An important part of the work of an actuary consists in making and testing graduations of mortality statistics. Much space has been devoted in the Journal to methods of graduation, but for many years, apart from the recent paper by H. L. Seal (J.I.A. Vol. lxxi, p. 5), little attention seems to have been paid to the testing of graduations. Although statistical methods are usually employed in making the tests, consideration has not often been given to ascertaining whether mortality statistics fulfil the conditions necessary for the tests to be strictly applicable. It is the purpose of this paper to set out some investigations into this question. Such matters may be thought to be of only theoretical interest, since, in practice, the tests work satisfactorily as a general rule; but actuaries should not employ their tools in a mechanical fashion without realizing fully their limitations and implications, and the question therefore takes on a practical as well as a theoretical aspect. It is hoped that this paper will show how far the tests of a graduation are satisfactory in theory and practice and indicate where modifications are required.

I have limited this paper to the consideration of appreciation or depreciation in fixed interest-bearing securities resulting from a fall or rise in the general level of interest rates and not from any alteration in the intrinsic value of the securities, i.e. there is assumed to be no change in the probabilities that the terms of the contracts will be fulfilled. My object is to discuss how this appreciation or depreciation should be treated in order to obtain the maximum practicable degree of equity between the different generations of policyholders in an office which distributes its surplus by means of a uniform reversionary bonus.

The problem can be most easily discussed by showing the effect on a model office of adopting various methods of treating this appreciation or depreciation. I propose to limit the discussion in the first place to the question of depreciation in an office employing a bonus reserve valuation.