Understanding Actuarial Practice Stuart A. Klugman Editor Jeff rey A. Beckley Patricia L. Scahill Matthew C. Varitek Toby A. White SSOOAA__ffmm..iinndddd ii 0022//0011//1122 1111::5599 AAMM Copyright © 2012. Society of Actuaries. All rights reserved under U.S. and international laws. No part of this publication may be reproduced or distributed in any form without the express written permission of the Society of Actuaries. Th is publication is provided for informational and educational purposes only. Th e Society of Actuaries makes no representation or guarantee with regard to its content, and disclaims any responsibility or liability in connection with the use or misuse of any information provided herein. Th is publication should not be construed as professional or fi nancial advice. State- ments of fact and opinions expressed herein are those of the individual author and are not necessarily those of the Society of Actuaries or its offi cers, directors, staff or representatives. Th e Society of Actuaries does not endorse or make any guarantee with regard to any prod- ucts, services or procedures mentioned or advertised herein. Library of Congress Cataloging-in-Publication Data Understanding actuarial practice / Stuart A. Klugman, editor. p. cm. ISBN 978-0-9759337-5-6 (alk. paper) 1. Actuarial science. I. Klugman, Stuart A., 1949– HG8781.U495 2013 368’.01—dc23 2011050636 ISBN 978-0-9759337-5-6 First Edition Printed in the United States of America 16 15 14 13 12 1 2 3 4 5 SSOOAA__ffmm..iinndddd iiii 0022//0011//1122 1111::5599 AAMM Contents PART 1: INTRODUCTION 1 1 Introduction 3 1.1 Purpose of This Textbook 3 1.2 Prerequisites 5 1.3 How to Use This Textbook 5 1.4 Actuarial Work and the Actuarial Profession 6 2 Actuarial Science and the Actuarial Profession 7 2.1 A Brief History of Actuarial Science and the Actuarial Profession 7 2.2 What Actuaries Do and What Sets Them Apart 9 2.3 Financial Security Systems 13 2.4 Insurance Industry Overview 23 2.5 Actuarial Areas of Practice 26 2.6 Key Competencies for Actuaries 34 3 The Actuarial Control Cycle 39 3.1 Introduction 39 3.2 Versions and Evolution of the Actuarial Control Cycle 40 3.3 An Expanded Discussion of the Control Cycle 45 3.4 Control Cycle Examples 47 3.5 Some Conclusions about Actuarial Work and the Control Cycle 51 4 Principles of Actuarial Science 53 PART 2: INVESTMENTS 55 5 Introduction and External Factors 57 5.1 Overview of Investments Section 57 5.2 External Factors Aff ecting Investment Decisions 57 iii SSOOAA__ffmm..iinndddd iiiiii 0022//0011//1122 1111::5599 AAMM iv Contents 6 Interest Theory 65 6.1 Types of Interest Rates 65 6.2 Two Approaches to Interest 69 6.3 Capital Budgeting 71 6.4 Annuities 75 7 Asset Types 85 7.1 Underlying Assets 85 7.2 Derivatives 92 7.3 Assets Used in Insurance Company Portfolios 100 8 Investing/Portfolio Management 103 8.1 Introductory Investment Issues 103 8.2 Mean-Variance Analysis 107 8.3 Other Issues 113 9 Finance Models and Data 121 9.1 Capital Asset Pricing Model 121 9.2 Other Financial Modeling Frameworks 126 9.3 Data and Estimation 133 10 The Term Structure of Interest Rates 139 10.1 Interest Rates 139 10.2 Yield Curves 143 11 Asset and Liability Management 151 11.1 Interest Rate Sensitivity 151 11.2 Immunization 159 11.3 More on Asset and Liability Matching 162 11.4 Asset and Liability Management Risk Measures for Life Insurance Companies 164 SSOOAA__ffmm..iinndddd iivv 0022//0011//1122 1111::5599 AAMM Contents v PART 3: LIFE INSURANCE AND ANNUITIES 169 12 Introduction 171 13 Types of Coverage 173 13.1 Life Insurance 173 13.2 Annuities 213 14 External Forces and Life and Annuity Products 231 14.1 Cultural and Social Factors 231 14.2 Demographic Trends 232 14.3 Economic and Business Environment 235 14.4 Government Infl uences 236 15 Pricing 241 15.1 Measuring Profi tability 241 15.2 Profi t Measures 244 16 Profi t Testing 253 16.1 Approaches to Profi t Testing 253 16.2 Pricing Tools 261 16.3 Asset Shares 261 16.4 Analysis of Book Profi ts 267 16.5 Sources of Profi t 280 16.6 Company Models 282 17 Inputs for Profi t Testing 289 17.1 Investment Income 289 17.2 Equity Returns 289 17.3 Mortality 290 17.4 Persistency 290 17.5 Expenses 291 SSOOAA__ffmm..iinndddd vv 0022//0011//1122 1111::5599 AAMM vi Contents 18 Regulatory Infl uences on Profi t Testing 295 18.1 Reserves 295 18.2 Reserve Model 298 18.3 Nonforfeiture Requirements 321 18.4 Income Taxes 331 18.5 Required Surplus 331 18.6 Premiums 332 19 Monitoring Results 337 19.1 Why Monitor Experience 337 19.2 What to Monitor 337 20 Closing 341 PART 4: RETIREMENT BENEFITS 343 21 Introduction to Retirement Plans 345 21.1 External Forces Underlying the Need for a Retirement Income System 345 21.2 History of Retirement Plans 355 22 Overview of Retirement Financial Security Systems 359 22.1 Most Common Types of Formal Retirement Plans 359 22.2 Government-Sponsored Social Security Systems 362 22.3 Employer-Sponsored Retirement Programs 375 22.4 Tax Structure of U.S. Employer-Sponsored Pensions 376 22.5 The Role of the Courts in Retirement Plans 382 22.6 Canadian Employer-Sponsored Pensions 383 22.7 U.K. Pension System 385 22.8 Mexican Pension System 386 22.9 The Actuary’s Role in Employer-Sponsored Defi ned Benefi t Pensions 386 22.10 Advantages of Having Retirement Income from Multiple Sources 387 23 Retirement Plan Design 389 23.1 Defi ned Benefi t and Defi ned Contribution Plans 389 23.2 Hybrid Plan Design 394 SSOOAA__ffmm..iinndddd vvii 0022//0011//1122 1111::5599 AAMM Contents vii 23.3 Allocation of Risks in Retirement Plans 396 23.4 U.S. Pension Plan Design 400 23.5 Canadian Pension Plan Design 403 23.6 Using Retirement Plans to Manage an Employer’s Workforce 404 24 Funding for Employer-Sponsored Retirement Plans 407 24.1 Overview of Employer-Sponsored Defi ned Benefi t Plan Funding 407 24.2 Actuarial Assumptions Used in Defi ned Benefi t Plan Valuations 410 24.3 Terminology Commonly Used in Pension Funding 411 24.4 Funding Methods 412 24.5 Asset and Participant Data Needed for the Actuarial Valuation 415 24.6 Selecting the Amount to Fund 417 24.7 Actuarial Valuation—Stakeholders and their Views 418 25 Pension Accounting in the United States 419 25.1 Policy Reason for U.S. Pension Accounting Requirements 419 25.2 Pension Accounting Requirements 420 25.3 Inputs into Pension Accounting Calculations 420 25.4 Responsibility for Company Financial Statements 421 25.5 Pension Expense 421 25.6 Pension Disclosure 422 26 Modeling Actuarial Costs and Expense 425 26.1 Actuarial Forecast Modeling System 425 26.2 Uses of Actuarial Forecast Modeling for Retirement Plans 425 27 Retirement Plan Solvency 427 PART 5: GROUP AND HEALTH INSURANCE 429 28 Introduction to Group Insurance 431 28.1 Principles of Insurable Groups 431 28.2 Buyers of Group Insurance Products 431 28.3 Sellers of Group Insurance Products 434 SSOOAA__ffmm..iinndddd vviiii 0022//0011//1122 1111::5599 AAMM viii Contents 28.4 Overview of Health Economics 437 28.5 Key Infl uences on Health Care Funding Models 443 28.6 Overview of Disability Insurance 445 28.7 Overview of Long-Term Care Insurance 446 28.8 Overview of Group Life Insurance 447 29 External Factors 449 29.1 Forces Driving the Need for Benefi t Plans 449 29.2 Cultural and Social Values 450 29.3 Demographics 451 29.4 Impact of Policy and Regulation 452 30 Pricing for Group Benefi t Plans 457 30.1 Data and Assumptions 457 30.2 Network Management and Plan Design 459 30.3 Estimating Claims Costs 459 30.4 Projecting Costs to the Rating Period 466 30.5 Calculating Benefi t Factors 469 30.6 Impact of Benefi t Changes 472 30.7 Calculating Manual Gross Premiums 473 30.8 Experience Rating 477 31 Reserving 487 31.1 Defi nitions of Terms 487 31.2 Short-Term Reserves 490 31.3 Long-Term Reserves 498 31.4 Evaluating Claim Reserve Adequacy 503 31.5 Guidelines and Practice Standards for Reserves 504 Bibilography 505 Index 509 SSOOAA__ffmm..iinndddd vviiiiii 0022//0011//1122 1111::5599 AAMM Preface A critical point in an actuary’s education is the transition from understanding the mathemat- ical underpinnings of actuarial science to putting them into practice. Th e problems become less well-defi ned and the solutions less clear-cut. Th is is not only a challenge for candidates who are making the transition but also a challenge for those who are guiding their learn- ing and assessing their performance. In 2003 the Society of Actuaries Board of Governors took the inspired step of moving a candidate’s education in this transition from a self-study reading of textbooks followed by a proctored exam to delivery of the candidate’s education through a supported e-Learning environment. Starting in 2006, candidates for the ASA des- ignation began taking the Fundamentals of Actuarial Practice Course (FAP). Th e FAP Course brought several new features to the education and assessment process. Among them were: • Self-paced learning through online modules. Th e modules were designed to guide candidates through the material. Th is would be done through readings (both online and offl ine), review questions, case studies, activities, and exercises. • Rather than organize the course by function or practice area, the course was organized around the control cycle. Th is is a framework for problem solving and decision making that begins with defi ning the problem, continues with designing the solution and concludes with monitoring the results. Candidates are made aware that external forces aff ect the process and that the work must be completed in a professional manner. • Formal assessments evolved to become take-home open book problems that o ft en required making judgments and recommendations to be communicated to the intended audiences, usually in the form of memos. Fortunately, a suitable text was available (Bellis, et. al., 2003) covering the application of the control cycle to solving actuarial problems. In order to supplement the overview provided by this text, course candidates were asked to purchase several additional texts covering risk management, property and casualty insurance, investments, retirement benefi ts, health in- surance, and life insurance and annuities. Because these texts were written for other purposes, disjoint sections of each text were used for FAP. Th is was both inconvenient and expensive for candidates. In 2010 a project was undertaken to create a text that would be purpose-written for FAP candidates with coverage of fi nance, life insurance and annuities, retirement benefi ts and health insurance. Four authors with extensive experience were recruited to write the sections. Biographical information about each appears elsewhere in this book. Th ey were asked to ensure that all the information on their subject that is covered in FAP appears in their section. However, while the FAP Course makes reference to readings in this text, the text itself does not reference other aspects of the FAP Course. Th us, this text also provides a stand-alone introduction to actuarial practice in each area. ix SSOOAA__ffmm..iinndddd iixx 0022//0011//1122 1111::5599 AAMM x Preface Th e text begins with an introductory section that has a brief review of the actuarial profes- sion, some comments on what it means to be a professional and a discussion of the Actu- arial Control Cycle. It is designed to provide context for FAP candidates and for the rest of this book. Each of the four practice area sections of this book are self-contained and can be studied in any order. FAP candidates will skip from some parts of this book to others as their study in FAP is organized by the Actuarial Control Cycle and not by practice area. As you read this book there will be references to “online resources.” Th ere is a dedicated webpage for this text. At it, you can download additional readings, spreadsheets that support various examples and exercises, and solutions to the book’s exercises. Th ese resources can be found at www.soa.org/FAP. To both FAP candidates and those who want an introduction to how actuarial science is prac- ticed in the four areas covered, I hope this book is both illuminating and enjoyable. Stuart Klugman, FSA, CERA Jan uary 2012 SSOOAA__ffmm..iinndddd xx 0022//0011//1122 1111::5599 AAMM