MR. T. G. ACKLAND, in the course of the discussion upon Mr. Manly's paper “On the Valuation of Staff Pension Funds”, presented the following problem for solution by the members of the Institute—” In the case of a superannuation fund, established—“ in connection with a municipality or corporation, to which the “employees contribute at a fixed rate, what will be the probable “annual charge upon the rates of the City during the next ten “years, during the following ten years, and so on for fifty years, “supposing that the present staff of the Corporation is adequate “in number for the needs of the Corporation, and that new “entrants come in only in replacement of those who die, “withdraw, or retire” ? (J.I.A., xxxvi, p . 283).

It is sometimes the case that a commercial undertaking merely guarantees the stability of its staff pension fund, without making an adequate annual contribution from which to build up the reserve necessary to meet the actuarial liability, or, more usually, it is the practice of a corporation to meet the current claims under its pension scheme out of the current income from its employees' contributions and to use any excess of income in relief of the rates, and to charge any deficiency, when arising, upon the rates. In such cases the ordinary actuarial valuation is of little practical use, but the main question is that put by Mr. Ackland—“ What will be the charge upon the employer, or the rates, at a given date, or over a given period”?

The recommendations made to and approved by the Select Committee of 1852 on Friendly Societies, with reference to the abolition or reduction of the duties payable in respect of policies for life assurance, have been acted upon more promptly than could well have been hoped for. The duties, it is true, have not been partly abolished in the way suggested, but the reduction now effected is so considerable as to make them fall very lightly upon those who will hereafter have to pay them.

I have limited this paper to the consideration of appreciation or depreciation in fixed interest-bearing securities resulting from a fall or rise in the general level of interest rates and not from any alteration in the intrinsic value of the securities, i.e. there is assumed to be no change in the probabilities that the terms of the contracts will be fulfilled. My object is to discuss how this appreciation or depreciation should be treated in order to obtain the maximum practicable degree of equity between the different generations of policyholders in an office which distributes its surplus by means of a uniform reversionary bonus.

The problem can be most easily discussed by showing the effect on a model office of adopting various methods of treating this appreciation or depreciation. I propose to limit the discussion in the first place to the question of depreciation in an office employing a bonus reserve valuation.

Many years ago it was suggested—I cannot remember by whom—that instead of graduating lx or qx or some such function it might be preferable to graduate annuity values. When I was fitting frequency curves to many kinds of statistics some fifty years ago, I noticed that the expectation of life from birth onwards looked something like the ordinates of a very skew frequency curve with a mode at age 4 or thereabouts. Partly because it seemed difficult to bring expectations of life within a definition of frequency distributions and partly because the example was neither a straightforward graduation nor helpful to the work on which I was then engaged, the notes I made were put aside and have long since been destroyed. From time to time, however, I have wondered whether life annuity values and expectations of life could be expressed roughly by one of the algebraic expressions used for frequency curves, and whether there would be advantages in working from joint expectations of life for n lives of the same age rather than for one life. Such a device, or the use of annuity values, may be taken to mean that we are using a series of values that could represent an expectation of life from a mortality table with heavier but related mortality. Approximations even if they are as rough as I had to anticipate in this case may be useful in unexpected ways, and that thought supplied me with some sort of justification for taking up the subject again and making some fresh calculations.

The great value of quadrature formulæ for the calculation of survivorship and other benefits involving three or more lives has been already illustrated in the pages of the Journal. From certain remarks made by Mr. G. F. Hardy and Mr. George King in the discussion which followed the reading of Mr. King's paper (J.I.A., xxvi, pp. 297, 301), I inferred that it would be of interest to examine the errors involved in these formulæ, and to compare the results yielded by them and by other methods of approximation, such as the substitution of an equivalent life. Mr. Sheppard has shown (Proceedings of the London Mathematical Society, xxxii, p. 258) how most of the best-known quadrature formulæ can be readily derived from the Maclaurin Summation Theorem, with expressions for the errors in terms of differential coefficients. In a recent paper (Proceedings of the London Mathematical Society, xxxiv, p. 335), I have obtained similar formulas by direct integration from Everett's Interpolation Theorem, with expressions for the errors in terms of central differences.

The importance of this subject may be indicated by the fact that more than half a million a year is paid by the British Life Offices to their assured, as surrender values on the discontinuance of their policies. Competition also, and the increasing interest which is being taken in the subject by the insuring public, have a tendency to induce companies to make these surrender values a prominent feature in their prospectuses; perhaps also it may be an inducement to some companies to offer large values in order to bid for larger patronage.

The lecture begins by outlining the differences in lifetime earnings between men and women, and between women with different levels of skill and with different numbers of children. It continues with a discussion on wrongful conception and wrongful birth, and the legal implications when damages are sought when children are born who were not meant to have been born. Many examples of claims for damages brought before the courts, over a period of time, are used to illustrate various aspects of this. Cases concerning both healthy and disabled children are discussed, and the changes that occur for all women who have given birth and the mother's responsibility of care are considered.

The present effort does not profess to be complete. It deals with the main problems that come before the Consulting Actuary in connection with Staff Pension Funds, but does not go into the details of what may be called the fancy benefits which are occasionally met with. The solutions of the general problems here given will, however, indicate the methods to be applied in attacking other, and sometimes more complex, questions, which, when the principles have been grasped, will not present serious difficulty.

The Presidential Address covers various aspects of the actuarial profession; past, present and into the future. It considers mutual life companies and their current situation. There needs to be improved education in investment and more actuaries should be involved in this area. The codes of conduct and disciplinary procedures of the profession have to be kept under constant review. The international actuarial scene is of great importance, with mutual recognition of qualifications, the various groupings of actuaries and of actuarial associations world wide and the expansion of the profession into further countries all part of current activities. Various alternative options for the future of the profession in the U.K. are suggested.

The distinguishing feature of the New Experience which differentiates it from all others, is the division of the observations into various classes of assurance; and when our President did me the honour of asking me to contribute a paper, I thought I could not do better than invite your attention to the premiums which, according to that experience, ought to be charged for these classes, as it is of the greatest importance to insurance companies generally that the risks which they undertake should be at adequate rates. Some of us have suspected, others have known, that the fate of mortality varied according to the class of assurance, and that one table of mortality applied to all was not satisfactory; but it is now possible for the first time to arrive at definite conclusions on the subject, and to determine in many cases what the difference between them really is.

Most of the published actuarial literature in the U.K. on immunization has been applied to the valuation of a life office. The authors have shown how the immunization techniques first introduced by Redington (3) in 1952 can be used to match the liability outgo of the office, to a greater or lesser extent.

The purpose of this paper is to introduce the student to the underlying concept of immunization and to show how it can be utilized to produce a guaranteed rate of return with a high degree of probability, irrespective of the future course of interest rate levels.

The term to maturity and duration (mean term) of a bond are discussed in §2. The maturity is only of limited help in characterizing a specific bond. The duration—a measure of the average time until the bond payments are received—is an easily determined figure which is more informative about a bond than maturity. The price sensitivity of a bond (i.e. volatility) is linearly related to the duration.