VOLUME LI NUMBERS 95 AND 96 PROCEEDINGS OF THE Casualty Actuarial Society DEZINAGRO 1914 1964 VOLUME LI Number 95- May 1964 Number 96- November 1964 1965 Year Book COPYRIGHT-- 1965 CASUALTY ACTUARIAL SOCIETY ALL RIGHTS RESERVED Printed for the Society by MAlL AND EXPRESS PRINTING COMPANY, INC. 225 Varick Street New York, New York 10014 CONTENTS OF VOLUME LI Page PREVIOUSLY PRESENTED PAPERS An Approximation for the Testing of Private Pas~nger Liability Territorial Rate Levels Using Statewide Distribution of Classification Data--James F. Gill (Nov. 1963) .............................................................................................. 1 Discussion By: Philipp K. Stern (May 1964) .......................................... 16 David A. Tapley (May 1964) ...................................... 20 Peter B. Zory (May 1964) ......................................... 22 Some Fundamentals of Insurance Statistics--Harry M. Sarason (Nov. 1963) ...... 25 Discussion By: Charles C. Hewitt, Jr. (Nov. 1964) ......................................... 44 Author's Review of Discussion .......................................................................... 45 PAPERS PRESENTED AT THE MAY 1964 MEETING A Glance at Group Dental Coverage--James H. Durkin .................................... 46 Discussion By: Roger A. Johnson (Nov. 1964) ......................................... 64 George E. McLean (Nov. 1964) .......................................... 66 MINUTES OF THE MAY 1964 MEETING .................................................................. 70 20, PRESIDENTIAL ADDRESS----NOVEMBER 1964 Thomas E. Murrin .................................................................................................. 77 PAPERS PRESENTED AT THE NOVEMBER 1.964 MEETING A Bayesian View of Credibility--Allen L. Mayerson ............................................ 85 Estimating the Cost of Accident Insurance as a Part of Automobile Liability Insurance----Herbert E. Wiltick .......................................................................... 105 Discussion By: Carl L. Wilcken (Nov. 1964) ......................................... 122 How to Tell A Pure Actuary From a Lay Actuary-- Matthew Rodermund ........................................................................................ 126 On Some Essential Properties of a Tariff Class-- Edward Franckx .................................................................................................. 131 Early Actuarial Studies in the Field of Property and Liability Insurance-- Laurence H. Longley-Cook ................................................................................. 140 The First Fifty Years--Dudley M. Pruitt ........................................................... 148 iii CONTENTS OF VOLUME LI (Cont,) Page The Optimal Management Policy of an Insurance Company-- Karl H. Botch ...................................................................................................... 182 Size of Loss Distributions in Workmen's Compensation Insurance-- Lester B. Dropkin .............................................................................. 198 Discussion By: Roy H. Kallop (Nov. 1964) .......................................... 243 LeRoy J. Simon (Nov. 1964) ........................................ 244 PANEL DISCUSSION---NOVEMBER 1964 MEETING Motor Insurance in Foreign Countries--Norton E. Masterson, Chairman • Hans Ammeter • Robert E. Beard • Karl H. Borch • B. Christoffersen * Edward Franckx • A. Tr6bliger .................................... 260 REPORT Observations on Casualty Insurance Rate-Making Theory in The United States -----Thomas O. Carlson ................................................................................. 282 GREETINGS FROM OTHER ACTUARIAL ORGANIZATIONS Hans Ammeter--ASTIN and the Swiss Actuarial Society ................................... 299 Robert E. Beard--lnstitute of Actuaries, England .......................................... 301 Karl H. Borch--Norwegian Society of Actuaries .......................................... 301 B. Christoffersen--Danish Association of Actuaries ............................................ 302 Gilbert W. Fitzhugh--Society of Actuaries ........................................................... 302 Edward Franckx--Royal Association of Belgian Actuaries ............................ 302 MINUTES OF THE NOVEMBER 1964 MEETING ..................................................... 304 OBITUARIES ................................................................................................................. 317 1964 EXAMINATIONS OF THE SOCIETY ................................................................... 330 INDEX TO VOLUME LI ....................................................................................... 359 INDEX TO VOLUMES THROUGH L ......................................................................... 365 1965 YEAR Boor: .......................................................................................................... NOTICE The Society is not responsible for statements or opinions expressed in the articles, criticisms, and discussions published in these Proceedings. iv VOL. LI, Part I No. 95 PROCEEDINGS MAY 18, 19, and 20, 1964 AN APPROXIMATION FOR THE TESTING OF PRIVATE PASSENGER LIABILITY TERRITORIAL RATE LEVELS USING STATEWIDE DISTRIBUTION OF CLASSIFICATION DATA JAMES F. GILL A previous paper ~ by Philipp K. Stern presented an excellent descrip- tion of basic ratemaking procedures for Automobile Liability insurance. To utilize this procedure, it is necessary to have territorial exposures by classification. Independent companies writing a large volume of private passenger liability business could use this method to test their private pas- senger liability territorial rate levels as they would probably have a suffi- cient volume of data in the necessary detail. Many small independent com- panies, however, would not have a sufficient volume of their own data and probably would not have a readily available source of data in the detail required by the procedure described in Mr. Stern's paper. A method is needed ,by statisticians and others responsible for rate levels of small inde- pendent companies so they may more easily determine the adequacy of their rate levels. The purpose of this paper is to explore the possibility of developing a method of testing private passenger liability territorial rate levels by sub- stituting the statewide distribution of classification data for the actual dis- tribution by rating territory. Such a method should be useful to small independent companies and could be used by company actuaries as a basis for estimating the adequacy of their rate levels. ATAD USED NI YDUTS The annual compilation of Automobile experience prepared by the National Association of Independent Insurers provided readily available data for such a study. 1 Current Rate Making Procedures for Automobile Liability Insurance, PC, IS XLIII, .p 112. 1 2 PRIVATE PASSENGER TERRITORIAL RATE LEVELS The NAIl calls for Automobile private passenger liability experience require data to be reported by coverage and classification statewide and by coverage and territory for all classifications combined in all states except Louisiana, New Jersey, New York, North Carolina, Texas and Virginia. Private passenger data for these six states are reported by coverage and classification for each territory. In order to determine the effect of substituting a statewide distribution for the actual territory distribution, statewide and territorial rate level changes were developed for the states of Lousiana, New Jersey, North Carolina and Virginia. The indicated rate level changes for each state were determined both on the basis of a statewide distribution of classification data and classification data by territory. Indicated rate level changes were also determined for the states of Alabama, Arkansas, Florida, Illinois, Ohio and Washington on the basis of each state's distribution of classification data statewide. It was decided to use only calendar/accident year ~- data and to test the results. The NAIl experience da.ta prior to 1958 was compiled on a policy year basis so that calendar/accident year experience was only available for the years 1958, 1959, 1960 and 1961. 1961 rate levels would ordinarily be developed in 1960 from experience data for the years 1957, 1958 and 1959 as this three-year period would be available for review in 1960. As calendar/accident year 19613 was to be used for testing the rate levels, the experience data to develop the rate levels was limited to calendar/accident years 1958' and 1959.' The three-year period 1958, 1959 and 1960 would have been used if calendar/accident year 1962 had beert available to test the rate levels. It is suggested that if the statewide distribution method is used, a three-year period should be considered as the longer period should provide a more stable base. DEVELOPMENT OF EARNED PREMIUM AT PRESENT RATES Earned premium at present rate level is required in order to deter- mine both the statewide rate level changes and the territorial rate level changes. To compute the earned premium, rates for basic limits are re- quired. The National Bureau of Casualty Underwriters rates were used as they were readily available. However, an independent company's rates or another rating bureau's rates could have been used. The developed rates -~ Exposures and premium compiled on a calendar year basis. Incurred losses, number of incurred losses .and allocated adjustment expense compiled by year of accident. a Incurred losses valued as of March ,13 .2691 • L Incurred losses valued as of~March ,13 .0691 ETAVIRP REGNESSAP LAIROTIRRET RATE SLEVEL 3 and loss ratios for 1961 would have been substantially the same regard- less of the basic limits rates used, provided the rate class differentials were the same. If a different set of basic limits rates had been used, they would have produced different rate level changes by state and territory, however, the application of these rate level changes to the rate schedule utilized should produce approximately the same revised rates as the method actu- ally used. The earned premium was calculated by multiplying N.B.C.U. private passenger car basic limits rates in effect in December of 1960 by the 1958 and 1959 earned car year exposures within each territory for each private passenger classification based on calendar/accident year 1959 distribution by class in each territory. The December 1960 rates were used on the assumption that 1958 and 1959 data would not be available until late in the fourth quarter of 1960. RATE LEVEL CHANGES To develop the statewide rate level changes for each of the ten states used in the study, factors were used to include unallocated loss adjustment expenses, to adjust losses to reflect changes in average paid claim costs sub- sequent to the experience period and to reflect the development of the in- curred losses to 63 months for bodily injury and 39 months for property damage. The factors used in this study have been utilized in past rate revi- sions. However, their accuracy is not important for the purpose of this study as the prime interest at this time is to determine the degree of rela- tionship between rates determined on the basis of the actual class distribu- tion by territory and rates developed .by substituting a statewide class dis- tribution for the actual territory distribution by class. The losses used to determine the territorial rate level changes were adjusted to include the un- allocated loss adjustment expenses using factors of 1.10 for bodily injury and 1.16 for property damage. The incurred losses including all adjust- ment expenses used to compute statewide rate level changes were devel- oped to 63 months for bodily injury and 39 months for property damage by application of the following development factors: Calendar/Accident Bodily Property Year Injury Damage 1958 .974 .989 1959 1.006 .962 4 PRIVATE PASSENGER TERRITORIAL RATE LEVELS The calendar/accident year weights, expected loss and loss adjustment ratios, loss trend factors and limits used for each state are as follows: Calendar/ Accident Expected Year Loss and Loss Loss Trend Weight Adjustment Factor State 8591 9591 Ratio B.I. P.D. Limits Alabama .15 .85 .645 1.051 1.104 5/10/5 Arkansas .15 .85 .630 1.035 1.053 10/20/5 Florida -- 1.00 .630 1.072 1.020 10/20/5 Illinois -- 1.00 .655 1.029 1.040 10/20/5 Louisiana .15 .85 .651 1.076 1.045 5/10/5 New Jersey -- 1.00 .636 1.014 1.065 10/20/5 North Carolina .15 .85 .650 1.119 1.110 5/10/5 Ohio -- 1.00 .625 1.040 1.028 10/20/5 Virginia .15 .85 .646 1.036 1.087 10/20/5 Washington -- 1.00 .655 1.107 1.054 10/20/5 The various calculations necessary for developing Louisiana statewide and territorial rate levels using classitication data by territory are set forth in Exhibits I and II. Exhibit I shows the development of the following statewide bodily in- jury and property damage rate level changes: Bodily Injury -- 9.1% Property Damage -- 13.5 Total -- 0.1% DEVELOPMENT OF 1961 RATES Exhibit II shows the development of the bodily injury rate level changes by territory. The indicated 1A bodily injury and property damage ~ rates were used to determine rates for the other private passenger classifications by application of the following differentials: 5 Property damage rates were developed using the procedure shown in Exhibit II for bodily injury. PRIVATE PASSENGER TERRITORIAL RATE LEVELS 5 Differentials to Class IA Rural and Small Large City ssalC City Territories Territories 1A 1.00 1.00 1B 1.00 1.10 IC 1.45 1.45 2A 1.90 1.90 2C 3.60 3.10 3 1.50 1.50 1AF .70 .70 2AF 1.33 1.33 2CF 2.52 2.17 The differentials for Classes 1A, 1AF, IB, IC and 3 were reduced 20% to reflect the discount for "two or more cars". The differentials were also reduced 10% to reflect the discount for compact carsf' All rates were rounded to the nearest dollar except for those states subject to the dis- count. Louisiana Statewide Distribution by Class 1959 Calendar/Accident year ssalC Earned Car Years Percentage 1A 42,811 32.8 1B 53,680 41.1 1C 6,272 4.8 2A 9,702 7.4 2C 1,087 .8 3 4,376 3.3 1AF 10,834 8.3 2AF 1,656 1.3 2CF 270 .2 Total 130,688 100.0 1A rates were also developed for Louisiana using the same procedure except that calendar/accident year 1959 statewide classification distribu- o The compact car discount si not applicable ni Louisiana dna North Carolina. PRIVATE PASSENGER TERRITORIAL RATE LEVELS tion percentages shown were multiplied by the total 1958 and 1959 earned car year exposure to determine the earned car year exposure by classifica- tion within each territory. The assumed earned car year exposures by class and territory were then multiplied by the December 1960 N.B.C.U. basic limits rates to develop earned premium at present rates. The indicated statewide rate level changes for Louisiana on the ,basis of the statewide distribution by class were as follows: Bodily Injury + 9.4% Property Damage -- 13.2 Total -1- 0.2% The effect of using the statewide distribution by class is reflected by an increase of 0.3% for bodily injury and property damage combined. TESTING FO SETAR The rates developed on both bases were used to determine the earned premium for calendar/accident year 1961. The premium was calculated by multiplying the rates by the earned exposures for each classification within each territory. The 1961 calendar/accident year basic limits in- curred losses were adjusted to include unallocated loss adjustment expenses by use of the factor of 1.10 for bodily injury and 1.16 for property damage. The adjusted basic limits losses for calendar/accident year 1961 were then divided by the earned premium to obtain territorial loss ratios on the basis of ,both sets of rates. The loss ratios were as follows: