No CrossRef data available.
Article contents
Bonus Distributions: A Study in Differences
Published online by Cambridge University Press: 27 November 2014
Extract
In America distributions of bonus are made on a “contribution” method, but in Great Britain most of the offices use a bonus system of the compound reversionary or the simple reversionary type. To an actuary practising in England a contribution method seems to entail a great amount of work and may not reach exactitude in the end; while an actuary practising in America must, I think, feel inclined to ask English actuaries how they reach fairness between different classes and different ages at entry.
If we define “fairness” for our present purpose as such a distribution as leads to an equation at the outset between the present values, on an experience basis, of benefits on the one hand and of premiums (less expenses) on the other, then a complete contribution method will provide “fair” bonuses whatever the basis of valuation; and this is true though the valuation basis may be far removed from actual facts and though the “profits” in the valuation sense, from interest, loading, withdrawals and mortality, bear no relation to the premiums or the facts assumed in calculating those premiums.
- Type
- Research Article
- Information
- Copyright
- Copyright © Institute of Actuaries Students' Society 1932
References
page 73 note 1 Lever, E. H.. Trans. Internat. Congress, Stockholm, vol. 1, p. 181 Google Scholar. The point made by Lever may be put: a “fairness” that alters appreciably the type of bonus allotted from the type canvassed may be deemed unfair by the policyholder. Mere equations of present values do not necessarily provide a complete solution of the problem.
page 73 note 2 See Morgan's Addresses to the Equitable Society (a collected volume in 1854 included also those by his son) and his “View of the rise and progress of the Equitable Society,” London, 1829 Google Scholar. The method has been adversely criticised by writers in J.I. A. and elsewhere. The critics seem to have overlooked that the premiums fitted the bonus system so far as Morgan's office was concerned. This may not have been equally true in the case of other offices which used the same bonus system.
page 74 note 1 See King, G., Text Book, Part II, Life Contingencies, pp. 327 Google Scholar, etc.
page 74 note 2 See Jones, D., “Values of Annuities, etc.” 1843, vol. i, p. 916 Google Scholar.
page 75 note 1 P. L. Newman pointed out in 1891 that there were at least five offices using the method in 1865, but exact information was not available prior to the Act of 1870. See “The principal Methods employed in the Distribution of the Surplus of Life Assurance Companies”, a paper to the Insurance Institute of Yorkshire.
page 76 note 1 Actuaries varied in their description of the figures and some seem to have allowed something for incidental profits. Moreover, many statements refer to the with-profit premiums in general use at the time without much consideration of whether those premiums were suitable either to a simple or a compound system and, strictly speaking, the same scale cannot be suitable to both except in the limiting case where there is no bonus.
page 77 note 1 See, for instance, Coutts, C. R. V., J.I. A., vol. lvii, p. 159 Google Scholar; Recknell, G. H., J.I. A., vol. lvii, p. 192 Google Scholar; Maltby, C. H., J.I. A., vol. liii, p. 167 Google Scholar.
page 80 note 1 See previous remarks as to this table. It may be suggested that actuaries are inclined to use a standard table without considering its applicability to a particular business.
page 80 note 2 In other words, we make something closely resembling a bonus reserve valuation (see Coutts, , J.I.A., vol. xlii, p. 161 Google Scholar).
page 80 note 3 It seems probable that this suggestion must have been made before, but I have not yet found a reference to it.