The Pamphlet Collection of Sir Robert Stout: Volume 54
Mistaken Methods of Valuation
Mistaken Methods of Valuation.
Those writers who have undertaken to defend the net premium method of valuation as the proper one to be applied in all cases, have found themselves forced to admit that in the case of young companies a smaller reserve is quite consistent, not only with solvency, but with prosperity. In order to get over this difficulty, they have argued that in such companies we may, in regard to the special circumstances, make a smaller reserve than is theoretically necessary. The more correct view, however, appears to me to be that those companies which make their valuations by the net premium method of valuation make a larger reserve than is theoretically necessary; in fact, that they set up a reserve fund which, although concealed from view, is none the less real. This method of procedure may be regarded as erring on the safe side, and, therefore, unobjectionable; but it has the inconvenience that in calculating the surrender values of policies, and in reasoning as to the rights of policyholders, if the larger reserve given by the net premium method is taken as the basis of our calculations, instead of the smaller one, which is obtained by making proper allowance for the expense of obtaining new business, we shall often be led to erroneous conclusions. Perhaps I may also venture to cite, as another instance of the same kind, the doctrine very strongly held in some quarters that the cash bonuses declared upon the same policy at successive divisions of profits should cæteris paribus be approximately constant, and that the reversionary bonuses should therefore form a diminishing series. This is, I believe, not a page 12 popular doctrine with the public, and it seems contrary to the suggestions of common sense, which would lead us to believe that the longer a policy remains in force, the larger in proportion to the time must be its contributions to the profit fund, and that, therefore, the bonuses allotted to it should form an increasing series. This commonsense view is found, upon examination, to be supported by theory when we introduce certain conditions which are neglected by the imperfect theory on which the above-mentioned doctrine is based. As a last instance of the way, in my opinion, too rigid an adherence to an imperfect theory may lead us astray, I take graduation of mortality tables. All attempts hitherto made to express the law of mortality by a mathematical formula have had only partial success, and I think I may say, without fear of contradiction, that no formula that has yet been proposed has been found entirely satisfactory. It is, therefore, in my opinion, unwise to attempt to force a set of observations on mortality experience into conformity with any assumed law, such as Gompertz's, which, although satisfactory enough for long periods, is not satisfactory throughout the whole of life. It is also a mistake to adopt any mechanical method of averages, or to use a formula by which the irregular facts given by observations are rendered less irregular by substituting for each one a new value obtained from a larger or smaller number of the adjoining values. I hope to show on some future occasion that any method of this sort virtually assumes that the law which the observations follow is of a particular kind, and it follows that if the method be applied to a series of figures following that particular law, it will leave them unaltered, whereas if it be applied to a series that follows any other law, it will alter the progression more or less; in fact, it will introduce an error into the series. If we assume, as seems reasonable, that the rate of human mortality follows a certain law that would be represented by a regular curve, if we could only ascertain what the law is, our present position is that we do not yet know what is the nature of that curve. It is, therefore, unwise to attempt to force our facts into correspondence with any known curve which is certainly not the correct one, and the better course is to adopt the graphic mode of graduation, which is the outcome of educated common sense, and according to which we draw a curve which represents approximately the observed facts, and we then correct it until we obtain a sufficient accordance between it and the facts. In making these remarks, I have no wish to undervalue the teachings of theory, but only to warn you against too exclusive a reliance upon them. I consider that theory is a most useful assistant, but not a guide to which we should trust ourselves blindfold. We must, on the contrary, always be on the watch to see whither it is leading us, and refuse to follow it when it is bringing us to conclusions that do not commend themselves page 13 to our educated common sense. I would, therefore, caution the actuary against being too much a man of theory, and would urge him to take every possible opportunity of testing, by the teachings of experience, the doctrines of his theory. If our companies are to be successful, the theoretical advice of the pure actuary or the man of science must always be carefully scrutinised by the man of business from a practical point of view before they are acted upon; it should, therefore, be the aim of every actuary to combine these different qualifications in himself; in other words, to aim at being at the same time a skilled actuary and an experienced man of business, so as to be able to apply his mathematical knowledge to solve any new problem that may present itself in the course of his business, and then to submit the theoretical result given by his formulas to a searching scrutiny in the light of his business experience. Passing on now to consider