the influence of expenses and selection on reserves for recently-effected policies [with discussion]

Institute and Faculty of Actuaries

The Influence of Expenses and Selection on Reserves for recently-effected Policies [withDISCUSSION]Author(s): James BuchananSource: Transactions of the Faculty of Actuaries, Vol. 2, No. 18 (1903-1905), pp. 195-206Published by: Cambridge University Press on behalf of the Institute and Faculty of ActuariesStable URL: http://www.jstor.org/stable/41217540 .

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The Influence of Expenses and Selection 195

The Influence of Expenses and Selection on Reserves for recently-effected Policies. By James Buchanan, D.Sc., F.F.A., F.I.A., of the Scottish Widows' Fund Life Assurance Society.

[Read before the Faculty, 28 November 1904.]

IN a paper read before the Actuarial Society of Edinburgh more than thirty years ago, the late Mr. D. Deuchar discussed the question of expenses and its relation to new business, and advocated the subdivision between new and renewal premiums of the items Premiums received, Expenses, and Commission in the revenue account. From a table compiled by him, relating to fifteen Scottish offices, it appeared that commission and expenses amounted to 13¿ per cent of the premium income ; or that, if 1' per cent be allowed for renewal expenses, initial expenditure absorbed about 80 per cent of the (estimated) new premiums. The question subsequently received much attention from Dr. Sprague, who stated (/. /. A., xix, 313) that about *l' per cent of renewal premiums was "generally amply sufficient for the purpose of administering the existing business of a company that pays commission and employs agencies ; and that any expenditure beyond this must be considered as incurred exclusively on account of the new business " ; while more recently (Transactions of the First International Congress of Actuaries, p. 190) he has expressed the opinion that "the average expenditure of prosperous and well-managed offices may be taken as 80 per cent of the new premiums and 7 ' per cent of the renewal premiums'".

With the object of comparing these figures with the actual expenses of a representative group of twenty-five British offices transacting ordinary life business, particulars of the new business for each year of the last completed valuation period were extracted from two or three well-known insurance publications ; and from the consolidated revenue accounts were taken the amounts of premiums received net of reassurance premiums and of annuity considerations, and the amounts absorbed in commission and expenses ; and the average of these figures for each year of the valuation period was taken. The analysis was limited to offices which state their new business net of reassurances, which pay commission, and which charge the whole of their life expenses to the life assurance account. For this group of offices we have the following figures : -



196 The Influence of Expenses and Selection

Average Annual New Business. Average Annual Premium Income and Expenses.

a.'!S¥ sag ;<g xs~ -- 27,945 £15,317,940 £648,678 £7,308,600 £915,513 £339,375 £665,938

Of these twenty-five offices, five keep a separate annuity account, and this enables us to estimate what proportion of the total expenses should be set against the working of the annuity business. In these five offices, all of which make quinquennial valuations, the total annuity considerations received in the quinquennium amounted to £2,382,615; the amount paid as commission was £19,039,. and the amount absorbed in expenses £40,492. Together the last two items amount to £59,531, which is almost exactly 2J per cent of the annuity considerations. If we make a similar allowance for the annuity expenses of the whole group, the balance amounts to 13*4 per cent of the premium income; or, allowing 7¿ per cent of renewal premiums for the working of the existing business, the initial expenditure amounts to 74*4 per cent of the new premiums - that is, nearly in the ratio of ten to one.

It is evident, however, that a fair apportionment of expenses between new and renewal premiums can not be made unless the net figures of the new premium income are used, and a subdivision of that income is made between single and annual premiums; but the published figures do not enable us to say what portion consists of single payments. In the paper already referred to, Mr. Deuchar advocated the subdivision in the revenue account of the premiums received into new annual and single premiums, and renewal premiums ; but few offices have adopted the suggestion, and where no subdivision is made in the annual reports we are not justified in assuming in every case that no single payments have been received. The high average premium per £100 assured in the above statement of new business, suggests that the proportion is considerable, and the published figures of several offices which do give this information showed that this is the case, so that the figures brought out above for new and renewal expenses would be correspondingly modified; but they seem to show that Dr. Sprague's estimate quoted above is very near the truth.

The effect of this incidence of expenses is to throw part of the cost of new business on the accruing profits of older policies ; and the pressure is greatest in young offices, where the burden is spread over a smaller total premium income. In view of this, it has been suggested that some allowance for initial expenses-



on Reserves for recently-effected Policies 197

should be made in office valuations ; but the present object is to examine whether, in the case of an office making ordinary pure- premium reserves, the cost of new business is not largely balanced by mortality profit accruing during the early years following selection. This question was discussed by Mr. Sorley in a paper read before the Actuarial Society in* 1878 (/. /. A., xxi, 192), and he arrived at the conclusion that, "if a company acquire new business at a moderate cost, there is nothing unfair to any section of the policyholders in a pure valuation ", but that it may rather be regarded as " a compromise or via media, where selection, expenses, occupation, residence, and other influences - some affect- ing the result in one way and some in another - are all alike ignored, and whose defence takes its stand on the broad principle of averages, which lies at the foundation of all actuarial questions ". The rates of expenditure assumed in that paper were only 50 per cent for new premiums and 7 per cent for renewals ; and, in view of all that has happened since these words were written, doubts have been expressed of their validity at the present time. It may therefore be of interest to examine the question afresh in the light of the new British Life Offices Experience, In what follows it is necessary to assume some scale of office premiums, and the following were adopted, these being the average premiums charged for whole-of-life participating policies by the group of offices whose new business has been analysed : -

Table 1.

Age at Office Premium I Age at Office Premium Entry. percent. Entry. percent.

20 £1 19 10 45 £3 16 1 25 2 4 0 50 4 10 9 30 2 9 6 55 5 11 3 35 2 16 4 60 6 18 6 40 3 5 0 65 8 15 11

A comparison of the rates of mortality shown by the new select tables and by aggregate tables used in office valuations, shows that there is a great " saving of claims " during the early years following selection. The general effect of this light mortality on the fortunes of a life office may be well seen by comparing the expected claims in Mr. King's Model Office, according to various tables of mortality. In finding the expected claims, it is usual to make corrections for new entrants and withdrawals; but in the model office that for new entrants is not required, as all policies are supposed to be effected at the beginning of the year, and if

VOL. II. T



198 The Influence of Expenses and Selection

we omit that for withdrawals we practically assume them to take place at the end of the year. On these assumptions, the expected claims during each of the first ten years are as follows :-

Table 2.

Expected Claims.

. Year. - ~ - - '-

OM OM<5) HM OM OtNMl

1 1,106-4 1,2628 1,290*2 567'4 841*5 2 2,236-9 2,534-5 2,5926* 1,3948 1,9121 3 3,337'6 3,756-3 3,8467 2,2893 3,088*6 4 4,429*3 4,955-6 5,0781 3,2289 4,3362 5 5,521*5 6,141-3 6,296*3 4,2097 5,615'5 6 6,619*8 7,323*5 7,511*5 5,232*8 6,896*8 7 7,730*3 8,508-3 8,729*8 6,300*4 8,180'2 8 8,855-4 9,7002 9,955'4 7,4129 9,468*5 9 9,976*8 10,881*6 11,170*6 8,549*7 10,742*7

io 11,118*8 12,077*0 12,400*5 9,732*5 12,031*9

Confining our attention for the present to whole-of-life participating assurances, it is reasonable to assume that for this class the OIM] claims are the true expected claims, and these show a very great saving as compared with those based on aggregate tables. It is true that a " claim saved " is not avoided, but only deferred ; but the office instead of paying the claim has to put aside a reserve, which with other reserves, together with the corresponding net premiums, will provide the sums assured under policies which become claims according to the valuation table, and increased reserves for policies which remain in force. To put it differently, the loss to an office by the occurrence of a claim is not the sum assured, but the difference between that sum and the value held in reserve against it; and the gain resulting from favourable mortality is represented by the amount by which that loss - or " death-strain " - falls short of its expected value. The following table illustrates the financial effect to the office of experiencing O[M1 mortality when its reserves have been made on the basis of an aggregate table : -



on Reserves for recently-effected Policies 199

Table 3.

Expected Death-Strain Reserves

in office ^S^^^fA * basing Reserves on * bagin« Reserves on

Year.

OM3%. OM(«3%. HM3% OM3%. OM(5)3%. HM

1 1,085-4 1,240-4 1,266*9 556 8 557*0 556'9 2 2,1727 2,466-4 2,5221 1,353*5 1,3549 1,354*3 3 3,209-4 3,621-4 3,706 9 2,1980 2,200*8 2,2000 4 4,2159 4,732-1 4,846 6 3,066 '7 3,071*4 3,0700 5 5,201-0 5.806-9 5,950-1 3,953*8 3,960*7 3,958*5 6 6,169*3 6,855-0 7,026-4 4,858*5 4,868*0 4,864*6 7 7,125-6 7,881-5 8,081*1 5,780*7 5,793*4 5,788*6 8 8,071*4 8,890*3 9,117*1 6,719*3 6,735*3 6,728*6 o 8,9919 9,866*8 10,120'l 7,655*5 7,675 2 7,666*7

10 9,906*3 10,830-6 11, 1103 8,606-1 8,6293 8,618*7

If, now, we assume that an office spends 75 per cent of new premiums and TJ per cent of renewals, we may fairly set this gain from favourable mortality against the amount by which the actual expenditure exceeds a low equalised expenditure, such as 10 per cent of the premium income; and the comparative figures are shown alongside the loading of the net premiums in the following table : -

Table 4.

LoadinrfcSmittms received. ää^ä S£ .. pr(mi1-11TTia Premiums

received. and basing 6 Reserves on and 7*% of .. £ pr(mi1-11TTia Premiums 6

Renewal ¿J •* Received. Premiums •*

over 10% of

0*3%. O««>8% HM3%. OM3%. OM(S)3%. HM 3%. S^T

1 3,908-5 926*1 8630 817*1 5286 683*4 710*0 2,540*5 2 7,702*0 1,824*0 1,699*9 1,609*7 819*2 1,111*5 1,167*8 2,445*7 3 11,2083 2,652-6 2,472*5 2,341*6 1,011-4 l,420'6 1,506*9 2,358*1 4 14,5103 3,4324 3,199*7 3,0305 1,149*2 1,660*7 1,776'6 2,275 5 5 17,6410 4,171*7 3,889*6 3,683*8 1,2472 1,846*2 1,991*6 2,197 2 6 20,626*5 4,876*7 4,547*4 4,306*7 1,310*8 1,987*0 2,161*8 2,122*7 7 23,4872 5,552-7 5,1780 4,904*1 1,344-9 2,0881 2,292*5 2,051-1 8 26,233-7 6,203*0 5,784*3 5,478*7 1,3521 2,1550 2,388*5 1,982*5 o 28,832*2 6,819*2 6,359*2 6,023*4 1,336*4 2,191*6 2,453*4 1,917*5

IO 31,337*1 7,414*2 6,914*3 6,548*9 1,300*2 2,201*3 2,491*6 1,854*8

It will be seen that in an office basing its reserves on the HM table with 3 per cent interest and experiencing O[M] mortality, the mortality profit just balances the excess expenditure after six



2OO The Influence of Expenses and Selection

years ; while in one valuing by OM(5 3 per cent the amount by which it falls short is rather more than met by the additional margin of loading. In the case of an office using the OM table in valuations, mortality profit is very much reduced, and after a period actually decreases. This is due to the fact that at the younger ages the continual influx of new entrants is more than sufficient to counter- act the wearing out of the benefit of selection, so that after the first year or two the expected claims by the aggregate table are actually less than by the select table. But while profit from mortality is diminished, the loading is increased. Thus it will be seen from the figures of Table 4 that the loading of the OM pure premiums exceeds the HM loading by about 2| per cent of the premiums received ; and if in the last column we take the excess above 12J instead of 10 per cent of the premiums received, practically the same margin of loading is left intact, and the balance is established about the seventh year, so that the combined effect of loading and mortality profit is much the same as with the other tables.

From the figures for the expected claims by the O[NM] table (see Table 2), it is evident that in the case of uon-participating policies these results will be considerably modified, and a longer time must elapse before the office can write off its initial expenses. But if the class taken as a whole can, after providing for its own claims and expenses, show a margin, there is no injustice in throwing part of the cost of new business on the older policies, for no bonus rights of these policies have to be considered.

Much of the favourable mortality experience of life offices is without doubt due to selection, and, in view of its importance as an offset to the cost of new business, the question suggests itself whether it would not be instructive to analyse that mortality in years of duration during the early years following selection. A comparison of the actual with the expected claims made in this way would throw much light on the extent to which new business was self-supporting.

DISCUSSION.

Mr. John Nicoll. - The subject of expenses is a very important one- one might say it is of vital importance to life offices. There is no doubt, too, that the conclusions arrived at on the subject in this hall and at the meetings of the Institute of Actuaries have at least a tendency to exercise a beneficial and restraining effect upon life office expenditure. We are all familiar with the conclusion Dr. Buchanan has quoted from Dr. Sprague, that 80 per cent of the first year's premiums and 7j per cent of renewals may be looked upon as a fair average rate in well-managed offices, and most of us have come to regard that rate as fairly correct. The balance of 20 per



on Reserves for recently -effected Policies 201

cent of the first premium would just about provide for the risk of the first year, and in that case the new business, if discontinued, causes at least no loss to the office ; and that is so far satisfactory. Dr. Buchanan has arrived at a slightly dilferent conclusion from Dr. Sprague, but his procedure does not seem to me to be so likely to lead to trustworthy results. His figures are the average of the years of the valuation period ; but would it not have been better to take the central year of the period? We should then have had actual figures. Then the commission paid on annuities seems very small, being less than one per cent on the purchase money. Of course a certain amount of business is obtained without commission, but that is generally small. Then the expenses, exclusive of commission, seem to be very large. We do not know how the offices arrive at the expenses applicable to the annuity business. Probably in most cases they will simply charge to that head as much as the annuity branch will bear. It would therefore seem that the practice of one office, or of five offices together, cannot form a guide to the expenditure of offices generally in connection with annuities. I presume that all the twenty-five offices dealt with do annuity business? In connection with Dr. Buchanan's expense ratios, I find that Mr. Monilaws in his book Companion to Surplus Funds gives the rates of commission and expenses for the years 1882 and 1904, without excluding the offices which pay no commission, and without making any allowance for the commission on annuities. Dr. Buchanan has allowed for commission on annuities, and taken out of the way offices which allow very small commissions. Mr. Monilaws has made no adjustment whatever. The expense ratio of eighty- two offices in 1904 is given by Mr. Monilaws as 13*66 per cent of the premium income, being commission 5*18 per cent and other expenses 8*48 per cent. In 1882 the ratio for ninety-nine offices was 13*49 per cent- 4*22 per cent commission and 9*27 per cent expenses. It would seem from this too that there has been an appreciable increase in the expense ratio since 1882. In making his comparison with the expected claims, I think Dr. Buchanan does well to call attention to the fact that a claim saved is not a claim avoided. If lighter mortality is experienced at one period, that is just a reason for anticipating later on a heavier mortality which should be provided for. This seems to me a strong argument against making special allowance for initial expenditure. A certain course of mortality and a certain rate of interest have to be assumed in making reserves, and a certain rate of bonus is desired to be maintained ; and these ought to be provided for as nearly as possible, and the rate of expenditure ought to be regulated by what remains thereafter. The opposite course ought not to be pursued, of providing for the reserves after the expenditure has been arranged for. One would have been glad if Dr. Buchanan had carried his tables a little further than ten years- when the effect of selection is just supposed to be exhausted. It is to be noticed, too, that he assumes 75 per cent of new premiums as expended, but Dr. Sprague's estimate of 80 per cent is generally admitted to be more correct, and if so, the time required to clear off initial expenditure will be considerably prolonged. Table 4 is very interesting. It is most important to notice from it that in an office valuing by the OM table and experiencing O[M] mortality (and these circumstances are likely to apply hereafter to perhaps the majority of offices), the profit from mortality is very much reduced, and the balance of profit as compared with the valuation by the HM table has to be met out of the increased loading on the OM pure premiums. It is noticeable in connection with this point, that certain offices which have lately changed the basis of their valuation from HM to OM call special attention to the fact that, whereas the loading on their premiums at a former valuation was only say 18 per cent all over, it is now 20 per cent. Dr. Buchanan's



2O2 The Influence of Expenses and Selection

table goes to show that such a statement requires at least to be qualified in some way, if it is to convey quite a correct impression to those who read it.

Mr. J. Chatham.- I think Dr. Buchanan is to be congratulated upon his appearance as the author of the two papers submitted tonight. He has taken a great deal of trouble and care in this paper, and as an instance I may mention the analysis of the expenditure of the twenty-five offices which he has made. He says the analysis was limited to offices which state their new business net of reassurances, which pay commission, and which charge the whole of their life expenses to the life assurance account. Now, even after all this trouble has been taken, we must not regard the result as showing the real rate of expenditure. There are ways - I will not say of concealing - but of reducing the apparent rate of expenditure of offices. For instance, a company with branches throughout the country possessing buildings partly let off to other tenants, may credit its invest- ments with the rents received from them for the property, and not charge to the expenses account any rent for the portion it occupies itself. I agree with Mr. Nicoli that the apparently high expense charged against annuity business, is an instance of how some offices may reduce the expenditure of the life assurance account. Dr. Buchanan refers to the high average premium on the new business as likely to be caused by the single payments. I do not think that is the reason. I think the high average premium is really due to the large amount of endowment-assurance business now being transacted. Formerly, the average premium used to be about three per cent ; but now it is generally regarded as four per cent or slightly over. I think if Dr. Buchanan investigates the matter further, he will find that this is really due to endowment assurances. He also refers to Dr. Sprague's estimate of 80 per cent of new premiums as being spent, and says it is very near the truth. Now, I should like to point out that the expenditure of life offices has increased very much since Dr. Sprague made his estimate, but that it is hidden by the fact to which I have referred, namely, the larger amount of the endowment-assurance business. The ratio may still be the same, but the new premiums on the sums assured are larger. The initial expenditure is pretty much the same whether it is a whole-life policy or a limited-payment policy or an endowment-assurance policy. The initial commission, the over-riding commission, the policy stamp, etc., are all calculated on the sum assured, so that the expense is to a great extent regulated by the sum assured, irrespective of class. As the new premiums per cent of the sums assured are larger, and the ratio of expenses to them remains the same, it is obvious that the expenditure must have increased very considerably without the accounts showing it. Dr. Buchanan has arranged his tables in a different form from that adopted by Mr. Sorley. I have no doubt that he has considered it very carefully and thinks it the better way ; but I had some difficulty in following his table. After all, Dr. Buchanan deals only with whole-life policies, but as endowment assurances now form a very large portion of the business transacted - 50 to 75 per cent and in some cases even 90 per cent - it is very desirable to get results for such policies. In a paper I submitted about two years ago to the Faculty, I referred to the high reserve required for whole-life policies of five years' duration according to the select table I used, when compared with the value according to an aggregate table, and I added that when an office employed an aggregate table in its valuation a considerable allowance is thereby made for the" heavy initial expenditure incurred for new business. I dealt not only with whole-life policies, but also with endowment assurances. I said regarding the latter, that the policy- values according to the HM table approximate more closely to those of the select



on Reserves far recently-effected Policies 203 than in the case of whole-life policies, and that the values according to the OM table approximate still more closely to those of the select. Let me give a few figures. I will read the percentages in the two classes by which the select value is greater than the aggregate : -

Duration 5 years. Whole Life.

Age at entry. Percentage. 32 12*2 37 123 42 13-5

20 Years' Endowment Assce. Age at entry. Percentage.

30 3*3 35 4*4 40 4*6

There is thus a great difference when we come to endowment assurances ; and I think that it would be very desirable if Dr. Buchanan's paper were extended so as to include that class. If he thinks of doing it, I shall be only too glad to furnish him with all the particulars of the investigation I made. This is not said as in any way detracting from the value of his paper, for we are greatly indebted to him for this interesting paper and for the valuable results obtained.

Mr. A. D. Lindsat Turnbull. - I have recently, in preparing a paper to be read to the Insurance Society of Edinburgh, brought out several rates connected with expenses and the relative size of premiums. Mr. Chatham said that the higher average premium nowadays is caused by the large number of endowment assurances issued, rather than by single premiums. I came to a similar conclusion, and I find that fifty-two English and Irish offices have an average premium of 4*466 per cent, and that the average premium of Scottish offices is 4*297 per cent. Mr. Deuchar, in 1874, took the average premium at 3 per cent. Of the different classes of offices some get higher premiums than others. One class has an average premium of 5*201 per cent, while the lowest average premium for any class is 4*053 per cent. With regard to expenses, I may mention that I got information from many managers which is not usually published, so that many of the figures I was able to bring out are of special interest. Dr. Buchanan's rates of expenditure, which I understand he assumes at 75 per cent on the first premium and 7¿ per cent on renewals, are hardly in accordance with present business conditions. In my paper I have treated the division of expenses in a somewhat different manner. I charged a rate on the funds for the management of the funds, collection of interest, etc., and another rate on the renewal premiums for their collection, an allowance being made for the initial expense of annuities. I think 7£ per cent on renewals is too much for large offices ; particularly as now seldom more than 2 J per cent is paid in renewal commission, as against the 5 per cent of former days ; and, besides, the large number of endowment assurances enables one to reduce the average cost per cent of collecting premiums. After making such allowances for working existing business, I find that the total expenditure of British offices is 13*1 per cent, and the cost of new business is 3*6 per «£100 assured, or 80*2 of the average first premium. The total cost of managing existing business, I make 6*2 per cent of the renewal premiums. The expenses of American offices are higher. My results show that 75 per cent is not enough to allow for the cost of new premiums obtained by ordinary life offices. More than 75 per cent of the first premium is spent in securing new business ; and so it is doubtful whether the " profit from mortality", or rather the apparent profit from suspended mortality, would in even seven years meet the extra ■expenditure on new policies written by the average office. I do not think



2O4 The Influence of Expenses and Selection

it would, especially in those offices which press for business. Some are so extravagant that one wonders how they make both ends meet at all. I think there is a tendency to look too favourably on liberal expenditure. This item of expenses is becoming serious. I fear the tone of Dr. Buchanan's paper will be apt to encourage expenditure, as some extravagant offices may point out that he, an eminent actuary, has shown that the additional cost of new business (which with them will be large) is met by " profit from mortality".

Mr. A. Hewat. - We are much obliged to Dr. Buchanan for having brought before us such an interesting subject, and having presented it in such a practical form. It should be an object lesson to our students and younger members, letting them see something of the relation of the three fundamental elements in the finance of life assurance - interest, mortality, and loading - to one another. Even our students know that a change in the base-rate of interest, from a higher to a lower, has the effect of decreas- ing the loading ; and Dr. Buchanan's figures let us see how a change in the base-rate of mortality- say from HM to OM - has the effect of increasing the loading. From this it is evident that changes may be so made at an office valuation as to leave the fundamental result practically unaffected by those changes. I am rather sorry to see that a change from an HM to the new OM basis indicates a larger loading or margin for expenses, at the sacrifice of mortality profit; as that may afford some temptation to increased expenditure, when the desire among most of us is rather to see an effort being made in a contrary direction.

Mr. D. Paulin. - I should also like to express to Dr. Buchanan my sense of obligation for his excellent and interesting papers. The only criticism that occurs is in the selection of the subject : the rationale of pitting a saving from selection against a high outlay in getting new business is not clear. It would be as reasonable to set the profits from lapses and surrenders, or the profit from interest, against the initial outlay in obtaining new business. As a Faculty we must be careful not to give weak and fallible men like myself who manage companies any excuse for extravagant outlays in extending the business. Thirty years ago the average premium on business was about 3 per cent. It now slightly exceeds 4 per cent ; and this rise in the rate I attribute to the growing popularity of limited-payment and endowment-assurance policies. Men nowadays do not care to burden their old age with the payment of premiums. This change, however, ought to produce a somewhat lower ratio of expense than Dr. Sprague and Mr. Deuchar indicated when they wrote on the subject many years ago. I am inclined to think Mr. Sorley's figures are nearer the mark. My own view, however, is that 66 per cent on new premiums and 7£ per cent on renewals, cannot be termed extravagant.

Mr. J. M. Warden. - Mr. TurnbulPs remarks as to the allocation of expenses between old and new business, and particularly his suggestion that the management of the funds should be charged for in some way, remind me of a precisely similar plan which, for certain purposes, I have made use of for the last dozen years in assessing expenses. More recently I have seen the same principle advocated by an American actuary. It is, I think, proper to consider that a portion of the expenses is incurred for the management of the existing business, with the funds belonging to it, and their re-investment from time to time, and the collection of interest income. Further, an office may, in certain classes of assurance, have a large number of fully paid-up policies in force, but under the ordinary methods of assessing expenses, nothing would be charged against these in respect of such expenses as I have mentioned; and erroneous conclusions might con- sequently be drawn as to the amount of profit derived from such classes



on Reserves for recently-effected Policies 205 of policies. Another case in which this question arises, is where the profits are distributed according to the " contribution plan ". For any such purpose as those indicated, it is, of course, necessary to divide the total expenses of an onice into those relating to old business and those applicable to the new business. The results obtained are very much in accordance with the figures quoted by Mr. Turnbull, but point to a rather lower charge for the expense of collecting renewal premiums - say 3 or 4 per cent at the most. The remainder of the expenses applicable to the old business would be fairly met by charging against the interest received about 5s. to 7s. 6d. per cent per annum on the funds, making the net rate of improvement of the funds less by that figure. The new business expenses are practically at a uniform rate on the new sums assured : it is easy to allow for the few classes of policies in which they can be better charged on the premium. With a suitable division of the expenses as suggested, I believe the percentage of new business expenses, calculated on the sum assured, will be found at the present time to be very close to Mr. Turnbull's figure. Of course this method would be used for internal office purposes only, as the public could not be expected to appreciate the sub-division proposed.

The President (Mr. N. B. Gunn). - In bringing the discussion to a close, I desire, in your name, to thank Dr. Buchanan for the two valuable papers he has given us. Combining as they do the practical and theoretical sides of life assurance, they form a contribution of considerable importance to our Transactions; and, as Mr. Hewat has said, the papers have the additional value that they are object lessons to other members, who, I hope, will follow Dr. Buchanan's example. I cannot say that I agree with Mr. Paulin in his idea that the union of the two elements of expenses and selection is objectionable. If each is treated by itself, you cannot so- readily do justice to the problem ; and in Mr. Sorley's paper I see he lays, emphasis on that point. I agree with Mr. Warden and Mr. Turnbull that strict exactness would require the expenses to be analysed by a three-fold test, taking into account funds, renewal premiums, and new sums assured. But whatever actuaries may say, the method that appeals to the public,, and the one by which assurance offices will be judged, is the rough-and- ready method to be found in vade mecums and similar publications - namely, the percentage to premiums paid. What I am sure we would all like, is to bring down the expense-rate as much as possible. It may be a counsel of perfection, but it is much to be desired that the offices would unite in reducing expenses. We have tried in the past to effect this, and perhaps we may succeed in time. I wish to convey the thanks of the meeting to Dr. Buchanan for his papers, before we close what has been an interesting discussion.

Dr. Buchanan, after thanking the Faculty for their reception of his papers, and the gentlemen who had spoken for their criticisms, said - Mr. Nicoli has referred to the amount paid on annuity business in commission and expenses, which appeared to him to be small. The actual figures were taken from the accounts of five offices doing a large annuity business, and it is worth noticing that the total annuity considerations, received by these five offices amount to about one-half of the total of the twenty-five offices ; so that, although the expenses of the rest of the offices, might be considerably higher, that would not have much effect on the- balance which is left for the assurance business. Mr. Chatham has. referred to my statement that the high average premium suggests that the proportion of single premiums is considerable. There is no doubt that a- large endowment-assurance business is now transacted, increasing the average premium, but this alone does not account for the high average. In fact, I may say that in five offices of this group the single premiums

VOL. IT. TJ



2o6 The Influence of Expenses and Selection

amounted to £ 133,181 out of a total new premium income of ¿£427,602. The single payments included in the total of the premiums of all the offices must have been considerable, though no doubt much less than this thirty per cent. Then, as regards the average premium for endowment assurances and their influence on the average premium of the offices, I made an analysis of the business in force in this group of offices, from the particulars given in the sixth schedule of the Board of Trade returns. The total original sums assured in this group amounted to about «£225,000,000. About four-fifths of this were with profits, and about two-thirds of this proportion were on the whole-life scale ; rather less than a quarter were endowment assurances. The average premium was, for whole-life policies 3 0 per cent ; for endowment assurances 4*5 per cent. The average premium for the whole of the participating business was 3*3 per cent ; for the whole of the business in force 3*2 per cent. Now, although endowment assurances amounted to one-quarter of the total participating business, and the premiums to about one-third of the corresponding premium income, it only had the effect of raising the average premium to 3*3 per cent. This seems to suggest that the average rate per cent for assurances taken out at annual premiums is, for this group of offices, something under 4 per cent. How- ever, it seems to me that in considering expenses we should look not so much to the average premium per cent, as to the average premium per policy. In this group the average whole-life policy was .£553, and the average endowment-assurance policy «£315. When we come to deal with the average premium per policy, we get 1 6*6 and 1 4*2 per policy respectively. Initial expenses seem to fall under two heads : (1) expenses on sum assured, such as commis sion and policy stamp ; and (2) expenses, such as medical fee, practically the same whatever the amount of the policy. Expenses of the first kind absorb a larger proportion of the whole-life premium ; but expenses of the second kind form a larger percentage of the endowment-assurance premium ; and I think it probable that the proportion which the cost of new business bears to the average premium does not differ so much for the different classes as is generally supposed. Mr. Paulin has referred to the scope of my paper, as dealing with both expenses and selection. Mr. Sorley, in his paper to which I have referred, has shown the influence of selection and expenses separately and combined. The effect of making allowance for expenses was to diminish reserves in the early years. The effect of selection, if you make your reserves by select tables, was to increase them. To com- bine these two elements gave practically HM reserves. What I have done is to take ordinary reserves, show the profit from mortality, and set that off against initial expenses. Mr. Turnbull has suggested that this paper may tend to encourage expenditure ; but it was written with the object of say- ing a word against the suggested weakening of reserves for recently effected policies ; and it has always appeared to me that one of the strongest defences of a pure-premium valuation rests in the fact that, in imposing upon offices the obligation of making reserves for policies of all durations on the same basis, it affords a very effectual safeguard against excessive expenditure.



the influence of expenses and selection on reserves for recently-effected policies [with discussion]

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