1.1. The concept of the matching of assets to liabilities is fundamental in matters of finance. In its broadest sense matching is relevant both to the investment of life office and pension funds and to actuarial calculations in relation to those funds.

1. In a paper to the Institute of Actuaries (JIA 107, p. 49) Heligman and Pollard fitted certain mathematical curves to Australian national mortality. They showed that a good fit could be obtained throughout the whole of life with the following curve:

By courtesy of the Government Actuary, the preliminary data relating to the proposed English Life Tables (No. 14) were made available to the author. In this paper we describe briefly the graduation of the underlying crude mortality rates by cubic splines and give an outline of the salient features of the graduations finally adopted. Complete details of the English Life Tables are given in reference 1, which also includes historical comparisons.

1.1. This paper developed from an earlier paper given by the authors to the New Zealand Society of Actuaries. The authors were involved in acquisitions and mergers at a time when there was very little actuarial literature on the subject. Since then, the 1980 International Congress of Actuaries had as one of its subjects “Estimating the Value of Insurance Companies and Portfolios” and a wealth of papers appeared on the subject of pricing life funds. However, the aspect of merging life funds does not appear to have been covered to the same extent.

1.1.1. In the course of the discussion of the paper by Praetz at the International Congress of Actuaries in Sydney, reference was made to the existence of the ongoing Expense Investigation conducted amongst life offices in the United Kingdom. Considerable interest was aroused and it was subsequently suggested that a paper describing this investigation be presented to the actuarial bodies in order that data on life office costs might be made available to the profession and its significance discussed. In agreeing to present such a paper the authors considered that its scope should be extended to include a study of the attitudes of offices and actuaries to expense analysis and control and of the uses made by offices and actuaries of the results of the Expense Investigation and other expense analyses.

1.1. As every actuarial student is taught:

“Pay-as-you-go is acceptable for a State pension scheme because the State is, for practical purposes, assured of a continuing existence”.

However:

“The position is quite different in the case of an occupational scheme, since an employer's business may cease to exist”.

Nearly 60 years ago, the late C. M. Douglas F.F.A. published a classical paper “The Statistical Groundwork of Investment Policy” (T.F.A. 12 p.173).

The main policy consideration, discussed by Douglas, was the extent to which offices should invest in equities. He maintained that funds should only be invested in equities if greater security was therefore obtained. From a study of index numbers covering the period 1924-28 Douglas concluded that share prices were related to the level of business activity i.e. to the progress of the ‘Trade Cycle’; equity prices following the cycle directly, the debenture prices following the cycle inversely, but with a different tempo and interval. If, therefore, an investor could judge the future trend of business activity, a sound investment policy could be pursued.

1.1. The work for the paper was carried out by the authors as members of the Bonus and Valuation Research Group of the Faculty of Actuaries. The previous paper produced as a result of work done in the Bonus Research Group (Studies of Reversionary Bonus using a Model Office, TFA 37, 91) used a deterministic model office. Future interest rates and returns from equity investment were assumed known and the effects on reversionary bonus of variations in the valuation bases, rates of expansion and inflation of expenses were examined. The assumption of an exact knowledge of future investment returns was a great simplification and begged many of the important questions facing a life office actuary. In this paper the Research Group has paid attention to the change in the value of the assets under variations in financial conditions.