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Mortality Tables

( Originally Published 1911 )



The basis of mortality tables.—Premium payments and the interest return are, of course, important matters in connection with life insurance. The real, underlying plan of life insurance, however, is founded on what are known as mortality tables. These tables in turn are based on actual statistics and aim to show the general rate of mortality and, in particular, the rate at each age of life. Insurance companies may derive mortality tables from two sources : (a) the general population of any territory as shown by the census returns, including, of course, the births and deaths within the territory, and (b) , so far as the life insurance companies are concerned, tables derived from their own experience.

Halley's table.—In the beginning, naturally, insurance companies had no previous experience as a guide so that all tables of mortality had to be founded upon such general statistics as were available. The earliest attempt—and it is interesting historically-to derive such a table in what might be called modern times, was that made by Halley, the English astronomer, in 1692. For some years the journal published by the Royal Society had been dormant. Halley, among others, was interested in its revival and offered to contribute an article to the first revived number. In casting about for some topic, he hit upon the idea of preparing a table of mortality. When he came to look for his statistics he found no information which he could use outside of Breslau in Silesia. Accordingly, he based a table on their records, which are the oldest known records of this form.

So far as the source is concerned, tables of some value can be derived from a limited range of data. For example, the length of life of the rulers of a country, such as Great Britain, might be used as a foundation. A some-what broader table, but still in the same class, could be based on statistics covering the peerage of Great Britain. In this latter case, more lives would be involved, which would make the table of greater value. In the same way, certain bodies, such as municipalities where employes are fairly steadily employed under civil service rules, furnish comparatively good data for the compiling of mortality tables. This same principle would also operate in the case of large corporations, especially those maintaining benefit funds.

Principles of compilation.—To compile a mortality table, the following essential facts must be known:

(a) the number of people,
(b) their ages,
(c) the death record,
(d) the ages at death.

Given these statistics and assuming that the population was stationary, a fairly reliable table could be computed. If, however, the tabulation is affected at all by emigration or immigration or by other factors, then the results may be quite deceptive although the first set of facts may exist.

The Northampton table.—An error of historic interest may be found in the Northampton Table of Mortality, published in 1783. This table, which enjoys the unique distinction of being the first to be used by life insurance bodies, was compiled by Dr. Price and was based on two parishes in the town of Northampton. It was, in fact, a record of the deaths in these two parishes, with the ages at death. There was also a record of the baptisms which had taken place. In the period under observation, 1735-1780, Dr. Price noted that the number of deaths exceeded the number of baptisms. The additional deaths, he assumed, were caused by immigration into Northampton at the age of about twenty. As a matter of fact, his assumption was erroneous, as there were a large number of Baptists in the community whose children were not baptised. The wrong assumption led to wrong conclusions. As a result of the error, Dr. Price's table over-estimated the death rate and, while it was safe for a life company for annuity purposes, it was grossly in error because it under-estimated the term of life. For a long time this table was the only one in use. It may even be found in use today in certain parts of the United States.

The Carlisle table.—The second table, more scientific and still in use, is the Carlisle Table, so called because it was based on the statistics of two parishes in the town of Carlisle, England. It was compiled in 1815 by Joshua Milne, who based his figures on the census of 1780 and the deaths in the two parishes from 1779 to 1787. Although using only a few lives, Milne's table proved remarkably accurate and is to-day held in high esteem for some purposes.

Other tables.—There have been as many as five other tables based on population statistics in England. One of the most important was that of 1851, based on statistics of births and deaths from 1848 to 1853 in sixty-three districts of England and Wales.

It is evident that, however valuable such tables as have just been described may be when based on general statistics, the data cannot be as exact, even within a small compass, as the carefully kept records of a life insurance society.

As soon as such a plan was practicable, the insurance companies turned to their own previous experience for data. Mr. Arthur Morgan, actuary of the old Equitable society, published the experience of that company in 1834. This was a valuable contribution to the subject, although, as the experience of merely one company, it was necessarily narrow. Some seventeen English life insurance companies combined their experience in 1843 and published a table generally known as the Actuaries or the Combined Experience Table. This new table was based on 84,000 policies running from 1762 to 1833, some 14,000 of the policies having terminated by death. The table brought out several interesting facts which have been verified by later experience—that the mortality among women between the ages of twenty and fifty was greater than that among men, and that above that age the reverse appeared to be the case. These facts do not hold good, however, when dealing with annuity experience, and that fact must be noted in the two forms of contract. The conditions under which the two forms are taken out are usually quite different.

The American Experience tables.—In the United States, the English tables were, with adaptations, the best guide until sufficient experience had developed to compile tables on this side of the Atlantic. Probably the most famous—perhaps because the first, but also because it has stood the test of years—is the American Experience Table of Mortality, which ranks as the standard table in the United States. It was compiled by Sheppard Homans and appears to have been published originally in connection with an act of the Legislature of the State of New York, May 6, 1868. Much interest was aroused as to how the table was compiled, although the exact manner is still more or less a matter of conjecture. One assumption was that the statistics of the Mutual Life Insurance Company of New York were used as a basis; in this connection, however, it has been observed that the statistics available for the older ages could hardly have been sufficient to serve as the basis for such a table. Some adaptation, evidently, must have been made, but just what or how extensive is not known. In any event, the table stood the test well and answered the purpose admirably. In fact, it made a very important place for itself on this side of the Atlantic and is the table usually prescribed by all the State laws.

There have been many other important tables based on different periods and used for different purposes. Investigations have been and are still being conducted both in England and in this country, and we may look for improved tables as the work progresses, just as we may expect changing conditions in the length of life itself under improved sanitary and hygienic conditions.

The American Table of Mortality, which is now in general use for computing the premium of American companies, is here reproduced. It assumes that there are 100,000 living at the age of ten and for each year up to 95, when the table runs out, shows the number surviving at the succeeding year. The percentage of mortality is also shown, that is, the number who died within the year in proportion to those living. The life expectancy is also shown. As yet, these percentages are, of course, tentative and provisional, but they are of considerable interest in connection with a study of the general subject. It should be remembered that the chief concern of the actuary is not in the expectancy of life, but rather in the chance of loss when a policy is issued.

Computing the premium.—A simple illustration will show the principles according to which an insurance premium is computed. It is desired, say, to insure 1,000 persons for $1,000 each. We will assume that they wish to pay for this in one payment. We will also assume that each member of the entire group is fifty years of age at the time the insurance is taken out and that all will die within a three-year period, the deaths being at the rate of 200 the first year, 300 the second and 500 the third. To meet this condition it is evident that the company must have on hand at the end of the first year $200,000 to pay one thousand dollars to each beneficiary for each of the 200 deaths. In the same way, there must be $300,000 at the end of the second year and $500,000 at the end of the third year. But only these respective parts—that is, $200,000, $300,000 and $500,000-will be required at the end of the first, second and third years respectively. The company need not, therefore, collect the entire $1,000,000 at the beginning, since only a proportion will be demanded at the close of that year. Let us further assume that the interest will be 3 per cent. At the close of the first year, as we have seen, $200,000 must be paid. But what is the present value of this sum? The present value of $1 for one year is .970874, and for $200,000 would be $194,174.80. The present value of the $300,000 due at the end of two years is $282,778.80; the present value of $500,000 needed at the end of the third year is $457,571. Totalling these three amounts at their present value, then, we have $934,524.60, and as there are one thousand persons whose lives are insured, each would pay one-thousandth part of this, or $934.53. This sum, then, at the beginning of the three-year period would provide for the payments of the whole group.

Passing now to an example taken directly from the American Mortality Table, suppose you wish to find the sum of money for which a policy can be issued for a per-son, age fifty, providing for a $1,000 payment at death. Refer to the table on the preceding page and you will find that out of 100,000 persons who were aged 10, only 69,804 reached the age of 50. You will further note, on looking at the 51st year, that 962 is the estimated number of those who will die within the year. Accordingly, if a company insured the whole group, it should be in a position to pay out $962,000 for the deaths of this year. But the present value of this sum is only $933,981, since with interest at 3 per cent it would amount at the end of the year to $962,000. Now, likewise, for each succeeding year the table shows the amount required and the present worth is easily ascertained. The sum of all these will show that each person at the age of fifty would pay $555.22 to insure $1,000 being paid to each person at death.

The law of increasing mortality.--The fact that the death rate increases in the older ages is provided for by adjusting the insurance premium so that in the younger ages an increased sum is collected in order that the proper reserves may be set aside. The annual premiums normally exceed the death claims for the first thirty or forty years; after that, the losses by death largely exceed the annual premiums. Failure to recognize this law of increasing mortality in the older ages has brought most of the trouble to the assessment insurance companies. If enough is not, collected at the younger age to establish the proper reserve for the older age, it naturally becomes necessary to increase the assessment or premiums at the older age.



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