INSURANCEINSURANCE is the system or machinery by which it is sought to guard against the pecuniary consequences of certain accidents to which men are liable, such as the loss of property by fire or shipwreck, or the loss of future earnings through disablement or premature death. Insurance does not attempt to prevent these accidents, nor even to protect men against all the consequences of them. It deals only with the main pecuniary loss which such accidents are fitted to occasion, provides for it beforehand, practically distributes it among the persons who are more or less exposed to the same risk; and so, when the accident does light on any one of them, its pecuniary effects are neutralized or greatly mitigated.
The three chief developments of this system—Fire, Life, and Marine Insurance—are separately treated in the following articles. A very important application of the principle has been treated under the heading Friendly Societies.
Besides the above branches of insurance, which have attained immense proportions in almost all civilized, countries, there are many other applications of the principle which have been tried with greater or less success. The conditions which seem necessary to success (in addition to good administration) are chiefly these :—there must be a risk of real loss which it ought to be beyond the power of either the insurer or the insured to avert or to hasten; a large number of persons must be liable to the like risk; the accident contemplated must be likely to fall on a comparatively small number of the persons exposed to the risk of it; the probabilities of its occurrence must be capable of being estimated beforehand with some approximation to certainty; the loss apprehended must be so considerable when it does occur as to be worth providing against; and the cost of that provision must be comparatively so small as not to be prohibitive.
Accident Insurance.— Ordinary life assurance protects against the pecuniary loss arising to a man’s family or creditors or others by his death, whether that arise from accident or disease; but it has been found that a separate insurance against the consequences of accident meets the requirements of a large class of persons. A company was established in London in 1849 for insuring against the consequences of railway accidents,—the Railway Passengers Assurance Company. In return for a payment of 3d., 2d,, or Id. made by first, second, or third class passengers respectively, for insurance during a single journey, it undertook to pay £1000, <£500, or £200 in case of death by such an accident, or a certain weekly allowance in respect of personal injury not resulting in death. In 1856 the business was extended to embrace accidents of all kinds, and there came into use a system of yearly payments proportioned to the degree of risk supposed to attach to various occupations or other conditions of life. Many other similar companies have since been established, and at the present time (1881) there appear to be about eleven such offices in the United Kingdom. The amount insured by them is estimated at nearly £100,000,000 sterling, and their yearly income is between £400,000 and £500,000. The claims absorb about 50 per cent, of the premiums, the remainder, after paying expenses necessarily large, being the profit. Various schemes are at present being organized, in consequence of recent legislation, to enable employers to insure against risk from injuries suffered by their work-people.
The business of insuring against accidents has been developed in Canada, Victoria, and New South Wales, as well as in France, Germany, Switzerland, and the United States. In the country last mentioned the premium income of the principal office engaged in this business was in 1879 close on a million of dollars.
Fidelity Guarantee.— The guarantee of employers against the fraud or insolvency of their servants has of late years become a considerable and useful department of insurance business. Private suretyship is attended by many evils, and a bond of indemnity by a joint-stock company, although it has to be purchased by a yearly payment, is now generally preferred. Such a bond is not granted without previous inquiry as to the character of the applicant and the checks which the employer is to use. Seven institutions in the United Kingdom undertake this description of business; some of them insure only against loss arising from embezzlement, while others protect the employer against any failure to make good the sums entrusted-to an employé. The yearly premiums required range from 10s. to 60s. per cent of the sum guaranteed.
Various Minor Forms of Insurance.— In those parts of the British Isles which are exposed to violent hail-storms offices have been established successfully for insurance against the loss which these often occasion. Efforts have been made also, not always with equal success, to protect farmers and other owners of horses and cattle against the loss arising from accident or disease among these animals. It has been attempted also to insure traders against loss from bad debts, and house-owners against loss of rent and against defective titles. No fewer than thirteen offices, mostly local in their operation, insure against loss from the breakage of plate glass, and three against the loss from explosion of boilers. In former times, when men were liable to be drawn to serve in the militia but might purchase a substitute, a system of insurance was established to provide them with the necessary funds. These developments of insurance, however, are of an importance quite insignificant compared with the three great departments now to be dealt with.
I. Fire Insurance.
Fire insurance is a matter of practical interest to a far larger number of persons than either of the other two great departments of insurance—life or marine. There are few persons to whom, in the absence of insurance, the destruction of their dwellings or of their household goods would not be a serious calamity, while to the merchant or manufacturer the burning of his premises or stock or machinery might be ruinous. No age or country has been exempt from such fatalities, and no watchfulness has been able to prevent them. Some protection against the pecuniary consequences seems an essential condition of any extended system of manufactures or commerce.
Fire insurance, however, as an organized system, has had an origin comparatively recent. There are traces, indeed, in earlier times of enforced or voluntary contributions towards the relief of sufferers by fire, but it is only about the beginning of the 17th century that we hear of proposals being made for a more systematic provision, and it was not till after the great fire of London in 1666 that these proposals took practical shape. This seems at first to have been in the form of underwriting by individuals or by clubs, and some attempts were made to engage the corporation of London in a scheme of fire insurance; but in 1681 the first regular office for insuring against loss by fire was opened by a combination of persons “at the back-side of the Royal Exchange,” and it was followed shortly afterwards by another Of the insurance offices that still survive, only one, the Hand-in-Hand, dates from the 17th century (1G96); five date from the first half of the 18th century, the Sun (1710), Union (1714), Westminster (1717), London (1720), and Royal Exchange (1720); while only three date from the second half of that century, the Salop (1780), Phoenix (1782), and Norwich Union (1797). The first fire office in Scotland was established in 1720, the first in Germany in 1750, and the first proprietary company in that country in 1779; the first office in the United States was established at Philadelphia in 1752, one of its early directors having been Benjamin Franklin; the first in France dates from 1816, and the first in Russia from 1827.
The growth of fire insurance business in Britain did not receive much assistance from Government. At a very early period, in 1694 under William & Mary, a stamp duty was imposed on fire policies (now reduced to the nominal rate of one penny), and in 1782, during the administration of Lord North, fire insurances were made liable to an annual duty at the rate of Is. 6d. for each <£100 insured. This tax, which was collected by the offices along with their premiums and accounted for by them to the exchequer, was increased in 1797 to 2s. per cent., in 1805 to 2s. 6d., and in 1816 to 3s., at which rate it continued for about fifty years. It was strongly objected to as a discouragement to prudence, and as disproportionate in rate to the cost of insurance which it was tacked to; but as it was easily collected, and yielded nearly two millions a year (£1,714,622 in 1863), it naturally died hard. In 1864 it was partially remitted, and it expired finally in 1869. The returns of the duty enable us to measure in some degree the progress of fire insurance in the United Kingdom during the eighty-five years of its incidence. Some descriptions of property, such as agricultural produce, were exempt from duty and do not appear in the returns, nor do the sums insured on property situated out of the United Kingdom; but the amount insured by British offices on which duty was paid was [table]
At the present time (1881) there appear to be about sixty offices established in the United Kingdom for insuring against loss by fire either alone or in conjunction with life or marine insurance. A few of these are of very recent origin. The number does not include several foreign companies doing business in Great Britain.
Excepting by the imposition of the duty now repealed, the British legislature has not interfered with the business of fire insurance. Any number of persons may at the present time engage in this business with or without capital, nor is there a necessity even for the publication of their accounts. By the Life Assurance Companies Act of 1870, a deposit of £20,000 is required on the establishment of a life office; certain returns also must be made to the Board of Trade for presentation to parliament, and these regulations apply to offices which conduct fire in conjunction with life insurance, as well as to purely life offices. One consequence is that, while the results of the fire insurance business of these compound offices are published regularly, those of purely fire offices need not be published, and several of the oldest and most important fire companies do in fact keep their accounts strictly private. There is no reason to suppose, however, that their experience differs materially from that of the compound offices whose figures are open to us. From the returns of thirty of these it appears that their aggregate income from fire premiums in the seven years 1870-76 was as follows :— [table]
The increase in six years was therefore nearly two millions and a half of yearly income, the premiums in 1876 being about 63 per cent, more than in 1870. There are no means of ascertaining how far this increase arises from the insurance of property abroad, which is no doubt a considerable item, or from an increase in the quantity of insurable property within the United Kingdom, or in the proportion of it which is insured, or in the average rates charged for insurance, but no doubt all of these causes were at work. It may be mentioned here that the thirty offices to which the above returns relate have a subscribed capital of about 40 millions, and cash assets available for fire losses, not including their life assurance funds, amounting to 20 millions. They have therefore funds in hand equal to more than three years’ income from premiums. Another return gives the premium income of forty-five’JBritish offices in the year 1879 as £8,271,000, their losses as £4,349,000, their expenses as £2,426,000, and their net profits irrespective of interest as about £1,500,000, or 18 per cent, of the premiums. The whole premium income of British fire offices is probably nearly 10 millions sterling, and the amount insured may be taken at from four to five thousand millions.
The returns of the London Fire Brigade enable us to approximate to the amount of insurances effected on property within the metropolitan area. In 1866 the sum insured was about 316 millions; in 1871, 440 millions; in 1878, 605 millions; and in 1879, 624 millions.
The essential principle of fire insurance is the distribution of loss. It does not aim, directly at least, at the prevention and only in a secondary way even at the minimizing of loss; but what it seeks to accomplish is that such losses as do occur shall not fall exclusively, and possibly with overwhelming effect, on the owner of the property destroyed, but shall be borne in easy proportions by a large number of persons, who are all alike exposed to the risk of a similar catastrophe. This work of distribution is capable of being effected in more ways than one. It might be undertaken by the state or by a municipality, and this plan has been tried in several countries, notably in the canton of Zurich. There it applies to buildings only, not to their contents. The Government insures, and raises the necessary funds for meeting losses by a ratable tax on the owners. Where, as in this case, the exact sum needed is raised and no more, the system is practically one of mutual insurance administered by the cantonal authorities. Such a system yields this collateral benefit that the authorities, and indeed all house owners, become interested in the prevention and extinction of fires, and in Zurich accordingly the construction of buildings is carefully watched and regulated; but the results do not indicate any remarkable measure of success. The rate of assessment in 1870 was nearly equal to 2s. 6d. sterling per cent. The difficulties of carrying out such a system with equity, especially in a great community, seem almost insuperable. To assess the cost fairly it would be necessary, not merely to value each individual building, but to measure the degree of risk it was exposed to from its construction, its surroundings, its uses, and its contents. To place in the hands of public functionaries the power to do this, as well as to adjust the amount of compensation to be paid in the event of a fire, would be a course attended with manifest evils. Still greater would be the difficulty of applying the same principle to household goods, merchandise, and machinery; and, if these must be insured on some other plan, there seems little to be gained by setting up a different system for the insurance of buildings alone.
There is, however, a natural temptation presented to particular classes or communities to speculate in the insurance of their own property, in the hope of making a profit, or at all events of saving for themselves what would go as profits to the companies which would otherwise insure them. Sometimes this temptation seizes the inhabitants of a particular town, sometimes the persons interested in some particular trade, sometimes an ecclesiastical body. A community which has taken out of the hands of joint-stock companies the supply of its own gas or water, and finds itself as well served as before, perhaps better served and more cheaply, is apt to think that it may insure itself against fire as well. But, besides the complications in the problem which have been already alluded to, and which require technical skill and extended experience for their equitable solution, there are few bodies or communities which possess a sufficiently wide area to make insurance profitable or even safe. If there had been such a system at Boston or Chicago or St John’s when these considerable cities were ravaged by fire, the effects would have been still more disastrous to them than they were. Certain classes of property again seem liable almost to epidemic fires, from causes which are often not far to seek; and if, for example, the owners of any particular class of mills were to combine in a scheme of mutual insurance, they might find that, besides the great difficulty of agreeing on how each mil], was to be rated, or on the compensation to be awarded on the occurrence of a fire, they were exposed to exceptionally numerous claims just when their own trade was most depressed, or when their relations with their work-people already loaded them with sufficient anxiety. Schemes of so-called mutual insurance are tried from time to time, but scarcely ever without being based on a subscribed or paid-up capital (the contributors to which have to be remunerated), or without looking for outside business to give breadth and ballast to the enterprise.
Accordingly the system of fire insurance which has virtually superseded all others, and has contributed most to the public benefit, is that which is conducted by joint-stock companies, offering to the insured the guarantee of their capital and other funds, and looking to make a profit by the business. It is a department of commercial activity eminently suited for joint-stock enterprise, requiring for its success, and indeed almost for its safety, that its transactions should be various in character and spread over wide areas of space and time, and be invested with a certain amount of publicity, and enjoy that prolonged existence which attaches more to corporate than to individual effort.
Fire insurance as a business consists in undertaking a certain risk more or less considerable in amount, in return for a comparatively small sum, received beforehand, called the premium. While the amount of risk undertaken is strictly limited to the sum insured, the degree of risk is an element extremely difficult to measure, and liable to much fluctuation. Whether of ten thousand houses or shops, or stores, or factories, ten will be more or less injured every year by fire or a hundred is a matter partly of experience, but partly also of conjecture and, as we say, of chance. Assuming that the proportion would always be the same under precisely the same circumstances, not perhaps every year but ou an average of years, the questions remain whether the circumstances will always be the same, and whether if they be the one thousand cases on which we have made our own calculations are a sufficient basis for dealing with ten thousand cases. The slightest observation reveals an endless diversity in the risks undertaken, and, even if an absolute law could be reckoned on, the risks would require careful and accurate classification before the law could be deduced. But, in point of fact, the risks are always changing. If we take what from an insurance point of view is the simplest and safest “risk,” a private dwelling house in a large town, the question suggests itself, How has this risk been affected by the age of the building, the character of the occupants, the introduction of gas or paraffin or lucifer matches, by the proximity of more dangerous property, and by the improvement or deterioration in the public supply of water and the public arrangements for extinguishing fires 2 Infinitely greater changes take place in the degree of risk attending warehouses and manufactories, and many of these developments are of an unexpected character. The great fire in Tooley Street, London, in 1861, was aggravated by a prodigious escape of burning tallow, which literally set the Thames on fire, and long defied all efforts to extinguish it. More lately at Leith a highly inflammable spirit recently introduced into trade exhibited similar characteristics. At Newcastle a fusion of nitrates of soda or potash mixed with burning timbers caused a prodigious aggravation of a fire; and at Glasgow and elsewhere the fine flour dust of a corn mill, when mixed with a certain quantity of atmospheric air, was unexpectedly found to be as explosive as gunpowder.
But the speculative hazard of fire insurance as a commercial enterprise is limited by a very important circumstance. The contracts, in the United Kingdom at least, are seldom made for a longer period than one year, and often for less, and need not be renewed on either side unless their safety and reasonableness are confirmed by experience, so that from day to day the insurance company is able in a measure to revise its terms, and to correct the errors arising from imperfect data or a too sanguine generalization. The business on the whole has been a profitable one. There have been comparatively few absolute failures of fire insurance offices in Great Britain, and none of any magnitude ; nor do British companies regard it as any distinction that “they have always paid their losses in full.” The returns of those companies whose accounts are published indicate general prosperity, and the quotations of the share market and other circumstances show that the companies whose accounts are not made public have had at least equal success. The thirty companies whose experience has been already quoted received in fire premiums during the seven years 1870-76 about 37 millions sterling, and paid away for losses by fire about 22 millions, or 58 ’ 7 per cent, of the premiums received. After providing for expenses, there must have been a satisfactory balance of profit in proportion to the capital at risk.
The conditions of the contract between a fire office and the insured are regulated partly by the terms of the document known as the policy, which embodies them, and partly by law outside these terms, resulting from custom, from statute, or from legal decisions. We will endeavour to set forth as succinctly as possible some of these conditions, having regard chiefly to British contracts.
It is in the first place a contract of indemnity. The insured is guaranteed against loss by fire to the extent of the sum agreed on, but he is in no event to receive more than he has lost, or to make any profit by the occurrence of a fire. The sum named in the policy is not the measure but the limit of what he can recover. Nor does his policy cover all the loss he may sustain, for it will not in any case protect him against consequential damage, such as the loss of trade or of prospective profit; and if he desire to recovcr, not merely the value of a building, but the loss he will sustain through its being temporarily untenantable, he must insure specially against that risk. He must have some substantial interest in the property he insures, but it need not be that of ownership, for, if he might lose as tenant or mortgagee or in any other capacity, he may insure against that loss; and he may insure against the loss which others would sustain for whom he holds the property in any fiduciary character. It is loss by fire only that is insured against, not loss by a fall in the market value of property or by natural tear and wear. If property which was worth .£1000 has come to be worth only £700, and is then destroyed by fire, it is £700 and not £1000 that is recoverable under the policy. In some cases loss by lightning and by explosions of gas are insured against, even where there has been no fire in the ordinary sense. It is the value at the time of the fire, or rather the difference in value which the fire has occasioned, that becomes the sum payable, provided it do not exceed the sum insured. It has been sometimes tried to have “valued policies” by which the sum to be paid in the event of the property being destroyed is fixed definitely beforehand; but the system has been felt to be open to grave objections; for, apart from the labour and cost of valuing a thousand properties in preparation for the total destruction of four or five, it is obvious that, if the value fixed is less than the real value, there is no advantage to the insured, but the contrary; and if it is greater than the real value, then no doubt the insured might make a profit by a fire, but this would offer an inducement to carelessness, if not to incendiarism. In the United States, however, several State legislatures have been so imprudent as to enforce the issue of “valued policies.”
According to the general practice of insurance in Great Britain, the insured recovers his loss up to the amount of the policy, although the property may not have been insured to its full value. A different rule prevails on the Continent and elsewhere, and even in England under exceptional circumstances, and wherever several unconnected properties or parcels of goods are insured under one sum. In these cases the rule of “average” is applied, by which the insured recovers only such proportion of his loss as the total sum insured bears to the total value of the property covered. The effect of this rule is virtually to compel persons to insure their property to the full amount of its value, unless they are willing when any loss occurs to bear a share of the loss. Under either system, if property is not fully covered, the owner is to the extent of the deficiency his own insurer; but under the one plan his liability to loss begins only after that of the insurance company has been exhausted, under the other his liability and that of the company run parallel from the first. The difference is most material where the loss is only partial, and practically the English rule is equivalent to a considerable reduction of rate. There are weighty reasons for believing that it might be for the advantage both of the insurance offices and the public to introduce more widely the pro rata principle, with a corresponding reduction of the nominal scale of premiums, or even to enforce a participation of risk on the part of the insured.
The contract of insurance is one of good faith. The insured is bound to disclose all special circumstances of risk attaching to his property, and ought to have them described in the policy, otherwise its validity may be endangered. He is bound, moreover, to communicate any change of circumstances which may affect the degree of risk. Special hazards affecting particular kinds of property are often specially warranted against.
Companies do not insure against the loss occasioned by invasion, foreign enemy, civil commotion, riot, or any military or usurped power; and there are some kinds of property which they will not insure,—ready money, books of accounts (their value as documents), bank notes, stamps, bills, bonds, and other written securities.
The almost universal practice in England is to insure a separate sum on each distinct kind of property insured, as on a building and on its contents, on mercantile stock, and on furniture in private use. The same rule prevails with respect to all properties not involved directly in the risk of one fire. Thus two contiguous buildings or their contents may be insured for one sum if the buildings communicate with each other internally or have a common roof, but otherwise they must be separately insured.
Very important questions arise out of the circumstance that the same building or goods may be insured by different persons, with various offices, and under dissimilar conditions. Thus a house may be insured by the landlord, the tenant, and the mortgagee; goods may be insured by the owner, by a creditor holding a lien over them, and by the warehouseman or other person who may be responsible for their custody. Where the owner alone has effected insurances, these may be so varied in their character as to give rise to perplexing questions. A merchant may have insured with one office wines in a specified warehouse A; with another, wines and spirits in the same warehouse for one lump sum; and with a third, wines only, but in all or any of the warehouses A, B, and C, subject to the conditions of average. The questions that arise under such circumstances owe their solution as much perhaps to the honour and fair dealing of the several offices interested as to any settled rules of law, but the general practice may be shortly stated. As between a policy covering a specific parcel of goods or goods in a specified place and another embracing a wider range subject to average, the former is exhausted before liability attaches to the latter. As between a policy covering goods in A and B and another covering goods in A, B, and C, if a fire occurs in A or B liability attaches first to the more restricted policy, provided the more extended liability of the other is not merely nominal. On the other hand, if one policy insures stock and machinery together (but without the condition of average), and another insures one or both of these separately, liability attaches to both policies pari passu ; but the former is placed at some disadvantage in being obliged to contribute ratably to its whole amount with certain limitations, as against each of the separate items of the other. Where the same property is insured under similar conditions with more than one office, it has been the aim of the companies to provide that the loss shall be borne by each in proportion to the sum insured, whether the several insurances may be in favour of the same person or of several persons having different interests. It is plain that if it were in the power of two persons, having each some sort of insurable interest in the same parcel of goods, so to insure them as that each might recover their full value, the goods might come to be paid for by the offices twice over, and it might become the interest of one or both of the persons that they should be burned. The “contribution clause.” of policies is intended to guard against this. It has lately received an unexpected interpretation which limits its application to insurances in which the interests insured are identical, while protection against double payments is afforded by another principle, namely, that each person insures only his own special interest. The utmost possible interest which M, N, and P can have in any given property cannot exceed the present value of the property; each may recover what he himself has lost by its destruction, whether he be owner, or mortgagee, or depositary, but he deals separately with the office that insures him, without reference to what other insurances may have been effected by other persons having a different kind of interest in the same property. The application, however, of these principles is often matter of extreme difficulty, and has scarcely yet been definitely settled.
The adjustment of a loss when a fire occurs is not unattended with difficulty, even where there are no such complications as those just referred to. To ascertain the quantity, the quality, and the value of property injured, and the degree of injury, is often a work of no little anxiety. Its destruction has swept away the readiest proof which could have been given; or, where partial damage only has been sustained, it is often scarcely capable of exact measurement. The insured is naturally bound to state and prove his claim; and the office, while exposed on the one hand to exaggerated and even to fraudulent demands, may on the other endeavour to exact from an honest claimant details and evidence which it is scarcely possible for him to give. Fortunately for both parties to the contract, there are strong motives on either side tending towards a reasonable adjustment. In most cases the office is guided by the advice of an independent professional valuer, who, while attending to the interests of his employers, has a natural desire, even apart from his instructions, to conciliate the claimant, and to avoid landing the company he represents in troublesome controversies. Claims which cannot be adjusted in this way are usually submitted to arbitration, and it is a condition of most policies that both sides must refer the quantum of loss to an arbiter or arbiters. Few claims find their way into the courts of law, and those only where some principle is involved, or where the claim is thought to be fraudulently overstated, or where the still more serious objection is taken that the fire has been the wilful act of the insured.
Many troublesome questions are rendered more easy of solution by the condition that it is in the power of the company to reinstate property rather than to pay the value of it. The insured has not the option of requiring reinstatement. In general an office prefers to settle a claim by payment in cash, but an offer to reinstate may be a convenient as it is a perfectly fair reply to an exaggerated demand, and may adjust the pretensions of competing claimants. The insured is not entitled to “abandon” his property, and the company is not bound to take on itself the care or risk of damaged property; it is for the insured to make the most of the “salvage,” and to deduct the value of it from his claim, but in practice it is sometimes found desirable to relieve him of this duty.
A part of the insurance system which has developed into great magnitude is the practice of reinsurance. No one company, however large its resources, deems it prudent to undertake a risk to an unlimited amount in connexion with any one set of goods or one locality. An office might restrict its liabilities by refusing to insure to a larger amount than what it pleased to run the risk of, but the convenience of the insured and the interest of its own agents, to say nothing of other considerations, make it difficult for any office so to limit its responsibilities. It therefore issues a policy for the amount proposed to it, but reinsures a part with some other office or offices. Business to a very large amount is exchanged in this way, and there are some offices which professedly, and some which practically, live by the premiums paid over to them by other offices. The principal British offices have established a code of laws for the regulation of these transactions, and a court of arbitration for the decision of such questions as may arise among themselves in connexion with them. They are often also matter of special contract between office and office. The system is of some benefit to the public. In the earlier periods of fire insurance, when a large sum had to be insured, a higher rate was charged; but this has long ceased to be the rule. A man who wishes now to insure a large amount has not only no extra rate to pay, but has not to take the trouble of arranging with numerous offices, or, if a fire occurs, of adjusting his loss with numerous offices. He can usually, if he pleases, obtain a policy from one company for the full sum he needs to insure, and the company takes all the trouble and risk of distributing the liability, a distribution with which he has nothing to do. He may even benefit in another way, for when a loss occurs he has on the whole, perhaps, a better chance of being liberally dealt with than if he had to make a direct claim on many offices.
What has been said hitherto has had reference chiefly to one side of the fire insurance contract—the obligations undertaken by the company. The consideration they receive in return is the payment made by the insured called the “premium.” The premium is calculated at so much per cent, of the sum insured, and is usually paid once a year, at one or other of four quarter days; but many insurances are effected on mercantile property and on ships for periods less than a year—ten days, one, three, or six months—the rate in such a case being higher than an aliquot part of the yearly rate; and insurances may be effected for seven years by a payment of six times the yearly rate, and for other periods at a proportionate discount. Insurances effected for a year, and stated to be renewable, practically remain in force for fourteen or fifteen days after the expiry of the year; that is, they may be renewed by payment of the premium within these “days of grace,” and if a fire occurs in the meantime the company will be liable. This will not happen, however, if an intention not to renew has been manifested on either side.
The rate of premium varies with the supposed risk, and in Great Britain runs from Is. 6d. per cent, yearly, the rate for first-class dwelling-houses and ordinary private furniture, to six or seven guineas per cent. The highest British rates are what are charged for some descriptions of corn-mills and sugar refineries, and for Turkey-red dyeworks. Large classes of property are insured at the ordinary “hazardous” rate of 2s. 6d., or “extra hazardous” rate of 4s. 6d., but certain descriptions of property are specially and more elaborately rated. This has been done to a considerable extent by common agreement amongst the offices, and the arrangements are known as the “tariff system,” which requires here a few words of explanation.
We may suppose the question to arise, What ought to be paid for insuring a cotton-mill, or a flax or woollen mill, or a weaving factory, or a wharf or warehouse in some large city? The experience of any one office scarcely affords adequate data, and a rate based on the combined experience of many offices has a greater chance of being at once safe and fair. The problem, indeed, is a more complicated one than what has been already said would indicate. The property to be insured may consist of several distinct buildings and the contents of them: one building may be devoted to operations involving in a high degree the risk of fire; in another the processes carried on may be more simple and safe; a third may be used only for the storage of materials having little tendency to burn. These several buildings may be more or less connected with each other—under the same roof, under different roofs but with internal communications, contiguous but without any communications, detached but still within reach of fire. Of two mills one may work on fine materials, the other on coarse; in one the machinery may be driven twice as fast as in the other; in one the most hazardous processes may be carried on in the heart of the building, in the other they may be so treated and so guarded as to involve the rest of the property in no peculiar danger. Fairly to measure these various hazards it has been found necessary that the experience and skill at the command of many companies shall be combined, and that the rates shall be the result of consultation and a common understanding.
Now it is clear that no office will contribute its skill and experience to such a common stock if the effect is to be that other offices may avail themselves of the information in order to undersell it. Consultation about rates and a common understanding necessarily involve a reciprocal obligation to charge not less than the rates thus agreed on; in other words, a tariff of rates is developed to which each office binds itself to adhere. The system tends to restrain and moderate the competition for business which inevitably and to some extent properly exists among the companies, and its value to them is manifest. But it is also of service to the insuring public. At first sight it might seem that free competition would suit the public best, and that a combination among the offices must tend to keep up rates, and to secure for the companies excessive profits, but a little consideration will show that this is a mistake.
It is an unquestionable truth, though one often lost sight of, that all losses by fire must ultimately be borne by the public. The insurance companies are the machinery for distributing these losses, nothing more. If the losses fell on them, their funds, large as they are, would speedily be exhausted, and the service which they render to the public would come to an end. To those who require insurance against loss by fire it must be a manifest advantage that they should have many sound and prosperous offices ready to accept their business, and no less able than desirous to earn or to retain the public favour by fair and liberal conduct. A necessary condition of this state of things is that the rates of premium paid for insurance should be remunerative to the offices, and the main object of the tariff system is to secure such remunerative rates.
This it endeavours to do by two methods,—by an agreement as to what rates are to be charged, and by affixing such a penalty to dangerous constructions, substances, and processes as to induce, if possible, a lessening of the danger. In other words, and reversing the order, it seeks to diminish the risk of fire, and to secure adequate payment for what risk remains. There can be no doubt as to the benefit the public derive from the former of these, in having pointed out to them, not on the authority of one office, still less on hesitating and contradictory authority, but with all the weight arising from the combined experience of numerous companies, that this or that method of construction, this or that combination of materials, this or that mode of conducting a manufacturing process, is attended by imminent hazard of fire, and in having the lesson enforced by a heavy pecuniary penalty. On the supposition that the offices are correct in their estimate of risks, the effect, and indeed the intention, of their rule is not so much to put money into their own coffers as to lessen the danger, and to save themselves in the first instance, and the owners of property ultimately, from the consequences of preventable fires.
These rules, as will readily be seen, must have powerful influences on trade and manufactures. Many individual warehouses and mills are, with their contents, insured for very large sums, £10,000, £20,000, £50,000, £100,000, and more. An additional charge of 5s. or 10s. per cent, in respect of a supposed increase of risk may mean ^ a payment by the owner of several hundred pounds a year, and may operate as a complete veto on some arrangement or some machine which it might otherwise be desirable to resort to. The occurrence of a few severe fires in one town, followed by an increase of insurance rates, may have, and indeed has had, the effect of driving some branch of trade away to another locality, the seat of greater caution or better fortune. It is therefore obviously desirable that so important an influence should be exercised, not precariously or capriciously, but according to the combined wisdom and experience of those associations which may be supposed to understand the subject best, and which obtain their experience in the way that makes it perhaps of most value, by paying for it.
It is equally for the public benefit that rates of insurance should be fixed on some common scale. Suppose the system of unrestricted competition to be tried, the first effect will be a general and great reduction in rates. But it may be said, “So much the better for the insured; if the offices can afford this reduction of rate, it will only bo a fair result of competition ; if they cannot afford it, they will be the losers, but the public will gain; will the effect not be simply to reduce the rates to the paying point, and no further ?” This would be all very well if the paying point could be absolutely ascertained or determined in any way beforehand, but the rate comes first and the losses come afterwards. In other businesses prices are based on "some certainty as to the cost of production, but in selling fire insurance the cost is not known till after it has been sold. In a free competition it is the sanguine man’s views which regulate the market price, and the rates therefore cease to be remunerative. The consequences are that some offices disappear altogether, others take fright in time to avoid ruin, though not to escape serious loss, persons who might establish new offices are deterred from doing so, the business gets the character of being a highly speculative and hazardous one, requiring extravagant profits to induce men to carry it on at all, and the public have to bear the cost. Unrestricted competition therefore is not for their advantage.
The combination we are considering has another beneficial effect; it serves to distribute the burden of losses fairly. If it is a just thing that cotton-spinners should bear all the losses that arise in cotton-mills, and not leave them to be borne by the owners of private dwelling-houses, or vice versa, it is well that the loss by each class of risks should be measured fairly. But, while the experience of any one office, taken by itself, furnishes a very imperfect criterion, each contributes its quota of knowledge and experience to the common stock, and the public get the benefit both of broad and trustworthy data and of that peculiar and intimate acquaintance with each different class of property or process which the conductors of one company or another are sure to possess.
On the other hand, it is beyond question that no association of the kind will ever hold together a large body of independent societies, except under the pressure of some necessity. No conventional or excessive rates can be maintained for any length of time. Some member of the union is sure to perceive that popularity and profit may be gained by introducing a lower rate, if a lower rate is manifestly sufficient, or a new company starts into existence to remedy the grievance. It is to be remembered, too, that the directors and shareholders who control the offices are likewise insurers, quick to raise the question of how far the rates they have to pay as individuals are justified by the risks run; and if it cannot be shown that these rates are a true measure of the risk, offices are soon constrained by a sense of justice or by self-interest or by pressure from without to mitigate them. In short, the association is a union bound together by necessity and tempered by competition.
Adequately to measure the risk of loss by fire demands not merely reference to an extended experience but a watchful regard to current changes. While the profits of fire insurance business fluctuate considerably from year to year, and seem even to follow cycles of elevation and depression, the tendency on the whole appears to be towards a growth of risk, although excessive competition among offices prevents the rates from rising in proportion. Among the causes are the prodigious increase in the use of lucifer matches; the introduction into commerce of such articles as jute and esparto grass and mineral oils, which are either highly inflammable, or have by themselves, or in combination with other substances, a tendency to generate combustion; the great speed of machinery; and the vast accumulation of property exposed to the risk of one conflagration, owing to the larger size of mills and warehouses’ and their concentration in particular localities. The very development of the insurance system may conduce to heighten the risk by lessening the motives to carefulness. It is difficult to form an estimate of the average rate of premium paid for property in the United Kingdom, but it is probably not much above or below 4s. or ’ 2 per cent, yearly.
When insurance companies were first established, and for a long time afterwards, they undertook not only to reimburse the insured for losses, but to extinguish fires. In one of the earliest prospectuses put forth (in 1684), there is the promise that “watermen and other labourers are to be employed at the charge of the undertakers to assist at the quenching of fires.” A writer in 1690, describing the ingenious and useful invention of a fire insurance office, says, “They have a great many servants in livery with badges, who are watermen, and other lusty persons dwelling in several parts of the city, who are always to be ready when any sudden fires happen, which they are very laborious in and dexterous at quenching ”; and De Foe, in an essay published in 1697, refers to the same subject. In 1708 when the Sun Fire Office was first projected, it was proposed that all persons insured with it should have a mark representing the sun nailed up against their houses, that the men whom it employed to extinguish’ fires and save property might direct their efforts specially for the benefit of the houses so distinguished. Marks of this sort were afterwards generally adopted by the offices, and are often to be seen even at the present day, though they no longer serve their original purpose. For more than a century and a half the insurance offices provided and kept up fire-engines at their own expense, not only in London but in many provincial towns, where frequently no other means of extinguishing fires were available. At first each office provided its own engine, and much rivalry prevailed among the several brigades; but in London ultimately the offices combined to support in common a very effective and very costly fire brigade. This arrangement, however, came to be regarded as objectionable from public points of view, as it had long been distasteful to the offices themselves; and in 1866 the offices handed over their whole establishment to the Metropolitan Board of Works, by whom it has been greatly enlarged and extended, the cost being provided for partly by a contribution from the offices, partly out of the Consolidated Fund, and partly by the rates.
The views of the insurance offices on this subject have undergone a material change, and they have ceased to regard it as any part of their duty to extinguish fires, or to bear the cost of extinguishing them. That ought to be undertaken by the public through municipal or other local authorities, and it is understood that the law regards it as their duty to do so. Parliament is always ready to confer the necessary power of assessment; but there is a disposition on the part of municipal bodies to exact from the insurance offices, directly or indirectly, as much of the expense as they can. Considerable contributions are in this way levied in Liverpool, Manchester, Glasgow, and other towns, but the system is eminently to the disadvantage of the public. Whatever the offices are compelled to pay forms a portion of their general expenditure, which they must recover from the public, at least the insuring part of it, in the form of premiums. The amount would be more equitably levied by means of a general assessment, and would be more likely to be advantageously expended. The business of fire insurance is to meet the losses which happen by fire, not to prevent them; if losses are heavy, the rates of premium must follow; if by care and well-organized appliances losses are diminished, the competition among the offices will inevitably reduce the rates of premium. In other words, if the public themselves bear the cost of these appliances, they obtain the benefit of it in a reduced cost of insurance; if they transfer the burden to the offices, they have in the end to bear it themselves in the form of increased insurance rates. If there were, as there ought to be, an efficient fire brigade in every town and village, it is obvious that the insurance offices could neither bear the cost nor undertake the care of them, and the best arrangement would be that they should be wholly under local management and wholly at local expense.
But, while it is the business of the public authorities to extinguish fires, the insurance offices regard it as within their province to promote in other ways the safety of the property endangered, and accordingly in London, Liverpool, Glasgow, and other cities they have established at their own expense salvage corps, which act in alliance with the fire brigades, but whose special duty it is, not so much to quench a fire, as to diminish as far as they can the damage which may be occasioned to the property whether by the fire or by the water used to extinguish it.
It only remains to add, with reference to fire insurance in the United Kingdom, that public attention has from time to time been directed to the serious question of how far the crime of arson may be regarded as a consequence of the insurance system, and what can be done to prevent it. There can be no doubt that wilful fire-raising, with a view to defraud insurance offices, is not only a very common offence, but is probably on the increase. In 1867 the subject was inquired into by a committee of the House of Commons, and evidence was submitted to show that between 1852 and 1866 the proportion of fires which were suspicious, doubtful, and unaccounted for had gradually increased from 34∣ to 52⅛ per cent., while well-informed persons testified that the number of fires in insured property is greater in proportion than in uninsured. There is a general agreement that in the interests of the public the origin of all fires should be made the subject of organized inquiry, but there is a difference of opinion as to the proper machinery and as to the incidence of the expense. Of existing functionaries the coroner in England and the procurator-fiscal in Scotland seem the natural persons to conduct the needful investigations, but in neither case is the subject free from difficulties, which in England are enhanced by the want of a public prosecutor. Several attempts have been made to legislate on the subject, but hitherto without success, nor is the public feeling sufficiently strong to give the required impulse. Other crimes than arson thrust themselves on public notice, and all men see the necessity for inquiry and detection. This crime, when successful, too often destroys, not merely the evidence which would go to prove it, but the very circumstances which would indicate that a crime has been committed. The immediate sufferer, too, is probably some wealthy insurance company, whose case naturally excites little sympathy; it is seldom prudent and sometimes scarcely safe for the sufferer to insist on exceptional inquiries, and there is a general disposition rather to put up with a loss than to raise disagreeable questions likely to lead to nothing. But, as the honest portion of the community pay for all dishonest claims, it may be hoped that a due inquiry into the causes of fires will some day come to bo regarded as a matter of grave public interest.
The general principles and practice of fire insurance are, in their main features, the same in most parts of the world. In the United States the business has been pursued with characteristic energy, and with some peculiarities of law and practice. As already stated, the earliest American fire insurance company was organized in 1752, and its policies during the first year covered a sum of $108,360 at an average rate of 147 per cent. At the present time there are within the State of New York alone upwards of eighty fire offices, having assets amounting to about 54 millions of dollars, and in the Insurance Year-Book for 1880 there is a list given of about four hundred different native offices in the various States, but this does not include a large number of local offices of small dimensions, mostly established on the mutual principle. The number of fire insurance offices in the United States is probably about nine hundred. Of these a large proportion have a merely nominal existence, but on the other hand important foreign offices—British, French, German, Swiss, and Canadian— transact business in the States.
If sixty offices suffice to transact the insurance business of the United Kingdom and a great deal of foreign business besides, the existence of more than four hundred offices in the States indicates of itself that a large number of them must have very limited resources, quite unfit to cope with the disastrous fires which sometimes occur in the rapidly developed cities of America. The failure of an insurance office is therefore a more familiar event than in England, and it is this perhaps partly which has led to a system of Government supervision intended to guard the public against such misfortunes. Each State of the Union has its own regulations about insurance companies, its insurance department, its insurance commissioner, superintendent, or auditor, its system of accounts and checks and public notices, its fees, taxes, and requirements as to deposits. The trouble and expense to which offices are thus exposed, especially where they do business in many States, is very great indeed, while the resulting benefits are problematical. All attempts of this sort are attended with these disadvantages, that they interfere injuriously with honest and well-conducted companies, and afford but a feeble protection against those of a different class; that they involve the Government in the odium of failures which it is supposed to be their duty to prevent; that they lessen the sense of responsibility among those who control the offices, and the spirit of prudence and watchfulness among the public; and that they place in the hands of public officials a power and influence which are apt to be abused, and are always open to suspicion. More to be admired and imitated are the State regulations in America with respect to building operations, the extinguishing of fires, and the inquiring into their origin. The business of an insurance agent in America is more recognized than in England as a distinct profession, and the agent is entrusted with greater powers. More has been done to facilitate the working of insurance by the surveying and mapping of large cities, and there has been a greater development of periodical literature, devoted to the subject.
Since 1866 a national board of fire underwriters of the United States has existed, and has proved of great service to the insurance offices and to the public. At the present time it is unfortunately suffering from disorganization, and there has been a consequent “shrinkage ” of rates. It appears from the reports of the superintendent of the fire department in the State of New York that in the year 1879 the sums insured in the United States by the companies reporting to him amounted to 6767 millions of dollars, and the relative premiums to nearly 61 millions of dollars, so that the average rate of premium was ’ 9 per cent., or 90 cents for each hundred dollars insured. Fourteen British fire offices doing business in the States received in the year 1879 premiums to the amount of 11 millions of dollars, and paid losses of 7 millions. Their losses that year were 63 per cent, of their premium, and their expenses in America 31 per cent.
In Canada twenty-seven companies—Canadian, British, and American—made returns, which showed that in 1879 they had insured in Canada, including the maritime provinces, sums amounting to 385 millions of dollars. In the eleven years ending in 1879, the premiums received had amounted to nearly 33 millions of dollars, and the losses to 27⅜ millions, and the ratio of loss had been 84 , 16 per cent. This included the loss arising from the great fire at St John’s, New Brunswick, in June 1877, which cost the insurance offices 6∣ millions of dollars.
In France there were at a recent date thirty-two proprietary and about twenty mutual fire insurance offices. Of the thirty-two offices founded on capital three are provincial offices, and the others are established in Paris. Two confine themselves to reinsurance. From the returns made by twenty-three of these offices, including all the more important, it appears that in 1879 their income from premiums was about 92 millions of francs, and their losses 47 millions. The average loss during eleven years was 50 per cent, of the premiums. Many of the French offices have been extremely successful; and recently there has been a remarkable increase of new offices in that country.
The Insurance Cyclopaedia of Mr Cornelius Walford, a work now in progress, and of prodigious industry and completeness, is the best and almost the only available literary authority which covers the whole subject of this article. The Law of Fire Insurance, by Mr C. J. Bunyon, is also of value. (J. Μ. M , C.)
II. Life Insurance.
The system of life insurance embraces a variety of contracts by which the insurers engage to pay capital sums on the decease of policy holders or nominees, in consideration of other sums received during their lifetime. These contracts may be divided into two classes,—(1) those in which the sum insured is certain to become payable, provided only the insurance is duly kept in force, and (2) those which are of a temporary or contingent character, so that the sum insured may or may not become payable according to circumstances.
To the first of those classes belong the great bulk of the transactions of life insurance offices, namely :—
1. Whole-Term Assurances on Single Lives.· —These are simply contracts on the part of the insurance office to pay a certain sum (with or without “bonus additions,” as the case may be) on the death of the person named in the policy, whenever that may occur. The premium, or consideration for the insurance, is in most cases an annual sum payable during the whole continuance of the policy. It may, however, be arranged in various other ways,—as, for example, by a single payment at the commencement of the transaction; or by a limited number of contributions, each larger in amount than the annual premium for the whole of life; or by payment of a modified rate during a limited period and a correspondingly higher rate thereafter. Insurances for the whole term of life are more common than any other kind.
2. Endowment-Assurances.— Next to insurances for the whole term of life, these constitute the most numerous class of insurances on single lives. The sum insured is payable to the person named in the policy, if he should survive a certain period or attain a specified age, or to his representatives at his death, if that should occur before the time has expired.
3. Insurances on Joint Lives.— In these transactions two or more lives are included in the policy, and the sum insured is payable when either or any one of them fails.
4. Longest-Life Insurances, or Insurances on Last Survivor. —These also are effected on two or more lives, but, instead of falling in by the death of any one of the parties, they do not mature until both or all are dead.
The second class of insurances described above consists principally of two kinds :—
1. Temporary or Short-Period Insurances.— These arc effected for limited periods to cover special contingencies, the sum insured becoming payable only if death should occur within the time specified in the policy. Such insurances may be effected on single lives or on two or more lives, and (in the latter case) may be payable either if one life or all the lives should fail within the period, or only if one life should fail before another, as in the case to be next mentioned.
2. Survivorship Insurances, or Insurances on one Life against Another.— In these the sum insured is payable at the death of A if that should happen in the lifetime of B, but not otherwise. Should B predecease A, the transaction falls to the ground.
Besides these there are transactions of other kinds dealt in by life insurance offices—such as deferred insurances, where the risk does not commence until the expiry of an assigned period; deferred and survivorship annuities; insurances against issue, for the benefit of expectant heirs; and the like. The system is indeed adapted to nearly every contingency of a pecuniary nature connected with human life.
It may be observed that, while life insurance has much in common with fire and marine insurance, there are some essential differences between it and them. The insurance 1 of houses and goods against fire, or of ships and merchandise against the casualties of the sea, is a contract of indemnity against loss, and in like manner an insurance on human life may be regarded as indemnifying a man’s family or his creditors or others interested against the loss of future income by his premature death. But it does not necessarily take the value of such income into account, nor does it relate to any intrinsic value of the subject of the insurance —the life of the insured party. Again, in fire and marine insurance loss may be either total or partial. In life insurance the event insured against cannot take place in any limited degree, and there is thus no partial loss. And again (in the first and larger of the two classes into which life insurances are divided) the event is certain to occur, and the time of its happening is the only contingent element. In the other kinds of insurance the events are wholly of a contingent character.
The idea of distinguishing in terms between contracts which differ so widely in reality appears to have early suggested itself. Mr Babbage in his Comparative View of the various Institutions for the Assurance of Lives, published in 1826, says—“The terms insurance and assurance have been used indiscriminately for contracts relative to life, fire, and shipping. As custom has rather more frequently employed the latter term for those relative to life, I have in this volume entirely restricted the word assurance to that sense. If this distinction be admitted, assurance will signify a contract dependent on the duration of life, which must either happen or fail, and insurance will mean a contract relating to any other uncertain event, which may partly happen or partly fail. Thus, in adjusting the price for insurance on houses and ships, regard is always had to the chance of salvage arising from partial destruction.”
The distinction proposed by Mr Babbage has not always been observed. Some writers appear to prefer the term insurance where life is concerned as well as in other cases; some continue to use the terms indiscriminately; while other recent writers have sought to establish distinctions of a novel character between them. One of these is that a person insures his life, his house, or his ships, and the office assures to him in each of these cases a sum of money payable in certain contingencies. Another is that assurance represents the principle and insurance the practice. Of these two suggestions we prefer the former; but, as the more conventional distinction of Mr Babbage is still very widely recognized, we shall adhere to it throughout the remainder of this article.
Calculation of Premiums.— The general principles of life contingency calculations are explained in the article Annuities, and it is there shown that such calculations are made by means of mortality tables, which exhibit the numbers of persons who out of a given number born or living at a particular age live to attain successive higher ages, and the numbers of those who die in the intervals. A full account of the numerous tables of this kind which have been framed from time to time does not fall within the scope of the present article, but, before passing on to show the application of mortality tables in the various calculations relating to assurances upon lives, it may be useful to mention those tables which have been chiefly employed by assurance offices.
Passing over the earlier tables of Halley, De Parcieux, and others, which for all purposes of calculation have long been obsolete,—and which, however much they contributed in their day to the development of assurance, possess now onlyanhistoricalinterest,—we pausefirstat the Northampton Table. This was constructed by Dr Thomas Price from the registers kept in the parish of All Saints, Northampton, for the forty-six years 1735 to 1780. Owing to certain faults in its construction, the table gives the chances of death too high at the younger ages, and consequently requires large premiums for assurances; while at the more advanced ages the chances of death are disproportionately low. For a long time, however, this table occupied the foremost place as a basis for life contingency calculations of all kinds, and even after the introduction of other tables, which are now recognized as more accurate, it continued to receive a large share of popularity. The rates of many assurance offices of high standing were calculated from it, and until a comparatively recent date it remained in use by not a few of them.
The Carlisle Table was constructed by Mr Joshua Milne from materials furnished by the labours of Dr John Heysham. These materials comprised two enumerations of the population of the parishes of St Mary and St Cuthbert, Carlisle, in 1780 and 1787 (the numbers in the former year having been 7677 and in the latter 8677), and the abridged bills of mortality of those two parishes for the nine years 1779 to 1787, during which period the total number of deaths was 1840. These were very limited data upon which to found a mortality table, but they were manipulated with great care and fidelity. The close agreement of the Carlisle Table with other observations, and especially its agreement in a general sense with the experience of assurance companies, won for it a large degree of favour. No other mortality table has been so extensively employed in the construction of auxiliary tables of all kinds for computing the values of benefits depending upon human life. Besides those furnished by Mr Milne, elaborate and useful tables based upon the Carlisle data have been constructed by David Jones, W. T. Thomson, Chisholm, Sang, and others. The graduation of the Carlisle Table is, however, very faulty, and anomalous results appear in the death-rates at certain ages.
The mortality experience of the Equitable Assurance Society, the pioneer of the modern system of assurance, has formed the basis of several tables. Of these two in particular have been used to a considerable extent by assurance companies. The first was a table constructed by Mr Griffith Davies and published by him in 1825. It was deduced from accounts given by Mr W. Morgan, the actuary of the society, of the ratio which the death-rates among the members bore to those indicated by certain well-known tables at different ages. The other table was constructed by Mr Arthur Morgan from the statistics of membership of the society from its commencement in 1762 down to 1829. This table was published in 1834.
Shortly afterwards a desire began to be pretty generally felt for a table of observations more extended than the statistics of any single office could supply, and accordingly a movement was set on foot in 1838 by a number of actuaries and others for collecting the experience of various offices “to afford the means of determining the law of mortality which prevails among assured lives.” Seventeen offices agreed to contribute their statistics, which were found to embrace in all 83,905 policies, of which 44,877 were in existence at the time of giving in the returns; 25,247 had been “discontinued”; and 13,781 had fallen by the death of the persons assured. The results of the inquiry were in due time published, and upon them was founded a mortality table known as the Seventeen Offices’ Experience Table, which came to be used to a considerable extent by assurance companies. A peculiarity of this table is that it is based upon the experience of the offices in regard to the number of policies which existed and became claims, and not the number of persons who were assured and died. There having been in many cases two or more policies issued on one life, the results are not necessarily the same as those which would have been obtained had each life been reckoned only once. The general agreement of the results with those derived from other data referring to persons, and not to policies, seems to show, however, that the peculiarity referred to does not materially affect the accuracy of the table as an exponent of the value of assured life.
Three English Life Tables have been constructed by Dr William Farr from the official records of the registrargeneral for England and Wales. The first, contained in the Fifth Report of the Registrar-General (1843), was founded on the census returns of 1841, and the deaths recorded in that year. The second table, contained in the Registrar-General's Twelfth Report, was based on the same census and the deaths of the seven years 1838 to 1844. The third table had a much wider basis than either of the others. It embraced the census returns of 1841 and 1851 and the deaths of seventeen years (1838-1854). This table, with an extensive series of monetary and other tables deduced from it, was published as a separate work in 1864.
The next set of tables demands more special notice in an article like the present, as being the most important collection of observations yet made in regard to the mortality of assured lives. “Nearly a quarter of a century having elapsed since the period to which the combined experience of seventeen life assurance offices was collected, it began to be felt amongst actuaries and the managers of companies that a large mass of valuable materials had accumulated which, if combined, would tend to throw further light on the law of mortality amongst assured lives, and on other points affecting the interest and prosperity of assurance companies.” Accordingly steps were taken by the council of the Institute of Actuaries, in co-operation with committees of the Association of Managers of Scottish Life Assurance Offices and of the Faculty of Actuaries in Scotland, “to collect and combine, as far as possible, the experience of the life assurance companies of the United Kingdom to the present time.” This movement was begun in 1862, and in 1869 the results of the inquiry were published in a volume containing 282 pages of tabular matter, with a preface (from which the above quotations are taken) by Mr Samuel Brown, then president of the Institute of Actuaries. The preface details the processes employed in collecting and arranging the statistics, and indicates the more important conclusions to be drawn from them.
The experience collected on this occasion embraced the returns of twenty offices—ten English and ten Scotch—the total number of lives assured being 160,426, of whom 26,721 had died, 45,376 had discontinued their policies, and 88,329 remained on the books of the several offices at 31st December 1863, the date to which, as a rule, the observations were brought down.
From these statistics several distinct mortality tables were constructed, viz.:—
Table H mf , comprising all the healthy lives, male and female, included in the observations,—the word “healthy” being used ^to denote those lives which had been considered eligible for assurance at the ordinary rates of premium.
Table H m , comprising the healthy male lives only.
Table H m < 5 ), comprising healthy male lives, but excluding from observation the first five years of assurance in every case.
Table H f , comprising the healthy female lives.
Other tables of a subsidiary character were constructed, but they do not appear to have been put to any practical use.
The completed tables were published in 1872, together with an extensive series of monetary values deduced from them, and explanations by Mr W. S. B. Woolhouse and Mr Peter Gray respectively, as to the method of graduation employed in the formation of the tables, and as to the construction and application of tho monetary values. In 1873 Mr R. P. Hardy published a series of Valuation Tables based upon these data.
It appeared to the two bodies in Scotland already men- ∣ tioned that considerable advantage might result if the ex-1 perience of the Scotch offices were separately ascertained, ' besides being merged in the general inquiry. This was ' accordingly done, and the results, arranged and tabulated by Mr James Meikle, were published in a report (1869) by the joint committee appointed to collect the information. The investigation embraced 115,254 policies on 94,749 lives, of whom 12,443 had died, 19,284 had discontinued their policies, and 63,022 remained on the books of the ten offices at 31st December 1863. These separate Scotch statistics were intended more particularly to illustrate the effects of the selection of lives for assurance. They have not been commonly employed as a basis for the calculations of offices. In 1872 Mr Meikle published Observations on the Rate of Mortality of Assured Lives ,in which the materials furnished by these statistics are exhaustively treated. This work forms a most valuable contribution to our knowledge of the subjects with which it deals.
The following tables will serve as a means of general comparison between the various mortality tables that have been mentioned.
I.— Table showing the Number of Persons who, out of 1000 living at the age of 10, will live to attain the ages of 20, 30, 40, <t∙c., according to the undermentioned Mortality Tables. [table]
II. — Table showing the “Expectation of Life” or “Mean After-Lifetime” of persons aged 10, 20, 30, <t∙c., according to the τvnder∙ mentioned Mortality Tables. [table]
Having given this table for the purpose of comparing in a general way the characteristics of the several mortality tables to which it relates, it is right we should say, in order to avoid misconception, that the “expectation of life” does not enter into calculations for determining the value of sums dependent on human life, or for ascertaining the premiums required for life assurances. The nature of these latter calculations will be explained presently.
As a specimen of a mortality table deduced from actual observation of assured lives, we give in full the last of the tables from which the foregoing particulars are deduced, viz. :—
III. — The H m Table of the Institute of Actuaries. [table]
In order to show the method of calculating assurance premiums, we shall first suppose the premiums to be payable in one sum, and shall employ an illustration founded on the above table. We learn from the table that, of 96,223 persons living at the age of 20, 609 will die before reaching the age of 21; of the 95,614 persons remaining alive at the latter age, 643 will die before reaching the age of 22; and so on. Let it be supposed that 96,223 persons of the age of 20 are desirous to have their lives assured, each for the sum of £1 to be paid at the end of the year in which he shall happen to die; and let it be further assumed that the H m table represents correctly the number of deaths that will occur among these 96,223 persons in each successive year, until the last of them dies between the ages of 97 and 98. According to the hypothesis, 609 payments of £1 each will fall to be made at the end of the first year, 643 at the end of the second, 650 at the end of the third, and so on until finally 9 payments fall to bo made at the end of the seventy-eighth year. In order, therefore, to ascertain the “present value” of the whole 96,223 payments to be made after the decease of the persons whose lives are to be assured, we must find the value of £609 due one year hence, £643 due two years hence, £650 due three years hence, and so on to the last payments. The sum of all these values will be the total value required. Suppose the interest of money to be 3 per cent, per annum. Then (as explained in the article Annuities) the value of 1 to be paid at the end of one year is J- ; of 1 to be paid 1*03
at the end of two years —θ^ 3 ; and so on. Consequently the total value of the supposed assurances will be the sum of the following terms :—
Value of first year’s payments £609 χ ∙γ^g- = £591'26 ,, second ,, ,, 643×p^g 2 = 606 , 09
„ third „ „ 650 ×Γ⅛ β 594 ' 84
&c. = &c.
The sum of all the terms in this series is £31,644.
We have thus found that £31,644 is the present value of 96,223
assurances of £1 each on as many lives, of the same age 20, according to the H m mortality table, reckoning interest at 3 per cent. It follows that, if all these persons are to contribute at the same rate for their several assurances, the share payable by each—or the single premium for an assurance of £1 on each life—will be £31,644 ÷96,223, or £'32886. If twice the number of persons were to be assured, there would be just double the number of claims to satisfy at the close of each year, and the contribution payable by each person would remain the same; and so in proportion for any smaller or larger number of persons. We conclude, therefore, that the single premium at age 20 for a whole-term assurance of £1 according to the H m mortality table, reckoning interest at 3 per cent., is £32886, or 6s. 7d. 1
Passing from numerical illustration to general symbols, the process displayed above may bo stated as follows. The number of persons living at any given ago (a:) is represented by the symbol l x , and the number dying in the next year (that is, between the ages of x and ae + Ι) by d x , which is the equivalent of l x -l x+ ∖. Hence the number of claims to be made at the end of successive years in respect of l x assurances of 1 each, effected at the age of x, is represented by the series
⅛⅛ ⅛4-ι, d x +% .... d x+z , where z is the difference between x and the highest age completed by any of the lives in the mortality table. The sum of all the terms in this series is of course l x , since every person living at age x must die at one time or another within the period embraced in the table. If money made no interest, l x would be the present value of all the assurances, and the premium payable by each person would be lχ÷lx, or 1. To allow for the operation of interest, it is necessary to discount the several yearly payments for the periods during which they are respectively deferred. The series representing the present value of all the assurances thus becomes u⅛+ι>⅛ + ι+t)⅛ +3 + .... +v*+ 1 ⅛ +ie , where v=-—-.,—i being the interest of 1 for a year. Hence the l+⅛
premium payable by each of the l x individuals is vd x + νhl x+ - i + ν i d x+ ∙ι + . . . . +ν ss + 1 d x+ z lx which is usually represented by the symbol A x ,
The same result may be arrived at by a process of reasoning based on the doctrine of probabilities. Since out of l x persons alive at the age of x, and all (as we must suppose) equally exposed to the risk of death, d x will die before completing another year of age, the chance that any one in particular.of those l x persons will die within the first year is as d x to l x . Similarly the chance of any particular person dying within the second year is as d x j r ∖ to l x ; within the third year as d x+ % to l x ; and within the nth year as d x ± n -ι to l x . In any particular case, therefore, the probabilities of the sum assured becoming payable at the end of the first, second, third, nth years, are , , ⅛^, - j"- 1 , respectively; and the present Cχ *x ^x *x value of the expectation of receiving 1 at the end of any year, as the nth, is ι"~÷ n ^3 . Hence the value of 1 to be paid at the lx end of the year in which death occurs is the sum of all the terms in the series v⅛ + ≠⅛± +v 3⅛ 2 + . . . . + φ *+L⅛ , lx lx lx lx an expression which is identical with that given above.
Reverting to the previous expression, it will be seen that by multiplying both numerator and denominator by the same quantity v x we obtain, without altering the value of the formula,
⅛ c + 1 ⅛÷¾ z +⅞ + ι + -υ x ÷ 3 ⅛4. 2 + .... +tf c + z + l d x + z v x lx
In this new expression the denominator is the product known as D z in the commutation method (see again the article Annuities) ; and the successive terms in the numerator are of the general form ν n + i d n . This latter product is called C„; so that the whole expression may be written C x + Cχ4-1 + C a r-j-2 + . . . . + C x -∖-z
D x
In a commutation table the sum of C x , C x +↑, C x+ 2, .... Qr+z is placed in a column headed M x ; so that the single premium for an assurance payable after the death of a person aged x is —' .
The single premium for an assurance on the same life “deferred” for m years —that is, to be payable only if death should occur after that period—is ^ g+ -**; which is equivalent to Hx
Cχ-∣-m ÷ C≈+m+l ÷ · . · . + Cχ+z
D x and hence to v"^d, +M +t^+ i <? x+ . + i+ .... +υ 3c + z + 1 d x+z I»
By subtraction, the single premium for a “temporary” assurance for m years on the same life is , which is equivalent to l√x
Cχ + C x -∣-1+ .... + Cχ+m-l
D x and hence to vd x + υ i d x+ ι+ .... +W x+m -ι
l x
A column R is sometimes inserted in commutation tables to facilitate calculations relatingto “increasing” assurances. R z is the
J> sum of the terms M x , M x ψι, . . . M x 4- z ; so that jy is the value of an assurance the amount of which shall be 1 if the life fails during the first year, 2 if during the second year, 3 if during the third year, and so on.
When the value of any immediate annuity, calculated at a given rate of interest, is known, the value of a sum payable one year after the last instalment of the annuity may be readily deduced from it. The value of any deferred payment is the difference between the sum to be ultimately paid and the discount for the period during which it is deferred. Let a be the value of an annuity of 1 at the rate of interest i, and let it be required to find the value of 1 due at the end of the year following the last payment of the annuity. The discount of 1 for one year at the rate of interest i is —-‰-=l-v! and the present value of such annual 1 +∣
discount (payable in advance) for the whole period covered by the annuity and one year more is (1-«) (l + α). Hence the value of the deferred payment of 1 is 1 - (1 - v) (1 + a). Putting a x for the value of an annuity on a life aged x, we have for the present value of a whole-term assurance on a life of that age 1 - (1 - v) (1 + a x ).
The agreement of this result with those formerly deduced from the numbers dying in each year may be seen by substituting for d x , d x +ι, &c., their equivalents (l x -l x +ι), (L+ι - l x +2), &c., when the foregoing expression υd x + υ i d x+1 + .... +v z +' l d x+t l x becomes
ι>G¾-⅛+ι) + ι> 2 (⅛+t-⅛+2)+ .... +¾ g + 1 (⅛+⅛-0) l x vl x +υ t l x+ ι+ .... +tf+ 1 l x +z l x vlx+l + v^l x +2 + . . . . + V z lx+z l x ≈υ(l + a x )-a x ; as will be seen from the article Annuities. By a simple transposition this expression takes the form v - (1 - υ)a x ; which in its turn becomes 1 - (1 - υ)(l + a x ).
Assurances, as formerly mentioned, are usually paid for T>y annual contributions or premiums, continuing either during the whole subsistence of the assurance or during a limited period only. The annual premium for an assurance is deduced as follows. Since the present value of all the annual payments must be equal to the single premium, and since premiums are always payable in advance, we have (putting P for the annual premium required) P(l +α) = A; whence P=≈^A- . In this expression A may represent the single premium for any benefit whatsoever, whether depending on single or joint lives, or on any other description of status; and (1 + a) may represent the value, in any such case, of an annuity payable in advance during the period over which the payment of premiums is to extend. The annual premium, payable during the whole of life, for a whole-term assurance on a life aged x is l-(l- ι ,)(l + αχ ) 1
f+^ Ï+^" (1 - V)î or ¾(l+α x )-α x , y a x
1 + a x 1 +a x or it may be expressed in a variety of other ways by substituting different equivalents of the single premium and the annuity.
When the premium is to be payable for m years only, its amount is expressed by —— , where the syml>ol ∣ m -ια represents the 1 +1« - 1Λ value of a temporary annuity for m -1 years; and 1 + | m _ 1 α is therefore the value of an annuity for m years payable in advance.
When the premium for the first m years is to lie —th of that for r the remainder of life, the ultimate annual payment is found by the expression - — where βi -ι∣α is the value of an
—(1 +∣≡-ια)+m-ι∣α
annuity deferred for m - 1 years, and therefore of an annuity deferred for m years, but payable in advance.
By the commutation method the annual whole-life premium is ΓΓ÷⅞-=v∏ i - · The premium limited to m annual payments, •1 x Hx ∙W x -1
for a whole-term assurance, is — . The premium pay-
N x -ι-N a , +m -ι
able after m years, when the payment during that period is —th of the ultimate annual payment, is — , ! A(N x -i-N x+w . 1 ) + N≈ +w - 1 or -
N x -ι + (r-l)N x+1 ,-ι
We do not propose to enter further on the investigation of formulae for the calculation of premiums for the various descriptions of life assurances. These will be found in the works of Milne, Baily, Jones, and other authors who have treated of the subject of life contingencies. The student will find a very clear exposition of the nature and modes of calculation of the more ordinary kinds of premiums in a paper by Mr James Meikle, The Rationale of Life Assurance Premiums, reprinted by the Actuarial Society of Edinburgh in 1879.
In the practical calculation of life assurance premiums various devices have been suggested for shortening labour and ensuring accuracy. Mr Peter Gray’s method of calculation, by means of logarithmic tables on the plan originated by Gauss, may be specially mentioned. His Tables and Formulae, in which this method is explained, is a work of great value to the student of life contingencies.
When the requisite annuity-values are available, the tables of assurance premiums constructed by Mr William Orchard afford great facilities, either in forming scales of premiums or in isolated calculations. The foregoing expressions for the single premium in terms of the corresponding values of annuities are of such a character as to be applicable to a great variety of cases—to nearly every case, in fact, where the risk of the assurance is to be entered on immediately, and the sum assured is to be payable at the end of the year following the last payment of the annuity embraced in the formulae.
In like manner the formulae for the annual premium, — (1 - v),
1 ^τ^ Oj and its equivalents are applicable in all such cases, but only when the premium is to be payable during the whole continuance of the assurance, so that in the expression -— ~ ι, )Q∙ ^f^ a ) the annuity-
1 -r value a in the denominator corresponds with that in the numerator. Mr Orchard has tabulated the values of v - (1 - v)a and A— (l-ι?) for all probable values of α, and for the several values of v corresponding to eight different rates of interest. By means of these tables, when the annuity-value corresponding to any required single or annual premium is known, the premium itself may be obtained by mere inspection. The tables may be employed with annuities derived from any table of mortality, and, as the various cases to which they apply are by far the most frequent in practice, they are found extremely useful by computers.
We have throughout supposed that the payment of the sum assured is to be made at the end of the year in which death occurs. This supposition accords with the theoιy of annual mortality and annual conversion of interest into capital, upon which the usual system of calculation is based. It also agrees very nearly with fact when the sums assured are payable six months after death; for, if it be supposed that the deaths occurring within each year of age take place at equal intervals of time, or that they occur in equal numbers in the first and second halves of each year respectively, the persons insured will, one with another, complete about half a year of age in the year when they die. When it is thought desirable to make allowance, in the calculation of premiums, for the circumstance of the sums assured being payable earlier than at the end of the year of death, that maybe done by a simple modification of the usual formulae. For example, A(l + i)Hsan approximation sufficiently near for most purposes to the value of an assuhance payable as soon as death occurs.
The more scientific methods of calculation developed by Mr Woolhouse and others, and referred to in the article Annuities, eliminate both the hypothesis of payments being due at the end of the year and that of a uniform distribution of each year’s deaths, neither of which is strictly admissible. The lives assured, instead of being regarded as subject to successive yearly decrements, are considered to be diminishing in number continuously; and in like manner interest, instead of being payable annually, is supposed to be growing due from moment to moment. The methods referred to afford great facilities for the solution of various problems which can only be solved approximately, or with extreme labour, by the usual modes of computation, but they are not employed in the ordinary calculations of assurance offices.
The premiums obtained by calculation from the fundamental data of interest and mortality are called “net” or “pure” premiums. In calculating the premiums to be charged by an assurance office, it is to be borne in mind that, while fluctuations will undoubtedly occur in the rates of mortality prevailing at different times among the lives assured, and in the rates of interest realized on the invested funds, the terms on which assurances are undertaken are not subject to variation at the will of the office in order to meet such fluctuations. The office must hold itself absolutely responsible for the fulfilment of its part of the contract, but the premiums cannot be increased beyond the amount fixed at the outset. Hence it is obviously necessary that the premiums should be on such a scale as to. keep the office safe under all circumstances. Further, the premiums must contain a sufficient provision for the expenses necessarily incurred in carrying on business. Therefore the rates actually charged must be larger than those which would suffice if only a probable death-rate and a probable rate of interest had to be taken into account. In the earliest days of assurance it seems to have been the practice to make an addition for safety to the rates of premium deduced from the fundamental data, and certain payments were required as “entry-money” to help to meet expenses. Afterwards, when experience had shown that the tables of mortality then in use considerably overstated the death-rate likely to be experienced, the addition made to the premiums was removed, but the offices continued to use tables giving high death-rates in combination with a rate of interest well within that which might safely be expected. With the introduction, however, of mortality tables which approached more closely the death-rates among assured lives, there revived the practice of making an addition to the “pure” premiums, in order to provide for expenses, for fluctuations in the death-rate, and for other contingencies. This addition is called the “loading” or “margin,” and the premiums which include it are called “office premiums,” as being those which enter into the contract between the office and the assured.
Few if any of the older assurance offices continue to base their estimates of liability on the tables which were originally employed in the construction of their scales of premium; but many of them still charge the same rates as formerly, or at all events rates which have not been constructed from the tables of mortality now in use. Hence the terms “loading” and “margin” have come to bear a somewhat extended meaning. They are now used to designate the difference between the premiums payable by the assured and the net premiums deduced from any table that may be employed for the time.
There have been various theories as to the proper method of loading premiums. The plan most commonly employed at first was that of adding a constant percentage of the net premiums at all ages. Some actuaries objected to this method, holding it to be inequitable as between old and young lives, and proposed in its stead the addition of an equal sum for every age (that is, in effect, a constant percentage of the sum assured) as more in accordance with the object in view. By others a combination of these two plans was preferred. The premiums were loaded by a percentage for “profit” and contingencies, and a constant addition was made to cover the expenses of management. More recently other methods have been proposed, and it has been specially insisted on that the “loading” should be adjusted so as to give due weight to the fact that by far the larger proportion of expense is usually connected with the first year’s premium; but most of the scales of premiums now in use by assurance offices have been arrived at by one or other of the methods of loading mentioned above.
The rates of the Northampton Table, at 3 per cent, interest, furnish an example of a scale of net rates used as office premiums, without any specific addition by way of “loading.” These are shown in the following table. As an example of a scale of office premiums formed by loading with a constant percentage, we give that obtained by adding 25 per cent, to the net rates of the Carlisle table, reckoning interest at 3 per cent It will be seen that, owing to the lower death-rate shown by that table, the premiums even with the addition mentioned are lower than those of the Northampton Table up to age fifty. After that age the loaded Carlisle premiums are higher than the Northampton pure premiums, but still the Carlisle rates without loading are lower than the Northampton rates. For the sake of further illustration we give the net premiums deduced from the healthy males table (H M ) of the Institute of Actuaries at the same rate of interest; and in a separate column is shown what percentage of “loading,” on a comparison with those premiums, is contained in the Carlisle rates with their 25 per cent, addition. The premiums are those required for the assurance of £100 for the whole term of life. [table]
Constitution of Offices.— The nature of life assurance is such as to render impracticable its successful prosecution as a matter of individual or private enterprise. To secure a sufficiently uniform operation of the laws of average, the transactions must be carried out on a scale quite incompatible with the sufficiency of private credit for their fulfilment; while the indefinite and lengthened periods over which the engagements extend also mark them out as beyond the reach of individual responsibility.
Accordingly, with the limited exception of the insurance scheme of the Government, the business in the United Kingdom may be said to be entirely in the hands of public companies or societies. These bodies have been of three kinds—(1) the purely mutual offices, in which the assured themselves constitute the society ; (2) ↑ yroprietary offices, as they once existed, being joint-stock companies which carried on the business of assurance for the benefit of the shareholders, among whom were divided the whole “profits” or “surplus” arising from the contributions of the assured; and (3) the mixed offices, possessed of a share capital, but dividing among their assured a proportion (generally from two-thirds to nine-tenths) of the “profits” realized. In the present day there are but two kinds of offices, mutual and mixed, the proprietary companies either having disappeared or having adopted the plan of sharing profits with the policyholders.
Into the relative merits of the two classes of offices it is not our purpose to enter. The mutual offices take their stand on the advantage to the assured of sharing the whole profits among themselves, while the mixed offices point to certain features of their system which tend to neutralize the apparent disadvantage of the shareholders taking a portion of the surplus. We believe it will be found that the fact of an office belonging to one class or the other does not of itself afford a presumption either for or against its being an advantageous office to assure in. The comparative advantages of different companies must be sought out by a closer scrutiny than a mere reference to this distinction in the nature of their constitution.
Most assurances are effected on the plan of participating in profits. In both mutual and mixed offices, however, there is generally a class of policyholders who do not share in the profits, but who, requiring only a guarantee of a fixed sum on the happening of the contingency mentioned in their policies, effect their assurances at a reduced rate of premium calculated to cover fully the risk and expenses of business.
Selection of Lives.— It is well known that assurance companies exercise a selection among the lives proposed for assurance, admitting some on the ordinary terms and surcharging or rejecting others whose prospects of longevity appear to be below the average. The necessity for this has been sometimes called in question. Why, it has been asked, should the offices inquire so scrupulously into the state of health of those who offer themselves, if the mortality tables on which the premiums are based exhibit the death-rate among a number of persons in all the degrees of health and sickness? The answer is that without such selection on their part the offices could not reckon on the lives assured being as a body equal to those represented in the tables. It must be remembered that the inducement to become assured is not so great to the healthy and vigorous as it is to the weak and delicate, and if the offices were to open their doors to all comers, or were even to relax their vigilance in scrutinizing the applications made to them, they would inevitably admit an undue proportion of the latter class, and thus expose themselves to greater hazards than those provided for in their tables. Moreover, since the assured have a direct interest in the surplus remaining of their premiums, after providing the cost of the assurances, the admission of all lives on equal terms would be an injustice to those possessing a full measure of health. They would practically be called upon to contribute more than their own cases required, in order to provide a fund sufficient to pay the sums assured on lives having inferior prospects of longevity.
The means of selection employed by assurance offices are also well known. Each applicant is required to furnish information as to his own health and habits of life, and some particulars as to his family history, and he undergoes an examination by a medical man named by the office. In former days this examination was not always required, nor does it appear that the same attention was paid as now to the question of hereditary tendencies to disease; and yet, judging from the experience of the older offices, the precautions observed in those days seem to have been not without considerable effect. Unquestionably, however, the improvements which growing experience and the advance of medical science have brought to bear upon the means of selection have had an important influence in increasing its efficacy, although possibly they may have done little more than to defend the offices against a greater risk of the introduction of questionable lives. It is now well understood that hereditary tendencies have a marked effect in determining the chances of longevity of individuals; the degree of importance to be attached to particular deviations from health is better known than formerly; while the increased prevalence of assurance has led to a better appreciation among medical men of the duties required of them in the examination of proposers. In some of the medical schools special attention is now ^directed to the subject. Several excellent works on medical selection have appeared, one of the most recent in England being that of Dr Sieveking of London.
It may readily be supposed that selection has an important influence in determining the rates of mortality among assured lives. The extent and nature of this influence have formed a very fruitful and interesting subject of inquiry. So early as 1776 an investigation of the affairs of the Equitable Society revealed that the death-rate among the members had been much lower than that anticipated in the tables on which the premiums were based. Similar results appeared at the subsequent investigations of W. Morgan and A. Morgan, who were successively actuaries of the society; and in many other collections of the statistics of individual offices—those by Galloway of the Amicable (1841), Jellicoe of the Eagle (1854), Spens of the Scottish Amicable (1862), for example—the mortality among assured lives has been exhibited in comparison with the deathrates shown by the mortality tables in common use. Comparisons of this kind may be drawn from the tables on a preceding page. These do not, however, afford the means of observing what is a very marked peculiarity of the mortality experience of assurance companies, namely, the varying death-rates at different periods in the duration of assurances. Mr Spens devoted considerable attention to this subject, but it had been previously investigated in connexion with the statistics of the seventeen offices to 1843 already referred to. These statistics were analysed with this object by Mr E. J. Farren, who pointed out the extremely light mortality experienced during the first year of each assurance. A more exhaustive analysis is given by Mr Higham, in a paper “On the Value of Selection as exercised by the Policyholder,” contributed to the Assurance Magazine (vol. i. p. 179). Mr Higham traces the lives from their first year of assurance down to the time of their passing from observation, by death or otherwise, and shows that the mortality, light at first in consequence of the initial selection exercised by the offices, gradually increases until it becomes greater than that prevailing among the general population. This latter result he attributes to the selection which the assured exercise against the companies by dropping policies on healthy lives and retaining those on lives which have become bad or doubtful. A still more complete investigation of the subject of selection has been made by Mr Sprague (Assur. Mag., xiv. 328), who shows that the deterioration noticed by Mr Higham attains its maximum some time before the lives pass from observation, and is ultimately reversed after the full effect produced by the withdrawal of good lives has exhausted itself. Mr Sprague’s statistics are taken from the Twenty Offices’ Experience to 1863. In the collection of that experience the effects of the two kinds of selection that have now been referred to—selection by the assurance offices and selection against the offices—were kept in view as a subject to be investigated; and in the preface to the tables published in 1 The Assurance Magazine— or, as it is now called, the Journal of the Institute of Actuaries— continues to he, as it has been for many years, the principal medium of publication for what is new and important in actuarial science. Under the auspices of the Institute of Actuaries, a text-book is in preparation which, when completed, will no doubt bring within a convenient compass much that is now scattered throughout the Journal and other works. In the meantime the student will find it indispensable to make himself acquainted with many of the valuable papers contained in the Assurance Magazine.
1869 the subject is considered at some length, and several interesting tables are devoted to its illustration. The following figures, extracted from one of those tables, show the rates of mortality at different quinquennial periods of life among the “healthy lives, male and female,”—dividing the lives into groups according to the duration of their assurances. [table]
A prominent feature of this table is the divergence of the figures in column 3 from those in column 2, and on the other hand the comparatively close agreement of the figures in column 3 with those in column 5. This seems to indicate that among lives which have been less than five years assured the rate of mortality is materially lower than that prevailing among lives of similar ages who have been assured for longer periods, but that after the first five years the causes which bring about this lessening of the rate of mortality have in great measure ceased to operate. It was this peculiarity of the statistics that led to the construction of the H M(S) table,—the first five years of assurance being regarded as marking, although not in any strict or absolute sense, a distinct period in the value of assured life, after which “for all practical purposes the benefit of selection may perhaps be said to be lost.” Mr Sprague has since pointed out that this distinction is not altogether satisfactory, and he has sought by the construction of a series of “Select Mortality Tables” for separate ages at entry (Äss. Mag. xx. 95 and xxi. 229) to supply a more exact basis of calculation than the H m and H M(5) tables afford.
Besides its influence upon the rates of mortality, selection has also a very noticeable effect in regard to the causes of death among the assured. Diseases to which a predisposition may be inferred from family or personal history, or which admit of detection in an early stage by careful medical scrutiny, are less frequent among this selected class of lives than among the general population, while, on the other hand, assured persons seem to be more liable than others to particular forms of disease. This interesting subject is dealt with by Mr Meikle in his Observations, formerly referred to; and it is also illustrated in numerous reports on the experience of different assurance companies by their medical officers.
Valuations.— The business of life assurance being founded on well-ascertained natural laws, and on principles of finance which in their broad aspect are of the simplest description, there exists no necessity for frequent close scrutiny of the affairs of an assurance office, in so far as the maintenance of a mere standard of solvency is concerned. We have seen that the premiums charged for assurances are based on certain assumptions in regard to (1) the rate of mortality to be experienced, (2) the rate of interest to be earned by the office on its funds, and (3) the proportion of the premiums to be absorbed in expenses and in providing against unforeseen contingencies. If these assumptions are reasonably safe, an assurance office proceeding upon them may be confidently regarded as solvent so long as there is no conspicuously unfavourable deviation from what has been anticipated and provided for, and so long as the funds are not impaired by imprudent investments or otherwise. The ascertainment and division of profits, however, require that the affairs should be looked into periodically; but the fluctuations to which the surplus funds are liable within limited periods of time, from variations of the death-rate and other causes, are generally regarded as furnishing a sufficient reason why such investigations should not take place too frequently. Accordingly in most offices the division of profits takes place only at stated intervals of years,—usually five or seven years,—when a complete survey is taken of the whole engagements present and future, and of the funds available to meet these. The mode in which the liability of an office under its current policies is estimated requires explanation.
All statistical observations on the duration of human life point to the conclusion that, after the period of extreme youth is past, the death-rate among any given body of persons increases gradually with advancing age. If, therefore, assurance premiums were annually adjusted according to the chances of death corresponding to the current age of the assured, their amount would be at first smaller, but ultimately larger, than the uniform annual payment required to assure a given sum whenever death may occur. This is illustrated by the following figures, calculated from the H m mortality table at 3 per cent, interest. In column 2 is the uniform annual premium at age thirty for a whole-term assurance of <£100. In column 3 are shown the premiums which would be required at the successive ages stated in column 1 to assure <£100 in the event of death taking place within a year. Column 4 shows the differences between the figures in column 2 and those in column 3. [table]
From this table it appears that if a number of persons effect, at the age of thirty, whole-term assurances on their lives by annual premiums which are to remain of uniform amount during the subsistence of the assurances, each of them pays for the first year £1*130 more than is required for the risk of that year. The second year the premiums are each <£1*111 in excess of that year’s risk. The third year the excess is only £1*093, and so it diminishes from year to year. By the time the individuals who survive have reached the age of fifty-four, their uniform annual premiums are no longer sufficient for the risk of the following year; and this annual deficiency goes on increasing until at the extreme age in the table it amounts to £95*207, thedifference between the uniformannual premium(£1 *880) and the present value (£97*087) of £100 certain to be paid at the end of a year. Now, since the uniform annual premiums are just sufficient to provide for the ultimate payment of the sums assured, it is obvious that the deficiencies of later years must be made up by the excess of the earlier payments; and, in order that the assurance office may be in a position to meet its engagements, these surplus payments must be kept in hand and accumulated at interest until they are required for the purpose indicated. It is, in effect, the accumulated excess here spoken of which constitutes the measure of the company’s liability under its policies, or the sum which it ought to have in hand to be able to meet its engagements. In the individual case this sum is usually called the “reserve value” of a policy.
In another view the reserve value of a policy is the difference between the present value of the engagement undertaken by the office and the present value of the premiums to be paid in future by the assured. This view may be regarded as the counterpart of the other. For practical purposes it is to be preferred, as it is independent of the variations of past experience, and requires only that a rate of mortality and a rate of interest be assumed for the future.
According to it, the reserve value (n V x ) of a policy for the sum of 1, effected at age x, and which has been in force for n years—the (n + l)th premium being just due and unpaid—may be expressed thus, in symbols with which we have already become familiar.
nV x = A at -∣-n — P x (l + aχ- ∖ -n) (1).
If we substitute for A x -∣-n its equivalent P x 4- tl (l+ α x ⅛ n ) this expression becomes n V x =(P x+n -P x )(l+fl⅛ +n ) (2); whence we see that the sum to be reserved under a policy after any number of years arises from the difference between the premium actually payable and the premium which would be required to assure the life afresh at the increased age attained. By substituting for P x -∣-n and P x their equivalents —A (1 - v) and - - (1 - v), we obtain another useful form of the expression,
V x = l- 1+αa +" (3)
1 + α x
_ fl ⅛ — 0 ⅛+n. ·
1 + ax
The preceding forrnulae indicate clearly the nature of the calculations by which an assurance office is able to ascertain the amount of funds which ought to be kept in hand to provide for the liabilities to the assured. In cases other than whole-term assurances by uniform annual premiums, the formulae are subject to appropriate modifications. When there are bonus additions to the sums assured, the value of these must be added, so that by the foregoing formula (1), for example, the value of a policy for 1 with bonus additions B is (1 + B)A x+n - P(1 + α x+n ). But the general principles of calculation are the same in all cases. The present value of the whole sums undertaken to be paid "by the office is ascertained on the one hand, and on the other hand the present value of the premiums to be received in future from the assured. The difference between these (due provision being made for expenses and contingencies, as afterwards explained) represents the “net liability” of the office. Otherwise, the net liability is arrived at by calculating separately the value of each policy by an adaptation of one or other of the above formulae. In either case, an adjustment of the annuity-values is made, in order to adapt these to the actual conditions of a valuation, when the next premiums on the various policies are not actually due, but are to become due at various intervals throughout the succeeding year.
So far in regard to the provision for payment of the sums contained in the policies, with their additions. We now come to the provision for future expenses, and for contingencies not embraced in the ordinary calculations. In what is called the “net-premium” method of valuation, this provision is made by throwing off the whole “loading” in estimating the value of the premiums to be received. That is to say, the premiums valued, in order to be set off against the value of the sums engaged to be paid by the office, are not the whole premiums actually receivable, but the net or pure premiums derived from the table employed in the valuation. The practical effect of this is that the amount brought out as the net liability of the office is sufficient, together with the net-premium portion of its future receipts from policyholders, to meet the sums assured under its policies as they mature, thus leaving free the remaining portion—the margin or loading—of each year’s premium income to meet expenses and any extra demands. When the margin thus left proves more than sufficient for those purposes, as under ordinary circumstances it always ought to do, the excess falls year by year into the surplus funds of the office, to be dealt with as profit at the next periodical investigation.
There appears to be a decided preference among assurance companies for the net-premium method as that which on the whole is best suited for valuing the liabilities of an office transacting a profitable business at a moderate rate of expense, and making investigations with a view to ascertaining the amount of surplus divisible among its constituents. Under certain circumstances it may be advisable to depart from a strict application of the characteristic feature of that method, but it must always be borne in mind that any encroachment made upon the “margin” in valuing the premiums is, so far, an anticipation of future profits. Any such encroachment is indeed inadmissible, unless the margin is at least more than sufficient to provide for future expenses, and in any case care must be taken to guard against what are called “negative values.” These arise when the valuation of the future premiums is greater than the valuation of the sums engaged to be paid by the office, or when in the expression (P x+n - P x ) (1 + α x+ , l ) the value of P z is increased so as to be greater than that of P x+n . It is evident that any valuation which includes “negative values” must be misleading, as policies are thereby treated as assets instead of liabilities, and such fictitious assets may at any time be cut off by the assured electing to drop their policies.
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. At a period of valuation the policies are to be dealt with as if effected a year after their actual date, and at the increased age then attained.
Another modification of the net-premium method has been advocated for valuing policies entitled to bonus additions. It consists in estimating the value of future bonuses (at an assumed rate) in addition to that of the sum assured and existing bonuses, and valuing on the other hand so much of the office premiums as would have been required to provide the sum assured and bonuses at the time of effecting the assurance. This tends to secure, to some extent, the maintenance of a tolerably steady rate of bonus.
An essentially different method is employed by some offices, and is not without the support of actuaries whose judgment is entitled to every respect. It has been called the “hypothetical method.” By it the office premiums are made the basis of valuation. Hypothetical annuity-values, smaller than those which would be employed in the net-premium method, are deduced from the office premiums by means of the relation P ’ = —— - (1 - v), and the policies are valued according to the formula nV x = (P x -∣-n — Pχ)(l + α ⅛H-n) » where P x and P' a . +n are the office premiums at ages x and
