Basic Ratemaking Version 5 May 2016 2


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BASIC RATEMAKING
Fifth Edition, May 2016 Geoff Werner, FCAS, MAAA Claudine Modlin, FCAS, MAAA Willis Towers Watson
With significant contributions from: Alice Gannon, FCAS, MAAA; Serhat Guven, FCAS, MAAA; Christine Gennett, ACAS, MAAA; Jeff Kucera, FCAS, MAAA; Brett Nunes, ASA, MAAA; and Dave Otto, FCAS, MAAA
© Casualty Actuarial Society, 2016

Basic Ratemaking
Geoff Werner, FCAS, MAAA and Claudine Modlin, FCAS, MAAA Willis Towers Watson
With significant contribution from: Alice Gannon, FCAS, MAAA; Serhat Guven, FCAS, MAAA; Christine Gennett, ACAS, MAAA; Jeff Kucera, FCAS, MAAA;
Brett Nunes, ASA, MAAA; Dave Otto, FCAS, MAAA
VERSION 5, MAY 2016 © Copyright Casualty Actuarial Society, 2016
This text outlines basic property/casualty insurance ratemaking concepts and techniques. It is intended to be a single educational text to prepare actuarial candidates practicing around the world for basic ratemaking. A key concept in the text is the fundamental insurance equation, which balances the expected future income and outgo of an insurance operation. Various chapters discuss the individual components of the equation (e.g., premium, loss, expense, profit), and other chapters review how to assess whether the equation is in balance in the aggregate and by customer segment. The text focuses on quantitative analysis as well as practical considerations in the ratemaking process. Finally, the text provides consistent definitions of terms and examples that underlie the ratemaking techniques discussed.
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FOREWORD
Ratemaking is a key driver of property and casualty (P&C) insurance profitability and hence a primary actuarial responsibility. Actuaries employ a variety of ratemaking techniques depending on specific circumstances. For example, techniques used to price short-tailed lines of insurance (e.g., personal automobile) are different than techniques used in long-tailed lines (e.g., workers compensation). Even within the same insurance product, actuarial techniques may differ due to regulatory requirements and data limitations. Furthermore, actuarial techniques are constantly evolving due to enhanced information and advances in technology.
This text is not intended to document every technique used for P&C insurance ratemaking. Instead, the purpose of this text is to provide an overview of basic ratemaking techniques used in the industry. As such, actuaries should continue to increase the depth and breadth of their knowledge to be able to discern the most appropriate technique for a given situation.
ACKNOWLEDGMENTS
The completion of this text required significant effort from many individuals other than the primary authors. The authors want to acknowledge the following individuals for researching and summarizing existing ratemaking material, offering alternative ratemaking techniques, and reviewing countless drafts:
Catherine Taylor, FCAS, MAAA and her CAS committee, comprised of Nancy Braithwaite, FCAS, MAAA; Ginda Fisher, FCAS, MAAA; Chris Styrsky, FCAS, MAAA; Jane Taylor, FCAS, MAAA; Theresa Turnacioglu, FCAS, MAAA; and Ron Zaleski, Jr., FCAS, MAAA, dedicated to partnering with EMB to facilitate the successful completion of this text.
The following associates of EMB: Tom Hettinger, ACAS, MAAA; David Sommer, FCAS; Emily Stoll, ACAS, MAAA; Julie Walker, ACAS, MAAA; Sandy Wu, ACAS, MAAA; Harsha Maddipati; and Peter Quackenbush.
The following actuaries who were consulted for their expertise in specific ratemaking topics: Joseph Palmer, FCAS, MAAA; James Guszcza, FCAS, MAAA; and Will Davis, FCAS, MAAA.
All of the authors who developed the materials from the prior Ratemaking examination; EMB relied heavily upon that material when creating this text.
Howard Mahler, FCAS, MAAA for his valuable contributions to subsequent versions of the text.
REFERENCE MATERIAL
The objective of the CAS in creating a new basic ratemaking text was to replace the series of readings that existed on the syllabus of basic education as of 2007 with a single educational publication. As such, the authors relied heavily on a series of published articles and texts that are contained in the Bibliography at the end of the text. Specific references to each of these sources are also present in individual chapters.
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ROUNDING
Rounding procedures have been applied in a manner consistent with the number of decimals shown in the text and tables (or per rounding procedures specifically outlined in the text). Small discrepancies may exist between the text and table entries when the text is summarizing multiple calculations within a table or further dissecting calculations in a table for illustrative purposes.
ORGANIZATION OF THIS TEXT
This text is organized into sixteen chapters plus six appendices. The chapters discuss various ratemaking concepts and techniques, and provide simple examples. Each chapter concludes with a narrative summary as well as an outline of key concepts covered in the chapter. The appendices provide in-depth practical examples of some of the techniques discussed throughout the text. In order to reinforce the concepts and techniques discussed in the body of the text, the authors suggest Appendices A-D be read upon completion of Chapter 8, and Appendices E-F be read upon completion of Chapters 9-10.
Below is a summary of the content of each chapter and appendix.
Chapter 1 provides an overview of P&C insurance ratemaking, highlighting the unique relationship between price, cost, and profit. This overview includes basic P&C insurance terms and commonly used insurance ratios. This chapter also introduces the fundamental insurance equation, a key concept that is referenced frequently in other chapters. This concept states that premium charged for policies written during a future time period should be appropriate to cover the losses and expenses expected for those policies while achieving the targeted profit.
Chapter 2 discusses the P&C insurer rating manual, an aid for anyone who needs to understand the process of calculating an insurance premium. The four main components of P&C insurer rating manuals are rules, rate pages, rating algorithms, and underwriting guidelines. The chapter also includes three rating manual examples for different insurance lines of business.
Chapter 3 discusses ratemaking data, both internal and external to the insurance company, and introduces methods of data organization. An example of internal data requirements is provided, as well as sources of external data.
Chapter 4 discusses insurance exposures, the basic unit that measures a policy’s exposure to loss and therefore serves as the basis for the calculation of premium. The chapter outlines criteria for selecting exposure bases, methods and quantitative examples for defining and aggregating exposures, and circumstances requiring a measurement of exposure trend.
Chapter 5 focuses on premium, the price the insured pays for the insurance product and one of the key elements of the fundamental insurance equation. The chapter discusses different ways to define and aggregate premium (including quantitative examples) and introduces standard techniques to adjust historical premium data to make it relevant for estimating future premium in the context of ratemaking. These adjustments include current rate level, premium development in consideration of premium audits, and premium trend. These adjustments to premium are relevant in loss ratio analysis.
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Chapter 6 is dedicated to losses and loss adjustment expenses. Losses are amounts paid or owed to claimants under the provisions of the insurance contract. This chapter outlines the different types of insurance losses, reviews how loss data is aggregated for ratemaking analysis, and defines common metrics involving losses. This chapter also describes the various adjustments to historical loss data to make it relevant for estimating future losses. These include adjustments for extraordinary events, changes in benefit levels, changes in loss estimates as claims mature, and changes in cost levels over time. Finally, the chapter discusses the treatment of loss adjustment expenses in ratemaking.
Chapter 7 covers methods for projecting underwriting expenses and addresses how to incorporate the cost of reinsurance and an underwriting profit provision in the rates.
Chapter 8 demonstrates how to combine the various estimated components of the fundamental insurance equation (i.e., premium, loss, expense) to ascertain the appropriate overall rate level (or rate level change) for the future policy period. The two overall rate level methods discussed are the pure premium and loss ratio methods. The methods are mathematically equivalent, but each offers advantages and disadvantages in certain circumstances.
Chapter 9 covers rate adequacy at the individual risk (or risk segment) level. The chapter discusses the concept of risk segmentation via rating variables and outlines criteria to consider when using a certain risk characteristic as a rating variable. The chapter also reviews the application of univariate methods to historical data to calculate rate differentials (or changes to existing rate differentials) for each rating variable. This process is known as classification ratemaking.
Chapter 10 is an extension of Chapter 9 that specifically addresses multivariate classification ratemaking techniques. The chapter discusses the benefits of multivariate approaches and provides a basic explanation of the mathematical foundation of one commonly used multivariate method, generalized linear models (GLMs). Sample output with explanation is provided for GLM results as well as associated statistical diagnostics. The chapter also reviews some commonly used data mining techniques.
Chapter 11 addresses additional classification ratemaking techniques that were developed to address the unique qualities of some rating variables or risk characteristics. These include territory boundary analysis, increased limits factors, deductibles, size of risk for workers compensation insurance, and the concept of insurance to value and how it affects the adequacy of rates.
Chapter 12 provides a broad overview of the credibility procedures used in ratemaking. This includes methods for incorporating credibility in an actuarial estimate, desirable qualities for the complement of credibility (the related data that is blended with the original actuarial estimate), and methods and examples for determining the complement of credibility.
Chapter 13 explores other items company management should consider, along with the actuarial indications discussed in the previous chapters, to determine what rates to charge in practice. These considerations include regulatory constraints, operational constraints, and market conditions.
Chapter 14 discusses non-pricing and pricing solutions to an imbalanced fundamental insurance equation (i.e., current rates do not produce an average premium that is equivalent to the sum of expected costs and target underwriting profit). In regards to pricing solutions, the chapter discusses how to calculate final rates for an existing product, as well as how to develop rates for a new product by referencing other data sources. The chapter concludes with comments regarding the importance of communicating expected rate change results to key stakeholders and monitoring results after implementation.
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Chapter 15 covers additional ratemaking methods commonly used by commercial insurers. The methods are divided into two categories: those that alter the rate calculated from the rating manual and those that are employed by insurers to calculate a premium unique to a particular large commercial risk. The former category includes experience rating and schedule rating, and the latter category includes loss-rated composite risks, large deductible policies, and retrospective rating. Chapter 16 discusses the adoption of claims-made policies, with particular attention to the medical malpractice line of business. This alternative to occurrence policies shortens the time period from coverage inception to claim settlement. For the ratemaking actuary, this translates to a shorter forecast period and therefore reduced pricing risk. Appendices A-D provide illustrative examples of overall rate level analyses for personal automobile, homeowners, medical malpractice, and workers compensation lines of business. The examples incorporate many of the ratemaking concepts and techniques discussed in Chapters 1-8. Appendices E-F provide illustrative examples of classification ratemaking analysis using the univariate and multivariate techniques discussed in Chapters 9 and 10, respectively.
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TEXT NOTATION
The text contains a significant number of formulae. The following is a summary of the key notation that appears throughout the text. Actual references in the text may specify more precise definitions (e.g., L could be used to describe accident year reported losses, policy year ultimate losses, etc.).

X

= Exposures

P; P = Premium; Average premium (P divided by X)

Pc;Pc = Premium at current rates; Average premium at current rates (PC divided by X)

PI;PI = Indicated premium; Average indicated premium (PI divided by X)

PP;PP = Premium at proposed rates; Average premium at proposed rates (PP divided by X)

L;L = Losses; Pure Premium (L divided by X)

EL;EL = Loss Adjustment Expense (LAE); Average LAE per exposure (EL divided by X)

EF;EF = Fixed underwriting expenses; Average underwriting expense per exposure (EF divided by X)

EV

= Variable underwriting expenses

F

= Fixed expense ratio (EF divided by P)

V

= Variable expense provision (EV divided by P)

QC

= Profit percentage at current rates

QT

= Target profit percentage

BC

= Current base rate

BP

= Proposed base rate

R1C,i = Current relativity for the ith level of rating variable R1

R1P,i = Proposed relativity for the ith level of rating variable R1

AC

= Current fixed additive fee

AP

= Proposed fixed additive fee

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TABLE OF CONTENTS
FOREWORD ............................................................................................................................................................... I
ACKNOWLEDGMENTS........................................................................................................................................ II REFERENCE MATERIAL...................................................................................................................................... II ROUNDING ............................................................................................................................................................ II ORGANIZATION OF THIS TEXT ........................................................................................................................ III TEXT NOTATION ................................................................................................................................................. VI
TABLE OF CONTENTS ........................................................................................................................................VII
CHAPTER 1: INTRODUCTION..............................................................................................................................1
RATING MANUALS ...............................................................................................................................................1 BASIC INSURANCE TERMS .................................................................................................................................1 FUNDAMENTAL INSURANCE EQUATION........................................................................................................5 BASIC INSURANCE RATIOS ................................................................................................................................7 SUMMARY ............................................................................................................................................................11 KEY CONCEPTS IN CHAPTER 1.........................................................................................................................12
CHAPTER 2: RATING MANUALS ......................................................................................................................13
RULES ....................................................................................................................................................................13 RATE PAGES .........................................................................................................................................................14 RATING ALGORITHMS.......................................................................................................................................15 UNDERWRITING GUIDELINES .........................................................................................................................16 HOMEOWNERS RATING MANUAL EXAMPLE...............................................................................................17 MEDICAL MALPRACTICE RATING MANUAL EXAMPLE ............................................................................23 U.S. WORKERS COMPENSATION RATING MANUAL EXAMPLE ................................................................29 SUMMARY ............................................................................................................................................................34 KEY CONCEPTS IN CHAPTER 2.........................................................................................................................35
CHAPTER 3: RATEMAKING DATA...................................................................................................................36
INTERNAL DATA .................................................................................................................................................36 DATA AGGREGATION ........................................................................................................................................42 EXTERNAL DATA................................................................................................................................................44 SUMMARY ............................................................................................................................................................47 KEY CONCEPTS IN CHAPTER 3.........................................................................................................................48
CHAPTER 4: EXPOSURES ...................................................................................................................................49
CRITERIA FOR EXPOSURE BASES ...................................................................................................................49 EXPOSURES FOR LARGE COMMERCIAL RISKS............................................................................................51 AGGREGATION OF EXPOSURES ......................................................................................................................51 EXPOSURE TREND ..............................................................................................................................................61 SUMMARY ............................................................................................................................................................62 KEY CONCEPTS IN CHAPTER 4.........................................................................................................................63
CHAPTER 5: PREMIUM .......................................................................................................................................64
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PREMIUM AGGREGATION ................................................................................................................................64 ADJUSTMENTS TO PREMIUM ...........................................................................................................................71 SUMMARY ............................................................................................................................................................88 KEY CONCEPTS IN CHAPTER 5.........................................................................................................................89
CHAPTER 6: LOSSES AND LAE..........................................................................................................................90
LOSS DEFINITIONS .............................................................................................................................................90 LOSS DATA AGGREGATION METHODS .........................................................................................................91 COMMON RATIOS INVOLVING LOSS STATISTICS.......................................................................................93 ADJUSTMENTS TO LOSSES ...............................................................................................................................94 LOSS ADJUSTMENT EXPENSES......................................................................................................................121 SUMMARY ..........................................................................................................................................................123 KEY CONCEPTS IN CHAPTER 6.......................................................................................................................124
CHAPTER 7: OTHER EXPENSES AND PROFIT............................................................................................125
SIMPLE EXAMPLE .............................................................................................................................................125 UNDERWRITING EXPENSE CATEGORIES ....................................................................................................126 ALL VARIABLE EXPENSE METHOD ..............................................................................................................127 PREMIUM-BASED PROJECTION METHOD ...................................................................................................130 EXPOSURE/POLICY-BASED PROJECTION METHOD ..................................................................................133 TRENDING EXPENSES ......................................................................................................................................135 REINSURANCE COSTS......................................................................................................................................137 UNDERWRITING PROFIT PROVISION ...........................................................................................................138 PERMISSIBLE LOSS RATIOS............................................................................................................................139 SUMMARY ..........................................................................................................................................................139 KEY CONCEPTS IN CHAPTER 7.......................................................................................................................140
CHAPTER 8: OVERALL INDICATION ............................................................................................................141
PURE PREMIUM METHOD ...............................................................................................................................141 LOSS RATIO METHOD ......................................................................................................................................143 LOSS RATIO VERSUS PURE PREMIUM METHODS......................................................................................145 SUMMARY ..........................................................................................................................................................147 KEY CONCEPTS IN CHAPTER 8.......................................................................................................................149
CHAPTER 9: TRADITIONAL RISK CLASSIFICATION ...............................................................................150
IMPORTANCE OF EQUITABLE RATES...........................................................................................................151 CRITERIA FOR EVALUATING RATING VARIABLES ..................................................................................154 TYPICAL RATING (OR UNDERWRITING) VARIABLES ..............................................................................159 DETERMINATION OF INDICATED RATE DIFFERENTIALS .......................................................................159 WORKSHEET EXAMPLE...................................................................................................................................168 SUMMARY ..........................................................................................................................................................168 KEY CONCEPTS IN CHAPTER 9.......................................................................................................................169
CHAPTER 10: MULTIVARIATE CLASSIFICATION ....................................................................................170
A REVIEW OF THE SHORTCOMINGS OF UNIVARIATE METHODS....................................................................170 MINIMUM BIAS PROCEDURES .......................................................................................................................171
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THE ADOPTION OF MULTIVARIATE METHODS .........................................................................................174 THE BENEFITS OF MULTIVARIATE METHODS ...........................................................................................174 GLMS ....................................................................................................................................................................176 SAMPLE GLM OUTPUT .....................................................................................................................................177 A SAMPLE OF GLM DIAGNOSTICS.................................................................................................................179 PRACTICAL CONSIDERATIONS .....................................................................................................................183 DATA MINING TECHNIQUES ..........................................................................................................................183 AUGMENTING MULTIVARIATE ANALYSIS WITH EXTERNAL DATA....................................................185 SUMMARY ..........................................................................................................................................................185 KEY CONCEPTS IN CHAPTER 10.....................................................................................................................187
CHAPTER 11: SPECIAL CLASSIFICATION...................................................................................................188
TERRITORIAL RATEMAKING .........................................................................................................................188 INCREASED LIMITS RATEMAKING...............................................................................................................192 DEDUCTIBLE PRICING .....................................................................................................................................199 SIZE OF RISK FOR WORKERS COMPENSATION ..........................................................................................204 INSURANCE TO VALUE (ITV)..........................................................................................................................206 SUMMARY ..........................................................................................................................................................213 KEY CONCEPTS FOR CHAPTER 11 .................................................................................................................215
CHAPTER 12: CREDIBILITY..............................................................................................................................216
NECESSARY CRITERIA FOR MEASURES OF CREDIBILITY ......................................................................216 METHODS FOR MEASURING CREDIBILITY IN AN ACTUARIAL ESTIMATE .........................................216 DESIRABLE QUALITIES OF A COMPLEMENT OF CREDIBILITY ..............................................................223 METHODS FOR DEVELOPING COMPLEMENTS OF CREDIBILITY ...........................................................224 CREDIBILITY WHEN USING STATISTICAL METHODS ..............................................................................236 SUMMARY ..........................................................................................................................................................236 KEY CONCEPTS IN CHAPTER 12.....................................................................................................................238
CHAPTER 13: OTHER CONSIDERATIONS.....................................................................................................239
REGULATORY CONSTRAINTS........................................................................................................................239 OPERATIONAL CONSTRAINTS.......................................................................................................................241 MARKETING CONSIDERATIONS....................................................................................................................244 SUMMARY ..........................................................................................................................................................261 KEY CONCEPTS IN CHAPTER 13.....................................................................................................................262
CHAPTER 14: IMPLEMENTATION .................................................................................................................263
EXAMPLE IMBALANCE....................................................................................................................................263 NON-PRICING SOLUTIONS ..............................................................................................................................263 PRICING SOLUTIONS ........................................................................................................................................264 CALCULATING NEW RATES FOR AN EXISTING PRODUCT......................................................................264 CALCULATING NEW RATES BASED ON BUREAU OR COMPETITOR RATES ........................................285 COMMUNICATING AND MONITORING ........................................................................................................286 SUMMARY ..........................................................................................................................................................287 KEY CONCEPTS IN CHAPTER 14.....................................................................................................................288
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Basic Ratemaking Version 5 May 2016 2