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1881. NEW ZEALAND.

GOVERNMENT LIFE INSURANCE DEPARTMENT (REPORT BY THE CONSULTING ACTUARIES ON THE NET SURPLUS OF PROFITS OF THE).

Presented to both Houses of the General Assembly in pursuance of Section 45 of « The Government Insurance and Annuities Act, 1874." government

Ketobt by Ihe Consultinc Actuaries, Mr. Bmii and Mr. &u>Dr, on the Net Sum],,, »f P,™l». «. * , f'w" ° the n. ecessary dat* reached us early in February, but it was not until the 23rrl «f--«,£^4° (^^■siassr^a *ar for th«te untilTo" .'jtr," 1™ "■ P1 *""8 th" ""U"b° '» h"d ' mi "» «»l ™» «.-«t.in,d nnintonptedlj systematic checks, as well as test-valuations for the more important group? o f the^ risks Hent wJ have found ,t impracticable to present our report at an earlier period fand^ wftrust thafthe caTe bestowed at every stage of the processes, and the close examination to which tf,e results; bare been subjected, will be more apprecated than an earlier, but perhaps less maturely weighed report 3. Tne following is a summary m a convenient form, of the financial transactions of the deoart ment in the quinquennial period ending on the 30th June, 1880:— «ui B «,nons ot the departPund, 30th June, 1875 .. 8" d- ,*. "• dAdd Income from— 109,967 12 1 Premiums ~ 482 392 lg 1 Annuity purchase-money 22 228 7 5 nter eBt - !!' 66^238 7 3 oundnes oq c q * * * k/O O O 560,958 18 5 Deduct Outgo for- 670 >926 £ laims, ... 114850 0 0 .Surrenders Uosg lg Q Annuities _. 8716 16 Q iixpenses, including commission .. 76 964 17 8 211,590 12 8 Fund, 80th June, 1880

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Comparing the interest brought to account each year with the mean between the fund at the beginning and end of the year, we find that the rate of interest realized in the quinquennium has been as follows, viz.:— £ s. d. 1875-76 .. .. ..5 1 3"| 1876-77 ~ ..4 17 11 | 1877-78 .. 4 18 5 |- Per cent, per annum. 1878-79 ... .. .. 5 0 10 | 1879-80 ... ... 5 1 7J The question of the rate to be assumed in the valuation will be discussed in Article 6. 4. The sheets containing the data for valuation were subjected to a very complete analysis ; and, for Table 1., the facts were re-scheduled for males and females separately, and again, so as to show the amounts at risk, with corresponding premiums at each year of birth, distinguished for yearly, halfyearly, quarterly, &c, payments of premium. The following statement gives a summary of the most interesting facts elicited in the course of this examination, and derived from the risks under Table I.: —

Analysis of the Risks shown under Table I.

From a further grouping of the sums assured, according to the ages at entry, we ascertained that tbe mean age at entry was —for males, 36 74 years; for females, 3877 ; the mean present age being —for males, 40 45 years ; females, 4207 ; It will be seen, therefore, that the number of females is too small to justify their being treated separately; also the average duration of the contracts is too short, and the average age of the lives tod low, to enable us to arrive at any trustworthy conclusions as to the rate of mortality that will prevail in future among the assured. For Tables 11. and 111. no distinction of the sexes was attempted; but the facts were rearranged in groups, according to the number of premiums remaining to be paid, in order to obtain some idea of the period during which the assumed rates of mortality and interest might be affected, and of the time when the contributions for expenses in Class 11. would expire. 5. As on the occasion of the last valuation, there is no definite information respecting the deathrate that may be expected to prevail amongst assured lives in New Zealand, nor any mortality statistics for the colony generally, available for the purposes of the present investigation. From such tests as we have been able to make, there would not appear to be any great difference between the general rate of mortality experienced in the last quinquennium amongst the lives assured under Table 1., and similar lives in this country We do not, upon general grounds, see much reason for expecting a contrary result, but we consider that it would be wise to collect and tabulate all available information on this head, especially in regard to the death-rate of the older lives. After full consideration, we think that the Institute of Actuaries' H m Table is the most suitable table of mortality to adopt for the present valuation. Nevertheless, we have thought it prudent (as will be hereafter shown) to make a further provision beyond what an estimate on this basis would provide. We observe: that, in a large number of cases, additional premiums have been charged, the lives having been assumed to be a certain number of years older, upon the ground that they were deemed to be below the average in point of future longevity In these cases the risks have been classified according to the true, and not the assumed, ages, which we consider to be the most suitable method of procedure. The effect is that the surcharges, taken in the aggregate, form an annual fund applicable to meet the additional claims arising from the expected increased mortality in this class of lives. 6. At the last valuation the> rate of interest assumed was 4f per cent, per annum ; and, from Article 3, it will be seen that rather more than this rate was realized in the last five years. The question for consideration, however, is not what has been or is, but what will be the rate of interest realized by the fund during a period of time covered by the present, generation. This point has

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Males (6,542). imaies (202). Premium Payable Proportionate Distribution. Proportionate Distribution. Average Sum Assured. Average Sum Assured. Number of Sums Policies. Assured. Number of Policies. Sums Assured. £ £ "early 414 21-17 2343 286 21-78 21-78 talf-yearly 372 4511 44-78 275 43 56 4353 juartely 356 27-22 2591 268 34-66 33-76 loathly 339 6-50 5-88 All Classes £374 100-00 100-00 £275 100-00 10000

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received our very full consideration, and we have come to the conclusion that it would not be consistent with prudence to assume that the fund will earn a higher rate than 4§ per cent., which is fully £ per cent, beyond that obtained in the mother-country Indeed, we do not consider it free from doubt whether in after years this rate will not be too high, having regard to the marked and inevitable tendency to an equalization of the rate of interest throughout the world. Bearing in mind, however, that a fall in the rate of interest must be gradual, and that, if a reduction of § per cent, were made on the present occasion, the difference in the net liability would not be great, we think that this valuation, like the last, may be made upon a 4J per cent, basis. 7 Appended hereto is a summary of the several assurance and annuity contracts in force as at 30th June, 1880, with a valuation at 4£ per cent, interest, of the assurances by the H m Table of Mortality and of the annuities by the Carlisle Table. An additional reserve, amounting to £19,302, has been made, because the sums assured are payable one month after death, and also in respect of the 817 assurances under Table 11., where the premiums are payable for a limited term only, so as to make provision for the expenses of management and for profits after the premiums have ceased to be payable. The financial position is as follows: —■ The realized assets on the 30th June, 1880, were .. ... ... £459,335 The estimated net liability, as per valuation, was .. 381,740 Surplus .. .. £77,595 8. Having regard to a.ll circumstances, and especially to the necessity of proceeding cautiously for some time until the prevailing rates of mortality and interest have been better ascertained, we suggest that the whole of this amount be not divided on this occasion, but that the distribution should be restricted to a sum not exceeding £60,000. Apart from other considerations, we feel satisfied that some portion of the surplus has arisen through the operation of what is sometimes termed "suspended mortality," or the lightened deathTate resulting from the recent selection of so large a proportion of the lives. Experience has shown that an acceleration of the rate of mortality exhibited by any general table takes place when the lives are no longer of recent selection, and we think it is expedient that some further reserve should be made on this account. This, we recommend, should on the present occasion be done by leaving undivided some portion of the estimated surplus, rather than by assessing a part of the liabilities by another table of mortality 9. The next matter submitted to our consideration is " the best and fairest system by which the divisible profits should be distributed." Various methods, more or less elaborate, have been suggested and adopted by several companies, the applicability of which to the present case has received our full consideration. There can be little doubt, however, that the surplus proposed for division has been derived mainly from what is called the "loading," upon the premiums having been found to be more than sufficient for the expenses incurred ; and, therefore, we consider that it will do substantial justice to the policyholders, without a needless amount of labour in calculation, to divide that surplus in proportion to the accumulated " loading." We deem it an unnecessary refinement to introduce the element of interest in this process, and that it will be sufficient to ascertain the amount of " loading" on the premiums received on each policy This being the first division of profits, the accumulation, on this occasion, should be taken as from the dates of the policies. It should be noted that the " loading " used for this purpose in the case of the whole-term policies should be that corresponding to the annual premiums under Table 1., taking the increased age where, the lives are under average ; so that, cwteris paribus, the sum apportioned as the bonus in cash will be the same, whether the policy be effected under Tables I. or 11., or the premiums be receivable by annual or more frequent instalments. The same principles are applicable to endowment assurances, and to policies of other classes. 10. If, as is commonly the case, it is desired to convert the cash bonuses into corresponding additions to the sums assured, a lower rate of interest than that adopted in the valuation should be assumed for the purpose. 11. We have examined the tables of rates given in the prospectus, and we consider them to be sufficient under the present circumstances. They are undoubtedly low, and especially so at the older ages; and, if the rate of interest in the colony were to fell materially, we think that the rates in question would require revision before new transactions were entered into. We notice, however, that the rates for single premiums given in Table 11. appear to be inconsistent with the other rates shown in the same table, and with those in Table I, being relatively higher. We have also tested the Table of Surrender Values, given on page 6of the prospectus; and we consider that on the basis of the present valuation the amounts promised to be allowed, whether in cash or as paid-up policy, can be granted with safety We do not think that either should be increased; and we recommend that, in applying them, the real, and not the increased, ages of the lives assured be taken. An both rates of premium and amounts of surrender-allowance must be ultimately determined by competition on the spot, we consider that, so long as the first are sufficient, and the second not too high, it is not necessary to propose, upon purely theoretical grounds, any revision of either, on the present occasion, beyond the rates for single premiums above adverted to. Theoretical perfection on such points as these must be subordinated to the practical considerations involved in meeting the public demands. 12. The results of our valuation show that the finances of the department are in a sound condition; and, considering the low rates of premium paid by the assured, the amount of the divisible

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surplus appears to us very satisfactory, and the business of the department to have been well conducted, and in such a manner as to reflect great credit on those who have been responsible for its management. We have, &c, Abthtie H. Bailey. The Hon. the Colonial Secretary, New Zealand. Ealph P Haedt. P.S. —-We have taken no account of the policies in the Industrial Branch, which we did not consider was included in the reference to us. The liability under these is, however, merely nominal.

Government Insurance Department of New Zealand. Summary and Valuation of the Assurance and Annuity Contracts as at 30th June, 1880.

Aethub H. Bailet Ealph P Haedt.

By Authority: Q-. Didsbuby, GWernment Printer, Wellington.—lBBl.

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Valua .tioit. Particulaes of ' Vaic, :nE Policies *ob ltiow. Ansurances 4s per ee] Mortality s: "Institui it. Annuit ', 4J * per cei te of Actuaries," Hm. lies Carlisle Table of at. Table. Description of Thawsactiob". Annual 'remiums. Vali Annual ] ie of 'remiums. No. of Policies Bums Assured. Net Hm. 4f p. cent. Value of Sums Assured. Hm. 4} p. cent. Set, Net Liability. Office. Office. ASSUBANCES. £ £ £ £ & £ £ I. II. III. IV, V. Whole term : Uniform annual premiums Ditto: Limited and commuted premiums Endowment assurances at various ages... Joint lives Children's endowments, without return of premium Ditto, with return of premium Temporary risks Extra premiums Additional reserve for payment of claims one month after death, and for profits and expenses of assurances under Table II. ... 6,744 817 3,916 14 5 2,504,775 417,199 1,221,845 5,150 1,500 69,863 14,786; 45,720 200 76 53,405 11,524 37,098 172 893,182 141,147 553,09! 2,470 575 5,314 975,885 106,827 533,387 2,266 741,264 8;i,775 431,004 1,957 151,918 60,372 122,087 513 575 5,314 VI. A. 113 11 13,585 6,950 682 123 607 62 304 62 304 19,30! Total amount of assurances ... 11,620 4,171,00 1 132,057 102,199 1,598,841 1,618,669 1,258,000 360,44! Annuities. VII. nil. IX. x. Immediate Contingent Deferred : Without return of premium Ditto: With return of premium 30 2 2 2,074 335 200 85 9 70 11 8 70 18,948 1,303 926 391 " 113 181 94 181 18,948 1,209 745 391 Total amount of annuities 36 2,694 p. annum 90 78 21,568 294 275 21,291 11,656 4,171,004 2,694 p. annum 132,147 102,277 1,620,409 1,618,963 1,258,275 381,7' Total of results...