Insurance Rates with Minimum Bias--Robert A
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VOLUME L NUMBERS 93 AND 94 PROCEEDINGS OF THE Casualty Actuarial Society ORGANIZED 1914 1963 VOLUME L Number 93- ~[ay 1963 Ntmd)cr 94--October 1963 1964 Year Book COPYRIGHT-- 1964 CASUALTY ACTUARIAL SOCIETY ALL RIGHTS RESERVED Printed for the Society by MAIL AND EXPRESS PRINTING COMPANY, 1NC, 225 Varick Street New York, New York 10014 CONTENTS OF VOLUME L Page PAPERS PRESENTED AT THE MAY 1963 MEETING Actuarial Note: Fixed and Variable Expenses--Lewis H. Roberts ................. I Discussion By: Paul S. Liscord (Oct. 1963) ....................................... 2 John H. Muetterties (Oct. 1963) ....................................... 3 Insurance Rates With Minimum Bias--Robert A. Bailey ................................... 4 Discussion By: James R. Berquist (Oct. 1963) ......................................... 11 Stephen S. Makgill (Oct. 1963) ......................................... 13 Rating By Layer of Insurance--Ruth E. Salzmann .......................................... 15 Discussion By: Robert L. Hurley (Oct. 1963) ......................................... 27 Robert Pollack (Oct. 1963) .......................................... 30 PANEL DISCUSSION--MAY 1963 MEETING An Analysis of the Adequacy of the Various Factors and Rating Values Used in Retrospective Rating--Chairman: Stephen S. Makgill ................................ 32 |NVITATIONAL ADDRESS--MAY 21, 1963 Medical Care Insurance--Compulsory or Freedom of Choice?--Gilbert W. Fitzhugh .................................................................. 50 DISCUSSIONS OF PAPERS PUBLISHED IN VOLUME XLLX Title and Author Discussion By An Introduction to Credibility Theory --Laurence H. Longley-Cook Arthur L. Bailey (May 1963) 59 Negative Binomial Rationale-- John W. Carleton (May 1963) 62 Thomas O. Carlson Kenneth L. Mclntosh (May 1963) 65 Author's Review (May 1963) 75 MINUTES OF THE MAY 1963 MEETING ............................................................... 78 iii CONTENTS OF VOLUME L (Cont.) Page PRESIDENTIAL ADDREss--OCTOBER 31, 1963 Laurence H. Longley-Cook .................................................................................... 82 PAPERS PRESENTED AT THE OCTOBER 1963 MEETING Commercial Package Policies--Rating and Statistics-- Robert A. Bailey • Edward J. Hobbs ° Frederic J. Hunt, Jr. ° Ruth E. Salzmann ............................................................................................... 87 Comprehensive Medical Insurance--Statistical Analysis for Ratemaking--John R. Bevan ........................................................................ ll 1 Discussion By: Eldon J. Klaassen (Oct. 1963) ......................................... 129 Allen D. Pinney (Oct. 1963) ......................................... 131 MINUTES OF THE OCTOBER 1963 MEETING ....... ,.................................................... 133 REVIEWS OF PUBLICATIONS .......................................................................................... 146 OBITUARIES ....................................................... ".............................. ."................................. 156 1963 EXAMINATIONS OF THE SOCIETY ................................................................... 161 INDEX TO VOLUME L ................................................................................................... 189 INDEX TO VOLUMES XLI TO L ................................................................................. 193 1964 YEAR BOOK ............................................................................................................ NOTICE The Society fs not responsible for statements or opinions expressed in the articles, criticisms, and discussions published in these Proceedings. iv VOL. L, Part I No. 93 PROCEEDINGS MAY 20, 21 and 22, 1963 ACTUARIAL NOTE: FIXED AND VARIABLE EXPENSES LEWIS H. ROBERTS A variety of meanings appear to have been attached to the exPression "fixed expenses," with the result that we sometimes find ourselves talking at cross- purposes. The intent of this note is to see if any clarification is possible. A cost which does not depend upon a particular variable is by definition constant, or fixed, with respect to that variable. For example, administrative costs do not depend upon premium rates although both may depend upon the value of money. A rate increase or a rate decrease does not affect the cost of underwriting, bookkeeping, etc. Administrative costs can therefore be logically regarded as fixed with respect to premium rates. Such costs, however, are obviously not fixed with respect to time since they depend upon the value of money and other factors, such as technology, which change with time. It might be observed that administrative costs, although fixed with respect to premium rates, are not fixed with respect to premiums since policies with larger premiums often involve more underwriting expense than policies with smaller premiums. The dependence, however, is indirect. Where the larger premium is a consequence only of higher rates there is no necessary dependence. The controlling factor is the amount of work entailed which, although correlated to some degree with premiums, actually depends on such factors as the com- plexity of the risk, the need for inspection, expected costs of loss adjustment, etc. The degree of correlation between administrative costs and size of premium will therefore be negligible when variations in premium size are due only to variations in rate for a given kind of business. Where, however, variations in premium are associated with variations in exposure there will often be corresponding, but smaller, variations in administrative costs. Hence administrative costs are in some cases Unrelated to premium and in other cases weakly related. Care is necessary to avoid error. Another sense in which costs can properly be regarded as fixed is as a minimum. If, for'example, it is known that a cost of at least $4 is incurred for every policy of a certain kind put on the books, then the fixed cost of this policy is $4 in the sense that $4 is the constant term in a mathematical equation. As such it will contain some elements of administrative cost but not necessarily all. Inspection, for example, could hardly be included. 2 FIXED AND VARIABLE EXPENSES A third sense in which costs can properly be regarded as fixed is reflected in the "out-of-pocket" cost principle, to which reference is frequently made in ratemaking for public utilities. Here, if a given increment to a carrier's total business will produce more revenue than the resulting increment to expenses, the new business is said to cover out-of-pocket costs. Any excess is a contribution toward overhead and profit. Fixed expenses here are all those which are not increased. The problem of defining fixed expenses in such cases is complicated by the fact that, whereas an increment of one size may not affect certain costs, a larger increment will do so. Each case must be analyzed from its own facts. It is apropos to remark here that where competition leads to widespread use of rates sufficient only to cover out-of- pocket costs, financial failures can be expected. Contrasting with fixed costs, certain costs such as commissions, premium taxes, and assessments are clearly variable with respect to premiums. The correlation here is complete within a kind of business subject to the same tax rates. Another kind of variable cost is allocated overhead. This paradoxi- cal definition arises from the fact that important "fixed" expenses must be covered one way or another. One way is to allocate them arbitrarily as a function of premium, say as a constant percentage. If the allocation at every instant is in proportion to "standardized premium in force,"* then the fixed expenses so allocated are made a function of earned premium by fiat. It is no wonder, considering the foregoing, that different meanings have been attached to the expression "fixed expenses." Different things are meant in different contexts. The Author suggests that when we refer to "fixed" expenses we take pains to be sure that the sense in which the word is used is clear. The use of such expressions as "costs independent of premium," "minimum costs per policy," "costs independent of exposure," etc., would make for better understanding in many cases. DISCUSSION BY PAUL S. LISCORD As one who is constantly being tripped up by terminology I find Mr. Rob- erts' paper on Fixed and Variable Expenses extremely helpful. It should be required reading for those of us who are faced with the forthcoming study of expenses by size of risk for Workmen's Compensation on Liability lines. Such a study after all concerns itself with an analysis of "fixed expenses" which include those defined by Mr. Roberts as " '... costs independent of premium,' 'minimum costs per policy', 'costs independent of exposure,' etc." The fact that these expenses are subsequently related to premiums (by size) only makes it of increasing importance to recognize differences not only in terminology, but also in measurability and controllability. We are indebted to Mr. Roberts for what 1 hope is an introduction to many more contributions to our Proceedings on this subject. * An expression coined by the author to denote the value obtained by dividing each premium in force by the term which it covers and adding the quotients. Integration of this sum with respect to time yields earned premium. FIXED AND VARIABLE EXPENSES 3 DISCUSSION BY JOHN H. MUETI'ERTIES This actuarial note under discussion "Fixed and Variable Expenses" has as its closing remark a