When the net-premium method is employed, it is important that the office premiums be not altogether left out of view, otherwise an imperfect idea will be formed as to the results of the valuation. Suppose two offices, in circumstances as nearly as possible similar, estimate their liabilities by the net-premium method upon the same data, but office A charges premiums which contain a margin of 20 per cent, above the net premiums, and office B charges premiums with a margin of 30 per cent. Then, in so far as regards their net liabilities (always supposing the sum set aside in each case to be that required by the valuation), the reserves of those offices will be of equal strength, and if nothing further were taken into account they might be supposed to stand in the same financial position. But it is obvious, that office B, which has a margin of income 50' per cent, greater than that of office A, is so much better able to bear any unusual strain in addition to the ordinary expenditure, and is likely to realize a larger surplus on its transactions. Hence it appears that in order to obtain an adequate view of the financial position of any office it is necessary to consider, not only the basis upon which its reserves are calculated, but also the proportion of “loading” or “margin” contained in its premiums, and set aside for future expenses and profits.

Valuations may be made on different data as to mortality and interest, and the resulting net liability will be greater or less according to the nature of these. Under any given table of mortality a valuation at a low rate of interest will produce a larger net liability—will require, that is to say, a higher reserve to be made by the office against its future engagements to the assured—than a valuation at a higher rate. The effect of different assumptions in regard to the rates of mortality cannot be expressed in similar terms. A table of mortality showing a high death-rate, and requiring, consequently, large assurance premiums, does not necessarily produce large reserve values. The contrary indeed may be the case, as with the Northampton Table, which requires larger premiums than the more modern tables, but gives on the whole smaller reserve values. The amount of the net liability depends, not on the absolute magnitude of the rates of mortality indicated by the table, but on the ratio in which these increase from age to age.

If the values deduced by the net-premium method from any two tables be compared, it will be seen that

Vi >, =, or < n Vχ according as j _ 1 ÷<⅛+⅝ > _ or < 1 — 1 αχ ^^ n

1 + a ’ x ’ 1 + ax i, e ., as ⅛⅛ >, =, or < ⅛ . . . (1),

1 + a x 1 + a x or as J±⅛ >, =, or < }⅛ . . (2);

1 + aχ 1 + aχ+n where the accented symbols throughout refer to one table and the unaccented symbols to the other.

We have thus the means of ascertaining whether the policy-values of any table will be greater or less than, or equal to, those of another, either (1) by calculating for each table separately the ratios of the annuity-values at successive ages, and comparing the results, or (2) by calculating at successive ages the ratios of the annuity-values of one table to those of another, and observing whether these ratios decrease or increase with advancing age, or remain stationary throughout. The above relations will subsist whatever maybe the differences in the data employed, and whether or not the annuity-values by the different tables are calculated at the same rate of interest. When the same rate of interest is employed, any divergence in the ratios of the annuity-values will of necessity be due to differences in the rates of mortality. This interesting subject is investigated by Mr Meikle in a paper on Policy Life-Lines, one of the Actuarial Society’s publications, and by Mr Sprague in the Assurance Magazine, vol. xxi. p. 77.

The following table gives examples of the reserve values of policies for £100, calculated on the net-premium method by three different mortality tables, at a uniform rate of interest, 3 per cent [table]

Something may be said here as to the data on which assurance companies make their valuations. The rates of interest assumed by different offices may be said to range between 3 and 4 per cent., being in most cases lower than 4. It is, however, in regard to the tables of mortality that the greatest diversity exists. The Northampton Table has, for valuation purposes, been all but discarded. The Carlisle Table has so far lost its ground, since the introduction of the more recent Experience Tables, as to be now used by only a, minority of the offices as the chief basis of their calculations. The different tables based on the experience of the Equitable Society, the Seventeen Offices’ Experience, and the English Life Tables have still some adherents, and (besides those offices which value by the “hypothetical method”) a few companies employ tables constructed specially for their own use. But there is an evident tendency towards the general adoption of the Institute of Actuaries (twenty offices) Tables, which have been used by a large proportion of the companies in their latest valuations. Of these, the tables chiefly employed are H m and H M(5) , the latter being used by some offices in combination with the H m pure premiums, in order to eliminate as far as possible the effects of selection. Mr King (Ass. Mag., xix. 381 and xx. 233) and Mr Sprague (Ass. Mag., xxi. 229 and xxii. 391) have shown the construction of tables which would give in a more, direct and scientific way the result that is aimed at by using the combined H m and H M(5) tables. Mr King, to illustrate the results of his method, constructs a “model office,” assuming a uniform annual influx of new business and a rate of discontinuance of policies based on the experience of the twenty offices which contributed their statistics to the formation of the Institute of Actuaries Tables, and he shows the comparative reserves required by such an office at the end of successive quinquennial periods, according to various mortality tables and at different rates of interest. As these illustrative tables afford an admirable means of comparing the results of valuing by different mortality tables, we give the following extracts. It must be borne in mind, however, in seeking to apply the figures in these tables to estimate the strength of the reserves maintained by particular offices, that the soundness of the estimate may be a good deal affected by circumstances. In particular the rates at which new business has come in and policies have been discontinued must be taken into account, and, as before stated, the amount of “margin” contained in the premiums must not be lost sight of. Moreover, the supposed liabilities do not include bonus additions, and the presence of these will of course modify any conclusions drawn from the tables. [table]

Division of Surplus.— There are various sources from which a surplus of funds may arise in an assurance company :—(1) from the rate of interest actually earned being higher than that anticipated in the calculations; (2) from the death-rate among the assured being lower than that provided for by the mortality tables; (3) from the expenses and contingent outlay being less than the “loading” provided to meet them; and (4) from miscellaneous sources, such as profitable investments, the cancelment of policies, &c.

»Supposing a valuation to have been made on sound data and by a proper method, and to have resulted in showing that the funds in hand exceed the liabilities, the surplus thus ascertained may be regarded as profit, and either its amount may be withdrawn from the assets of the office or the liabilities may be increased in a corresponding degree.

Various methods are employed by assurance companies in distributing their surplus funds among the assured. In some offices the share or “bonus” falling to each policyholder is paid to him in cash; in others it is applied in providing a reversionary sum which is added to the amount assured by the policy; in others it goes to reduce tho annual contributions payable by the policyholder. A method of more recent introduction is to apply the earlier bonuses on a policy to limit the term for which premiums may be payable, thus relieving the policyholder of his annual payments after a certain period. Another method is to apply the bonuses towards making the sum assured payable in the lifetime of the policyholder. The plan of reversionary bonus additions is most common, and when it is followed the option is usually given of exchanging the bonuses for their value in cash or of having them applied in the reduction of premiums.

Not only are there different modes of applying surplus, but the basis on which it is divided among the assured also varies in different offices. In some the reversionary bonus is calculated as an equal percentage per annum of the sum assured, reckoning back either to the commencement of the policy in every case, or (more commonly) to the preceding division of profits. In others the rate is calculated, not only on the original sums assured, but also on previous bonus additions. In others the ratio of distribution is applied to the cash surplus, and the share allotted to each policy is dealt with in one or other of the ways above indicated. The following are some of tho ratios employed by different offices in the allocation of profits:—(1) in proportion to the amount of premiums paid (with or without accumulated interest) since the last preceding valuation; (2) in proportion to the accumulated “loading” of the premiums so paid; (3) in proportion to the reserve values of the policies; (4) in proportion to the difference between the accumulated premiums and the reserve value of the policy in each case.

Some offices have a special system of dealing with surplus, reserving it for those policyholders who survive the ordinary “expectation of life,” or whose premiums paid, with accumulated interest, amount to the sums assured by their policies. This system is usually connected with specially low rates of premium.

The various bonus systems which have been mentioned yield different results to policy holders of different ages, and whose assurances have been in force for longer or shorter periods. A person seeking to effect an assurance may exercise a wise discretion in selecting that office whose bonus system appears most advantageous, considering his own age and circumstances.

From a paper by Mr A. ∏ewat in the Assurance Magazine (xxii. 286) it appears that , the average amount of surplus annually divided among the assured by seventyseven offices which have rendered valuation accounts to the Board of Trade since the passing of the “Life Assurance Companies Act, 1870,” has been £2,285,000, cr 23 per cent, of the annual premium income of the offices. The following average specimens of reversionary bonuses are taken from the returns of forty-one of those offices, whose average rate of annual premium is shown in the second column. [table]

Surrender Values.— In those branches of insurance where the contract is one of indemnity against loss, the risk remaining the same from year to year—and where the consent of both parties, insurer and insured, is required at each periodical renewal—no question of allowance in respect of past payments can anse when one party or the other determines to drop the contract. It is quite recognized that the premiums are simply an equivalent for the risk undertaken during the period to which they apply, with a certain margin for expenses and for profit to the insurer, and that therefore a favourable issue of the particular contract supplies no argument for a return of any part of the sums paid. In life assurance, however, we have shown that the premiums contain a third element, namely, the portion that is set aside and accumulated to meet the risk of the assurance when the premium payable is no longer sufficient of itself for that purpose.

When a policyholder withdraws from his contract with a life assurance office, the provision made for the future in respect of his particular assurance is no longer required, and out of it a surrender value may b. allowed him for giving up his right to the policy. If there were no reasons to the contrary, the office might hand over the whole of this provision, which, as we have seen, is in fact the reserve value of the policy. No more could be given without encroaching upon the provision necessary for the remaining policies. But the policyholder in withdrawing is exercising a power which circumstances give to him only and not to the other party in the contract. The office is bound by the policy so long as the premiums are duly paid and the other conditions of assurance are not infringed. It has no opportunity of reviewing its position and withdrawing from the bargain should that appear likely to be a losing one. The policyholder, on the other hand, is free to continue or to drop the assurance as he pleases, and it may fairly be presumed that he will take whichever course will best serve his own interest. If he is in failing health he is the more likely to make an effort to keep the assurance on foot; if he has also fallen into adverse circumstances, his friends may aid him to maintain his policy for the benefit of those dependent on him, or he may dispose of it to some one who, knowing the circumstances, may be willing to give a high price for it, speculating on the chance of its becoming an early claim. All these things do happen, and the tendency obviously is that policies on deteriorated and unhealthy lives are kept in force, while those on lives having good prospects of longevity are more readily given up. Again, the retiring policyholder, by withdrawing his annual contribution, not only diminishes the fund from which expenses are met, but lessens the area over which these are spread, and so increases the burden for those who remain. Considerations like these point to the conclusion that, in fairness to the remaining constituents of the office, the surrender value to be allowed for a policy which is to be given up should be less than the reserve value. The common practice is to allow a proportion only of the reserve value. Some offices have adopted the plan of allowing a specified proportion of the amount of premiums paid. This plan is not defended on any ground of principle, but is followed for its simplicity and as a concession to a popular demand for fixed surrender values.

Another mode of securing to retiring policyholders the benefit of the reserve values of their assurances is that known as the nonforfeiture system. This system was first introduced in America, whence it found its way to the United Kingdom, where it was gradually adopted by a large proportion of the assurance companies. In its original form it was known as the “ten years non-forfeiture plan.” The policies were effected by premiums payable during ten years only, the rates being of course correspondingly high. If during those ten years the policyholder wished to discontinue his payments, he was entitled to a free “paid-up policy” for as many tenth parts of the original sum assured as he had paid premiums. The system, once introduced was gradually extended first to assurances effected by premiums payable during longer fixed periods, and ultimately, by some offices, to assurances bearing annual premiums during the whole of life. The methods of fixing the amount of paid-up policy in the last-mentioned class of cases vary in different offices, but the principle underlying them all is that of applying the reserve value to the purchase of a new assurance of reduced amount.

Conditions of Assurance.— An office, in entering on a contract of life assurance, does so in the faith that all circumstances material to be known in order to a proper estimate of the risk have been disclosed. These circumstances are beyond its own knowledge, and as the office for the most part (except as regards the result of the medical examination, which may reveal features of the case unknown to the proposer himself) is dependent on the information furnished by the party seeking to effect the assurance, it is proper that the latter be made responsible for the correctness of such information. Accordingly it is made a stipulation, preliminary to the issue of every policy, that all the required information bearing upon the risk shall have been truly and fairly stated, and that in case of any misrepresentation, or any concealment of material facts, the assurance shall be forfeited. In practice, however, this forfeiture is rarely insisted on unless there has been an evident intention to deceive. The other usual conditions of life assurance policies may be shortly noticed.

1. As to Payment of Premiums.— A certain period of grace is allowed, most commonly thirty days, after each premium falls due. If payment is not made within that time, the presumption is that the policyholder intends to drop the contract, and the risk of the office comes to an end. It may, however, be revived on certain conditions, usually the production of evidence of health and payment of a fine in addition to the premium. An impression used to prevail among the public that the offices were interested in encouraging the forfeiture of policies. If any such impression was ever shared by the offices themselves it must have long since passed away, as it will be found that every reasonable effort is now made on their part, not only to secure assurances but to retain them, and to afford all the facilities that can be extended to policyholders with that object.

2. As to Foreign Travel and Residence, and as to Hazardous Occupations.— When Mr Babbage wrote his Comparative View of Assurance Institutions in 1826, voyaging abroad was scarcely permitted under a life policy. The Elbe and the Garonne, Texel and Havre, Texel and Brest, the Elbe and Brest, were the limits prescribed by most of the English offices. Even at a much later period the extra premiums charged for leave to travel or reside abroad were very heavy. But improved means of conveyance—in some places better sanitary appliances, and habits of living more suited to the climatic conditions—and, more than all perhaps, the knowledge that has been gained by experience as to the extent of the extra risks involved and the relative salubrity of foreign climates—have enabled the offices to modify their terms very considerably. The limits of free residence and travel have been greatly widened, and where extra premiums are still required these are, as a rule, much lower than formerly. The assured are now commonly permitted to reside anywhere within such limits as north of 35° N. lat. (except in Asia) or south of 30° S. lat., and to travel to and from any places within those limits, without extra premium.

Military men (when on active service) and seafaring men are of course charged extra rates, as are also persons following specially dangerous or unhealthy occupations at home.

3. As to Suicide.— The policies of most companies contain a proviso that the assurance shall be void in case the person whose life is assured dies by his own hand. This proviso is analogous to that which renders void a fire policy if the insured becomes guilty of arson, or a policy of marine insurance if the vessel is wrecked intentionally by the owner. The event contemplated in the policy being brought about by the voluntary act of the assured, and not in the natural course of events, is a contingency not included in the scheme of insurance. In the case of life policies the general rule of law appears to be (see The Law of Life Assurance, fy C. J. Bunyon) that the contract will be avoided unless the suicide takes place when the assured is insane and not accountable for his acts. Sometimes the proviso “whether insane or not” is inserted in policies. In the case of...