In the course of the discussion at the meeting at Staple Inn last October one speaker regretted the absence of any reserve figures from the notes then under discussion. This comparison of reserves under a new table with those under a table to which we have become accustomed is something of a habit which we tend to do perhaps without asking ourselves why we do it. What does a comparison between A1924–29 and A1949–52 reserve values tell us? Does it really tell us what change to expect in our liability as a result of a change of valuation basis or are these figures merely calculated as a matter of interest, serving in practice no useful purpose?

The answer to that must depend, at least as far as reserves under the main classes are concerned, on the extent to which we use a true net premium valuation. Interesting information is to be found in the paper recently given to the Faculty by J. M. Beattie.

This paper sets out those considerations which appear to the author to be of major importance in the formulation of economic policy and some of the history of the development of thought on these matters. It should be emphasized at once that it represents the knowledge acquired by an actuary, with no formal training in economics, in the course of attempting to appraise the policies actually adopted in recent years, and that it is addressed primarily to those setting out with the same equipment on the same path.

The only other introductory remark necessary is that, inter alia, considerations of space prevent any lengthy discussion of non-economic factors which influence economic policy. This does not imply that technological, moral or social problems may be ignored, but that, for this purpose, they are regarded as parameters in the economic equation.

In recent years there have been a number of papers read to statistical societies and much written on the place of the statistician in business. In the fields of quality control and operational research the position of the mathematical statistician is unchallenged. That of the statistician employed in the day-to-day running of a business is, however, very different. He may have had a mathematical training but is more likely to be an accountant or an economist. This has tempted the author to analyse the extent to which he, as a statistician in business, makes use of his mathematical and actuarial training and employs the mathematical techniques of the statistical textbook. Most of the energies of such a statistician are employed in the collection and tabulation of data; in the main his especial skills are based on an intimate knowledge of the sources of his information (which range from the firm's accounting system for internal statistics to the almost newspaper reporter tactics needed by the market intelligence statistician) and on a familiarity with the needs of the users of the figures (psychology can play its part too in their presentation).

The object of this paper is to provide a basis for a discussion on the advisability or otherwise of life offices issuing ‘variable annuities’ in this country on a commercial basis.

As this is a relatively new subject it is, perhaps, as well to define our terms at the outset. The form of contract which has come to be referred to under the name of ‘variable annuity’ is one under which the annual amount payable is not a fixed sum in terms of money, but a fixed number of annuity units the cash equivalent of which varies from time to time in accordance with the variations in the market value of the assets in which the fund is invested.

The substance of the paper was originally written about a year ago as an internal office memorandum summarizing reports and notices appearing in the financial and insurance press both here and in the U.S.A. about this new American idea, and the authors were of the opinion that as the subject had received little other attention in this country it would form a suitable topic for discussion at one of the Students' Society meetings.

The Friendly Societies Act 1896 provides for two methods of combining the membership, the assets and the liabilities of separate registered friendly societies. Following the procedure of §70 (1) of the Act the societies may amalgamate as one society. For this, the written assent of five-sixths, in value, of the members of each society must be obtained; the value of the members is defined by giving one vote to every member, with an additional vote for each 5 years of membership up to 20 years.

Alternatively, under §70 (2) of the Act, one society may transfer its assets, engagements and liabilities to another. If this procedure is followed, the written assent of five-sixths, in value, of the members of the society transferring its engagements is necessary, but the society receiving those engagements can do so on the resolution of the Managing Committee alone, provided that the Committee has the requisite powers under the rules of the society. For this reason, if one of the societies is large or if it is difficult to contact the members, a transfer of the engagements of the smaller society to the larger is more practicable than an amalgamation.

At the meeting of the Institute of Actuaries on 26 March 1956, it was brought out very clearly that the population problem for the world in general is very different from anything within the present experience of this country. In many areas the population is already outstripping the capacity for food production, and the rate of population increase, consequent upon improving mortality, gives cause for fears about the future.

One of the areas where this problem is becoming acute is the British Caribbean, where the island territories are already thickly populated, and there is no prospect that the rapidly increasing population can be adequately provided for. Lord Simon of Wythenshawe illustrated this very effectively in his 1954 report on the Population and Resources of Barbados. The report was printed privately, but the paper presented to the Institute described the position.

A table of for m = 1 (1) 20 and t = 1 (1) m was supplied by the writer in J.S.S. x (facing p. 64). The present table gives values of for m = 21 (1) 52 and t = 1 (1) n, where n = ½m if m is even, or ½(m — 1) if m is odd. By virtue of the identity I , it is unnecessary to tabulate the argument for higher values of t.

The table was constructed by means of the relation

,

and each column was checked by casting and using the relation

.