1.1. The concept of matching assets and liabilities has for many years been recognized as a crucial aspect of our professional work. Its importance is emphasized in the Institute's guidance notes entitled “Actuaries and Long-Term Insurance Business” and in many papers published in the Journal.

1.2. A particular form of matching, namely immunization, was developed by F. M. Redington in his paper “Review of the Principles of Life-Office Valuations” (J.I.A. 78, 286). Immunization signifies the investment of assets in such a way that the existing business is immune to a change in the rate of interest. One of the consequences of immunization is that the mean term of the asset-maturity dates is appreciably longer than the mean term of the value of the asset-proceeds and of the liability-outgo; and, at other than low rates of interest, a perpetuity can be too short to immunize a long-term contractual liability.

The Address is a journey in three parts. The first part describes the world scene in the last century when the Institute was founded and traces the development of actuarial work to the present day. The current U.K. pension scene is then broadly reviewed and the journey ends with vistas of the future. The concentration of actuarial work towards life assurance and pensions is attributed to meeting the needs of the past and encouragement is given to the urgent extension of the work of the profession into wider fields.

The U.K. pension scene is described as being complex, confused and filled with uncertainty. The profession is urged to assist government actively and positively, to examine the expected future growth of pension funds, and to compare the financing of retirement benefits in the U.K. with other methods adopted in Europe.

Work in wider fields is envisaged as embracing general insurance, the health and care of the aged, banking and finance, and the appraisal of capital projects.

It is now June 1959—only eight years after the first magnetic tape computer was put to work in the U.S. Bureau of the Census. But it was not until mid-1954 that the appropriate auxiliary machines needed to complement this computer became available. In a very real sense, magnetic tape data processing facilities suitable for business operations are only five years old at this time.

Yet, in so short a time, possibly 300 or more tape-operated data processing systems have already been installed in the United States. A great deal has been written and said regarding the use of this equipment and its impact on current practices. There is much yet to be said. As we come to grips with the immediate and difficult job of putting it to work we can be encouraged by the very substantial progress already achieved by both manufacturers and users. In just a few years, the initial approach to computers has changed so much that the key question ‘Can electronic computers be relied upon?’ has become for many ‘Which one should I get?’

Mr. Sprague, in his report on Mr. Finlaison's Tables of Mortality among Government Life Annuitants, states as the result of his study of the subject of graduation that the most satisfactory system of adjustment is the graphic method; and he supports this opinion by referring to the irregularities which he regards as a consequence of the use of Mr. Woolhouse's method of adjustment. I do not doubt that Mr. Sprague would conceive and correctly draw a curve to satisfy all the conditions of good graduation; but in my own hands the graphic method would be a failure, and there may be others who doubt if they have skill to draw the curve and patience to amend it by the successive trials which Mr. Sprague himself finds necessary.

From the fact that a very large amount of capital has been of recent years invested in loans to foreign governments, the question of sinking funds and other kindred matters has come prominently into notice; and matters which at one time were only looked upon as belonging to the theory of compound interest, are now become of great moment to thousands of persons who have invested, or purpose to invest, their money in the above-mentioned class of security. Various causes appear to have led to the large increase in the popularity of foreign loans among certain classes of investors. No doubt, the rapid growth of unemployed capital has considerably reduced the rate of interest realizable on first-class home securities, and has induced persons anxious to obtain a high rate of interest to invest their money elsewhere. From the nature of the case, however, even a fairly high rate of interest would not generally be sufficient inducement for an investor to lend money to a perfectly irresponsible foreign government, which might at any time, if it thought fit, renounce all its past financial obligations. Whether the general practice of providing for the repayment of loans has arisen from the scruples of foreign governments to accumulate a large national debt like our own, or whether, on the other hand, it has been found necessary to give an undertaking to repay the loan over a term of years, in order to make the loan at all palatable to investors, I cannot say; but the fact none the less remains, that very generally provision appears to be made, in the case of loans by foreign governments, for repayment in a shorter or longer period of time.

As far as we are aware there have been no life insurance demutualizations in the U.K. in recent times, that is conversions from mutual to proprietary form. There has been movement in the other direction: in the 1960's a number of U.K. proprietary companies converted to mutual form to escape the unwelcome attentions of the corporate raiders of the time.

In the U.S. and South Africa however, the two countries which give us the demutualization examples in this paper, there have been in recent years a number of significant demutualizations. In the next chapter we give a sketch of the background to demutualization in these countries.

In Section 3 we explore why a mutual might wish to undergo such a lengthy, costly and probably painful process. The motivation will vary from country to country, depending on the particular economic and institutional background. We have tried to be as general as possible.

In the Introduction to his famous Théorie Analytique des Probabilités, Laplace, after an eloquent summary of the progress of Astronomy from the days when every rare celestial phenomenon was regarded as a portent of human misery, to the verification in April 1759 of the perihelion passage of Halley's Comet, proceeds to say :—

“The regularity which Astronomy shows us in the movement of Comets exists, beyond doubt, in every phenomenon of nature. The curve described by a simple molecule of air or of vapour is regulated in a manner as certain as the planetary orbits: there is no difference between the two cases save our ignorance.

When interpolations are made between values of a function by any of the ordinary interpolation formulae, there are generally discontinuities in the slope and curvature of the successive interpolation curves, and when, as often happens in practical work, the given values are themselves derived from rough data, these discontinuities may be considerable. To remove these breaks of continuity T. B. Sprague in 1880 devised his osculatory interpolation formula, and in the present Paper is given a brief review of subsequent contributions to the subject. From the practical point of view, the most important of the earlier contributions were those of Mr. 6. King, who successfully applied the method to the construction and graduation of national and other life tables; but while two sets of national life tables have since been constructed on the lines proposed by him, there has, for the last fifteen years, been no further development in this country either in the theory itself or in its application.

In contrast to this has been the interest in the method shown by American actuaries, particularly in recent years. Their work is briefly reviewed, and special attention is directed to that of Mr. W. A. Jenkins, who, in 1926, put forward a method of greater generality than that underlying the earlier formulae.

The weak point of the osculatory method, regarded as a smoothing agent, rests on the fact that the graduated curve is required to pass through certain predetermined points. The curve will, in fact, be constrained to take a form similar to that assumed by a flexible steel wire which is clamped at fixed points, so that, while the curve is free from discontinuities, any departure of these points from the smooth curve will be reproduced with resulting undulations. To remove this tendency to waviness, Jenkins has devised his modified osculatory method, which, while requiring the successive interpolation curves to have the same slope and curvature at their common points at the ends of each interval, does not require the curves to pass through the points corresponding to the calculated values.

His fifth difference formula has been applied to regraduate the English Life Table No. 9, Males, and in connection therewith it is pointed out that the success of the method must depend to some extent on the provision of a good set of guiding values ; for, while the curve is not required to pass through the points corresponding to these values, the closer they lie to the smooth curve the better is the graduated curve likely to be. The method recommended for adoption is one based directly on summations in fiveyear groups of the unadjusted rates of mortality. By means of a formula derived from the modified osculatory formula quinquennial values are obtained. These are treated as first approximations, and the formula is again applied to them in order to produce rates which are treated as the graduated rates. The results are satisfactory both from the point of view of smoothness and of fidelity to the data, as measured by the agreement between actual and expected deaths.

An interesting point which emerges from the various graduations and from the comparisons of actual with expected deaths is that the crude rates of mortality appear always to exceed the graduated rates for ages centering about 24, 34 . . . and to fall below them for ages centering about 29, 39 . . . ; and it is suggested that this is due to some persistent tendency to misstatement of age, and that it is also largely responsible for the waviness of graduations of population data which is generally characteristic of the application of the ordinary osculatory method.

As a further test of the possibilities of the method, and, in particular, of its smoothing powers, it has been applied to graduate the data of the Government Female Annuitant Experience 1900-1920. These data had proved very intractable to curve-fitting methods, but had been found to show an element of periodicity up to about age 90 with an apparent change in the form of the curve after that age. In connection therewith, formulae are given for applying the method to the data at the ends of the experience where the main method is inapplicable. The result is to produce a curve which is almost perfectly smooth and which closely follows the original data.

The method is essentially a graphic method in which the curves are drawn in accordance with mathematical formulae instead of being drawn by hand, and the work is arranged in such a way that it can be carried out practically from beginning to end by purely mechanical processes.

I am always happy to be back where my Institute life started and I am grateful to your Committee for fitting me in at short notice.

When you start to write, ideas take on a being of their own. Life is a shy child which hides its face when you stand aloof, but is soon at your elbow to help when you kneel to build with its bricks. Then other bricks begin to appear. As it turns out, my helper is concerned about imagination so ‘imagination’ shall be our subtitle.

First, a brief reference to my 1972 paper: the winning themes were—in reverse order, as for beauty queens—third prize to the imminent collapse of our society, second prize to the essential unity of the universe, but an easy winner was double faults at tennis.

The object of the following notes is to state somewhat more fully and formally a method (first published in the Insurance Record for 10 March 1905) of approximating to the reserves required for whole-life assurances, with due regard to the influence of selection; and to illustrate the practical application of the method.

In the Diary for 1850 the following; mathematical query was proposed by the Rev. T. P. Kirkman, of Croft, near Warrington:—

Two answers were printed in the Diary for 1851; one by the proposer and another by Messrs. Samuel Bills, of Hawton; Thomas Jones, of Chester; Thomas Wainman, of Burley; and W. H. Levy, of Shalborne.