A hundred years ago last Saturday, on 24 November 1884. Dr Thomas Sprague. my sometime predecessor in this office, delivered an Address. He opened by announcing that, after prolonged and painful negotiations, a Royal Charter had been granted to the Institute placing it, in his words “…as a professional body publicly recognized as representing, and entitled to speak in the name of, actuaries in the United Kingdom”. It was impossible, he wisely added, to predict exactly what new duties would devolve upon the profession as a consequence of this change.

1.1. For a number of years now it has been a commonplace amongst actuaries actively involved in unit-linked business that it was time someone wrote a paper dealing adequately with the subject of unit pricing. To those not actively involved with the subject the absence of such a paper may seem unimportant, but the fact is that the price-making process is central to the whole conduct of linked life business. It exerts a major influence upon the profitability and solvency of the office, and upon the relative interests of different classes and generations of policyholders and shareholders. In this respect, it is analogous to the bonus policy of a with profits office.

1.1. The Institute has discussed papers on most aspects of institutional investment in recent years, with the notable exception of property. This is not due to the lack of importance of this investment sector to pension funds and life offices, but perhaps to the greater role of actuaries (rather than surveyors) in the other investment media and to the interest in mathematical models for gilts and equities.

1.2. In this paper we have not tried to produce a mathematical model of the property market, a new valuation method for property or solutions to the extensive problems of property performance measurement and indices. We have, however, tried to pull together, in a single paper, the volumes of material on the property market and property valuation methods. We have also tried to set down some of the pitfalls of property performance measurement, which often tend to be overlooked in the relentless pursuit for more statistics in this important area.

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.

1. In the following experiments I simplify enormously, by assuming that the only benefit provided is a pension on retirement at age 65, that there are no benefits at all on death, not even a return of contributions, and that there are no ill-health retirements or early retirements. I also assume that all salaries, contributions and retirement pensions are paid annually in advance. This simplifies the calculations and hardly affects the results. I also assume complete certainty of inflation. salary increases and investment returns. The purpose of the experiment is to investigate the relationship between the amount of pension that may be deemed to have ‘accrued’ each year, and the amount of contribution (as a percentage of salary) needed to purchase the extra pension that has accrued in each year. under both a final salary defined benefit scheme and a revalued average salary scheme.

1. Salary scales have been widely used in actuarial literature about pension schemes, but they do not seem to have been developed beyond the idea first introduced by Manly (1901) and used in a series of papers following this, including McGowan (1901), Manly (1902, 1903 and 1911), and M'Lauchlan (1908). King (1905), Bacon (1907) and M'Lauchlan (1914) discuss the construction of a salary scale from records of individual employees. King made some valuable observations on how a salary scale may change with time if the observed population is not a stationary one, for example, because the firm is growing or declining, which Bacon also commented on, and M'Lauchlan went into considerable detail about the separation of different grades. Thomas (1913) gave an example of an organization with six ranks, within each of which there was a salary scale, and showed explicit probabilities of promotion in each year of age. His development comes closest to what I shall discuss below. Text books on Life Contingencies, such as Jordan (1952), Hooker & Longley-Cook (1957) and most recently Neill (1977), have followed essentially the definition introduced by Manly, as also have papers and text books on pension funds, such as Porteous (1936), Marples (1948), Heywood & Marples (1950), Crabbe & Poyser (1953) and Lee (1973). Curiously Spurgeon (1922) does not mention salary scales, although his book was written after they had come into use.

1.1 The actuarial profession has for decades, indeed centuries, used age-related tables, particularly (although not exclusively) of mortality, which in preparation have been subjected to the process known as graduation. Five purposes of such graduation have recently been set out by Vallin, Pollard and Heligman and these may be summarized as follows:

(1) to smooth the data, make them easier to handle, remove irregularities and inconsistencies;

(2) to make the result more precise on the reasonable assumption that the real mortality underlying the observations is a smooth curve, i.e. to remove sampling and other errors;

(3) to aid inferences from incomplete data;

(4) to facilitate comparisons of mortality;

(5) to aid forecasting.

Of these purposes, (1), (2) and (3) may all be paraphrazed as implying that the purposes are to make the table smooth, and (4) and (5) as indicating uses to which a table may better be put if smoothed. So the purposes of what the profession has come to term ‘graduation’ all boil down to the production of a smooth table, and for the rest of this paper until the last section I shall use the word ‘smoothing’ rather than ‘graduation’. But what is smooth?

This note continues an annual series on mortality rates in Great Britain; the previous note in the series appeared in J.I.A. 111, 181 and dealt with mortality in 1981.

Following the 1981 Census, revised estimates of the ‘home’ population of England and Wales since 1961 have been published. These allow for revision of past estimates in the light of the Census and also for a new definition of ‘home’ population, which brings the concept closer to that of ‘resident’ population. The ‘home’ population is now defined as including residents temporarily outside the country but excluding foreign visitors. It includes members of both H.M. and foreign forces stationed in the United Kingdom but excludes members of H.M. forces who are stationed abroad.

1. The Universal or Variable Linked Life Assurance policy has been issued by a number of companies in the United States of America and in the United Kingdom, and it is now reasonably familiar in the marketplace. It does not appear to have received much attention in actuarial literature, perhaps because of its simplicity, though a paper has been presented to the Institute of Actuaries Students' Society (Sheraton, 1984). So far as I know the corresponding Variable Linked Life Annuity has not been issued by any office, and some of its features are slightly different from those of the Life Assurance policy.

The new series of Financial Times–Actuaries fixed interest indices commenced in 1977 with the first publication in the Financial Times of the British Government Securities Indices. These were described on behalf of the Joint Index and Classification Committee of the Institute and the Faculty in the paper by G. M. Dobbie and A. D. Wilkie, “The F.T.–Actuaries Fixed Interest Indices”, J.I.A. 105, 15 and T.F.A. 36, 203. Subsequent notes in J.I.A. and T.F.A. have given annual reviews, the last, for 1980, appearing in T.F.A. 37, 327. Part 1 of the present note continues the history of the B.G.S. Indices up to the end. of 1984.

1. This note was inspired by the paper ‘The Matching of Assets to Liabilities’ presented by A. J. Wise to the Institute in March 1984 (Wise. 1984b). In it he presented a method of looking at the problem of matching which I claimed in the discussion was essentially a portfolio selection approach. However, his approach had a number of novel features. I wish to discuss one of these, approaching it from the conventional portfolio selection viewpoint. I am not aware that this problem has been considered elsewhere in the substantial literature that exists on portfolio selection. Full discussion of the mathematics of the conventional portfolio selection problem is contained in Sharpe (1970) and Szegö (1980), and a general explanation is available in many modern financial text books, and in the Institute paper by Moore (1972).

From the very outset of the formation of pensions schemes in the United Kingdom, actuaries have been involved in their design, investment, valuation and solvency. A review of issues of the Journal of the Institute of Actuaries in England and the Transactions of the Faculty of Actuaries in Scotland over the last 40 years would show how schemes have become more complicated and more comprehensive, how the economic and equity problems have increased and how the actuarial profession has successfully adapted its theory and practice to accommodate change. After World War II the rapid growth in occupational pension schemes together with the post-Beveridge expansion in State social security led to concerns about the overall effect on the national economy. As a consequence, in 1954 a report on “The growth of pension rights and their impact on the national economy” was presented to both the Institute and the Faculty of Actuaries by Bernard Benjamin, Francis Bacon and Donald Elphinstone.

Edmond Halley, who was born in 1656 and died in 1742, is well known generally because of the Comet which bears his name. He is not, however, associated to any great extent with other activities and if it were not for the Comet it is likely that most people today would never even have heard of him. Outside the actuarial profession, and perhaps to some extent even within it, it is not generally known that in 1693 he constructed a life table from the bills of mortality in the German city of Breslau and then went on to calculate from that table annuity rates on one, two and three lives. Reference to this was formerly included in the introduction to the Year Book, but this has now been shortened and the reference to Halley has disappeared.