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1994 Spring Forum, Volume 1 / CASUALTY ACTUARIAL SOCtETY FORUM Spring 1994 Volumb One i .- Including SelectedPapers from the -” 1994 Variability in Reserves Prize Pro&m .,C - CASVALTYACTVARI~ SOCIETY ORGANnED j, _/ CASUALTY ACTUARIAL SOCIETY Date: March 1994 To: CAS Readership Re: _The Forum, 1994 Soecial Edition This special edition of The Forum includes Stephen Philbrick’s “Accounting for Risk Margins,” a paper that was commissioned by the Committee on Reserves. Mr. Philbrick’s paper is preceded by a brief introduction by Paul O’Connell, explaining the committee’s charge in funding this paper. The main body of this issue is devoted to ten papers submitted for the Committee on the Theory of Risk prize on how to measure the variability of loss reserves. Gary Venter gives an introduction and summary of the ten Theory of Risk papers. He ends his introduction by listing outstanding issues that merit further research. As always, any submissions, question or comments may be directed to me, or anyone on the Committee on The Forum. Very Truly Yours, airperson, The Committee on The Forum The Casualty Actuarial Society Forum The Casualty Actuarial Society Forum is a non-refereed journal printed by the Casualty Actuarial Society. The viewpoints express in it do not necessarily reflect the views of the Casualty Actuarial Society. The Forum is edited by the committee for the Casualty Actuarial Society Forum. The committee for the Forum invites all members of the CAS to submit papers on top- ics of interest to the actuarial community. Articles need not be written by a member of the CAS, but should have content of interest to the CAS membership. The Forum is printed on a periodic basis, based on the number of articles submit- ted. Its goal is to publish two editions during the calendar year. Comments or questions about the Forum may be directed to the committee for the Casualty Actuarial Society Forum. Casualty Actuarial Society Forum Joel M. Kleimnan, Chairperson George R. Busche, Vice Chairperson Paul E. Lack0 James C. Wilson Stephen W. Philbrick’s paper “Accounting for Risk Margins” was edited by the CAS Committee on Reserves. The Committee on Reserves Paul G. O’Connell, Chairperson Raja R. Bhagavatula Mark I. Sobel Charles F. Cook Chris M. Suchar Todd J. Hess Ronald J. Swanstrom Jefkey P. Kadison John P. Tiemey Stephen P. Lowe Ronald F. Wiser Steven D. Marks The Theory of Risk call papers were edited by the CAS Committee on the Theory of Risk The Committee on the Theory of Risk Isaac Mashitz, Chairperson Roger M. Hayne, Vice Chairperson John G. Aquino Rodney E. Kreps Robert J. Finger Glenn G. Meyers Lmise A. Francis Gary S. Patrik William R. Gillam John P. Robertson Philip E. Heckman Richard J. Roth, Jr. Stuart A. Klugmsn Gary G. Venter VOLUME ONE OF TWO VOLUMES Correction The paper “A Quantification of Snader’s Deductible Safety Factor,” by John Rol- lins and Monty J. Washburn, which appeared in the 1994 edition of the Forum, In&d- ing the 1994 Ratemaking Call Papers, is a copyrighted paper. The copyright notice was inadvertently deleted in printing the Forum. The copyright notice should have read as follows: Copyright 1993. National Council on Compensation Insurance. All rights reserved. The material contained in this paper represents the ideas of the au- thors and not necessarily those of the National Council on Com- pensation Insurance. We regret the error, and apologize to all affected parties. Spring 1994 CAS Forum Table of Contents Paper/Author. RageNumber Volume Accounting for Risk Margins, StephenW. Philbrick with an introductionby Paul G. O’Connell . 1 . 1 SelectedPapers from the Variability in ReservesPrize Program Introduction, GaryG.Venter.. , . 91 . 1 Measuring the Variability of Chain Ladder ReserveE&mates, ThomasMack . , , . 101 . 1 Unbiased Loss Lkveiopment Factors, DanielM. Murphy . 183 . , 1 Correliuion and the bieasurement of Loss ReserveVariabiBty, RandallD. Holmberg . 247 . 1 Varkzbili@ of Loss Reserves, RobertL. Brown , . 279 . 1 A Method to Estimate Probability Levelfor Loss Reserves, RogerM.Hayne . 297 . 1 A Note on Simulation of Claim Activity for Use in Aggregate Loss Distributions, DanielK. Lyons . 357 . 1 StatisttM Methods for the Chain Ladder Tech&gut, RichardJ.Verrall . , 393 . 1 Probabilistic Development Factor Models with Applications to Loss ReserveVariability, Prediction Intervats and Risk Based Capital, BenZehnwirth , . , . + . 447 . 2 IBNR ReserveUnder a Loglinear Location-Scale RegressionModel, LouisDoray . 607 . 2 A Generalized Fmmework for the Stochastic Loss Reserving, ChangseobJoeKim . , . 653 . , , 2 Accounting for Risk Margins by Stephen W. Philbrick with an introduction by Paul G. 0’ Connell Introduction by Paul G. O’Connell The CAS Committee on Reserves is pleased to present a funded research paper titled “Accounting for Risk Maigins”, authored by Stephen W. Philbrick. The committee’s charge to Mr. Philbrick was to explore possible ways to adapt statutory and GAAP accounting to reflect formal existence of margins for adverse deviations in loss reserves. The focus was not to be on methods for calculating margins, but rather on proper accounting treatment for the calculated margin. In his paper he has accomplished this and more. Mr. Philbrick demonstrates the conflict between profit recognition and the true economic reality of the insurance transaction under both current accounting principles and in an environment where losses are discounted at a risk-free rate. Through his research in this area, he has advanced a theoretical framework that addresses the appropriate accounting technique for reflecting and amortizing a risk margin, which when used with discounted loss reserves, results in a more accurate formula for profit recognition. Mr. Philbrick’s paper is a valuable addition to casualty actuarial literature. It is certain to prompt debate among actuaries, accountants and others as well as to inspire additional research on the appropriate method or methods for calculating risk margins. The current and former members of the CAS Committee on Reserves who assisted on this project are as follows: Neil A. Bethel (Chairperson 1991-1993) Paul G. O’Connell (Chairperson 1994) Raja R. Bhagavatula Charles F. Cook Linda A. Dembiec Todd J. Hess Russell T. John Jeffrey P. Kadison Stephen P. Lowe Steven 13. Marks Richard J. Roth, Jr. Mark J. Sobel Chris M. Suchar Ronald Swanstrom John P. Tiemey Ronald F. Wiser Accounting for Risk Malgins By Stephen W. Philbrick Introduction The importance of risk margins is growing rapidly. Not long ago, the subject of risk margins was not considered a burning issue within the actuarial profession, much less the insurance community at large. The recent insolvencies in the industry and the attendant search for causes and solutions, however, have led to heightened interest in risk margins. Risk margins, whether in pricing or in loss reserves, have always been easy to understand superficially but difficult to pin down precisely. It is well known that case reserves and IBNR reserves are estimates of unknown future loss payments. Actual results will differ from estimated amounts, and the concept of risk margin reflects that fact. A risk-averse individual or corporation would prefer a fixed liability of $100 to a liability whose expected value is $100, but whose actual payout amount is uncertain. “The greater the uncertainty, the larger the risk margin,” Beyond that statement, however, there is little universal agreement. Methods vary not only for calculating uncertainty, but also for determining risk margins from uncertainty measures. 4 Furthermore, assuming a risk margin has been calculated, it is not obvious how that risk margin should be incorporated into statutory accounting, and it is arguable whether it should be incorporated at all. The purpose of this paper is to explore how such a risk margin should be incorporated in statutory accounting. Rather than researching methods of calculating risk, this paper will assume that a satisfactory method for calcuiating risk margins will be separately developed. Nevertheless, a discussion of the accounting treatment of risk margins can hardly proceed without a clear understanding of what we mean by the term “risk margin”. Unfortunately, the actuarial profession not only needs to develop methods to calculate a risk margin, but it also needs to agree on a common definition. There are three common situations where the term “risk margin” is used: undiscounted loss reserves, loss portfolio transfers, and self-insurance trust funds. Each of these situations will be discussed briefly. Undiscounficd Loss Reserves The term risk margin is commonly used in the observation that stating the loss reserve at nominal (rather than discounted) values provides an implicit risk margin. It is clear that the amount of the risk margin in this circumstance is the difference between undiscounted and discounted reserves. This observation, however, does not 5 provide much insight into the purpose or definition of a risk margin. Compounding the problem is the fact that there is no general agreement regarding which discount rate should be used in such a calculation; thus, the specific value of the implicit risk margin is not clearly defined. Loss Portfolio TmnsfetdCommutalions There is a market (albeit tiny) for loss reserves. A company retiring from business may sell a portfolio of reserves to another company. In theory, the amount of the purchase price less the present value of the expected payments represents a risk margin. Unfortunately, this does not provide a good empirical
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