Carlisle

Do.

3.354
7.517

Do.

-10.151
-14.426
-18.453

1.223

-10.780
-13.609
- 21.137

2.938
•627

+ 5.432

+ 1.362

2.520
*557

4.630
8.499

+ 5.253

+ 1·174

1.546

5.300

8.812
9.107

Hypothetical Tables.

I have extended the table to show the results for a Society of the standing of 50, 55, and 60 years respectively, but it is hardly worth while to give the figures. It will be sufficient to say that the comparative results differ but little from those of an office 45 years old.

A few words now upon the comparison of other results with the standard proposed. The figures speak for themselves; much comment is, therefore, unnecessary.

The reserves at 4 per cent. interest by all other tables of mortality are below the standard.

The reserves at 3 per cent. interest by the Carlisle, Davies' Equitable, and English No 3 Tables, are below the standard throughout; by the HM and the 17 Offices' Tables below it up to and including 15 years, but above it for a Society more than 15 years old.

The reserves at 3 per cent. interest by the Carlisle, Davies' Equitable, Northampton, and Hypothetical Table No. 3, are also below the standard throughout; but by the English Tables, by Edmonds' Mean Mortality, and the Hypothetical Table No. 4, the reserves at this rate of interest are above the standard, except for the first period of 5 years, and by the HM, 17 Offices', and Hypothetical Table No. 5, above the standard throughout.

From the Returns made by Offices to the Board of Trade, it appears that the Carlisle and Davies' Equitable Tables are frequently employed for valuation purposes. It may not be unimportant, therefore, to ask special attention to the reserves brought out by these tables. Tested by our standard, it will be seen that these are invariably too low. Even when the calculations are made at 3 per cent. interest, this is found to be the case. If our standard, then, be near the truth, these tables are not appropriate for valuations. And yet, when they are adopted along with interest at 3 per cent. or 3 per cent., we find it stated in valuation reports that not only is the table of mortality employed a suitable one, but that the office has an unvalued source of profit in the difference between the rate of interest assumed, and that which may be fairly expected to be realized. Such statements can only mislead as to the real position of an office, and it is to be hoped that they will soon cease to be made thro' the recognition and adoption of the new Institute Experience as a true measure of mortality. Altho' the frequency with which the above tables are used has caused me to specially

mention them, my remarks, of course, apply equally well to all tables which bring out reserves under what I have set up as our standard.

Speaking of valuation reports calls to my mind what no doubt everybody has noticed, that they sometimes contain a statement to the effect that the number of deaths which has actually happened has approached very closely to the number expected according to the table by which the liabilities have been valued, and there seems to be a tendency to jump to the conclusion that the table therefore is an appropriate one. It is possible, however, as is well known, that this conclusion may be very untrue. Take, for instance, the case of an office with a good many old lives on its books, which uses the Carlisle Table. It is not unlikely that the total number of deaths will be much the same as that expected by the table. If, however, a division be made between the younger and the older lives, drawing the line say at age 60, the agreement will cease. The actual deaths among the younger lives will be less than the number expected, while, among the older lives, the reverse will hold good, and the Carlisle Table, although showing a total mortality approaching the truth, will be seen to be inapplicable for the valuation of policies, because it is not correct at particular periods of life.

I have only further to say, that it is necessary to bear in mind that no account of reversionary bonuses has been taken in the comparisons which have been made. The position of an office reckoning a large amount of such bonuses among its liabilities would be materially affected according as the table employed in its calculations brought out values for reversionary payments greater or less than the standard. To take one example. The Northampton Table brings out too small policy values, but, on the other hand, too high values for reversionary payments, and, therefore, if an office using that table had a considerable proportion of its liabilities in the form of reversionary bonuses, the result would be that the deficiency on the one part of its reserves and the excess on the other would so far balance one another. But this introduction of a fresh element of uncertainty into the calculations is only another argument in favour of the employment of true data, by which alone the real position of an office can be satisfactorily ascertained.

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

The CHAIRMAN said that the subject of the paper was perhaps the most important that could engage the attention of actuaries, and as the matter must have been thought over by many gentlemen in the

room, he would be glad to hear the result of those thoughts from any of the members present.

Mr. H. A. SMITH remarked that there are many instances of the older established companies being obliged in the last few years to retrace their steps in the rate of bonus-giving payments; and it would have been well for them if in their early days they had had such data before them as are now available. If they had taken pencil in hand and computed what would have been the premiums necessary, according to the bonuses they were declaring, it might have kept them in the right way. It would be a useful exercise to some of the younger members to work out such a problem as the following: Suppose an office to be established with a large enough number of lives on its books to form an average, then suppose the books to be closed, not allowing for any new lives. It would be found-supposing the premiums required were in excess of the demands upon them-that the surplus in the first periodical term of investigation would yield a very large bonus; at each periodical investigation afterwards it would become "smaller by degrees and beautifully less." This has only been kept out of the sight of many of our contemporaries by the large influx of new lives still coming in. He hoped there would be no more extravagant bonuses, and no more retrograding from the large amounts that have been so frequently declared.

Mr. DAY stated that several offices are beginning to think about a change of basis in their valuations. In some of the large Scotch offices there is a practice of having what is called “ a check valuation", and the Carlisle 3 per-cent table has ceased to be that infallible guide that it was formerly considered. He thought that the standard of valuation proposed by Mr. Valentine, was of somewhat too complicated a character for general adoption—i.e., taking the HM(5), combining it with the H", and then assuming the 4 per-cent rate of interest. A simpler method, and one more intelligible to the public, would be the HM 3 per-cent. With regard to the basis adoptedthat of the imaginary office in Mr. Manly's paper-the probability is, that the lives enter at younger ages than Mr. Manly assumed. It would be very interesting if Mr. Valentine or Mr. Manly would take up the subject further, and work it out with the greater information furnished by the returns made under the 5th and 6th Schedules of the Life Assurance Companies' Act. There were certain other matters arising out of Mr. Valentine's paper which are very interesting; and one of those is the confirmation obtained by the comparisonbringing out results of an almost identical character of the two experience tables-i.e., the Institute Experience table and the Seventeen Offices Experience table. One conclusion to be derived from the paper is, that there will be in the future few actuaries who will be content to recommend the adoption of the hitherto generally accepted valuation by the Carlisle 3 per-cent, or Davies's Equitable.

Mr. MACFADYEN said that if by calling the combined HM and HM(5) 4 per-cent table the standard, Mr. Valentine means that it is the best to adopt in all cases, he must demur to that conclusion. He was not prepared to admit that 4 per-cent interest should be used universally by companies realizing that rate. In a large number of offices there are strong reasons for thinking 3 per-cent preferable.