JOURNAL

OF THE

INSTITUTE OF ACTUARIES

AND

ASSURANCE MAGAZINE.

On Reversionary Life Interests as Securities for Loans. By T. B. SPRAGUE, M.A., Vice-President of the Institute of Actuaries. [Read before the Institute, 25 November 1872.]

OF all the securities proposed to insurance companies, reversionary life interests are the most troublesome to deal with in the ordinary way of mortgage; and the objections to so dealing with them have been considered by many actuaries so serious, that they have laid down the rule that the only safe way of making an advance on the security of a reversionary life interest is by way of reversionary charge. The transaction, they think, should be in the nature of a sale rather than a mortgage, a portion of the reversionary life interest being sold in consideration of the present advance.

When a borrower applies for a loan on a reversionary life interest, he generally expects to be called on to effect an insurance of about the same amount as would be required to secure a loan on an immediate life interest; and it is difficult to make him understand why a greatly larger insurance is necessary to protect the lender. The reason becomes obvious enough when we consider what remedy a lender has in the event of the borrower failing to pay his interest and premiums. In that case, there appear to be three possible courses open to the lender. First, may, by agreement with the borrower, allow the premiums and

he

VOL. XVII.

interest to accumulate at compound interest; or, secondly, he may sell the reversionary life interest; or, thirdly, foreclose. Suppose the amount of the insurance that has been effected to be such as would be required in the case of an advance on the security of a life interest in possession, or to exceed the sum lent by about 20 per-cent. Then, if the first of the above courses is adopted, and the interest and premiums are allowed to accumulate at compound interest, it is clear that in a very few years, (probably within three years, under the circumstances supposed) the accumulated amount of the loan will exceed the insurance, and a further insurance will become necessary to protect the lender from loss by the death of the borrower. Should the borrower be still in good health, no difficulty arises. If, however, he has fallen into bad health, and his life is only insurable at a greatly increased premium, the value of his reversionary life interest will be much reduced; and unless the sum originally lent was but a small fraction of the value, the lender may probably find that the security is worth less than he has lent upon it. But it may happen that the borrower's life has become wholly uninsurable. If it were then certain that he would die within a short term of years, the difficulty would be met by increasing to a moderate extent the original amount of the insurance; but, as is well known to all persons familiar with life insurance business, a person whose life is practically uninsurable may nevertheless live for ten or even twenty years; and if the borrower's life in the case supposed should be extended in this way, the accumulations at compound interest would make his debt very greatly exceed the amount of the insurance, so that the lender would receive on the death of the borrower only a small part of the sum due to him. It appears then that, in this case, in order to protect the lender completely, the full insurance that will be ultimately required should be effected (or arranged for) at the outset when the loan is originally granted. Secondly, suppose that the lender attempts to sell the reversionary life interest; then since the purchaser will in no case receive any income until the death of the life tenant, and will receive nothing at all if the reversioner should die before the life tenant, he will of course require to have an insurance on the reversioner's life sufficient to cover the probable amount of the accumulations at compound interest of his purchase money and the premiums which he may pay before he comes into possession of the reversionary life interest. Here the same difficulty meets us; for, under the circumstances supposed, a new insurance will have to be effected when

the reversionary interest is put up for sale, and it may happen that the reversioner's life has become uninsurable; in which case the reversionary life interest will be perfectly unsaleable. Lastly, if the lender forecloses, he practically becomes the purchaser himself, and the same remarks apply.

From these considerations we conclude that, in order to make a loan in the ordinary way of mortgage on the security of a reversionary life interest, an insurance on the reversioner's life must be either effected or arranged for at the outset, of sufficient amount to render the reversionary life interest practically saleable, at such a price as to return the lender the amount of his advance with all arrears of interest and premiums and legal costs. Suppose, for example, that the life tenant is 60 and the reversioner 30, then a reversionary annuity of £1000 will be worth £4276, and the policy necessary to protect a purchaser fully will be £14,286 (see the tables appended to my paper "On the Valuation of Reversionary Life Interests" vol. xiv, pp. 432, 3). The annual premium on this policy will be £319. 13s.; and the very largest sum that could be lent on the security of the annuity would be £3500. In this case, then, the amount of the insurance exceeds four times that of the advance, even when we take the smallest margin consistent. with safety. Taking the interest at 5 per-cent, the annual sum which the borrower is required to pay is £495, or more than 14 per-cent on the advance. If the loan is to be allowed to accumulate at compound interest, of course the amount that could be advanced is greatly reduced. Thus, for example, if in the above case the interest and premiums are to accumulate at 5 per-cent compound interest for 5 years, the sum to be lent must be so fixed that the accumulated amount of the debt at the end of the five years shall be so much less than the then value of the reversionary annuity that there is no doubt, in the event of that annuity being sold, the lender will receive the full amount of the debt and The value of the reversionary annuity of £1000 and the policy of £14,286, at the end of the five years will be very nearly the same as that of a similar annuity on a life of 30 expectant on the death of 65, which the table referred to above gives as £5227. The accumulated amount of the debt at the end of five years should therefore not be more than about £4700; whence it follows that the original loan should not be more than £2229, so that the insurance is no less than 6.4 times the sum lent.

costs.

In all the cases we have considered, it is to be observed that the large policy is not required at the outset of the transaction, but is

only necessary for the purpose of guarding against the risk of the borrower's life becoming uninsurable. If the loan is to accumulate at compound interest, it appears at first sight as if an increasing insurance, which should always exceed the amount of the accumulations by a fixed sum, would meet the requirements of the case, as being sufficient to protect the lender and calling for the smallest possible payment from the borrower. But on closer examination this will, I believe, be found to be impracticable. In order to meet the borrower's convenience, the term of the accumulation would have to extend until the death of the life tenant; but unless the latter were of a very advanced age, probably no insurance company could be persuaded for any reasonable consideration to grant an insurance increasing yearly until his death. If the term of accumulation and the term for which the policy increases is to be a moderate term of years only, some new arrangement will have to be entered into at the expiration of that term; and whatever the nature of that arrangement may be, a further insurance would be required beyond the insurance already arranged for, and we are thus again met by the risk of the life having become uninsurable. If instead of effecting at once the full insurance that is necessary to protect fully the security, an increasing insurance is effected which increases by annual steps thro' a course of, say, 20 years, till it reaches the full amount, the cost to the borrower will be somewhat reduced. If, in this case, the premium on the increasing insurance is a uniform one, the saving to the borrower will, I believe, be comparatively unimportant. This, however, is a point which appears to require further investigation. On the other hand, insurance companies would be reluctant to grant such an increasing insurance at a premium increasing proportionately. The immediate cost to the borrower may be reduced by effecting the insurance on the ascending scale of premium or on the half-premium plan; but this involves a still greater increase of his ultimate payments, if the reversion does not fall in early.

The foregoing arguments appear to prove beyond all question that in general it will be much more satisfactory, both for borrower and lender, that the advance should be made by way of reversionary charge rather than by way of mortgage. Altho' the necessity of a large insurance is amply demonstrated, the terms of the mortgage appear so onerous to the borrower that the transaction is likely to bring a lender into disrepute. Generally speaking, the borrower is not in a position to pay the interest on the loan and the premiums on the heavy insurance necessary to secure the advance properly;

and the only way in which he can practically find the means to do so is by borrowing further sums from year to year as his payments grow due, by which means his indebtedness accumulates at a truly frightful rate. If, however, the advance is made by way of reversionary charge, he is called on for no payment until he comes into possession, and he knows exactly what payments he will then have to make out of the income he receives. On the other hand, the lender will receive nothing until the death of the life tenant. This circumstance renders the transaction almost always an unsuitable one for an individual lender, but forms no objection when the lender is a life insurance company; in fact, almost all life insurance companies, and more particularly the young and growing companies, have constantly sums coming into their coffers from premiums, interest, and repayment of loans, for which they are seeking investments; and it is only in the case of a very old company, in which the outgo largely exceeds the income, and the invested funds have to be realized in order to pay the claims, that transactions of this nature are quite unsuitable.

I shall, therefore, throughout the remainder of this paper, consider that the lender is a life insurance company; and I take this opportunity of repeating what I have said on a former occasion, that I think transactions of this nature are extremely well suited for the investment of the funds of well established and prosperous life insurance companies. Altho' an office making large advances by way of reversionary charge runs the risk in every case of sustaining a loss on the investment, through the life tenant and the reversioner jointly living beyond their expectation, yet it is fully compensated for this risk by the chance it has of making a profit by the early death of the life tenant in other similar transactions, and the increase of its insurance business caused by the large insurances they introduced.

Assuming, then, that the advance is made by way of reversionary charge, it is to be observed that the arrangement admits of various modifications, which I propose to consider briefly. It may firstly be stipulated that the borrower shall pay an annuity, to run from the day of the death of the life tenant until that of his own death; and in this case it is usual to name beforehand a sum for which the annuity can be redeemed, at the option of the borrower, at any time after it has become payable. It may, secondly, be stipulated that the borrower shall, upon coming into possession, pay a fixed sum to the office; and in this case it is necessary to add that, until he pays such sum, he shall pay interest