according as 1 + a'_(x+n) 1 + a_(x+n)
1 - ------------ >, =, or < 1- -----------
1 + a'_x 1 + a_x
1 + a_(x+n) 1 + a'_(x+n)
i.e. as ----------- >, =, or < ------------ (1)
1 + a_x 1 + a'_x
1 + a'_(x) 1 + a'_(x+n)
or as ---------- >, =, or < ------------ (2)
1 + a_x 1 + a_(x+n)
where the accented symbols throughout refer to one table and the
unaccented symbols to the other.
We have thus the means of ascertaining whether the policy-values of
any table will be greater or less than, or equal to, those of another,
either (1) by calculating for each table separately the ratios of the
annuity-values at successive ages, and comparing the results, or (2)
by calculating at successive ages the ratios of the annuity-values of
one table to those of another, and observing whether these ratios
decrease or increase with advancing age or remain stationary
throughout. The above relations will subsist whatever may be the
differences in the data employed, and whether or not the
annuity-values by the different tables are calculated at the same rate
of interest. When the same rate of interest is employed, any
divergence in the ratios of the annuity-values will of necessity be
due to differences in the rates of mortality.
Fallacy of single-policy reserve.
A prevailing fallacy in the popular mind, which has grown out of the
practice of net valuations, is the inference that the average technical
reserve represents the value of the individual policy. Each risk is
properly assumed at its probable or average value at the time. But from
that moment its circumstances are constantly changing in directions then
unforeseen, and the expectation that such changes will occur is the
motive for insuring. To treat them singly as unchanged in value at any
later time is as illogical as it would be after some have matured. The
actual value of any one risk borne by a company is indeterminate. It may
become a claim to-morrow, or not for a generation to come. In the former
case the company must now hold funds to pay in full; in the latter, the
future premiums will perhaps more than suffice, so that no present
reserve is needed. An entire reserve for the whole body of risks is
essential, and its amount is definite, upon the reasonable assumption
that the general average remains undisturbed by individual changes. A
distinct reserve for a single policy is inconceivable. 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. The
practical consequences are serious when, as often, many of the insured
cease to pay premiums, and each demands the amount of the supposed
individual reserve. His right to claim it is countenanced by a
widespread public opinion, which has inspired statutes in Massachusetts
and some other states, requiring companies to redeem all policies
lapsing after the first two or three years of insurance at a price
founded on the technical reserve. Yet, in by far the majority of
instances, the lapse of policies is of itself a loss to the company. It
is deprived of business secured at much expense before it has derived
any of the advantage expected from the accession. It is compelled to pay
numbers of its profitable contributors for ceasing to contribute. The
burden falls in a mutual company upon the insured who fulfil their
contracts. Such laws favour those who withdraw after few payments at the
cost of those who maintain their insurance to the end, or for many
years. The American companies formerly yielded to the pressure of a
mistaken public sentiment, and competed for favour by promising
excessive values in case of surrender.[2] Similar conditions exist in
Switzerland, Austria, and other countries in which the business is
minutely regulated by government bureaus. But in Great Britain the
companies are largely free from such influences, while an open market
exists for policies which have a commercial value, with results on the
whole more satisfactory to all parties interested than any rule of
compulsory purchase which could be enforced on the companies.
Industrial Insurance.
A special form of life insurance, which has wonderfully developed, is
the family insurance of the labouring people by the so-called industrial
companies. Until recently this class of people had no satisfactory share
in the benefits of insurance, although the friendly societies in Great
Britain, and many forms of beneficial associations in the United States,
were attempts, often in part successful, to provide for special wants,
mainly for maintenance of the sick and for the costs of burial. Most of
them, however, lacked a scientific basis and an efficient and permanent
organization, while thousands of them were grossly mismanaged. In
Germany an elaborate scheme of compulsory insurance for labourers was
established by a law of the empire in 1883, and extended in subsequent
years; and similar legislation has been enacted in several other
countries, most thoroughly in Switzerland and Austria. The ultimate
value of this great social experiment cannot yet be determined. That it
relieves much want and does a great service in preventing pauperism is
not disputed; but that it also undermines the independent spirit of the
people, and that it imposes a burden upon the national industry, which
not only hampers it in the world's competition, but reacts with special
injury upon the class it aims to benefit, are criticisms not
satisfactorily answered. No scheme of government insurance, certainly,
is adapted to a people impatient of paternalism in its rulers and
thoroughly habituated to voluntary association for all common interests.
The solution of the great problem, how to apply the insurance principle
to the most pressing needs for protection of the class supported by the
wages of labour, is now sought in Great Britain and America mainly in
the universal offer to them of industrial insurance. The Prudential
Assurance Company of London was the pioneer in this work, beginning it
experimentally in 1848, but gradually adapting its methods to the new
field, until a generation later they showed themselves so efficient that
an extraordinary growth resulted, and has continued without
interruption. This company and others upon a similar plan insure whole
households together for burial expenses in case of death, and a small
provision for dependants or for old age, charging as premiums small
fractions of a day's wages, which must be collected weekly. The great
difficulties encountered were the cost of small and frequent
collections, and the high rate of mortality, which is from 40 to 90%
more than that in the experience of the older companies. This high
death-rate is due not so much to the fact that life is shorter in the
labouring class as to the lack of efficient medical selection, which
would be too costly. The premiums, at best, must be made higher than in
offices insuring for annual payments, but the demand for insurance
extended as rapidly as the system could be explained, and the Prudential
is said to have now in force some 12,000,000 policies, with an average
premium of twopence a week, secured by an accumulated insurance fund of
L17,000,000. It has superseded a host of petty assessment societies of
various classes without scientific basis or business responsibility,
which deluded and disappointed the poor. The British government in 1864
undertook to administer a plan for the insurance of working men, but in
thirty years accomplished less than the work of one private company in a
year. In addition to the many insurance companies which transact
industrial business in the United Kingdom, a large number of friendly
societies have adopted similar plans.
The system of industrial insurance was introduced into the United
States in 1876. Its growth, though much more rapid than in Great
Britain, was at first slow compared with that of later years. The
following table, condensed from the Insurance Year-Book for 1900, is
an interesting exhibit of the character as well as of the extent of
this form of insurance among working men:--
_Industrial Insurance in the United States._
+------+------+-------------+------------+--------------+------------+------------+
| | | | Policies in| Insurance in | | |
| Year.|No. of| Insurance | force 31st | force 31st | Premiums | Losses |
| | Cos. | written. | December. | December. | received. | paid. |
+------+------+-------------+------------+--------------+------------+------------+
| 1876 | 1 | $400,000 | 2,500 | $248,342 | $14,495 | $1,958 |
| 1880 | 3 | 34,212,131 | 228,357 | 19,590,780 | 1,155,360 | 430,631 |
| 1884 | 3 | 89,150,302 | 1,076,422 | 108,451,099 | 4,486,612 | 1,499,432 |
| 1888 | 7 | 161,260,335 | 2,788,000 | 302,033,066 | 11,939,540 | 4,162,745 |
| 1892 | 11 | 276,893,923 | 5,118,897 | 582,710,309 | 24,352,900 | 8,847,322 |
| 1896 | 11 | 360,852,458 | 7,375,688 | 886,484,869 | 40,058,701 | 13,420,336 |
| 1899 | 16 | 519,789,085 | 10,048,625 |1,292,805,402 | 56,159,889 | 17,023,485 |
+------+------+-------------+------------+--------------+------------+------------+
It is remarkable that the average weekly premium in the United States
appears to be about 10 cents, or two and a half times as high as in
Great Britain. The average policy is also proportionally larger, and
the progressive increase in its amount deserves notice. At the rate at
which the practice of insurance is extending among working men, it
would require but few years for it to become as universal in these
countries as any paternal government has aimed to make it by
compulsion.
Division of surplus.
There are various sources from which a surplus of funds may arise in an
insurance company: (1) from the rate of interest actually earned being
higher than that anticipated in the calculations; (2) from the
death-rate among the insured being lower than that provided for by the
mortality tables; (3) from the expenses and contingent outlay being less
than the "loading" provided to meet them; and (4) from miscellaneous
sources, such as profitable investments, the cancelment of policies, &c.
Supposing a valuation to have been made on sound data and by a proper
method, and to have resulted in showing that the funds in hand exceed
the liabilities, the surplus thus ascertained may be regarded as
_profit_, and either its amount may be withdrawn from the assets of the
office or the liabilities may be increased in a corresponding degree.
Bonuses.
Various methods are employed by insurance companies in distributing
their surplus funds among the insured. In some offices the share or
"bonus" falling to each policyholder is paid to him in cash; in others
it is applied in providing a reversionary sum which is added to the
amount assured by the policy; in others it goes to reduce the annual
contributions payable by the policyholder. A method of more recent
introduction is to apply the earlier bonuses on a policy to limit the
term for which premiums may be payable, thus relieving the policyholder
of his annual payments after a certain period. Another method is to
apply the bonuses towards making the sum insured payable in the lifetime
of the policyholder. The plan of reversionary bonus additions is most
common, and when it is followed the option is usually given of
exchanging the bonuses for their value in cash or of having them applied
in the reduction of premiums.
Not only are there different modes of applying surplus, but the basis on
which it is divided among the insured also varies in different offices.
In some the reversionary bonus is calculated as an equal percentage per
annum of the sum insured, reckoning back either to the commencement of
the policy in every case, or (more commonly) to the preceding division
of profits. In others the rate is calculated, not only on the original
sums insured, but also on previous bonus additions. In others the ratio
of distribution is applied to the cash surplus, and the share allotted
to each policy is dealt with in one or other of the ways above
indicated. The following are some of the ratios employed by different
offices in the allocation of profits: (1) in proportion to the amount of
premiums paid (with or without accumulated interest) since the last
preceding valuation; (2) in proportion to the accumulated "loading" of
the premiums so paid; (3) in proportion to the reserve values of the
policies; (4) in proportion to the difference between the accumulated
premiums and the reserve value of the policy in each case.
Some offices have a special system of dealing with surplus, reserving it
for those policyholders who survive the ordinary "expectation of life,"
or whose premiums paid, with accumulated interest, amount to the sums
insured by their policies. This system is usually connected with
specially low rates of premium.
In the United States the so-called "contribution plan" has been
accepted in theory by many companies, though carried out with many
variations in detail by different actuaries. The principle is, that
since each of the insured is charged in his premium a safe margin
above all probable outlays, when the necessary amount under each head
becomes determinate the several excesses should be returned to him. It
is therefore sought to calculate what each member would have been
charged for net premium and loading had the mortality, rate of
interest, and expenses been precisely known beforehand, and to credit
him with the balance of his payments. As a corollary of the theory of
net valuations, which regards every life insured as an average life
until its end, and assumes the rigid accuracy and equity of all the
formulas employed to represent business facts, it is consistent and
complete. But many minds find it more curious than practical, and
prefer to seek equity in faithfulness to contract rights rather than
in adjustments which they deem too refined, if not fanciful. The plan
has met with little favour in England, where surplus is more commonly
distributed on general business principles. Enormous bonuses were
saved by the British offices out of the excessive premiums at first
collected, and by the American companies during the epoch of high
interest rates. But the use of more accurate tables, the decline in
interest, and the increased expenses of later years, have vastly
reduced the apparent profits. Former methods of distributing surplus,
when ascertained, have largely given way in America to novel and more
complex plans. The Tontine idea, historically familiar, was for many
years imitated by some offices in their insurance contracts. All
premiums above outlay, in a company or a class of policies, were
accumulated, only stipulated amounts being paid on death claims
meanwhile maturing, with no compensation to its members withdrawing,
until the end of a fixed term, when the whole fund was apportioned to
the survivors. Large returns were sometimes made, but many who could
not maintain their policies were dissatisfied. "Semi-tontines"
followed, partly meeting the difficulty by pooling only the surplus,
and allowing some return in case of withdrawal. But these cruder forms
of contract are now largely superseded by various "reserve-dividend,"
"accumulation," "bond," and "investment" policies, with options at
stated periods between cash withdrawals and continued insurance, the
simple inducement to provide against death being more or less merged
in that of making a profitable investment of capital.
Surrender values.
In those branches of insurance where the contract is one of indemnity
against loss, the risk remaining the same from year to year--and where
the consent of both parties, insurer and insured, is required at each
periodical renewal--no question of allowance in respect of past payments
can arise when one party or the other determines to drop the contract.
It is quite recognized that the premiums are simply an equivalent for
the risk undertaken during the period to which they apply, with a
certain margin for expenses and for profit to the insurer, and that
therefore a favourable issue of the particular contract supplies no
argument for a return of any part of the sums paid. In life insurance,
however, we have shown that the premiums contain a third element,
namely, the portion that is set aside and accumulated to meet the risk
of the insurance when the premium payable is no longer sufficient of
itself for that purpose.
When a policyholder withdraws from his contract with a life insurance
office, the provision made for the future in respect of his particular
insurance is no longer required, and out of it a surrender value may be
allowed him for giving up his right to the policy. If there were no
reasons to the contrary, the office might hand over the whole of this
provision, which is in fact the reserve value of the policy. No more
could be given without encroaching upon the provision necessary for the
remaining policies. But the policyholder in withdrawing is exercising a
power which circumstances give to him only and not to the other party in
the contract. The office is bound by the policy so long as the premiums
are duly paid and the other conditions of insurance are not infringed.
It has no opportunity of reviewing its position and withdrawing from the
bargain should that appear likely to be a losing one. The policyholder,
however, is free to continue or to drop the insurance as he pleases, and
it may fairly be presumed that he will take whichever course will best
serve his own interest. The tendency obviously is that policies on
deteriorated and unhealthy lives are kept in force, while those on lives
having good prospects of longevity are more readily given up. Again, the
retiring policyholder, by withdrawing his annual contribution, not only
diminishes the fund from which expenses are met, but lessens the area
over which these are spread, and so increases the burden for those who
remain. Considerations like these point to the conclusion that, in
fairness to the remaining constituents of the office, the surrender
value to be allowed for a policy which is to be given up should be less
than the reserve value. The common practice is to allow a proportion
only of the reserve value. Some offices have adopted the plan of
allowing a specified proportion of the amount of premiums paid. This
plan is not defended on any ground of principle, but is followed for its
simplicity and as a concession to a popular demand for fixed surrender
values.
Non-forfeiture system.
Another mode of securing to retiring policyholders the benefit of the
reserve values of their insurances is that known as the _non-forfeiture
system_. This system was first introduced in America, whence it found
its way to the United Kingdom, where it was gradually adopted by a large
proportion of the insurance companies. In its original form it was known
as the "ten years non-forfeiture plan." The policies were effected by
premiums payable during ten years only, the rates being of course
correspondingly high. If during those ten years the policyholder wished
to discontinue his payments, he was entitled to a free "paid-up policy"
for as many tenth parts of the original sum insured as he had paid
premiums. The system, once introduced, was gradually extended first to
insurances effected by premiums payable during longer fixed periods, and
ultimately, by some offices, to insurances bearing annual premiums
during the whole of life. The methods of fixing the amount of paid-up
policy in the last-mentioned class of cases vary in different offices,
but the principle underlying them all is that of applying the reserve
value to the purchase of a new insurance of reduced amount.
Conditions of insurance.
An office, in entering on a contract of life insurance, does so in the
faith that all circumstances material to be known in order to a proper
estimate of the risk have been disclosed. These circumstances are beyond
its own knowledge, and as the office for the most part (except as
regards the result of the medical examination, which may reveal features
of the case unknown to the proposer himself) is dependent on the
information furnished by the party seeking to effect the insurance, it
is proper that the latter be made responsible for the correctness of
such information. Accordingly it is made a stipulation, preliminary to
the issue of every policy, that all the required information bearing
upon the risk shall have been truly and fairly stated, and that in case
of any misrepresentation, or any concealment of material facts, the
insurance shall be forfeited. In practice, however, this forfeiture is
rarely insisted on unless there has been an evident intention to
deceive. Other systems and conditions of life insurance policies may be
shortly noticed.
The usual division of policies is into "non-participating" and
"participating." Non-participating policies are contracts for the
payment on death of a certain fixed sum in consideration of a given
premium, and these amounts are not affected by the profit made by the
company. Participating policies entitle the holders to a share in the
profits of the company. These profits are applied in various ways, as
described above. A policy may be a whole life one, that is, the
policyholder may pay a periodical premium throughout life, or it may be
a limited payment one (the holder paying a premium for a limited number
of years), or an endowment policy, under which the insurer receives the
amount he has insured for at a given age, say fifty-five or sixty; or if
death occur previously, the sum is paid to his representatives. There
are also endowment policies for children, under which parents or others
receive a specified sum on a child attaining a given age, the premiums
being returnable if the child dies before the specified age.
_As to Payment of Premiums._--A certain period of grace is allowed,
most commonly thirty days, after each premium falls due. If payment is
not made within that time, the presumption is that the policyholder
intends to drop the contract, and the risk of the office comes to an
end. It may, however, be revived on certain conditions, usually the
production of evidence of health and payment of a fine in addition to
the premium. An impression used to prevail among the public that the
offices were interested in encouraging the forfeiture of policies. If
any such impression was ever shared by the offices themselves it must
have long since passed away, every reasonable effort being now made on
their part, not only to secure insurances but to retain them, and to
afford all the facilities that can be extended to policyholders with
that object.
_As to Foreign Travel and Residence, and as to Hazardous
Occupations._--When Babbage wrote his _Comparative View of Assurance
Institutions_ in 1826, voyaging abroad was scarcely permitted under a
British life policy. The Elbe and the Garonne, Texel and Havre, Texel
and Brest, the Elbe and Brest were the limits prescribed by most of
the English offices. Even at a much later period the extra premiums
charged for leave to travel or reside abroad were very heavy. But
improved means of conveyance--in some places better sanitary
appliances, and habits of living more suited to the climatic
conditions--and, more than all perhaps, the knowledge that has been
gained by experience as to the extent of the extra risks involved and
the relative salubrity of foreign climates--have enabled the offices
to modify their terms very considerably. The limits of free residence
and travel have been greatly widened, and where extra premiums are
still required these are, as a rule, much lower than formerly. The
assured are now commonly permitted to reside anywhere within such
limits as north of 35 deg. N. lat. (except in Asia) or south of 30
deg. S. lat., and to travel to and from any places within those
limits, without extra premium.
Military men (when on active service) and seafaring men are usually
charged extra rates, as are also persons following specially dangerous
or unhealthy occupations at home.
_As to Suicide._--The policies of most companies used to contain a
proviso that the insurance shall be void in case the person whose life
is insured dies by his own hand, but it is now seldom inserted. Some
offices, acting on a sound principle, limit its operation to a fixed
period, the extent of which varies in different offices from six
months to seven years from the date of issue of the policy.
The practice of rendering policies _indisputable_ and free from
restriction as to foreign travel or residence, after a certain period,
has tended greatly to simplify the contract between the office and the
insured. A declaration of indisputability covers any inaccuracies in
the original documents on which a policy was granted, unless these
inaccuracies amount to fraud, which the law will not condone under any
circumstances.
A remarkable difference in the development of life insurance between
Great Britain and the United States is, that among the British
companies only one-third of the insurances in force is in purely
mutual institutions, while in America the proportion exceeds
four-fifths. In both countries there are also "mixed" companies, in
which policyholders receive a fixed percentage of the realized
surplus, often from three-fourths to nine-tenths of the whole, but the
control and management are in the hands of shareholders. These form
the great majority of the proprietary offices in the United Kingdom,
and the profits of the business have been large. The amount of capital
paid in by shareholders of forty-one joint-stock companies was
L5,931,000, but the capital authorized and subscribed was much more,
and the subscriptions have often been paid, wholly or in part, by
credits from surplus. The shares of these companies, at market prices,
represent a value of at least L50,000,000, but the dividends upon
these shares are drawn largely from other business, many of the
largest and most prosperous corporations conducting also fire
insurance, and some of them marine or casualty insurance.
No branch of social statistics has been more diligently studied than
life insurance, and several governments publish classified accounts of
corporations insuring lives within their jurisdiction. But the reports
are not uniform in method and in periods covered, and aggregates derived
from them must be used with reserve. By the Life Assurance Companies Act
1870, and amendments made in later years, each company issuing policies
in the United Kingdom must deposit with the Board of Trade every year
its revenue account and balance-sheet for the preceding year, and must
at fixed intervals cause an investigation of its financial condition to
be made by an actuary, and furnish the public through the Board of Trade
with the detailed results, in forms prescribed by the act. Thus these
returns are the highest authority for the conditions and operations of
the offices, which often supplement or anticipate them by voluntary
publications. In the United States the laws exact still more minute and
much prompter reports to the insurance departments of the states; and
every annual statement is required to show the results of an actuarial
investigation. All these facts are collected, classified and compared by
statisticians for several standard annuals in both countries, especially
the _Post Magazine Almanack_, _Bourne's Directory_ and _Manual_ and the
_Insurance Blue Book_ in London, and _The Insurance Year-Book_ of the
Spectator Company in New York.
The reports of the insurance department of New York cover more
companies than those of any other state. The institutions not included
in them are about thirty-five in number, mostly small and local. The
New York reports represent very nearly 95% of the entire business of
the United States. While the amount of life assurance done by British
and other foreign offices in the United States is insignificant,
fourteen companies of the United States have agencies in Canada (ten
for new business), and four transact business in Europe and in other
parts of the world. The home business of the American companies is in
the aggregate about 87(1/2)% of the whole.
In the principal countries of continental Europe life assurance is
offered by the chief international institutions of Great Britain and
the United States, and their policies are in force probably to the
aggregate amount of L140,000,000. The domestic companies have been
stimulated to increased activity by the aggressive canvassing of the
foreign agencies, and the business in recent years has grown rapidly,
until now the total sum insured upon lives on the continent of Europe
is little less than a milliard of pounds sterling. Much information
about life assurance in the different countries of Europe will be
found in Ehrenzweig's _Assekuranzjahrbuch_ (Vienna).
(C. T. L.; T. A. I.)