|
|
Table of Contents |
Next |
COMMON CHARACTERISTICS OF PUBLIC TABLES
The methods discussed in this chapter for applying the laws of probability to life insurance have produced a multitude of mortality tables for a variety of purposes. Generally, proprietary company tables are used for premium and dividend calculations. Different tables are used for solvency accounting and reporting to regulators. In the remainder of this chapter we describe important and interesting characteristics of some public tables. Table 13-10 provides a summary of these and other tables developed over the past century.
Two principal kinds of public mortality tables exist. First is the set of United States Life Tables published as a by-product of the decennial census. Census data are used to construct a table for the total population and for each of several sub-populations. The purpose of these tables is to display the public health of the country and to provide a general model for the uncertainty of length of life.
The other principal kind of public table is required by statute in the various states for use by insurance companies for specific purposes. Sections of these codes, which usually follow model laws developed by the National Association of Insurance Commissioners (NAIC), specify how the assets and liabilities on the annual statements of the insurance companies will be calculated. Insurance and annuity contracts in force create liabilities for life insurers. Valuing these liabilities requires reasonable assumptions about several factors, including mortality. The statute specifies a reasonable assumption for the mortality rates of insureds by naming a specific mortality table�the statutory table.
Until 1941 the statutes required tables that were selected from among those in existence in the actuarial profession. The 1941 CSO Table was the first constructed at the request of the NAIC for calculating minimum reserves and surrender values. In keeping with this purpose it was also the first to have an explicit margin added to the mortality rates.
Of the mortality tables listed in table 13-10, those described in rows 3 through 9 are descendants of the 1941 CSO. The 1958 and 1980 CSOs are updated tables used for ordinary life insurance. The 1980 CSO (see table 13-9) differs from its predecessors in several ways. It was the first time actuaries developed and published separate rates for men and women. Another difference was in the treatment of the "hump" in the mortality rates for males around age 20. The raw data in most mortality studies show rates for males reaching a low near age 10, then rising to a maximum near age 21, and falling again to a minimum near age 29. After this, they start a long continuous rise to the end of life. In previous mortality tables, the smoothing process eliminated this hump in the initial rates. In the 1980 CSO, however, because the hump in the male data was more pronounced than ever (due to auto accidents, homicides, drug overdoses, and suicides) it was not eliminated. An examination of table 13-9 shows a hump of 1.91 per 1,000 at age 21, then a reduction to the low of 1.70 at age 28, and then a rise back to 1.91 at age 33. The slight hump apparent in the female data was lost in the smoothing process.
The 1980 CSO also was the first to include selection factors in a table developed for regulatory purposes.
The 1958 and 1980 CET Tables, intended for use with extended term insurance, illustrate the need for mortality tables appropriate to their intended use. There were insufficient data to derive mortality rates for extended term coverage at all ages, so the general level of the mortality was determined and then applied to the pattern of mortality for ordinary life insurance. The resulting tables are based on multiples of the ordinary mortality tables rather than being derived directly from the mortality of lives with extended term coverage.
Further illustrations of tables constructed to be appropriate for the relevant population are the 1961 CSG, CSI, and CIET Tables. These are tables constructed at the request of the NAIC for group, industrial, and industrial extended term policies.
The 1983 Smoker-Nonsmoker tables also were constructed at the request of the NAIC. At the time, companies did not possess sufficient experience on insured lives to construct a table in the usual way. The committee that developed there tables estimated the proportion of smokers at each age of the 1980 CSO population and the relative mortality of smokers versus nonsmokers. Combining this information, the committee estimated mortality rates of the smoking and nonsmoking components of the 1980 CSO populations that were consistent with the overall mortality rates.
The UP-1984 Table was constructed by actuaries to value pension benefits. The Pension Benefit Guarantee Corporation (PBGC) adopted this table to fulfill its mission of protecting defined-benefit pension plan participants with federal guarantees. The PBGC uses this table to value the obligations of pension plans that employers wish to terminate. The table is a unisex table and includes suggestions for complying with laws governing sex discrimination in the distribution of benefits.
Rows 10 through 15 of table 13-10 are tables used for annuity contracts. Only the 1971 and 1983 tables were constructed at the request of the NAIC. The mortality experience of lives covered under group annuities and pensions is different from that for lives covered under individually purchased annuities. These differences indicate a need for separate individual annuitant mortality (IAM) tables and group annuitant mortality (GAM) tables.
All public tables, like those described in this chapter, are intended to provide a minimum basis for valuation. Company solvency is the prime concern. For setting premiums and dividend scales, most major life insurance companies rely on their own recent experience.
|
TABLE 13-9 |
|||
|
Age (x) at Beginning of Year |
Number Living at Beginning of Designated Year (lx) |
Number Dying during Designated Year (dx) |
Yearly Probability of Dying (qx) |
|
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 |
10,000,000 9,958,200 9,947,545 9,937,697 9,927,958 9,918,526 9,909,599 9,901,077 9,893,156 9,885,637 9,878,322 9,871,111 9,863,510 9,855,126 9,845,369 9,834,047 9,820,968 9,806,138 9,789,762 9,772,336 9,754,159 9,735,626 9,717,031 9,698,666 9,680,626 9,663,007 9,645,903 9,629,216 9,612,750 9,596,408 9,579,998 9,563,425 9,546,402 9,528,932 9,510,732 9,491,711 |
41,800 10,655 9,848 9,739 9,432 8,927 8,522 7,921 7,519 7,315 7,211 7,601 8,384 9,757 11,322 13,079 14,830 16,376 17,426 18,177 18,533 18,595 18,365 18,040 17,619 17,104 16,687 16,466 16,342 16,410 16,573 17,023 17,470 18,200 19,021 20,028 |
0.004180 0.001070 0.000990 0.000980 0.000950 0.000900 0.000860 0.000800 0.000760 0.000740 0.000730 0.000770 0.000850 0.000990 0.001150 0.001330 0.001510 0.001670 0.001780 0.001860 0.001900 0.001910 0.001890 0.001860 0.001820 0.001770 0.001730 0.001710 0.001700 0.001710 0.001730 0.001780 0.001830 0.001910 0.002000 0.002110 |
|
TABLE 13-9 (Continued) |
|||
|
Age (x) at Beginning of Year |
Number Living at Beginning of Designated Year (lx) |
Number Dying during Designated Year (dx) |
Yearly Probability of Dying (qx) |
|
36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 |
9,471,683 9,450,466 9,427,785 9,403,461 9,377,225 9,348,906 9,318,148 9,284,975 9,249,042 9,210,289 9,168,382 9,123,274 9,074,738 9,022,649 8,966,618 8,906,452 8,841,435 8,771,057 8,694,661 8,611,540 8,521,377 8,423,722 8,318,510 8,205,461 8,084,266 7,954,271 7,814,753 7,664,788 7,503,368 7,329,740 7,143,418 6,944,474 6,773,084 6,509,613 6,274,160 |
21,217 22,681 24,324 26,236 28,319 30,758 33,173 35,933 38,753 41,907 45,108 48,536 52,089 56,031 60,166 65,017 70,378 76,396 83,121 90,163 97,655 105,212 113,049 121,195 129,995 139,518 149,965 161,420 173,628 186,322 198,944 211,390 223,471 235,453 247,892 |
0.002240 0.002400 0.002580 0.002790 0.003020 0.003290 0.003560 0.003870 0.004190 0.004500 0.004920 0.005320 0.005740 0.006210 0.006710 0.007300 0.007960 0.008710 0.009560 0.010470 0.011460 0.012490 0.013590 0.014770 0.016080 0.017540 0.019190 0.021060 0.023140 0.025420 0.027850 0.030440 0.033190 0.036170 0.039510 |
|
TABLE 13-9 (Concluded) |
|||
|
Age (x) at Beginning of Year |
Number Living at Beginning of Designated Year (lx) |
Number Dying during Designated Year (dx) |
Yearly Probability of Dying (qx) |
|
71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 |
6,026,268 5,765,331 5,490,613 5,201,587 4,898,907 4,584,446 4,261,105 3,932,489 3,602,553 3,274,541 2,950,885 2,633,724 2,324,920 2,026,726 1,742,478 1,475,966 1,230,823 1,009,829 814,659 645,788 502,572 383,472 286,281 208,381 146,721 98,309 60,504 31,450 10,757 |
260,937 274,718 289,026 302,680 314,461 323,341 328,616 329,936 328,012 323,656 317,161 308,804 298,194 284,248 266,512 245,143 220,994 195,170 168,871 143,216 119,100 97,191 77,900 61,660 48,412 37,805 29,054 20,693 10,757 |
0.043300 0.047650 0.052640 0.058190 0.064190 0.070530 0.077120 0.083900 0.091050 0.098840 0.107480 0.117250 0.128260 0.140250 0.152950 0.166090 0.179550 0.193270 0.207290 0.221770 0.236980 0.253450 0.272110 0.295900 0.329960 0.384550 0.480200 0.657980 1.000000 |
|
TABLE 13-10 |
|||||||
|
Name |
Purpose |
Database |
Gender |
Type |
Margins |
Comments |
|
|
1 |
79-81 US Life Table |
US mortality; general purpose |
1979�81 |
Combined and sex distinct |
Aggregate |
None |
For two centuries, life tables for U.S. population, with sub-populations by sex, race, and geographic region prepared as part of decennial census |
|
2 |
1941 CSO |
Company solvency and minimum nonforfeiture for ordinary insurance |
Insurance company experience, |
Male |
Ultimate |
Explicit by formula |
First table commissioned by the NAIC; first with explicit margins |
|
3 |
1958 CSO |
Company solvency and minimum nonforfeiture for ordinary insurance |
Insurance company experience, |
Combined; female equal to male with |
Ultimate |
Explicit; sufficient to cover experience of 33 small companies |
|
|
4 |
1958 CET |
Company solvency and minimum nonforfeiture for ordinary extended term |
58 CSO plus the greater of .00075 or 30% of mortality rate |
Combined |
Ultimate |
Proportional to 58 CSO |
First special table for extended term insurance |
|
5 |
1961 CSG |
Company solvency and minimum premiums for group insurance |
Insurance company experience, |
Combined |
Aggregate |
Explicit |
|
|
6 |
1961 CSI |
Company solvency and minimum nonforfeiture for industrial insurance |
Insurance company experience on white insureds, 1954�58; U.S. life table for ages >75 |
Combined |
Aggregate |
Explicit and substantial |
|
|
7 |
1961 CIET |
Company solvency and minimim nonforfeiture for industrial extended term |
61 CSI plus loading |
Combined |
Aggregate |
Proportional to 61 CET |
|
|
8 |
80 CSO |
Company solvency and minimum nonforfeiture for ordinary insurance |
Insurance company experience, |
Sex distinct |
Aggregate, policy years 6 and up |
Math formula using the life expectancy based on the basic table |
10-year selection factors were provided making this the first CSO Table available on a select basis |
|
TABLE 13-10 (Concluded) |
|||||||
|
Name |
Purpose |
Database |
Gender |
Type |
Margins |
Comments |
|
|
9 |
80 CET |
Company solvency and minimum nonforfeiture for ordinary extended term |
80 CSO plus the greater of .00075 or 30% of mortality rate |
Combined |
Ultimate |
Proportional to 80 CSO |
|
|
10 |
49A |
General use for annuities |
Group and industrial experience for several years about 1943 |
Combined |
Aggregate |
Only to bring it to 1949 |
First table with projection factors provided to update the table |
|
11 |
51 GA |
For employee annuitants |
49A rates for ages < 65; company experience 1946�50 for ages > 65 |
Male |
Aggregate |
Margin to make it safe for all occupations |
First table for employee annuitants; has projection factors as 49a |
|
12 |
71 GAM |
For minimum reserves on employee annuitants |
Insurance comfpany experience, 1964�68 |
Sex distinct |
Aggregate |
8% for males and 10% for females |
Had new projection factors |
|
13 |
71 IAM |
For minimum reserves on individual annuitants |
Insurance company experience, 1960�67 |
Sex distinct |
Aggregate |
10% reduction |
|
|
14 |
83 GAM |
For minimum reserves on employee annuitants |
Insurance company experience, 1964�68, with projections to 1983 |
Sex distinct |
Aggregate |
10% reduction |
83 IAM projection factors up age 82; lower reduction factors above |
|
15 |
83 IAM |
For minimum reserves on individual annuitants |
Insurance company experience, 1971�76 for ages >50; 71 IAM for ages <50 |
Sex distinct |
Aggregate |
10% reduction |
Had new projection factors |
|
16 |
84-UP |
Used by PBGC in pension termination cases and general pension work |
1965�69 noninsured pension plans and group life |
Combined 80% male |
Aggregate |
Developed by consul. to manage unisex regulations in the 70s |
|
|
17 |
83 Smoker-Nonsmoker |
Company solvency and minimum nonforfeiture for ordinary insurance |
Various |
Sex distinct |
Aggregate, policy years 6 and up |
80 CSO margins |
Mortality rates for smokers and nonsmokers consistent with 80 CSO rates were found for each age |
|
|
Top |
Next |