With these words Sir George Maddex, in his Presidential Address, directed our attention to the present system of taxation of annuity funds. M. E. Ogborn (1), on 27 October 1947, touched on the subject of uneven incidence of tax upon differing funds, and some uneasiness about the consequences was manifest in the discussion on that paper.

Much has been written in recent years upon the general subject of taxation of annuities. S. J. Rowland and F. H. Wales (2), A. H. Shrewsbury (3), and M. E. Ogborn (1) have fully described and commented upon the present method. Relatively little attention, however, has been devoted to the effects of the system upon annuity funds, probably because it is only recently that we have become aware of its full implications. There is some need therefore to review the consequences and to investigate more closely the actuarial problems which follow.

It is proposed here to analyse the effects of the system and, proceeding from some simple basic principles, to point to a method of solution of the actuarial problems connected with valuation, investment and the terms for new business and withdrawals.

Actuaries are closely interested in the economic state of the nation, both as ‘scientific financiers’ and as citizens of a democracy, but this interest involves them in a dilemma: although it is possible to obtain only a hazy picture of the whole, even by devoting all of one's time to the study of economic affairs, yet for the majority this subject can be only a sideline. Each actuary must therefore make his own decisions, first as to how much time he can spare, and second as to which aspects of the nation's economy he might most profitably study. These two decisions will depend on the particular actuary's interests and employment, and on the state of the nation's economy at the time.

This paper discusses one selection of economic data, comprehensive enough to give a reliable impression of the nation's economy, yet short enough to permit frequent examination.

The following communication is not an original paper, but the summary of an article published by the author in collaboration with H. Zimmermann in the Bulletin de l'Association des Actuaires Suisses, L, pt. 2 (1950). As the method of reserve calculation by grouping described below assumes a fundamentally new point of view and combines substantial advantages with great simplicity, it may, however, interest those actuaries who have no access to the original paper.

As is well known the individual valuation of every single policy, even for a medium-sized portfolio, is a long and arduous task. Therefore different methods for the valuation of policies grouped in certain ways have been in use for a long time. In this respect it is possible to distinguish methods giving the exact total of the individual reserves (e.g. the so-called Altenburger or Karup or valuation constant method) and those leading to approximate results (e.g. the Lidstone or Z-method). But most group methods have the evident disadvantage of a grouping which is in other respects inappropriate for the classification of the individual policy within the portfolio. Thus, in the valuation constant method, groups of equal age attained have to be formed, and the Z-method requires groups of the same remaining term. Yet one would much prefer a grouping which necessitates no sorting of the policies contrary to their natural grouping. Thus the putting together of all policies with the same year of entry for the purpose of collective reserve calculation is in some way a natural manner of grouping, and this was the procedure used in the t-method formerly proposed by the author.

Heavy taxation by Estate Duty and Income Tax has recently led to a serious consideration of the avoidance of this onerous liability by means of gifts made by a donor in his lifetime and, in the case of a settled fund, of an exchange of benefits where the Beneficiaries can come together and bring the trusts to an end.

If, in the case of a Settlement, Life Tenant and Reversioner can by mutual agreement arrange to divide the Fund between them, the Life Tenant may benefit considerably by realizing a sum in excess of the market value of his interest and using it to provide as much or more spendable money than before. He may also promote a smaller liability to Sur-Tax. The Reversioner may succeed in securing a cash sum larger than he could expect at a future date on the death of the Life Tenant reduced as it would be by Estate Duty at the aggregable rate applicable to the Life Tenant.