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assured, and during the continuance of this assuranee, grant, without further evidence of health, an increasing assurance on the life of the said assured, commencing at the sum of £1000 and increasing at the rate of £1000 a year up to £10,000, the premium on each £1000 of the said assurance being calculated according to the published rate of the said company for an age five years older than that of the said assured at the date of such application, provided that the said company shall not be bound to renew the said increasing assurance from year to year, unless the within written assurance is also continued in force.

For the protection of the offices granting this insurance, more especially considering its novel character, it was thought desirable to limit the option as far as is consistent with its being effectual for the purpose for which it is required, and for this reason it was stipulated that the right of exercising the option shall only continue during the lifetime of the tenant for life. On his death the borrower comes at once into possession of the income, and if it has not been necessary to sell his interest during the lifetime of the tenant for life, the original policy will be amply sufficient to secure the advance after the death of the tenant for life.

When a loan proposal is carried out in this way, it must not be overlooked that every year which passes without the option being exercised, increases the premium that would have to be paid on the new insurance, and consequently diminishes the value of the life interest supposed to be in possession. It is clear, therefore, that this could not be entered into as a permanent arrangement, except in cases where the margin is ample, and the life tenant is advanced in life.

It remains to consider on what terms such a policy might be practically granted by an office. It is clear that as an option is given to the holder of the policy, which option may possibly be exercised greatly to the detriment of the office, it is right that the office should receive a fair equivalent for this option. At present there seems no means of calculating the money value of this option with anything like scientific accuracy, but in the particular case to which I have already referred, it was considered sufficient to charge an additional 5s. per-cent per annum on the amount of the original policy, and on the above terms several first-class offices agreed to share the risk.

principles here adopted may without difficulty be extended to the case of advances made on contingent reversions, to which many of the preceding remarks apply with very little alteration.

The following account of the discussion which followed the reading of the paper is abridged from the Insurance Record.

Mr. A. H. BAILEY—The council having referred Mr. Sprague's paper to me, I at first thought I had an easy duty to perform-viz., to decide whether it was a suitable paper to be read in this room. I am sure the meeting will be unanimous in their opinion that it is very suitable for discussion by this Institute. But Mr. Sprague has informed me that the duty of referee extends beyond this—that he is expected also to

his opinion upon


submitted to him by the council, which adds considerably to the burden of the referee's duty. In turning the matter over in my mind, I have felt that there is a peculiar difficulty in discussing this subject here. Most of the gentlemen in this room are interested in these transactions on behalf of the lenders ; and if we could hear counsel for the borrowers, perhaps additional light would be thrown upon the subject. While I agree with Mr. Sprague that transactions of this nature are well suited for the investment of the funds of an assurance company, there are, notwithstanding, some difficulties in the way. One arises from the apparent, perhaps, rather than real severity of the terms on which these transactions are effected. It would be very difficult indeed to persuade any borrower that if, for every £1 he borrows, he has to pay, say, £4, he is not hardly used. The result is that an assurance company, rightly or wrongly, acquires a certain amount of repute for hard dealing. But there is a more serious difficulty, and that is how to deal with these transactions as a matter of book-keeping. If a considerable sum is advanced, a large amount has to be disbursed annually for life assurance premiums, and, as we all know, the value of reversions, looked at in the ordinary way, increases so slowly that it would hardly do not to credit the account with interest ; otherwise, if there are many of these transactions, the average rate of interest on the whole funds would apparently be reduced. I believe it is the practice of some offices to credit year by year 5 per-cent on their outlay. If they do that, the account in the ledger, in the words of the paper, "accumulates at a truly frightful rate," and the amount apparently advanced on these transactions is considerably in excess of the value by any ordinary estimate. This is an inconvenience for which I have never yet heard any practicable remedy suggested. Still, notwithstanding these difficulties, I am bound to say that I think the balance of advantage is in favour of the assurance companies, and that these are very desirable transactions for them. I cannot think they are equally desirable for the borrower.

The case which Mr. Sprague has instanced at the end of his paper, is an interesting, but an extremely rare case. As a rule, reversionary annuitants are in possession of but small immediate means, and it is very seldom indeed that there is any hope that the premiums and interest can be kept down by them. In former times attempts were made to carry these transactions out by way of mortgage, but they almost invariably broke down and proved unsatisfactory. Sometimes efforts were made to give sureties for the premiums and interest, but solvent sureties are not easily found if the borrower is not in a position to keep up the payments himself; and it


may be laid down as a cardinal rule in all investments, that it is unwise for an assurance company to enter into transactions with a borrower which there is no reasonable prospect of the borrower himself being able to carry out. I, like many others, have turned over in my mind whether any way could be devised by which loans could be granted on securities of this description on apparently less onerous terms to the borrower. There are two classes of reversionary interests, -one in which the borrower is tenant in tail ; the other in which he is tenant for life in reversion. In many of these cases he is tenant in tail;—because, as is well known, by the law of this country land can be settled only for twenty-one years beyond the life of any person in existence at the period of settlement;—and if he be tenant in tail, although he cannot grant a charge on the fee simple in reversion, if he succeeds to the property he then will be in a position to disentail; and before he succeeds, he can covenant to disentail. In this case it appears to me that the grant of a reversionary charge with an assurance effected on the life of the borrower against that of the tenant for life and for a sho term longer, would fairly well meet the

In the other case, where the borrower is only tenant for life, it has occurred to me that some such arrangement as this might be made. The advance might be made by way of reversionary charge, computed, not by the formula

1-(P+d)(1+ary), which Mr. Jellicoe first suggested, and which is one I have never used for myself, for the reason that in all these reversionary transactions, as far as I know, the lenders never do purchase these annuities, —but by the old-fashioned one

Ary-Alky, where Axy is the value of the reversion at the death of the joint lives at the current rate of interest, and A'ły the single premium for the contingent assurance; and then the borrower should endeavour to induce the assurance companies--(and I really see no reason why they should object)—to grant an assurance on the life of x against y by a single premium, and undertake to grant a whole term assurance on the life of x when y dies, without reference to the then state of health of x. Of course a higher premium than the ordinary one should be charged, but I se

no reason why they should not enter into a transaction o that sort.

Before I sit down, perhaps I may be permitted to express my opinion of the value of papers of this kind to students and younger members of the Institute. There is no difficulty in learning from any of the textbooks the theoretical investigations required to determine the value of reversionary life interests, but to deal with these interests in practice is matter of considerable difficulty. I have for one been a little surprised, as an examiner of the Institute, at finding that, whereas the candidates come up in large numbers for the first year's examination, and in respectable numbers for the second year's, they come up in very small numbers indeed for the third year's examination, which, it appears

to is by no means the most difficult of the three. The only reason I can find for this state of things is that the information re


quired for the third year's examination, which is very necessary

for the practice of an actuary, is not to be acquired by books; and therefore I conceive that the opportunity which Mr. Sprague has given us to-night, as well as on previous occasions, of getting at some of the knowledge which floats about and is current in assurance offices, is of great value to the junior as well as the senior members of the Institute.

Mr. MACFADYEN—The first part of the paper shows the onerous nature of the terms requisite to protect the mortgagee of a reversionary annuity,—the second indicates various modes in which the purchase of such annuities can be arranged,—and the third treats of the manner in which a borrower, if still obstinate enough to mortgage rather than to sell, may have the terms made, if not easy, at least as easy as they can well be. Examining, as the other parts are connected, the second section first, I find that Mr. Sprague, in commenting on the final disposal of the policies of assurance, though willing to hand them over to the seller on the payment of the charge, considers the purchaser should retain the bonuses. Looking at this in connection with the statement that profit policies for less amount than will be ultimately required shor'd be taken out, it seems to me scarcely fair to the seller if he has had deducted by the purchaser in the price given these profit premiums, to retain from him on settlement that part of the bonus equivalent to the difference between the full amount required at the non-profit rate and the sum actually assured. In short, whether it be bonus or otherwise, the seller, on redemption, is entitled to an insurance policy equal in amount to that which the premiums he paid would purchase by the non-profit rates of the office. If, beyond this, the buyer chooses to enter into a speculation by paying an additional premium for profits, of course, as the seller has not been charged this addition, he has no claim to the results. With reference to the first part of the paper, since it is requisite that the full ultimate assurance amount be secured from the first, it is obvious that the borrower is called on to pay a sum calculated on the assumption that he omits to pay premiums and interest from the commencement; and this, even though he make no such default whatever, or at most, for only part of the time. So it is clearly the borrower's interest to be what he is credited with being, and sell his reversion rather than retain it at such a cost. On the other hand, as is proved in the paper, the lender can demand no less. In fact, there is an à priori probability in favour of default and uninsurableness going together, as the one may be a direct consequence of the other. Since then, as in the credit system in ordinary business, the borrower must pay a higher price, however punctual he may be in his payments, simply because he might have been a defaulter, all that can be done for him is to make this extra payment as light as possible. Mr. Sprague considers the objections to doing this by an ordinary increasing assurance insuperable, but thinks it might be done by an optional increasing assurance. Taking the actual instance given in the paper, and comparing an insurance of £20,000 increasing to £40,000 with an insurance of £20,000 with an option to increase to £40,000, of the two risks, since there are no means of valuing this option, the former seems to me much the preferable to the society. No doubt the latter, if it can be obtained at a less rate, will be cheaper for the borrower. On the other hand, it is clear that in the former case the society gives value for the premiums received in the shape of a life insurance, and on the settlement of the transaction this assurance will become the property of the borrower. Of course, I am here assuming that the premiums and interest are paid regularly by the borrower, as if not, he has no grievance in the amount he has to pay. He may not want this large assurance any more than the gentleman, borrowing from certain money-lenders, wants the pictures given him as part of his loan, but at least, unlike the pictures, it is not sold him at a fancy. price, but its cost is the result of mathematical calculation. In the latter case, unless by instinct the right value of the option has been hit upon, somebody is aggrieved. Either the office has not sufficient remuneration for the risk undertaken, or the borrower has his pictures sold him at a fancy price. Indeed, if the option principle is to be introduced at all, it seems to me more thorough, if a dealer in such transactions is making the advance, to directly assume that a certain number of borrowers will become defaulters and uninsurable, and calculate accordingly. It may be urged that there are no data for fixing what this number will be. Very true, but there are just as many as for fixing the premium for an optional increasing assurance.

Mr. R. P. HARDY–Mr. Sprague, I believe, after the lengthened study he has given to this question, has been unable to suggest a method more generally applicable than that which is ordinarily adopted. In some cases a low rate of premium during the joint lives of the successive tenants can be charged; and in others, no doubt, an office would be disposed to grant an increasing assurance for a limited term. The particular case which Mr. Sprague instances must be the one case in a hundred. Borrowers always object to the advance being made by way of reversionary charge, and solicitors are very loth to take upon themselves the responsibility of advising a client to enter on a transaction which may ultimately prove detrimental to his interest. They all, therefore, naturally endeavour to make

you entertain the transaction by way of accumulation. I have seen some such cases so carried out, and I think they will be found to be safely based, but they are very difficult indeed to manage, and the personal covenant of the borrower must be of some value. [Mr. BAILEY, “That is very rare.

e."] Mr. Bailey thinks there is a difficulty in representing these transactions in the books of account, so as not to show a falling off in the interest revenue. I do not see that that ought to be the case. If you have a fair number of transactions of about equal amount, it is probable that a sufficient number will fall in in every quinquennium to justify the office allowing, say, 5 per-cent every year on the account. That is the case with offices dealing in moderate-sized reversions, and they will be found to fall in with some regularity; and if you look at the profit made, you will find it comes as nearly as possible to the rate of interest at which you have valued. Mr. Bailey says further, that most of these borrowers are tenants in tail, but I should say that eight out of every ten borrowers are tenants for life. The conveyancer, in framing a settlement, takes good care to give a tenant in tail no allowance out of the estate, so that when

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