PRINCIPLES OF INSURANCE from:

MODERN ECONOMIC PROBLEMS

BY

FRANK A. FETTER, PH.D., LL.D.

PROFESSOR OF ECONOMICS, PRINCETON UNIVERSITY

1916


CHAPTER 12

PRINCIPLES OF INSURANCE

Insurance Quotes , Insurance Quotations, Insurance Sayings

Sec. 1. Chance, unavoidable and average. Sec. 2. Uneconomic character of
gambling. Sec. 3. Borderland of gambling. Sec. 4. Insurance: definition and
kinds. Sec. 5. Insurance viewed as a wager. Sec. 6. Insurance as mutual
protection. Sec. 7. Conditions of sound insurance. Sec. 8. Purpose of life
insurance. Sec. 9. Assessment plan. Sec. 10. The reserve plan. Sec. 11. The
mortality table. Sec. 12. The single premium for any term. Sec. 13. Level
annual premiums and reserves. Sec. 14. Different features of policies.
Sec. 15. Insurance assets and investments as savings. Sec. 16. Excessive
costs of insurance operation.


Sec. 1. #Chance, unavoidable and average.# Every action and every
movement in life has in it some element of chance. There are what
may be called natural chances, arising from the uncertainties of the
seasons, or from rainfall, heat, hail, storm, flood, lightning, or
land-slides. Such chances must be taken both by the small enterpriser
and by the large. In earlier conditions of society natural chance
dominated industry, and it still remains and must always remain
important. There is the chance of unexpected political events, such
as war, riot, and legislation on money, tariffs, credit, and business
relations. These things are caused, it is true, by the action of men,
but it is a collective action out of the control of the individual.
There is the chance of human carelessness causing fire, explosions,
and wrecks on misplaced switches. There is the chance of physical or
mental collapse, as the sudden insanity or the sudden death of one
performing responsible duties. There is the chance of sickness that
often wrecks the plans and the fortunes of a whole family. There is
the chance of economic alterations in methods of production and of
transportation, in fashions and demand in this direction or for those
materials.

Some of these chances are more connected with money-lending, others
with manufacturing, some with agriculture, others with commerce; but
all are present in some degree in every industry. Some events are
unique in nature and seem unlikely ever to occur again; others are of
a kind occurring so irregularly that no reasonable prediction can be
made as to the time and frequency of their occurrences. Still others
occur frequently and to many different persons; but no individual can
tell when and how they will occur to him. A general average of chances
in different lines of business causes some to be called safe, others
extra-hazardous. Chance has its favorable as well as its unfavorable
aspects. Chances are averaged and added algebraically to the profit or
loss in an industry, for an extra-hazardous enterprise must in general
afford a higher average of profit in order to induce men to engage in
it. It is folly to take a risk without ascertaining its degree so far
as general experience enables one to choose. But inasmuch and in so
far as the gains and losses fall unequally upon different individuals,
income depends upon chance.

Sec. 2. #Uneconomic character of gambling.# This prevalence of chance
sometimes tempts men to say that business is "a gamble." But a
distinction in principle must be made between gambling and legitimate
risk-taking. The chances enumerated above are not sought, but avoided
as far as possible; yet they must be borne by some one if the collusion of
horse-owners or of horse-jockeys to deceive the betting public, are
so common that they seem often to be an essential feature. Gamblers
recognize fair as opposed to unfair methods. Fair gambling is a kind
of minor morality within the immoral field of gambling, like the
honor found among thieves. The chance-taking in gambling has no useful
purpose or result outside itself. Betting and gambling do not produce
wealth, but merely shift the ownership of existing wealth. The
gamblers constitute themselves a little fictitious economic circle,
and they transfer gains and losses on the turn of events that have no
practical objective result within their circle except to determine the
direction of the transfer. Even when fairest, gambling must, in its
average results, be uneconomic. In any economic trade each trader
gains by getting goods that are, on the marginal principle, to him
more valuable than the other kinds of goods he gives up.[1] But in
gambling the winner gets all, the loser gets nothing. If two men of
like incomes gamble the additional desires that the winner is able
to gratify are (by the principle of decreasing gratification) less in
amount than the desires which the loser must forego. As a result the
loser is often depressed and seriously injured by the loss of his
income, the winner makes reckless and extravagant use of his winnings.
Easy come, easy go, is the rule of gamblers.

Moreover, gambling reduces the amount of wealth by relaxing the
motives of economic activity, diverting energy from productive
enterprise, tempting men into dishonesty to offset their losses, and
leading them into speculation and embezzlement.

Sec. 3. #Borderland of gambling.# Ranging between the extremes of
unavoidable risk-taking and of gambling are a number of cases of a
mixed nature. In nearly all wagers, judgment in some degree influences
the choice of sides. One man bets on a horse whose pedigree and
performances he knows thoroly; another judges by the horse's
appearance as it comes upon the track. The professional bookmakers
have the latest possible and most exact information on which to base
their bids.

In the bets made on one's own prowess, as on speed in running, the
chance-taking is still on the uneconomic side of the borderland,
certainly if the running is for the sake of the wager, not for
pleasure or for a useful purpose. A premium won by a runner for speed
in delivering a message of economic importance presents an essential
contrast to the winnings in a wager.

Finally, the very borderland of difficulty is reached in the purchase
and sale of goods in the market with a view of profiting by chance
changes in price. The purchasing and holding of land, lumber, grain,
cattle, and other tangible and useful things, that need to be stored,
held for buyers, or taken to market, must be judged liberally. The
quality of gambling depends somewhat on the motive as well as on the
ability of the trader. The enterpriser dealing with real wealth, and
fitted to take the risks both because of his resources and of his
exceptional knowledge, needs the motive of gain in such cases, and in
a sense can be said to earn socially what he gets. The motive of the
uninformed must be a blind trust in luck, and a hope to gain from a
rise in prices which they are quite unable to foresee or to explain.

Sec. 4. #Insurance: definition and kinds.# The large element of luck in
industry due to unavoidable chances has something of the same evil
character as gambling. It brings unearned prizes to some and to others
unmerited losses. It must therefore be a benefit to the community, if
this element of unavoidable chance cannot be reduced as a whole,
at least to regularize it and make it exactly calculable for any
individual. In this way eac are property
insurance and personal insurance. _Property insurance_ is that which
indemnifies for loss of one's possession in specified ways, such as by
fire, by the elements at sea (marine), by hail, lightning, or cyclone,
by death (of valuable animals), by robbery, and by breakage (of window
glass). _Personal insurance_ is that which indemnifies the beneficiary
for loss of income as the result of various happenings to persons,
the chief being death, accident, sickness, invalidity, old age, and
unemployment. The principle of insurance is being constantly extended
to new subjects[2] and it is capable of further development in a
variety of directions.

Sec. 5. #Insurance viewed as a wager.# Insurance, without question a
highly useful thing, appears, paradoxically, to be in its outer form
a bet. The large merchant with many vessels used in many kinds of
business had in the days before marine insurance an advantage in
distributing his losses over a number of voyages. Antonio, the wealthy
merchant, is made thus to express his security:

"My ventures are not in one bottom trusted
Nor to one place; nor is my whole estate
Upon the fortune of the present year.
Therefore my merchandise makes me not sad."

In its early form marine insurance was the attempt of smaller
ship-owners to distribute their losses (as could the wealthy merchant)
over a number of undertakings, lucky and unlucky. It became customary
for a ship-owner to bet with a wealthy man that the ship would not
return. If it did come back, the owner could afford to pay the bet;
if it did not, he won his bet and thus recovered a part of his loss.
Gradually there came about a specialization of risk-taking by the men
most able to bear it. They could tell by experience about what was the
degree of uncertainty, and could lay their wagers accordingly. When
several insurers were in the same business, competition forced them to
insure the vessel and cargo of the ordinary trader for something near
the percentage of risk involved. The insurance thus tended to become a
mutual protection to the ship-owners; what had to be paid in premiums
to cover risk came to be counted as part of the cost of carrying on
that business.

Every legitimate form of insurance exhibits substantially the same
characteristics; it reduces loss at the margin where it is felt most
keenly. The difference between insurance and gambling, thus, lies
primarily in the purpose of insurance, which is not to increase
artificially the risk that any individual runs, but to neutralize or
offset an already existing chance. The insurance bet is what is called
a "hedge." The difference lies further in the collective method of
insurance, which combines the chances scattered among a number of
persons. Insurance does not increase the total of risks and of losses,
but merely combines, averages, and distributes them equally among all
the insured. This eliminates the chance element to the individual by
converting it into a regular cost.

Sec. 6. #Insurance as mutual protection.# Modern insurance is conducted
either by enterprisers for profit, or by mutual companies; but in any
case in large measure the losses in insurance are mutually shared,
as the premiums (plus interest earned) equal the total losses plus
operating expenses and profit, if any is made. Each insured gets a
contract of indemnity for the payment of a sum that will help cover
the losses of others. Such an exchange is mutually beneficial. The
premium comes from marginal income; the loss if it occurs would fall
upon the parts of income having higher value to the insured. The less
urgent needs of the present are sacrificed in order to protect
the income that gratifies the more urgent needs of the future. In
insurance each party gives a smaller va insured
sets fire to his own buildings, he makes an illegitimate use of
insurance. Constant efforts are made by insurance companies to guard
against these "moral risks," the least calculable of any. Merchants
whose stocks have been mysteriously burned two or three times find
difficulty in getting further insurance. Formerly insurance was not
paid in case of death by suicide; but now usually no such limitation
is contained in a policy after a period of one or more years. As men
rarely plan suicide years in advance, death by one's own hand some
years after taking life insurance is regarded as coming under the
ordinary rules of chance. Yet it is to be feared that this
liberal policy serves as a temptation at times to crime and to
self-destruction.

Sec. 8. #Purpose of life insurance.# Property insurance is mainly an
aspect of enterpriser's cost, whereas personal insurance is more
closely connected with the object of saving.[3] We shall in the rest
of this chapter limit the discussion to the one most important form
of personal insurance, that called life insurance (sometimes called
survivors' insurance).

Life insurance is that form of insurance in which partial indemnity
is provided for survivors against the financial loss incurred by the
death of the insured. Usually the insured is the breadwinner of
the family and the beneficiary is a member of his family, but in an
increasing number of cases the beneficiary is the surviving business
partner, a creditor, or a business corporation with an insurable
interest in the life of one of its employees.

Life insurance has been much used by persons mainly dependent on labor
incomes[4] rather than on incomes from capital, by those receiving
salaries, professional fees, and by active business men. It has of
late been extended rapidly, as "industrial insurance" to wage earners,
in policies never exceeding $1000, but averaging very much less,
and often being for no more than enough to pay funeral expenses. The
premiums on such policies are usually collected weekly and by agents
making personal visits. The cost to the insured is, therefore,
necessarily very high in proportion to the amount of insurance.


Sec. 9. #Assessment plan.# Life insurance plans may be distinguished,
with reference to the time and method of collecting the premiums, as
assessment and reserve insurance.

In the simple form of assessment insurance originally the losses were
paid by contributions taken after the losses occurred, each member
paying an equal share without regard to age. In a slightly improved
plan the assessments are made at the beginning of the year, based upon
the expected mortality for the year. The sum just sufficient for this
purpose (omitting expenses) is called the _natural premium_. The
cost of such insurance is closely related to the average age of
the members. The rates are very low in a new organization with a
membership of young men; but each year the average age, and therefore
the mortality of the membership, rises and the annual assessments must
be increased. By constant additions of young members, this rise of
cost may be retarded. But when these members grow older, a still
larger addition of young members is required to keep down the average,
and the mathematically inevitable result is an increasing rate of
assessment. This keeps young men from entering, and finally results in
failure or in some form of "reorganization" that drives out the older
members. The assessment plan carries with it the seeds of its own
decay.

To meet these difficulties in part, various modifications of the
flat-rate assessment plan are employed, such as classification by age
at entry, so that each member pays a flat-rate according to age
at entry; or large initiation fees at entry which f older members. Still others are struggling with difficulties that
presage dissolution. Many now have some form of reserve accumulations,
and some have so improved their methods that they closely resemble
reserve companies. The assets of all the assessment companies are
now $1.37 per $100 of insurance in force, while the legal reserve
companies have $22.66. The assessment companies now get 10 per cent of
their total incomes from their funded investments, as against 24 per
cent for the old-line companies. Even with the favorable conditions
under which the fraternal orders conduct their insurance business they
are doomed to failure unless they adopt rates and policies based upon
adequate reserve accumulations. Many thousands of present members
are paying for insurance at rates which will not suffice to meet the
future losses. The assessment plan fails to eliminate the one great
risk, that of leaving the survivors without insurance in advancing
years.


Sec. 10. # The reserve plan.# The reserve plan, if honestly administered,
gives complete protection against the difficulties just indicated. The
essential purpose of the reserve plan is to collect during the earlier
years of the insurance policy when the mortality is less, a sum larger
than is needed to meet the current losses. This sum, the reserve, is
kept invested and accumulating an income, sufficient to offset the
increase in losses as years advance. In reserve insurance, therefore,
the premium never increases from year to year, altho it may be so
arranged as to diminish or to cease entirely sometime within the term
for which the insurance continues.

The premium must always be fixed in advance. The calculations for
determining the premiums on different kinds of insurance policies are
many and complex, but all conform to a few general principles. The
three factors assumed are an average mortality table, a rate of
interest (or yield on investments), and an expense rate in proportion
to the premiums or outstanding insurance. Insurance on the reserve
plan is often called "scientific insurance" because, upon the basis
of these assumptions resulting from experience, it makes exact
mathematical calculations of the premiums and reserves needed for
insurance of any particular kind in respect to age of insured,
number of payments, method of paying the beneficiary, and any other
conditions. The premium thus fixed is, however, only a maximum, and
usually is reduced as the result of conditions more favorable than
those assumed.

Sec. 11. #The mortality table.# When large numbers of men are taken as
a group, a certain proportion of those at each age may be expected to
die. A mortality table starts with a group of persons, as 100,000, at
a given age, as 10 years, and shows the number who die and the number
who survive at each year of age until all are dead. The table most
widely used in the United States is the American Experience Table of
Mortality, constructed by Sheppard Homans in 1868. The figures of this
table, at different years, are given below:

Age Number Living Deaths each year Death rate
per 1,000

10 100,000 749 7.49
20 92,637 723 7.80
30 84,441 720 8.43
35 81,822 732 8.95
40 78,106 765 9.79
50 69,804 962 13.78
60 57,917 1,546 26.69
70 38,569 2,391 61.99
80 14,474 2,091 144.47
90 847 385 454.54
95 premium
for each year of insurance. Now, when it is possible to invest the
premiums so as to yield a minimum rate of income it is a simple matter
to determine the amount of a single premium, at any age, that is
adequate to pay for insurance covering any selected number of years
(term insurance) up to the entire period of each insured person's
life (full life). It is necessary only to apply the formula of present
worth and that of compound interest on investments.[6] Thus the
expected losses of any year according to the table of mortality,
divided by 1 + rate of yield on investments raised to the power of
years distant, equals the present worth of insuring the entire group
for that year. The sum of the discounted cost of insurance for all the
years of the term divided by the number living at the beginning of the
period, gives the single premium for each of the insured. Let P be the
present worth of all the policies for a group of the same age, p the
present worth of one policy, X the total insured at the beginning of
the period, f the natural assessment premium this year, or the natural
premium required for any year. Then

f f1 f2 fn
P = __________ + _________ + ________ + _________
(l + r) (l + r)^2 (l + r)^3 (l + r)^n

P
p = _________
X

The payment in advance of the single premium for any selected period
provides a reserve fund sufficient, on the assumptions made, to carry
all the insurance without further payments. Each year there is added
to the fund the income earned on investments, and there is subtracted
the amount of the losses for the year, until the death of the last
member of the insured group. If the deaths in the earlier years are
fewer than were expected in the mortality table, this will be offset
eventually by more deaths at the advanced years; but in the meantime a
reserve larger than was expected is yielding income, thus providing
a larger sum than is needed to pay all the policies at maturity. This
surplus might be distributed as so-called "dividends" from time to
time to those surviving, or be added pro-rata, at intervals, to the
amount of the policies as accumulated dividends.

Sec. 13. #Level annual premiums and reserves.# It is a matter of no very
abstruse mathematics (in principle) to find the equivalent of this
single premium in any one of many other forms of premium payment.
The processes are mainly but variations of present worth and compound
interest calculations. Such calculations, however, lead into many
complexities of practical detail difficult to explain in brief
compass, and are the special task of the actuary (the mathematical
expert dealing with such problems in the insurance business). The most
useful actuarial equivalent of the single premium is the level annual
premium for any period (term or life). Almost all policies now written
have the level annual premium as a feature. The amount of the level
annual premiums at first is greater than the losses; this causes for
a time the steady accumulation of a reserve which yields income. Then,
as the losses grow, they overtake and finally surpass the amount of
the annual premiums. Therefore, the total reserve for any group of
insured increases year by year to a maximum and then declines until
it reaches zero with the payment of the last claim. The individual
reserve for each policy not yet matured increases steadily the longer
it is in force. The total reserve is essential to the solvency of
the company and the payment of all the policies as they fall due. The
companies which issue policies on the level premium plan or reserve
plan are known as "old line" companies, or as "legal reserve"
companies, because the state laws require every company of this ty company sets aside a surplus and then divides the rest among
the policyholders. These returns, virtually but the refund of excess
premiums, are called "dividends" (a somewhat misleading term, not
to be confused with dividends on corporate stock). The policies
that receive dividends are called "participating" and are said to
participate in the earnings. Formerly the majority of policies paid
"deferred" dividends after 5, 10, or 20 years, according to various
tontine and semi-tontine plans, the survivors to these periods
receiving their dividends plus those of the other policyholders who
had died or had withdrawn from the company. This form of payment
having been found objectionable, it was made illegal in New York and
other states, and in most cases dividends are now paid annually. The
stock company, organized for profit, frequently charges lower premiums
for "non-participating" policies, and then retains such profits as may
result from keeping expenses below receipts.

The most popular policies are term policies (usually for 5, 10, 15,
or 20 years); ordinary life policies with annual premiums; limited
payment life policies (the policy payable at death, with premiums
fully paid up after 10, 15, or 20 years); and endowment policies (the
face of the policy payable after 10, 15, or 20 years if the insured is
still living). An endowment policy must be understood to be a regular
term policy of insurance for the specified number of years, plus a
plan of regular annual savings, which at compound interest, accumulate
to the face of the policy. Many persons are attracted to endowment
insurance by the oft expressed thought that "you don't have to die to
beat it." But this is a mistaken thought. For the premium in endowment
insurance is much higher than that for life insurance alone during the
same period, so that the endowment is merely a pretty convenient but
somewhat costly plan of saving, hitched on to an insurance policy,
with which "actuarially," it has no essential connection. In "scientific"
insurance the insured pays its full actuarial cost for each additional
feature of the policy that he buys. The various policies issued by a
company are approximately equivalent actuarially, on the basis of the
assumptions made, but they are of very different degrees of desirability,
in view of the circumstances of the insuring individual. The choice of
policies deserves a more careful investigation than it usually received.
Moreover, carelessness and ignorance in the choice of a company is
responsible for widespread loss and suffering.

Policies differ in respect to the mode of payment. The payment usually
takes the form of a lump sum payment at death or at the maturity
of the endowment. In recent times there has been a growing use of
optional forms of payment which give to the beneficiary annual or
monthly installments for a definite number of years or for life.

Sec. 14. #Insurance assets and investments as savings.# The discussion of
savings institutions in the last chapter left unmentioned insurance,
which probably is destined to be the most important of all. The assets
of life insurance companies in the United States have already attained
the enormous sum of $5,000,000,000, a sum equal to the reported
savings bank deposits. In the last twenty years life insurance assets
have more than doubled in each decade, and are now increasing by about
a quarter of a billion dollars every year.[7] These great funds,
which in equity nearly all belong to the policyholders, form already
approximately one thirtieth of all the private capital of the country.
They are invested in many ways, in real estate, in loans secured
by mortgages on real estate, in bonds--municipal, railroad, and
industrial. The problem of wise legislation for these organizations,
of their

It is probable that abstinence will more and more express itself not
in accumulating large capital sums to provide for one's old age or for
survivors, but in providing insurance for survivors, and invalidity
and old-age pensions for the insured and others, payable as terminable
annuities. In any case the results to be expected in the changing
forms and magnitude of private fortunes are certain to be great.

Sec. 15. #Excessive costs of insurance operation.# So beneficent is
insurance that the enormous cost of transacting the business under
present methods is much to be regretted. A very large part of the
premiums paid by the insured is retained by the companies.[8] In the
case of reserve life insurance a considerable part of what is not
returned is, however, set aside as reserve virtually held in trust for
the policyholders. In the case of the other kinds of insurance, nearly
all of the amount not returned is either cost of operation or profits,
tho it must be recognized that a part of the cost of some kinds
of insurance is for real services, such as inspection and fire
prevention. It is remarkable that the percentage returned by the life
insurance companies, accumulating, as they do, large reserves in trust
for the policyholders, is greater than it is for the other kinds of
companies (fire, marine, casualty, surety, liability, accident, and
health insurance).

It is a striking evidence of the importance of the marginal
principle[9] that insurance at such a cost should still be desired by
men. The use of insurance would be much wider and its benefits greater
if this "tare and tret" of doing the business could be reduced. It
seems a reasonable hope, now that the experimental stages are passed,
that this may be done. In the case of all kinds of insurance as yet a
large expense for agents has been necessary to educate men to see
the value of insurance and to purchase it, as well as for many other
competitive expenses. It has been found that much of this expense
can be saved by insurance in groups (for all employees in an
establishment), by compulsory insurance (as of all working men), and
by central state administration serving to regularize and unify the
organizations. This important question will be further considered in
connection with "social insurance" as a measure to benefit the working
classes.


[Footnote 1: See Vol. 1, ch. 5, sec. 7.]

[Footnote 2: The Jeffries-Johnson prize-fight was insured, against
rain, for $30,000. Frequently, race-horses, the fingers of pianists,
the lives of ball-players, and the throats of singers, are now
insured. Summer hotels in England regularly insure for large sums
against more than so many days of rain per season.]

[Footnote 3: On the former, see Vol. I, pp. 365 and 374; and on the
latter, below, sec. 14.]

[Footnote 4: See Vol. I, labor-incomes, in Index.]

[Footnote 5: There is an appearance of a slight discrepancy due to
the omission of fractions of cents. If premiums are collected at the
beginning of the year and losses are paid at the end of the year, and
if interest can be earned meantime at the rate of 3-1/2 per cent, the
natural premium for a one year term policy is about $8.64, that being
the present worth of $8.95 due a year hence, interest being 3-1/2 per
cent. In these calculations there is no allowance for expenses, the
necessary "loading," on which see below, sec. 14.]

[Footnote 6: See Vol. I, p. 279.]

[Footnote 7: The following are the chief statistical facts regarding
the life insurance business in the United States, Jan. 1, 1914,
showing separately legal reserve and assessment companies, and the total.
------------------------------------------------------------------
| Number of | Policies of
insurance companies reported (Statistical Abstract of the U.S., 1914,
pp. 549-557) were about $1,512,000,000, and the amount returned to
policy holders the same year was $918,000,000, or about 61 per cent
of all premiums, the amount not returned ($584,000,000) being 39 per
cent.

Premiums received Returned to policyholders
Amount Percent

Life insurance
reserve companies ..$715,000,000 $470,000,000 67
assessment companies 138,000,000 106,000,000 76
Other kinds ......... 659,000,000 342,000,000 52
------------- ----------- --
Total ........... $1,512,000,000 $918,000,000 61
]

[Footnote 9: See above, secs. 2 and 5.]