Endowment Assurances Research Articles

Numerical System of Rating

In considering the question as to whether an assurance can be granted to a particular proposer, the Chief Medical Officer and the Actuary of the Company have available the Medical and other reports of the life proposed. From the information given in those reports they have to form an opinion as to the present state of health and likelihood of longevity, taking into account all the factors before them. In some cases it does not require a doctor nor yet an actuary to decide that the policy can be issued at ordinary rates, but in other cases there will be some degree of impairment, varying from the case where a spin of the coin might be as fair a method as any, to the case which is obviously uninsurable at any rate. It is the border line cases which cause the most inconvenience. A certain proposer is slightly overweight, so we do not like the look of him, but this may be counterbalanced by favourable chest and abdominal measurements. Then, again, there may be a lack of longevity in the family history, but on the other hand he may only require a short term endowment assurance.

Valuations in Modern Conditions

A Net Premium Valuation is made when the sums assured and net premiums are valued at a given rate of interest and by a given table of mortality, and the net premiums are calculated at the same rate of interest and by the same table of mortality. Such a valuation leads to a reserve that starts with the net premium and ultimately reaches the sum assured for whole life assurances and endowment assurances; it cannot produce negative values unless the annuity value increases with the age, a case with which we are not concerned in this paper.

The Valuation of Ordinary Whole-Life Policies

The title to this paper deliberately restricts its field. Emphasis is essentially on “The Valuation” and the limitation to Whole Life Policies restricts these notes to the one class to the exclusion of all others, including special policies, which, in any event, would require in the valuation separate treatment. It is not intended to enter into the realms of Industrial Assurance.Essentially there is no difference between Whole Life and Endowment Assurance Policies, but by restricting the paper to the former it will simplify discussion. It has the advantage also that we have to consider the basic factors—namely, the rates of mortality and interest—in their extreme form, for whereas the terms of Endowment Assurances are comparatively short, thus minimising the effect of error, when dealing with Whole of Life Policies the Actuary has to consider the general trend of mortality and interest rates over a very much longer period, probably fifty or more years.

A Valuation of Non-Participating Policies without Classification

In a note to his paper on "the Approximate Valuation of Endowment Assurances" (J.I.A. Vol.XLVIII, p. 32) Mr Elderton suggested that it might be possible to approximate to the true net premium reserves by accumulating the premium at interest only without having any direct regard to mortality, and I have made an attempt in this paper to arrive at a suitable method of approximation.

Single Premium Policies.

For some time past there has been a large amount of business transacted by Life Insurance Companies under what is commonly known as the “Super Tax Saving Scheme.” A person who is liable for super tax effects with an insurance company a whole life or endowment assurance with or without profits by a single premium. The company then advances a large proportion of the single premium to the assured on the security of a first charge on the policy and bonuses, if any.

Surrender Values of Whole Life and Endowment Assurances.

The subject of Surrender Values is a wide one and it will be impossible in the course of these remarks to give more than an outline of a few of the points which arise. I shall, therefore, deal in the main with broad general principles and leave the lesser details untouched. The scales of surrender values actually allowed by offices in this country differ widely, and an examination of the figures indicates that some offices still retain the view that a policyholder who surrenders his assurance should be fined heavily. It is difficult to reconcile this view with present-day ideas, for if a policyholder is so unfortunate as to be unable to continue his premiums owing to financial or other reasons, it is surely harsh treatment on the part of the company to impose a heavy fine, the whole, or practically the whole, of which merely goes to swell the bonuses allotted to those more fortunate individuals who are able to continue and who could well dispense with this additional benefit.

Non-Profit Office Premiums

The following remarks refer to the determination of Non-Profit Whole Life Assurance and Endowment Assurance office premiums; many of the principles raised apply to the premiums for other types of policies.The office premium depends on the rates of mortality, interest, expense and loading for profit used in its calculation; we shall be concerned mainly to determine what values to give these factors, and the values chosen will form our premium bases. There is no reason to assume that we should give the factors the same values for all policies; for instance we might be justified in taking a lower rate of expense for policies of large sum assured than for policies of small sum assured.

Non-Forfeiture Regulations

When a premium on a life assurance policy falls due, a certain time, known as the Days of Grace, is always allowed in which it may be paid without loss or fine. This period is usually 30 days, but a calendar month may be allowed and in one case 15 days only are given. During the days of grace the policy is fully in force and should a claim arise, it would be paid in the ordinary way, the premium that has fallen due merely being deducted.If the premium is not paid within the days of grace, it is said to be overdue and if the policy has acquired a surrender value the non-forfeiture regulation then comes into operation. The regulations usually apply only to ordinary life business; for special policies special schemes are sometimes in force and in some cases, such as Sinking Fund Assurances, where the office is running no mortality risk, no regulation is called for. These remarks, throughout, will deal only with the ordinary non-forfeiture regulations as applied to Whole Life and Endowment Assurance Policies.

Net Premiums for Endowment Assurances and Temporary Assurances, also values of Temporary Annuities, in the case of three or four joint lives

Net Premiums for Endowment Assurances and Temporary Assurances, also values of Temporary Annuities, in the case of three or four joint lives

On the Valuation of Endowment Assurances by Select Tables

The question whether it is necessary to use select mortality rates in the calculation of office reserves was pronounced by Mr. R. P. Hardy during the discussion on the papers submitted by Messrs. King, Diver and Ackland to be a highly debatable one.The discussion disclosed two lines of thought on the subject, one admitting that a select valuation was theoretically correct, the other questioning the advisability of making a select valuation at all, the arguments in favour of the use of an aggregate table being crystallized in Mr. Warner's statement that the logical complement of a select table valuation would be the employment of a rate of interest representing to the nearest penny what had been actually realized during the quinquennium. Considered as a warning against undue striving after exactitude this is unanswerable, but when the calculation of the office reserves is viewed as a preliminary to the declaration of bonus, the conclusion might be drawn that an aggregate table valuation so entirely meets the case as to permit the full distribution of the resulting surplus.

A Group-Check for Endowment Assurance Net Premiums, by means of Mean Ages Based on the Z Method

A Group-Check for Endowment Assurance Net Premiums, by means of Mean Ages Based on the Z Method

An Analysis of the Profit from Endowment Assurance and Whole Life Policies

An Analysis of the Profit from Endowment Assurance and Whole Life Policies

Claim Acceleration Reserve for Endowment Assurances

Claim Acceleration Reserve for Endowment Assurances

Decreasing Debts on Endowment Assurances

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The Valuation of Double Endowment Assurances

The Valuation of Double Endowment Assurances

Select Net Premiums for Endowment Assurances

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Approximate Valuation of Endowment Assurances

In the discussion that followed the reading of a paper before the Institute of Actuaries Students’ Society, by E. A. Woodall on the valuation of special policies, F. Bedford explained that certain classes, such as joint life endowment assurances, could be valued conveniently by assuming that all the policies will mature at the same age, and calculating the net premium on the same assumption. This method is mentioned in the Students’ Journal, vol. I, No. 2, pp. 24–26, where Mr. Woodall, in giving the method in the abstract of his paper and the discussion, explains how the method applies to certain classes, and writes : “Since the reserve for an endowment assurance maturing at “70 or 75 is practically the same as the reserve for an endowment “assurance of the same term maturing at 50, 55, 60, or 65, the “error of 10 years in the equivalent age is of little importance,” “provided the net premium is calculated on the same assumptions.” This quotation may be taken as the text for the present paper, which discusses the application of the method to ordinary endowment assurances and the errors involved in its use.

Value of Policies in Force for Fractional Periods.

It is easiest to understand the subject by approaching it arithmetically and remembering that in practice tables give values ofnV for integral values ofn.Throughout these notes it is assumed thatnV =nV(m) ifnis integral. The error cannot exceed 1 per cent, of the true value where the entry age is 35, or 3 per cent, where the entry age is 60. As mentioned in the Text Book, Part II., p. 346, the maximum percentage error arises whenmbecomes infinite and is one-half of the net annual premium per cent, for Whole Life Assurances. For Endowment Assurances the differences are very small, increasing with the maturity age.

Double Endowment Assurances

(i) The characteristic feature of Double Endowment Assurances is that for a given term of years the annual premium is almost independent of the age, provided the age at maturity does not exceed a certain limit. If we assume it to be precisely true that the annual premium is independent of the age, it follows that the premium must be identical with that for a Capital Redemption Policy for the same term of years and assuring an amount equal to the Double Endowment.

Tables of the Values of Endowment Assurance Policies (OM(5) 3½ Per-cent)

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