Actuarial science

“ Actuarial science has been widely cultivated in the United States of late years, the numbers and zeal of its professional students having kept pace with the extraordinary growth of life insurance. The aggressive activity of the companies has brought the principles of the business home to the popular mind as in no other country, and a large number of periodicals are devoted entirely to the subject. ”

“ The result was a revolution in actuarial science. Milne's table, which, considering the narrow data from which he had to work, was remarkably accurate, was very generally adopted by insurance societies, and subsequent writers have been greatly indebted to his investigations. ”

“ The belief that the death-rate, especially among selected insured lives, is a fixed quantity, is still held by many experienced insurance men, notwithstanding much recent evidence to the contrary. The constant use of actuarial tables, both in business practise and in the statutes governing the maintenance of reserves by life-insurance companies, tends to give a certain fixity-and authority to such tables which they derive from no natural law. ”

“ To recognize it is to deny the first principle of insurance. The average amount by which the reserve of a company must be increased, because of the existence of policies of a given class, is to the actuary an important fact, and is commonly accepted as his best guide in the distribution of surplus. But a popular theory has seized upon the assignment of this average sum to each policy, in the technical shorthand of the actuary, and holds that it is in each case the special property of the owner of that policy. ”

“ It only represents the actuarial average expectation of all the lives. This may be useful enough for insurance dependent on the total experience, but it may be a shocking injustice to the individual in taxation. ”

“ But the risks of business enterprise are not often of this type. They conform more usually to the opposite type of a large chance of a relatively small gain, balanced by a small chance of serious loss or entire failure. Now for almost everyone the possibility of a great loss will count as a deterrent (just as the possibility of a great gain may count as an attraction) for much more than its strict actuarial value. ”

“ But a considerable number of professional actuaries have prosecuted their studies in a scientific spirit, and most of these since 1889 have been associated in the Actuarial 667 Society of America, which has established a high standard of professional competence in its examinations and transactions. The question how far the rate of mortality among insured lives in America is fairly represented by tables drawn from British experience has attracted much inquiry ”

“ Assuming, therefore, the necessary statistics to be attainable, the computation of suitable rates of contribution to be paid by the members of a society in return for certain allowances during sickness, or upon attaining a certain age, or upon death, can be readily made by an actuarial expert. Accordingly, to furnish these statistics, the act of 1875, in continuation of an enactment which first appeared in a statute passed in 1829, required every registered society to make quinquennial returns of the sickness and mortality experienced by its members. ”

“ Cost-of-living increases to retirees, as provided by law, provided the retirement system is approaching actuarial soundness as provided by law, and the granting of such increase does not cause an increase in the actuarially required contribution rate. ”

“ If entered at forty, by the actuary's table, at four per cent., its net single premium would be $511.15 for $1,000. At the age of forty, the natural net premium to insure $1,000 for one year is $9.96. This, at four per cent., will amount at the end of the year to $10.36, so that the company, exclusive of the party himself, by insuring $1,000, runs the risk of losing $989.64 if he dies, and of gaining $10.36, if he does not. There is in this case no reserve at the end of the year, and no occasion to use the term "self-insurance." ”

“ The actuaries, who are intelligent and accomplished gentlemen, must be propitiated, for they are in possession of a somewhat occult science, having justly the ear, the confidence, and the respect of their directors. And when it is borne in mind that these directors embrace, as a body, the first men in the city of London, that they possess a commercial, social, and, not seldom, a political consideration, it follows, that to conciliate them is as necessary to the well-being of any measure, as to conciliate the actuary is necessary to the co-operation of the directors. ”

“ Let the directors take the utmost pains to be independent of great conflagrations and pestilences, their actuaries can tell them that, according to the doctrine of chances, the time must come, at last, when their losses will bring them to a stop. They may tide over such a crisis by extraordinary means, but then they will start again in a weakened state, and the same thing will happen again all the sooner. An actuary might be inclined to deny this, because he knows that the expectation of his company is large, or perhaps (neglecting the interest upon money) is infinite. ”

“ His skill in experimental physics, in astronomical observations, and in practical mechanics was constantly placed at the service both of public bodies and private individuals. He made the actuarial calculations for an insurance fund established by law for the widows and children of the Scottish clergy and professors in the universities. ”

“ Each issuer assumes the risk of mortality from the moment the contract is issued. That risk is an actuarial prognostication that a certain number of annuitants will survive to specified ages. Even if a substantial number live beyond their predicted demise, the company issuing the annuity-whether it be fixed or variable-is obligated to make the annuity payments on the basis of the mortality prediction reflected in the contract. This is the mortality risk assumed both by respondents and by those who issue fixed annuities. ”

“ It is idle to explain that if it is to be looked upon in that light every one would have the right to draw upon it in proportion to their contributions, and the whole system would have to be rearranged upon an actuarial basis. ”

“ In recognition of the fact that a large proportion of the first year’s premiums is in most offices absorbed by the expense of obtaining new business, it has been proposed by some actuaries to treat the first premium in each case as applicable entirely to the risk and expenses of the first year. ”

“ Plans for the present generation have been formulated on the basis of future prospects as foretold by state and federal census data. The methods used were characterized by a member of the Cleveland Foundation Survey Committee as "the actuarial basis of vocational education." This is accurately descriptive, because the method of forecasting the number of men the community will need for each wage-earning occupation closely resembles that employed by life insurance actuaries in foretelling how long men of different ages are likely to live. ”

“ Prior to placement of any proposed increased benefits on the ballot, the retirement system shall prepare, or have prepared on its behalf, an actuarial study of the cost and the funded and unfunded actuarial accrued liability attributable to the retirement benefit changes proposed by the amendment. ”

“ But, though most business risks are not and cannot be a matter for premiums and policies, the principle, which the practice of insurance illustrates, applies none the less. In the light of their knowledge and experience, the promoters of a new undertaking must weigh up the chances of failure and success, though they will not do so by the precise methods of an actuary. They will require that any chances of serious loss should be balanced by such chances of exceptional gain, as would raise the expectation of profit well above the normal return on secure investments. ”

“ Part I. is theoretical. The tables of mortality are given, and we are shown how from these are obtained the expectation of life, and—assuming a given rate of interest the net premium and the reserve—or, as the author prefers to call it, the trust-fund deposit. The theory of annuities is discussed in a series of problems; and the mechanism of the commutation tables—those working-tools of the actuary—is explained.
Part II. is devoted to the discussion of such practical considerations as: the general management of companies; stock and mutual rates; the various plans of insurance ”

“ When it is found, and after making allowance for probable salvage value at the time of retirement, it is a mere matter of mathematics to compute under the straight-line method the rate of annual accrual.
This rate when applied to the cost of the depreciable property fixes two things: (1) The amount of the depreciation accrual to deduct from gross, before determining net, income. For this purpose a high rate works in favor of the taxpayer for any given year. (2) It also determines the amount by which the cost base must be reduced for application of depreciation rates the following year. ”

“ But the severest lesson was the loss of Barrett's Method, [327] now the universal instrument of the actuary in his highest calculations. It was presented to the Royal Society, and refused admission into the Transactions: Francis Baily [328] printed it. ”

“ The actual results of an investment over a long term of years very seldom agree with the initial expectation. Nor can we rationalise our behaviour by arguing that to a man in a state of ignorance errors in either direction are equally probable, so that there remains a mean actuarial expectation based on equi-probabilities. For it can easily be shown that the assumption of arithmetically equal probabilities based on a state of ignorance leads to absurdities. ”

“ The actuary is forced to observe that the interest factor in his calculations is much less definitely fixed by known facts than the mortality factor. The longer a contract has to run, the greater the effect of the difference in rate. The value of a payment to be made in thirty years is greater by above one-half with interest taken at 3% than at 41/2%, and one to be made in thirty-six years is more than twice as great. Hence the most careful study of the forces determining for long periods the average rate of interest is fundamental in life insurance. ”

“ To determine the present value of such remainder, use the appropriate factor in column 3 of Table A or B of § 81.10. If the present worth of a remainder bequeathed for a charitable use is dependent upon the termination of more than one life, or in any other manner rendering inapplicable Table A or B of § 81.10, the claim for the deduction must be supported by a full statement, in duplicate, of the computation of the present worth made, in accordance with the principle set forth in § 81.10, by one skilled in actuarial computations.' (Emphasis supplied.) ”

“ It is also to be remarked that it is found in general that the average amount of policies matured by death is higher than the average of all policies in force; and some actuaries incline to believe that tables of pecuniary loss might, for practical use, take the place of tables of mortality, since the actual claims are in units of money, not of lives. ”

“ An actuary in a large insurance company is obliged to stop work at such times, finding that he makes so many mistakes which he is only conscious of later that his work is useless. In a large factory from ten to twenty per cent less work is brought out on damp days and days of threatening storm. ”

“ Few seem to be aware how greatly the knowledge of what may be termed the actuarial side of heredity has advanced in recent years. The average closeness of kinship in each degree now admits of exact definition and of being treated mathematically, like birth and death-rates, and the other topics with which actuaries are concerned.
2. Historical inquiry into the rates with which the various classes of society (classified according to civic usefulness) have contributed to the population at various times, in 39ancient and modern nations. ”

“ Each is interested in the engagements of all; for out of the coexistence of many risks arises the law of average, which underlies the whole business. An essential feature of this scheme is the mathematical calculations referred to, on which the premiums and amounts assured are based. ”

“ It is to be hoped that a further gathering of statistics as to expectations of life of different assets under varying conditions will ultimately furnish tabulations, corresponding to insurance tables, according to which under known and expected conditions a fairly accurate rate of depreciation for a particular asset may be made. Unlike insurance rates, however, the depreciation rate once established will not necessarily remain constant, but must be subject to a periodic revision in the light of new data and conditions. ”

“ If the actuary of an insurance office infers from his tables that among a hundred persons now living, of a particular age, five on the average will attain the age of seventy, his inference is legitimate, not for the simple reason that this is the proportion who have lived till seventy in times past, but because the fact of their having so lived shows that this is the proportion existing, at that place and time, between the causes which prolong life to the age of seventy, and those tending to bring it to an earlier close. ”

“ The likelihood of presenting an inaccurate picture of yearly income from operations is particularly offensive where, as here, the taxpayers stoutly maintain that they are only in the business of renting and leasing automobiles, not of selling them. The alternative is to estimate the period the asset will be held in the business and the price that will be received for it on retirement. Of course, there is a risk of error in such projections, but prediction is the very essence of depreciation accounting. ”