PENNSYLVANIA COMPENSATION RATING BUREAU. Tail Factors for Loss Development

Transcription

1 Exhibit 7 As Filed PENNSYLVANIA COMPENSATION RATING BUREAU Tail Factors for Loss Development For a given calendar year, the PCRB collects financial loss development data for the current policy year and the twenty previous individual policy years. A single aggregate line of experience is reported for all older policy years combined. Thus, the 26 vs. 27, 27 vs. 28, 28 vs. 29 and 29 vs. 21 valuations in the tail factor calculation will use policy year 1986 as the earliest separate policy year and an aggregate line of experience for policy years 1985 and prior. The following discussion focuses on data with an earliest available policy year of 1978 for illustrative purposes. The discussion for data starting with later policy years would, however, be analogous. to 1995, the PCRB has computed incurred loss development for maturities older than policy year 1978 (i.e., the pre-1978 tail ) by comparing the total amount of dollar development in incurred losses occurring in a given calendar year to the incurred loss reported for policy year 1978 at the beginning of that same calendar period. As part of the Insurance Department s examination of the Bureau, the actuarial firm retained to perform portions of that review commented that the PCRB s approach effectively assumed that each policy year prior to 1978 had the same amount of ultimate losses as did policy year Since policy year losses have tended to increase from year to year in response to benefit and price changes, changes in employment volume and other features affecting loss trends, this assumption was noted as understating the true tail in the PCRB s loss development analysis. The contractor recommended that for future filings the PCRB add a growth adjustment to its tail factor calculation. In response to this recommendation the PCRB changed its derivation of tail factors for its 12/1/95 filing. That approach, used again for this filing, is applied separately for indemnity and medical loss experience and for each calendar year of experience, and outlined as follows: 1. A starting policy year loss amount based on the average reported incurred loss for policy years was computed. 2. An annual loss inflation factor was selected based on observed changes in incurred losses by policy year for the older policy years having separate experience data reported.

2 3. A historical series of estimated incurred losses by policy year beginning with policy year 1977 was computed using the starting point from #1 and the selected inflation factor from #2. 4. A calendar year loss development factor was selected for policy year 1977 based on observed developments for the oldest years with actual separate experience available. 5. A rate of decline in calendar year loss development factors by policy year was then computed such that when the resulting series of loss development factors was applied to the historical series of estimated incurred losses in #3, the total implied dollar amount of loss development for the calendar year balanced to the observed amount of development on policy years prior to The tail factor applicable to maturities prior to policy year 1978 based on that calendar year of experience was then computed as the cumulative product of the series of loss development factors constructed in #5. In general, this approach produced policy year incurred losses and loss development factors such that measurable development terminated for policy years in the mid- to early 193 s. Because the amount of calendar year development observed for policy years prior to 1978 varied considerably from year to year, some variations in the application of the initial selected loss development factor were necessary (i.e., whether the initial selection was applied to 1,2 or 3 prior policy years before beginning the application of the selected rate of decline in loss development). In addition, the selected rates of decline in loss development factors vary from calendar year to calendar year in order to achieve the desired balance with observed calendar year development. Recognizing the volatility of observed calendar year development for policy years prior to 1978 in the aggregate, the PCRB elected to use an experience period comprising four calendar years of loss development in computing indicated tail factors for this filing. A summary exhibit on page 1 presents results of both the previous and revised approaches to the derivation of tail development factors. Following the summary page, eight exhibits presenting the derivation of indicated tail factors using the procedure outlined above are attached (four for indemnity and four for medical). These exhibits are numbered as pages 2 through 9 respectively.

3 SUMMARY OF LOSS DEVELOPMENT TAIL FACTOR CALCULATIONS INDEMNITY MEDICAL Tail Tail VALUATION MATURITY Factor Factor 9V1 23RD TO ULT V9 23RD TO ULT V8 23RD TO ULT V7 23RD TO ULT AVERAGE OF LATEST 4 VALUATIONS

4 Inputs for Tail Factor Estimation Loss Cost Filing Indemnity: 9v1 Latest 12/31 to 1986 Incurred 4,768,295,55 Next Latest 12/31 to 1986 Incurred 4,766,671,573 1 Policy Yr 1985 Incurred = Average of 1986, 1987, 1988, reduced by PY Deflation ^ 2 CY Development of Yrs 1,623,977 2 PY 1984 & = Subsequent Yr x PY Deflation Next Latest PY 1986 Incurred 721,28, Development Selected Based on Observed 1986, 1987, 1988 # of 1986 Yrs in Data PY 1984 & Development = (Subsequent Yr - 1.) x Selected Decrement + 1. Selected Decrement, Development Factor.75 Selected Average PY Deflation Factor.95 TAIL = 1.41 vs ,623,977 Tail Factor Model Loss Cost Filing INDEMNITY Policy 12/31/1 Year Dollar Policy 12/31/1 Year Dollar 194 * 77,555, # 1976 * 491,545, , * 81,637, # 1977 * 517,416, , * 85,934, # 1978 * 544,649, , * 9,457, # 1979 * 573,315, , * 95,218, # 198 * 63,489, , * 1,229, # 1981 * 635,252, , * 15,54, # 1982 * 668,686, , * 111,57, # 1983 * 73,88, , * 116,92, # 1984 * 74,926, , * 123,55, # 1985 * 779,922, , TH TO ULT. 195 * 129,532, # ,419, RD TO ULT * 136,349, # ,117, * 143,526, # ,3, * 151,8, # ,15,653, Total 1954 * 159,31, # 199 1,183,312, Development: 1955 * 167,41, # ,37,355, ,623, * 176,212, # ,75, * 185,486, # ,167, * 195,249, # ,857, * 25,525, # ,363, * 216,342, # ,947, * 227,728, # ,533, * 239,714, # ,149, * 252,331, # ,297, * 265,611, # 2 682,963, * 279,591, # ,23, * 294,36, # ,924, * 39,796, ,46 1. # ,666, * 326,11, , # ,97, * 343,264, ,6 1. # ,997, * 361,331, , # ,215, * 38,348, ,58 1. # ,147, * 4,367, , # ,198, * 421,439, , # 29 42,16, * 443,62, , # ,595, * 466,968, , #

5 Inputs for Tail Factor Estimation Loss Cost Filing Medical 9v1 Latest 12/31 to 1986 Incurred 1,493,274,537 Next Latest 12/31 to 1986 Incurred 1,479,852,93 1 Policy Yr 1985 Incurred = Average of 1986, 1987, 1988, reduced by PY Deflation ^ 2 CY Development of Yrs 13,421,634 2 PY 1984 & = Subsequent Yr x PY Deflation Next Latest PY 1986 Incurred 318,181, Development Selected Based on Observed 1986, 1987, 1988 # of 1986 Yrs in Data PY 1984 & Development = (Subsequent Yr - 1.) x Selected Decrement + 1. Selected Decrement, Development Factor.75 Selected Average PY Deflation Factor.93 TAIL = vs ,421,634 Tail Factor Model Loss Cost Filing MEDICAL Policy 12/31/1 Year Dollar Policy 12/31/1 Year Dollar 194 * 14,29, # 1976 * 191,276, , * 15,85, # 1977 * 25,673, , * 16,221, # 1978 * 221,154, , * 17,442, # 1979 * 237,8, , * 18,754, # 198 * 255,699, , * 2,166, # 1981 * 274,945, , * 21,684, # 1982 * 295,64, ,38, * 23,316, # 1983 * 317,893, ,976, * 25,71, # 1984 * 341,82, ,828, * 26,958, # 1985 * 367,549, ,43, TH TO ULT. 195 * 28,988, # ,642, RD TO ULT * 31,169, # ,98, * 33,516, # ,333, * 36,38, # ,491, Total 1954 * 38,751, # ,149, Development: 1955 * 41,668, # ,14, ,421, * 44,84, # ,875, * 48,176, # ,276, * 51,83, # ,422, * 55,72, # ,64, * 59,894, # ,823, * 64,43, # ,156, * 69,25, , # ,191, * 74,462, , # ,36, * 8,67, , # 2 537,823, * 86,94, , # ,148, * 92,574, , # ,473, * 99,542, , # ,464, * 17,34, , # ,79, * 115,91, , # 25 66,44, * 123,754, , # 26 66,433, * 133,68, , # ,491, * 143,84, , # ,618, * 153,854, , # 29 51,793, * 165,435, , # ,468, * 177,887, , #

6 Inputs for Tail Factor Estimation Loss Cost Filing Indemnity: 8v9 Latest 12/31 to 1986 Incurred 4,723,492,361 Next Latest 12/31 to 1986 Incurred 4,72,82,988 1 Policy Yr 1985 Incurred = Average of 1986, 1987, 1988, reduced by PY Deflation ^ 2 CY Development of Yrs 3,49,373 2 PY 1984 & = Subsequent Yr x PY Deflation Next Latest PY 1986 Incurred 716,626, Development Selected Based on Observed 1986, 1987, 1988 # of 1986 Yrs in Data PY 1984 & Development = (Subsequent Yr - 1.) x Selected Decrement + 1. Selected Decrement, Development Factor.75 Selected Average PY Deflation Factor.95 TAIL = 1.51 vs ,49,373 Tail Factor Model Loss Cost Filing INDEMNITY Policy 12/31/9 Year Dollar Policy 12/31/9 Year Dollar 194 * 76,689, # 1975 * 461,751, , * 8,725, # 1976 * 486,54, , * 84,974, # 1977 * 511,636, , * 89,446, # 1978 * 538,564, , * 94,154, # 1979 * 566,99, , * 99,19, # 198 * 596,747, , * 14,326, # 1981 * 628,154, , * 19,816, # 1982 * 661,215, , * 115,596, # 1983 * 696,16, , * 121,68, # 1984 * 732,648, , * 128,85, # 1985 * 771,29, , RD TO ULT * 134,826, # ,39, * 141,922, # ,133, * 149,392, # ,43, * 157,254, # ,125,823, Total 1955 * 165,531, # 199 1,158,349, Development: 1956 * 174,243, # ,1,36, ,49, * 183,414, # ,493, * 193,67, # ,668, * 23,229, # ,497, * 213,925, # ,777, * 225,184, # ,857, * 237,36, # ,524, * 249,512, # ,315, * 262,644, # ,711, * 276,467, , # 2 668,77, * 291,18, , # ,48, * 36,335, , # ,218, * 322,458, ,83 1. # ,11, * 339,429, , # ,977, * 357,294, , # ,699, * 376,99, , # ,929, * 395,894, , # ,348, * 416,73, , # ,835, * 438,663, , # ,7,766 4

7 Inputs for Tail Factor Estimation Loss Cost Filing Medical 8v9 Latest 12/31 to 1986 Incurred 1,461,552,784 Next Latest 12/31 to 1986 Incurred 1,453,271,446 1 Policy Yr 1985 Incurred = Average of 1986, 1987, 1988, reduced by PY Deflation ^ 2 CY Development of Yrs 8,281,338 2 PY 1984 & = Subsequent Yr x PY Deflation Next Latest PY 1986 Incurred 314,873, Development Selected Based on Observed 1986, 1987, 1988 # of 1986 Yrs in Data PY 1984 & Development = (Subsequent Yr - 1.) x Selected Decrement + 1. Selected Decrement, Development Factor.75 Selected Average PY Deflation Factor.93 TAIL = vs ,281,338 Tail Factor Model Loss Cost Filing MEDICAL Policy 12/31/1 Year Dollar Policy 12/31/1 Year Dollar 194 * 13,66, # 1975 * 173,27, , * 14,688, # 1976 * 186,244, , * 15,794, # 1977 * 2,262, , * 16,983, # 1978 * 215,336, , * 18,261, # 1979 * 231,544, , * 19,636, # 198 * 248,972, , * 21,114, # 1981 * 267,712, , * 22,73, # 1982 * 287,862, , * 24,412, # 1983 * 39,529, ,219, * 26,249, # 1984 * 332,827, ,745, * 28,225, # 1985 * 357,879, ,498, RD TO ULT * 3,349, # ,426, * 32,634, # ,441, * 35,9, # ,475, * 37,731, # ,332, Total 1955 * 4,571, # ,785, Development: 1956 * 43,625, # ,548, ,281, * 46,99, # ,491, * 5,44, # ,416, * 54,236, # ,21, * 58,319, # ,45, * 62,78, # ,821, * 67,428, # ,963, * 72,53, # ,88, * 77,961, , # ,41, * 83,829, , # 2 521,32, * 9,138, , # ,31, * 96,923, , # 22 55,82, * 14,218, , # ,16, * 112,63, , # ,482, * 12,498, , # ,551, * 129,568, , # ,963, * 139,32, , # 27 61,937, * 149,86, , # ,22, * 161,82, , # ,23,556 5

8 Inputs for Tail Factor Estimation Loss Cost Filing Indemnity: 7v8 Latest 12/31 to 1986 Incurred 4,823,613,335 Next Latest 12/31 to 1986 Incurred 4,821,729,417 1 Policy Yr 1985 Incurred = Average of 1986, 1987, 1988, reduced by PY Deflation ^ 2 CY Development of Yrs 1,883,918 2 PY 1984 & = Subsequent Yr x PY Deflation Next Latest PY 1986 Incurred 73,672, Development Selected Based on Observed 1986, 1987, 1988 # of 1986 Yrs in Data PY 1984 & Development = (Subsequent Yr - 1.) x Selected Decrement + 1. Selected Decrement, Development Factor.75 Selected Average PY Deflation Factor.95 TAIL = 1.21 vs ,883,918 Tail Factor Model Loss Cost Filing INDEMNITY Policy 12/31/8 Year Dollar Policy 12/31/8 Year Dollar 1941 * 82,544, # 1975 * 472,156, , * 86,889, # 1976 * 497,6, , * 91,462, # 1977 * 523,165, , * 96,275, # 1978 * 55,7, , * 11,343, # 1979 * 579,684, , * 16,676, # 198 * 61,193, , * 112,291, # 1981 * 642,39, , * 118,21, # 1982 * 676,115, , * 124,422, # 1983 * 711,7, , * 13,971, # 1984 * 749,158, , RD TO ULT 1951 * 137,864, # 1985 * 788,587, , ND TO ULT * 145,12, # ,365, * 152,758, # ,47, * 16,798, # ,6,57, * 169,261, # ,164,88, Total 1956 * 178,169, # 199 1,191,295, Development: 1957 * 187,547, # ,49,568, ,883, * 197,418, # ,325, * 27,88, # ,91, * 218,745, # ,821, * 23,258, # ,311, * 242,377, # ,72, * 255,134, # ,718, * 268,562, # ,919, * 282,697, # ,59, * 297,576, # 2 76,572, * 313,238, , # ,847, * 329,724, ,73 1. # ,448, * 347,78, ,39 1. # ,77, * 365,345, , # ,194, * 384,574, ,78 1. # ,64, * 44,815, , # ,426, * 426,121, , # 27 46,887, * 448,548, , # 28 13,532,565 6

9 Inputs for Tail Factor Estimation Loss Cost Filing Medical 7v8 Latest 12/31 to 1986 Incurred 1,489,,219 Next Latest 12/31 to 1986 Incurred 1,474,478,859 1 Policy Yr 1985 Incurred = Average of 1986, 1987, 1988, reduced by PY Deflation ^ 2 CY Development of Yrs 14,521,36 2 PY 1984 & = Subsequent Yr x PY Deflation Next Latest PY 1986 Incurred 32,233, Development Selected Based on Observed 1986, 1987, 1988 # of 1986 Yrs in Data PY 1984 & Development = (Subsequent Yr - 1.) x Selected Decrement + 1. Selected Decrement, Development Factor.75 Selected Average PY Deflation Factor.93 TAIL = vs ,521,36 Tail Factor Model Loss Cost Filing MEDICAL Policy 12/31/8 Year Dollar Policy 12/31/8 Year Dollar 1941 * 15,27, # 1975 * 177,26, , * 16,159, # 1976 * 19,544, , * 17,375, # 1977 * 24,886, , * 18,683, # 1978 * 22,38, , * 2,89, # 1979 * 236,89, , * 21,61, # 198 * 254,721, , * 23,227, # 1981 * 273,893, ,43, * 24,975, # 1982 * 294,59, ,494, * 26,855, # 1983 * 316,676, ,138, * 28,877, # 1984 * 34,512, ,59, RD TO ULT * 31,5, # 1985 * 366,142, ,373, ND TO ULT * 33,387, # ,338, * 35,9, # ,883, * 38,63, # ,782, * 41,58, # ,672, Total 1956 * 44,632, # ,591, Development: 1957 * 47,992, # ,784, ,521, * 51,64, # ,613, * 55,488, # ,25, * 59,665, # ,643, * 64,156, # ,157, * 68,985, , # ,458, * 74,177, ,6 1.1 # ,64, * 79,761, , # ,382, * 85,764, , # ,64, * 92,22, , # 2 556,38, * 99,161, , # ,817, * 16,625, , # ,653, * 114,65, , # 23 53,585, * 123,28, , # ,59, * 132,559, , # ,326, * 142,537, , # ,217, * 153,265, , # ,53, * 164,82, , # ,952,32 7

10 Inputs for Tail Factor Estimation Loss Cost Filing Indemnity: 6v7 Latest 12/31 to 1986 Incurred 4,52,85,294 Next Latest 12/31 to 1986 Incurred 4,521,571,57 1 Policy Yr 1985 Incurred = Average of 1986, 1987, 1988, reduced by PY Deflation ^ 2 CY Development of Yrs -1,485,763 2 PY 1984 & = Subsequent Yr x PY Deflation Next Latest PY 1986 Incurred 691,536, Development Selected Based on Observed 1986, 1987, 1988 # of 1986 Yrs in Data PY 1984 & Development = (Subsequent Yr - 1.) x Selected Decrement + 1. Selected Decrement, Development Factor.75 Selected Average PY Deflation Factor.95 TAIL =.9987 vs ,485,763 Tail Factor Model Loss Cost Filing INDEMNITY Policy 12/31/7 Year Dollar Policy 12/31/7 Year Dollar 194 * 74,566, # 1974 * 426,522, , * 78,491, # 1975 * 448,97, , * 82,622, # 1976 * 472,6, , * 86,97, # 1977 * 497,474, , * 91,548, # 1978 * 523,657, , * 96,366, # 1979 * 551,218, , * 11,438, # 198 * 58,229, , * 16,777, # 1981 * 61,768, , * 112,397, # 1982 * 642,913, , * 118,312, # 1983 * 676,751, , RD TO ULT. 195 * 124,539, # 1984 * 712,369, , ND TO ULT * 131,94, # 1985 * 749,862, , ST TO ULT * 137,994, # ,8, * 145,257, # ,838, * 152,92, # ,98, Total 1955 * 16,949, # ,113,719, Development: 1956 * 169,42, # 199 1,148,748, ,485, * 178,337, # ,16,226, * 187,723, # ,157, * 197,63, # ,597, * 28,4, # ,623, * 218,951, # ,378, * 23,475, # ,287, * 242,65, # ,415, * 255,374, # ,357, * 268,815, # ,535, * 282,963, # 2 7,642, * 297,856, # ,99, * 313,532, , # ,229, * 33,34, , # ,22, * 347,44, , # ,44, * 365,689, ,71 1. # ,223, * 384,936, , # 26 4,31, * 45,196, , # ,763,184 8

11 Inputs for Tail Factor Estimation Loss Cost Filing Medical 6v7 Latest 12/31 to 1986 Incurred 1,372,85,87 Next Latest 12/31 to 1986 Incurred 1,358,187,617 1 Policy Yr 1985 Incurred = Average of 1986, 1987, 1988, reduced by PY Deflation ^ 2 CY Development of Yrs 14,663,253 2 PY 1984 & = Subsequent Yr x PY Deflation Next Latest PY 1986 Incurred 33,61, Development Selected Based on Observed 1986, 1987, 1988 # of 1986 Yrs in Data PY 1984 & Development = (Subsequent Yr - 1.) x Selected Decrement + 1. Selected Decrement, Development Factor.75 Selected Average PY Deflation Factor.93 TAIL = vs ,663,253 Tail Factor Model Loss Cost Filing MEDICAL Policy 12/31/7 Year Dollar Policy 12/31/7 Year Dollar 194 * 13,19, # 1974 * 155,536, , * 14,183, # 1975 * 167,243, , * 15,25, # 1976 * 179,832, , * 16,398, # 1977 * 193,367, , * 17,632, # 1978 * 27,922, , * 18,96, # 1979 * 223,572, , * 2,387, # 198 * 24,4, , * 21,921, # 1981 * 258,495, ,54, * 23,571, # 1982 * 277,951, ,59, * 25,345, # 1983 * 298,872, ,159, RD TO ULT. 195 * 27,253, # 1984 * 321,368, ,89, ND TO ULT * 29,34, # 1985 * 345,557, ,414, ST TO ULT * 31,51, # ,221, * 33,882, # ,533, * 36,432, # ,85, Total 1955 * 39,175, # ,173, Development: 1956 * 42,123, # ,52, ,663, * 45,294, # ,169, * 48,73, # ,592, * 52,369, # ,416, * 56,311, # ,26, * 6,549, # ,711, * 65,17, , # ,625, * 7,7, , # ,63, * 75,277, , # ,96, * 8,943, , # ,666, * 87,35, , # 2 55,53, * 93,586, , # 21 52,594, * 1,63, , # ,812, * 18,25, , # 23 52,53, * 116,349, , # ,612, * 125,17, , # ,322, * 134,523, , # 26 51,174, * 144,649, , # ,314,49 9