulated range can be expressed in a similar form as purely mathematical and easily evaluated functions of the initial age and interest in combination.It is claimed that the evaluation of such temporary functions at any rate of interest is thereby greatly facilitated.The retrospective and prospective values of an endowment assurance policy in terms of the formula are investigated, and check methods of valuation, continuous in process and independent of the working principles and practice of the principal method, are put forward.Numerical results and examples of the procedure are given in the paper.