TRANSACTIONS OF SOCIETY OF ACTUARIES 1959 VOL. 11 NO. 31 A NEW TABLE FOR ACCIDENTAL DEATH BENEFITS. NORMAN BRODIE Am) WILLIAM J.

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1 TRANSACTIONS OF SOCIETY OF ACTUARIES 1959 VOL. 11 NO. 31 A NEW TABLE FOR ACCIDENTAL DEATH BENEFITS NORMAN BRODIE Am) WILLIAM J. NOVEMBER roi)y of the combined experience of 17 large companies on accidental death benefits between 1951 and 1956 policy anniversaries was presented by the Committee on Disability and Double Indemnity in TSA 1958 Reports. The death rates were found to differ markedly from those in the Intercompany Double Indemnity Table. There was a substantial improvement at all ages, but since the percentage of reduction tended to increase with advancing age within the age range generally covered by the double indemnity benefits offered by life insurance companies, the curve of death rates in the new experience was much flatter than the Table. ~ This can be expected to result in a lower level of reserves than are required by the Table, which is at present generally recognized in the insurance laws for valuation purposes. It appears appropriate to use the more modern experience as a basis for a revised valuation standard. Even aside from the desirability of updating the laws in this respect, we can expect that the companies will turn to the new data as a basis for their operations, and this in itself will generate a need for replacing the Table with a new table. It is the purpose of this paper to present a table of accidental death rates, based on the new intercompany experience data, that we believe to be suitable for use as a valuation standard. Table 3 on page of the report contains a graduated set of accidental death rates for the aggregate experience entering the new study. We considered the appropriateness of using these published rates for valuation purposes, but concluded that it was essential that they be increased somewhat. This is in keeping with the comments which appear on page 52 of the report, where it is stated that the graduated rates "were produced for analysis purposes only, and not as a table deemed suitable for premium or valuation purposes." Several reasons are there cited why the graduated rates might not be appropriate for the latter purposes. The factors considered in arriving at our conclusion and in designing the suggested table are outlined and discussed below: 1. There were wide fluctuations in the experience among the 17 individual contributing companies, with a good number of them having an 1 See Tables 2 and 3 of the Committee's 1958 report, which will hereafter be referred to as "the report." 749

2 7 A NEW TABLE FOR ACCIDENTAL DEATH BENEFITS over-all result which was well over 100 7o of the average experience. Table 14 of the report shows that the over-all mortality ratios by amounts of insurance for the aggregate experience of each company relative to the graduated rates for all companies ranged from v-/0 to 169%. Of the 17 companies, seven had ratios in excess of ll0go. Thus the use of the graduated rates without adjustment would even fall short of covering the experience of a substantial number of companies that contributed to the study. Table 1 presented herewith shows the mortality ratios in five year attained age groups for each of the contributing companies, the companies being arranged in the same sequence as in Table 14 of the report. The range of the variation in the ratios as thus subdivided is noteworthy, and of some significance in establishing a table to be used for valuation purposes. The distribution of the mortality ratios appearing in Table 1 is summarized in Table It can be expected that many companies that did not contribute to this study will have an experience which departs significantly from the average of these 17 large companies. The distribution of the ratios shown in Table 2 for cells involving 10 to 24 claims, as compared with the distribution for cells with 25 or more claims, may be an indication of the fluctuations that are likely in small or medium size company data. In the 10 to 24 claim category, 35% of the cells had ratios of 0~ or more. 3. In addition to the variation in the distribution of mortality ratios by size of company, variation can also be expected because of the differences in the distribution of business among the companies by sex, geographic area, occupation and other factors correlated significantly with accidental death rates. By way of illustrating the variations that are possible in the matter of the proportion of business written on women, it may be noted that among the ten companies which contributed material in the intercompany study to the analysis of the results by sex, the proportion of the exposed to risk which was on female lives ranged from 27% to 8% by numbers of policies and from 14% to 4% by amounts of insurance. Because of the relatively favorable claim rates on women, the lower the female proportion the higher can we expect the over-all claim rates to be. Geographic area is of pertinence because of the higher accidental death rates which prevail in rural districts, as repeatedly evidenced by population statistics. It was noted in the report, for example, that "the two companies with the highest policy ratios [of actual to expected] do much of their business in farm states" (page 68). 4. As stated in the report, the period between 1951 and 1956 policy

3 TABLE 1 ANALYSIS BY" COMPANY--ALL YEARS OF ISSUE AND POLICY DURATIONS COMBINED MORTALITY RATIOS (BY AMOUNT OF INSURANCE) RELATIVE TO GRADUATED RATES Co~t- PANY COD~ A',t" rained AGE 5-9 l(~l,t! , , All I 3forCrALITY RATIOS A... * '/; B... * C... D... ~0 E Hilll illl L M... * N * P Q... * Z * % t 95 *% tlt lt lt0 114 I40 *% t5t ,% It t % % t % 66 6l t t35 85' I * % 68 8,I 94 9! t3,4 1,o4 217 * % t * % _m 94% tl5 202% 116 to3 *%,z 5o% t tl3 It;' lt ~'LrbIBER OF CLAIM'; (POLICIES) A.. B.. C.. D. E.. F.. (',.. a.. I... JIC I L., ~I P... Q t tl l t 630 t It t to t tl t l? (} It ~ t b t l lit O t 176 4,265 3, , ,249 8O 3, * Ratios not shown where number of claims was less than 10. Dashes appear where there was no exposure.

4 TABLE 2 DISTRIBUTION OF MORTALITY RATIOS OF INDIVIDUAL COMPANIES IN FIVE YEAR AGE GROUPS (Ratios Expressed Relative to Graduated Experience) NUMBER OF COMPANY-AGE Gltorfl" CELLS WITH SPECIFI~D RATIO.~,IORTALIYY RAT10 25 or More Claims in Cell 10 to or More Claims in Claims in Cell i Ceil 200% or more I i" i Less than or more to to Less than All... -f l ~

5 A NEW TABLE FOR ACCIDENTAL DEATH BENEFITS 753 anniversaries covered by the investigation was probably "a favorable one from a claim point of view because of the good economic conditions which prevailed. For example, companies are not always successful in excluding suicides when paying accidental death benefit claims, and in depressed times such claims are bound to be more frequent than in prosperous times." The Equitable's experience over the years is illustrative of this point. Its over-all crude claim rate (not adjusted for age) averaged. per 1,000 in the years 1925 to 1929, rose to an average of.53 in 1930 to 1934, and dropped back to. in 1935 to Changes adopted by companies in recent years in their definition of the benefit and in the underwriting of the coverage can be expected in themselves to result in higher claim rates than might otherwise emerge. Passenger aviation deaths are now more widely insured, and a trend toward the use of "accidental result" rather than "accidental means" in writing or administering the benefit will also admit more claims. There has in addition been a trend toward writing larger amounts of double indemnity benefits. This may have a significant effect in raising the level of claim rates as there is substantial evidence in the report and in collateral data that higher claim rates are associated with larger policies. Information in support of this statement will be found in Tables 7, 11 and 12 of the report. MARGINS ADOPTED RELATIVE TO EXPERIENCE RATES In view of the above considerations, it seemed clear to us that some margin should be added to the experience rates in the development of a new standard for the accidental death benefit. As to the extent of the margin, we considered the ratios set forth in Table I and the distribution in Table 2 to be of particular pertinence. In keeping with the thinking that went into the construction of the 1958 CSO Table, it was our view that the rates appearing in a standard table should cover a high proportion of the individual company variations from the average. Using the graduated aggregate experience rates in Table 3 of the report as a base, we have accordingly constructed a new table, proposed as the 1959 Accidental Death Benefits Table, by adding a margin equal to 30% of the experience rate, subject to a minimum addition of.10 per 1,000 and a maximum addition of 1.00 per 1,000. The 30% factor covers approximately 85% of the ratios experienced by the contributing companies in the five year age group cells with 25 or more claims, and about 65% of the cells in the 10 to 24 claim category. The combined proportion is of the order of 80%. There may be some question whether this goes far enough. Naturally there is room for judgment

6 TABLE ACCIDENTAL DEATH BENEFITS TABLE COMPARED WITH UNDERLYING EXPERIENCE TABLE AND INTERCOMPANY TABLE O'l AGE I Table (1) , ,ooo qz a Experience (2) MAROtlqIN 1959 TXBI~ RATIO 1959 TO Ac~ Percent Amount Table (1)-(2) (4) age + (2) TABLE Table (3) (4) (5) ] (1) " o~ 63%, I i M , , I 238 OF H 1,O00 ~z Experience (2) 362, ,442, Table (3) , ,448 1,519 1, ,844 1, O53 2, MARGIN IN 1959 TABLE Amount [ Percentage (1)-(2) (4)+(2) (4) (5) [ ~o9 30% , O RATIO o~ 1959To TABLE % O

7 TABLE 3--Continued ACE 1959 Table (1) I,O Experience (2) Table (3) MARGIN IN 1959 T~,BL~ RArzo of 1959 To AcE Percent- Amount age ] 1959 (1)-(2) (4)(+(2),5)1 TABLE Table (4) (1) 1,00o qgd MARGIn IN 1959 TABLZ Experience Table (2) (3) Amount (t)-(2) (4) Percent- age (4) + (2) (5) i RATIO O~ 1959 TO TABLg O , D, , , % ' 94% , , ,.. 2, ,, 2,88 l I , ,.. 6, I ! l 1, , i , , , , , o% 56~

8 TABLE ACCIDENTAL DEATH BENEFITS TABLE COMBINED WITH 1958 CSO COMMUTATION FUNCTIONS Carl OX 1000 AGz ~a 2~% 3% 1000 C 1000 M ad i, ooo C'g~ a looo M~ a AGE 1000 qgd O t% 3% 1ooo C~ a tooo M~ a i I looo c~ ~ iooo M~ a "/ M

9 TABLE 4--Continued Aaz ~5... ~,6... ~7... ~ ; to... ~I ~ to00 q,a ~% 3% i000 C~d lo00m~a tooo C~ 1ooo M~ I I Aoz ~illl , I000 q~a 1, , , ~ 1ooo C~ a looo M~ a I I % tooo c~ d! 10O0M~ a ~ l

10 758 A NEW TABLE FOR ACCIDENTAL DEATH BENEFITS here, but considering the requirements of companies with a favorable experience as well as the others and not overlooking the supplementary nature of the benefit, the 30~0 addition appeared to us to be justified. A uniform percentage loading was adopted rather than one varying by age since the data in Table 1 indicated that the median and quartile ratios were reasonably uniform by age group. The.10 per 1,000 minimum was deemed advisable to avoid negligible additions to the basic experience. It was recognized also that in the area where the minimum is effective---when the basic rate is less than.333 per 1,000--greater percentage fluctuations can be expected. The ages where the minimum comes into play are 3 to 14 and 27 to, inclusive. The 1.00 per 1,000 maximum is controlling when the basic rate is or higher. This happens above age 82 and therefore is of no practical effect for companies with a maximum coverage age of 65 or 70. The graduated rates in Table 3 of the report are based on company experience up to age 82, and thereafter are a blend from company experience to an assumed terminal rate, based on population data, of 15 per 1,000 at age I00. Because of the nature of the death rates at the high ages, a 30~o margin was not deemed necessary or desirable, and the 1.00 per 1,000 maximum was adopted as a practical method of grading the percentage down as the claim rate rose ACCIDENTAL DEATH BENEFITS TABLE The claim rates recommended for the 1959 Accidental Death Benefits Table appear in Table 3. Also shown in this table are the graduated experience rates, and the margins in the new table in relation to these rates. Table 3 includes in addition the Intercompany Table rates and the ratio of the new table to these rates. Table 4 contains commutation functions based on the proposed 1959 Accidental Death Benefits Table combined with the 1958 CSO Table and with interest at 23% and 3~. The payment of claims at the end of the year of death was assumed. Net annual premiums based on the commutation functions in Table 4 are presented in Table 5 for the Ordinary Life, 20 Payment Life and 20 Year Endowment plans at selected issue ages. The form of coverage for which the premiums are calculated is that which ceases at age 65. The limited range within which these net premiums fall is noteworthy. Separate tests indicated that if the proposed 1959 Accidental Death Benefits Table had been combined with the 1941 CSO Table, the resulting net premiums would have been very similar to those in Table 5.

11 A NEW TABLE FOR ACCIDENTAL DEATH BENEFITS 759 For comparison purposes Table 5 also shows the net annual premiums based on the Intercompany Table in combination with the 1941 CSO Table. The ratios of the net premiums based on the 1959 Table to those based on the Table evidence a percentage reduction which ranges from about 30% or 35% at the young ages to about % at the older ages. To gauge the impact of the new table on reserve levels, Table 6 has TABLE 5 NET ANNUAL PREMIUM PER $1,000 OF ACCIDENTAL DEATH BENEFIT 1959 ACCIDENTAL DEATH BENEFITS TABLE WITH 1958 CSO TABLE COMPARED WITH INTERCOMPANY TABLE WITH 1941 CSO TABLE COVERAGE CEASING AT AGE 65 23% 3% Isstr~ AGE Ratio Table Table Table Table Ratio ORD~A~Y LL~VE ~ % , % PAY~'t LIFE ~ % I YEAR ENIK~T ~ % ~%

12 TABLE 6 MEAN RESERVES PER ~I,000 OF ACCIDENTAL DEATH BENEFIT 1959 ACCIDENTAL DEATH BENEFITS TABLE WITH 1958 CSO 2~o COMPARED WITH INTERCOMPANY TABLE WITH 1941 CSO 2½~o COVERAGE CEASING AT AGE 65 POLICY YEAR ISSUE AGE [ 35 ] 55 ORDINARY LIFE 1959 ACCIDENTAL DEATH BENEFITS TABLE ,91 1,70, , , LNVTgRCOMPAIq'Y TABLE ] ,36,36,36,36, , ,40,81 RATIO OF 1959 TABLE TO TABI~ % % % % % % PAYMENT LIFE 1959 ACCIDENTAL DEATH BENEFITS TABI~ I ,26 3, O

13 TABLE 6---Conllnuat 20 x,a',,,mt~r upz--..ca~/nu~ POLICY Y~Am }! Iss~ Ao~ 5 I 15 [ n~'rerco~,'.~t~y TABL~ RATIO OF 1959 TABLE TO TABLE % % % % % % YEAR FACVOWMENT 1959 ACCIDENTAL DEATH BENEFITS TABLE INTERCO~EPANY TABLE RATIO o1~ 1959 TABLE TO TABLE % loo% % % % %

14 762 A NEW TABLE FOR ACCIDENTAL DEATH BENEFITS been compiled, showing mean reserves under the proposed table and the Table for the Ordinary Life, 20 Payment Life and 20 Year Endowment plans at the specimen issue ages and selected durations. This calculation has been confined to a 2½90 interest rate. The new table will require reserves that in the aggregate are less than % of the reserves under the Table. This sharp percentage reduction is a reflection of the fact that the accidental death rates do not increase by age nearly as rapidly in the new table as in the old.

15 DISCUSSION OF PRECEDING PAPER ROLAND F. DORMAN: The substantial improvement in accidental death rates since the study was completed indicates the need for a new valuation standard for accidental death benefits. The Experience Table is the logical starting point in the development of a table to serve as a valuation standard. There would seem to be no question that a table for use on an industry-wide basis should include margins over the experience rates. The main question, of course, is how large the margins should be. Certainly, the margins should be sutficient to cover the experience of a large portion of individual company variations from the average but should not be so large as to be unrealistic for those companies with good experience. I feel the margins in the 1959 Accidental Death Benefits Table satisfy this requirement. This would seem to be an appropriate time to adopt a new valuation standard for accidental death coverages in view of the fact that the 1958 CSO Table is currently being processed through the various jurisdictions. It is interesting to note that the experience indicates a higher death rate is experienced on the larger amounts of accidental death coverage. The current trend toward issuing large amounts of accidental death coverage, underwriting more liberally, together with changes in the definition of benefits, and the likelihood of further liberalization in interpretation by the courts, may very well lead to a reversal of past improvement in accidental death rates. We should, therefore, add adequate margins to the basic experience rates ff premiums are to be based on them. Messrs. Brodie and November have performed a valuable service by preparing the 1959 Accidental Death Benefits Table. (AUTHORS' REVIEW O DISCUSSION) NORMAN BRODIE AND WILLIAM ~'. NOVEMBER: We should like to thank Mr. Dorman for discussing our paper and endorsing our suggested valuation standard. It may be of interest to note that the Intercompany Double Indemnity Table is specified as the minimum valuation standard for accidental death benefits in the laws of 32 of the states. Of the other 18 states, have no applicable law and 5 have provisions such as "any recognized basis satisfactory to Commissioner." 763