PENSION MATHEMATICSwith Numerical Illustrations

Second Edition

Pension Research Council

Pension Research Council Publications

A complete listing of PRe publications appears at the back ofthis volume.

PENSION MATHEMATICSwith Numerical Illustrations

Second Edition

Howard E. Winklevoss, Ph.D., MAAA, EAPresident

Winklevoss Consultants, Inc.

Published by

Pension Research CouncilWharton School of the University of Pennsylvania

and

University of Pennsylvania PressPhiladelphia

© Copyright 1977 (first edition) and 1993 (second edition) by thePension Research Council of the Wharton School of the University of Pennsyl­vania

All rights reserved

Library of Congress Cataloging-in-Publication DataWinklevoss, Howard E.

Pension mathematics with numerical illustrations / Howard E.Winklevoss. -2nd ed.

p. em.Includes bibliographical references and index.ISBN 0-8122-3196-1I. Pensions-Mathematics. 2. Pensions-Costs-Mathematics. 3. Pension

trusts-Accounting. I. Title.HD7105.W55 1993331.25'2-dc20 92-44652

CIP

Printed in the United States of America

To my parents,

Marian and Howard Winklevoss,

my wife,

Carol,

and our children,

Amanda, Cameron, and Tyler

PENSION RESEARCH COUNCIL

Chairman and DirectorJerry S. Rosenbloom, Frederick H. Ecker Professor of Insuranceand Risk Management, Wharton School, University of Pennsyl­vania

Associate DirectorDwight K. Bartlett III, F.S.A., Visiting Executive Professor ofInsurance, Wharton School, University of Pennsylvania

Founding DirectorDan M. McGill, Chairman Emeritus, Department of Insuranceand Risk Management, Wharton School, University of Pennsyl­vania

Vincent Amoroso, F.S.A., Principal, KPMG Peat Marwick,Washington, DC

Zvi Bodie, Professor of Finance and Economics, School of Man­agement, Boston University

Gary I. Gates, Secretary, Department of Employee Trust Funds,State of Wisconsin, Madison

Michael S. Gordon, Esq., The Law Offices of Michael S. Gordon,Washington, DC

Donald S. Grubbs, Jr., F.S.A., Consulting Actuary, Grubbs andCompany, Inc., Silver Spring, MD

Ronald E. Keller, Executive Vice President, The PrincipalFinancial Group, Des Moines, IA

Judith F. Mazo, Senior Vice President and Director of Research,The Segal Company, New York City

Olivia S. Mitchell, Professor of Labor Relations, School ofIndustrial and Labor Relations, Cornell University, Ithaca,NY

Alicia H. Munnell, Senior Vice President and Director of Re­search, Federal Reserve Bank of Boston

Robert J. Myers, F.S.A., International Consultant on Social Se­curity, Silver Spring, MD

George J. Pantos, Esq., Partner, Vedder, Price, Kaufman,Kammholz & Day, Washington, DC

viii Pension Research Council

James E. Pesando, Professor of Economics, Institute for PolicyAnalysis, University of Toronto

Samuel H. Preston, Chairman, Department of Sociology, Uni­versity of Pennsylvania

Richard Prosten, Director, Coordinated Bargaining andResearch, Industrial Union Department, AFL-CIO,Washington, DC

Anna M. Rappaport, F.S.A., Managing Director, William M.Mercer, Inc., Chicago

Sylvester J. Schieber, Director, Research and InformationCenter, The Wyatt Company, Washington, DC

Ray Schmitt, Specialist in Social Legislation, Congressional Re­search Service, Library of Congress, Washington, DC

Richard B. Stanger, National Director, Employee Benefits Ser­vices, Price Waterhouse, Washington, DC

Marc M. Twinney, Jr., F.S.A., Director, Pension Department,Ford Motor Company, Dearborn, MI

Jack L. VanDerhei, Associate Professor of Risk and Insurance,Temple University

L. Edwin Wang, Retired President, Board of Pensions of theLutheran Church in America, Minneapolis, MN

Howard E. Winklevoss, President, Winklevoss Consultants, Inc.,Greenwich, CT

Howard Young, F.S.A., Adjunct Professor of Mathematics, Uni­versity of Michigan, Ann Arbor

PURPOSE OF THE COUNCIL

The Pension Research Council of the Wharton School of theUniversity of Pennsylvania was created in 1952 for the purpose ofsponsoring objective research in the area of private pensions. Itwas formed in response to the urgent need for a better under­standing of the private pension movement. Private pensions haveexperienced a phenomenal growth during the last three decades,but their economic, political, and social implications are yet tobe explored. They seem destined to playa major role in the questfor old-age economic security, but the nature of that role can beascertained only on the basis of more enlightened evaluation ofthe capabilities and limitations of the private pension mecha­nism. It was to conduct an impartial study into the facts and ba­sic issues surrounding private pensions, under the auspices of anacademic and professional group representing leadership in ev­ery phase of the field, that the Council was organized.

Projects undertaken by the Council are broad in scope andpredominantly interpretive rather than technical in nature. Ingeneral, attention is concentrated on areas which are not the ob­ject of special investigation by other research groups. Its re­search studies are conducted by mature scholars drawn fromboth the academic and business spheres. Research results arepublished from time to time in a series of books and monographs.

Contents

List of Tables xix

List of Figures xxiii

Foreword from the First Edition xxvii

Preface xxix

Chapter 1 Pension Plan Benefits 1

Retirement Benefits, 4Eligibility Requirements, 4Benefit Amount, 5

Vested Benefits, 7Eligibility Requirements, 8Benefit Amount, 8

Disability Benefits, 9Eligibility Requirements, 9Benefit Amount, 9

Death Benefits, 10Eligibility Requirements, 10Benefit Amount, 10

Chapter 2 Actuarial Assumptions 12

Decrement Assumptions, 12Mortality Decrement, 15Termination Decrement, 17Disability Decrement, 20Retirement Decrement, 23

Salary Assumption, 25Merit Component, 26Productivity Component, 26

xi

XII

Inflation Component, 27Total Salary Increase, 28

Interest Assumption, 28Risk Free Rate, 29Investment Risk, 29Inflation Component, 30Total Interest Rate, 30

Contents

Chapter 3 Basic Actuarial Functions 31

Composite Survival Function, 31Interest Function, 34Salary Function, 36Benefit Function, 40

Flat Dollar Unit Benefit, 41Career Average, 41Final Average, 41

Annuity Functions, 46Straight Life Annuity, 46Period Certain Life Annuity, 46Joint and Survivor Annuity, 47Refund Annuities, 48Temporary Annuities, 51

Chapter 4 Pension Plan Population Theory S6

Basic Concepts, 56Stationary Population, 56Mature Population, 58Undermature and Overmature Populations, 59Size-Constrained Population, 61

Model Plan Population, 64

Chapter S Pension Liability Measures 68

Plan Termination Liability, 69Plan Continuation Liability, 70Actuarial Liabilities, 71

Accrued Benefit Method, 73Benefit Prorate Methods, 74Cost Prorate Methods, 75

Contents xiii

Chapter 6 Normal Costs 79

Generalized Normal Cost Function, 80Normal Cost Under Actuarial Cost Methods, 83

Accrued Benefit Method, 84Benefit Prorate Method, 85Cost Prorate Method, 86Summary of Normal Costs Under Actuarial Cost

Methods, 89Plan Termination Cost Method, 94

Chapter 7 Supplemental Costs 96

Unfunded Actuarial Liability, 97Explicit Supplemental Costs, 100Implicit Supplemental Costs, 102

Accrued Benefit Method, 105Benefit Prorate Methods, 107Cost Prorate Methods, 108

Explicit and Implicit Supplemental Cost Combinations, 111Summary of Actuarial Cost Methods, 112

Chapter 8 Ancillary Benefits 114

Term Cost Concept, 114Vested Termination Benefits, 114

Term Cost, 114Present Value of Future Vested Termination

Benefits, 115Disability Benefits, 116

Term Cost, 116Present Value of Future Disability Benefits, 117

Surviving Spouse Benefits, 117Term Cost, 117Present Value of Future Surviving Spouse Benefits, 118

Numerical Illustration, 118Ancillary Benefits Under Actuarial Cost Methods, 118

Accrued Benefit Method, 119Benefit Prorate Method, 120Cost Prorate Method, 121

Ancillary Benefits for Alternative Liability Measures, 122Comparison of Ancillary Benefit Costs, 122

xiv Contents

Chapter 9 Multiple Retirement Ages 126

Actuarial Equivalence, 126Present Value of Future Benefits, 129Accrued Benefit Method, 131Benefit Prorate Methods, 132Cost Prorate Methods, 133Relative Cost of Early Retirement, 135

Chapter 10 Statutory Funding Requirements•••.•••••..•••.•..•.••.••.•••..•..139

Minimum Required Contributions, 140Statutory Funding Methods, 142

Unit Credit Method (Unprojected), 142Unit Credit Method (Projected), 145Entry Age Method, 145Attained Age Method, 145Individual Level Method, 146Frozen Entry Age Method, 146Frozen Attained Age Method, 146Aggregate Method, 147Individual Aggregate Method, 148

Statutory Amortization Periods, 148Additional Funding Charge, 151Current Liability, 151

Old Supplemental Costs, 153New Supplemental Costs, 154Contingent Event Supplemental Costs, 154

Actuarial Liability Full Funding Limit, 155Current Liability Full Funding Limit, 158Funding Standard Account, 159Additional Interest Charge Due to

Late Quarterly Contributions, 159Miscellaneous Credits, 161Alternative Minimum Funding Standard, 163

Maximum Tax Deductible Contributions, 164Numerical Illustration of Statutory Funding

Requirements, 167Statutory Asset Values, 171

Weighted Average Method, 172Average Ratio Method, 172N-Year Moving Average Method, 173Write-Up Method, 173Corridor Method, 174

Contents xv

Chapter 11 Pension Accounting 176

Liability Values, 176Accumulated Benefit Obligation (ABO), 177Vested Benefit Obligation (VBO), 180Projected Benefit Obligation (PBO), 180

Net Periodic Pension Cost, 182Service Cost, 183Interest Cost, 185Expected Return on Assets, 185Amortization Cost, 187

Future Service of Employees Expected toReceive Benefits, 187

Prepaid (Accrued) Expense, 188Transition Obligation (Asset), 188Prior Service Cost, 189Net Loss (Gain), 190

Disclosure of Net Periodic Pension Cost, 191Numerical Illustration of Net Periodic Pension Cost, 192

Balance Sheet, 194Minimum Additional Liability, 195Intangible Asset, 196Reconciliation of Funded Status, 196Numerical Illustration of Financial

Statement Disclosure Items, 196Critique of SFAS 87,199

Salary vs. Benefit Proration, 199Linear vs. Formula Proration, 200Interest Cost, 201Gain (Loss) Amount, 201Gain (Loss) Amortization, 201Amortization Periods, 202VBO Disclosure, 202Terminology, 202

Chapter 12 Alternative Actuarial Assumptions .203

Mortality Rates, 203Termination Rates, 205Disability Rates, 207Retirement Rates, 209Salary Rates, 210Interest Rates, 212Inflation Rates, 214

xvi Contents

Chapter 13 Alternative Plan Benefits ••••••••..•....••.••.•••••.••••••...•.......•218

Retirement Benefits, 218Alternative Benefit Formulas, 218Alternative Early Retirement Benefits, 221Cost-of-Living Adjustments (COLA), 222

Vested Termination Benefits, 223Disability Benefits, 224Surviving Spouse Benefits, 225

Chapter 14 Funding Policy 226

Economic Liability, 228Funding Policy Objectives, 230Financial Modeling, 230Target Cost Methodology, 232Statutory Methods and Assumptions, 234FASB Assumptions, 240

Chapter 15 Investment Policy: Asset Allocation 242

Capital Market Simulation, 244Capital Market Statistics, 245Illustrative Capital Market Parameters, 246Efficient Frontier, 247Real Return Simulations, 248

Stochastic Pension Simulations, 249

Chapter 16 Funding and Accounting for RetireeHealth Benefits 254

Economic Liabilities and Costs, 255Health Benefits Cost Function, 255Actuarial Assumptions, 257

Decrement Assumptions, 257Economic Assumptions, 258Inflation and Utilization, 259Employee Costs, 259Medicare Reimbursements, 260

Economic Liabilities, 260Economic Costs, 262Numerical Illustrations, 262

Funding Limits, 265Alternative VEBA Investments, 268

Contents

Numerical Illustrations, 270Accounting Requirements, 273

Liability Values, 273Net Periodic Postretirement Benefit Cost, 274Balance Sheet, 275Footnote Disclosure, 276Numerical Illustrations, 277

Critique of SFAS 106,279Salary vs. Benefit Proration, 279Proration Pattern and Period, 279Interest Cost, 280Gain (Loss) Amount, 280Gain (Loss) Amortization, 281Amortization Periods, 281Terminology, 281

xvii

Glossary of Mathematical Notation••••••.••.••••••••...••...••.•......••••.•..•..•.283

Index 303

Table1-1

1-2

1-32-12-22-32-4

2-52--62-72--82-92-102-11

2-123--1

3--23--33-4

3--5

List of Tables

Retirement Benefits as Percent of Salary atRetirement for 8-Percent-of-Salary DC Plan 2Retirement Benefits as Percent of Salary atRetirement for Alternative DB Plan Formulas 3Summary of Model Plan Benefits 111971 Group Annuity Mortality Rates for Males 16Mortality-Based Survival Probabilities 17Select and Ultimate Termination Rates 19Termination-Based Survival Probabilitiesfor Various Entry Ages 20Disabled-Life Mortality Rates 22Disabled-Life Survival Probabilities 22Disability Rates 23Disability-Based Survival Probabilities 23Early Retirement Rates 25Merit Salary Scale 27Salary Projections Inclusive of Merit, Productivity,and Inflation 28Investment Risk Estimates 30Probability of Surviving in Service toAge 65, 65_xP1T) 33

Service Table 35Compound Interest Function, v t ••••••••••••••••••••••••••••••••••••••• 37Salary Function per Dollar of EntryAge Salary, Sx7Sy•••••••••••.••.•••••••••••••••••••••••••••••••••• ••.•••••••••••••• 39Benefit Accrual and Accrued Benefit FunctionsExpressed as a Percent of the Projected Benefit 44

xix

xx

Table3-6

3-7

3--8

4-14-24-34-44-54-64-75-1

5-2

6-1

6-2

6-3

7-18-1

8-2

8-3

9-1

List of Tables

Annuity Values Under Alternative Interestand Mortality Assumptions 50Present Value of a Temporary Employment-Based

Life Annuity from Age x to Age 65, ii.~:65-xl 53Present Value of a Temporary Employment-Basedand Salary-Based Life Annuity from Age x to Age 65,s·· T 54ax:65~xl············································ .

Development of a Stationary Population 57Development of a Mature Population 59Development of an Undermature Population 60Development of an Overmature Population 61Development of a Size-Constrained Population 62Hiring Age Distribution and Salary Scale 64Population Statistics 66Plan Termination and Plan Continuation Liabilitiesas a Percentage of the Age-65 Value 72Actuarial Liability and T(PVFB)x Functions as aPercentage of the Age-65 Value 77Normal Cost Functions as a Percent of AttainedAge Salary 91Percentage of Projected Retirement BenefitAllocated to Each Age Under Various ActuarialCost Methods 92Cumulative Percentage of Projected RetirementBenefit Allocated to Each Age Under VariousActuarial Cost Methods 93Summary of Actuarial Cost Methods 113Ancillary Benefit Cost Functions: Term Costs as aPercent of Salary and PVFB Functions as a Percentof T(PVFB)x 119Ancil1ary Benefits Under Alternative Normal Costsas a Percent of Retirement Benefit Normal Cost 123Ancillary Benefits Under Alternative ActuarialLiabilities as a Percent of Retirement BenefitActuarial Liability 124Actuarial Equivalent Grading Function 128

Ust of Tables xxi

Table9-2

9-3

10-110-210-3

10-410-5a10-5b10-610-7

10-8

10-9

11-111-211-3

11-411-5

11-612-112-212-312-412-512-612-713-1

Relative Cost of Early Retirement With FullBenefit Accruals for Various Normal Costs 136Relative Cost of Early Retirement With ActuariallyReduced Benefit Accruals for VariousNormal Costs 137Statutory Funding Method Terminology 143Characteristics of Statutory Funding Methods 144Amortization Periods for Minimum RequiredContributions 149Minimum Required Contribution (End of Year) 156Funding Standard Account 160Development of Additional Funding Charge 161Valuation and Experience Assumptions 168Projection of ERISA Minimum Required andMaximum Tax Deductible Contribution 169Projection of ERISA Minimum Required andMaximum Tax Deductible Contribution UnderAlternative Funding Methods 170Effect of Alternative Asset Valuation Methodson the Actuarial Value of Plan Assets 175Net Periodic Pension Cost Components 183Disclosure of Net Periodic Pension Cost 192Projection of SFAS 87 Net Periodic CostDisclosure Items 193Reconciliation of Funded Status 197Projection of SFAS 87 Financial StatementDisclosure Items 198Reconciliation of SFAS 87 Values 200Effect of Alternative Mortality Rates 204Effect of Alternative Termination Rates 206Effect of Alternative Disability Rates 208Effect of Alternative Retirement Rates 209Effect of Alternative Salary Rates 211Effect of Alternalive Interest Rates 213Effect of Alternative Inflation Rates 216Effect of Alternative Benefit Formulas 219

xxii

Table13-2

13-3

13-413-5

13-6

13-714-114-214-314-4

15-115-216-116-216-316-4

16-516-6

16-7

List of Tables

Effect of Non-Reduced Benefits at AlternativeRetirement Ages as a Percent of Values forRetirement at Age 65 222Effect of Non-Reduced Benefits at AlternativeRetirement Ages as a Percent of Values ofActuarially Reduced Benefits 222Effect of Automatic Cost-of-Living Adjustments 223Effect of Alternative Service Requirementsfor Vesting 224Effect of Alternative Age and ServiceRequirements for Disability Benefits 225Effect of Alternative Surviving Spouse Benefits 225Economic Liability Definitioll 229Illustrative Funding Policy 230Funding Policy Assumptions 238Net Periodic Pension Costs Under AlternativeAssumptions 240Capital Market Statistics, 1971-1990 246Capital Market Assumptions 247Retiree Health Benefits Plan and Assumptions 263Health Benefits Cost Functioll 263Valuation and Experience Assumptions 271Net Periodic Postretirement Benefit CostComponents 274SFAS 106 Footnote Disclosure Items 276Disclosure of Net Periodic PostretirementBenefit Cost 277Reconciliation of Funded Status 277

Figure2-1

3-1

3-2

3-3

3-4

3-5

5-1

5-2

5-3

6-1

6-2

6-3

List of Figures

Single-Decrement Survival Probabilitiesfrom Age x to Age 65 24Survival and Interest Functions from Age xto Age 65 37Attained Age Benefit Accrual Functions as aPercent of the Projected Retirement Benefit.. 45Attained Age Accrued Benefit Functions as aPercent of the Projected Retirement Benefit.. 45Life Annuity vs. Annuity Certain for LifeExpectancy 51Unit-Based and Salary-Based Temporary AnnuityValues from Age x to Age 65 55Plan Termination and Plan ContinuationLiabilities as a Percentage of the Age-65 Value 73Actuarial Liabilities as a Percentage of theAge-65 Value 78Actuarial Liabilities as a Percent of PresentValue of Future Benefits Liability 78Normal Costs as a Percent of Salary UnderVarious Actuarial Cost Methods 91Percentage of Projected Retirement BenefitAllocated to Each Age Under Various ActuarialCost Methods 92Cumulative Percentage of Projected RetirementBenefit Allocated to Each Age Under VariousActuarial Cost Methods 93Normal Costs as a Percent of Payroll 94

xxiii

xxiv

Figure6-5

7-1a

7-1b

7-2a

7-2b

8--1a

8--1b

9-1a

9-1b

10-110-211-111-212-112-212-312-412-512-612-713-1

13-214-114-214-314-4

List of Figures

Normal Cost Under Plan Termination Method vs.Accrued Benefit Method 95Supplemental Costs per $100 of UnfundedLiability Under Alternative Methods l03Supplemental Costs per $100 of UnfundedLiability Under Alternative Methods 103Unfunded Liability Balance per $100 of InitialBalance Under Alternative Methods 104Unfunded Liability Balance per $100 of InitialBalance Under Alternative Methods 104Normal Costs With Ancillary Benefits UnderAlternative Actuarial Cost Methods 125Actuarial Liabilities With Ancillary BenefitsUnder Alternative Actuarial Cost Methods 125Normal and Early Retirement Under AlternativeNormal Costs 138Normal and Early Retirement Under AlternativeActuarial Liabilities 138Percent of Adjusted Unfunded Current Liability 154Maximum Tax Deductible Contribution I64Minimum Additional Liability Examples 195Valuation Year vs. Fiscal Year. I97Effect of Alternative Mortality Experience 205Effect of Alternative Termination Experience 207Effect of Alternative Disability Experience 208Effect of Alternative Retirement Experience 210Effect of Alternative Salary Experience 212Effect of Alternative Investment Experience 215Effect of Alternative Inflation Experience 217Contributions Under Alternative BenefitFormulas 220Effect of Ad Hoc Cost-of-Living Adjustments 224Pension Policy Components 227Comparison of Alternative Liabilities 229Deterministic Target Cost Methodology 232Stochastic Target Cost Methodology 234

List of Figures xxv

Figure14-5

14-6

14-714-814-9

14-10

15-115-2a15-2b15-2c15-3a

15-3b

15-3c

15-4a

15-4b

15-4c

16-116-216-3

16-4

16-5

16--6

Ideal Relation Between Statutory Limits andPlan Contributions 235Contribution Limits Under AlternativeActuarial Assumptions 238Deterministic Projection of Contribution Policy 239Stochastic Projection of Contribution Policy 239Deterministic Projection of SFAS 87 Expenseand Funded Status 241Stochastic Projection of SFAS 87 Expense andFunded Status 241Efficient Frontier 248One-Year Real Returns 250Five-Year Compound Real Returns 250Ten-Year Compound Real Returns 250Contributions in Year 5 Under AlternativeAsset Mixes 251Pension Expense in Year 5 Under AlternativeAsset Mixes 251Economic Liability Funded Ratio in Year 5Under Alternative Asset Mixes 251Contributions in Year 10 Under AlternativeAsset Mixes 252Pension Expense in Year 10 Under AlternativeAsset Mixes 252Economic Liability Funded Ratio in Year 10Under Alternative Asset Mixes 252Economic Liability Sensitivity Analysis 264Economic Cost Sensitivity Analysis 264Retiree Health Benefits Contributions UnderAlternative Funding Approaches 272Retiree Health Benefits Funded Status UnderAlternative Funding Approaches 272SFAS 106 Expense Under Alternative FundingScenarios 278APBO Funded Status Under AlternativeFunding Scenarios 278

Foreword from the First Edition

This book is the culmination of ten years of intensive inquiryby Howard Winklevoss into the intricacies of pension costs andactuarial liabilities. It is a welcome and much needed addition topension literature.

When I began my pension research activities in the early1950s, I sought in vain for explanations of pension cost behaviorof the type that abound in this book. I suspect that many of theserelationships were known, perhaps intuitively, by actuaries ac­tively engaged in pension consulting or the pension operations oflife insurance companies. If so, there insights and perceptionswere apparently treated as proprietary information, to be con­fined to internal communications or the inner recesses of theirminds. With some notable exceptions, the ideas did not findtheir way into published pension literature.

To a considerable degree, knowledge of pension cost behav­ior was constrained by the technology of the day. Pension costcalculations were laborious and many shortcuts and approxima­tions were used. With the development of sophisticated, high­speed computers, it has become feasible to refine pension actuar­ial techniques and assumptions. In particular, it has become fea­sible through the construction of computer models to simulatethe experience of a pension plan over many years, with a chang­ing population mix and a variety of actuarial assumptions, espe­cially those of an economic nature. The fruit of this improvedtechnology and refined actuarial approaches is a keener percep­tion of pension cost behavior under varied circumstances.

To a large extent this book simply quantifies and providesnew or improved actuarial notation for long recognized pensioncost concepts and procedures. In certain areas, however, new in­sights and techniques have been developed. Both types of con­tributions are useful and innovative. The book should serve the

xxvii

xxviii Forward

needs of pension actuaries of all persuasions, pension consul­tants, management and labor pension specialists, governmentalofficials with pension responsibilities, students, and others inter­ested in the dynamics of pensions. Dr. Winklevoss is to be com­mended for having completed this prodigious and scholarly task.

On a more personal note, it has been an intellectually reward­ing experience to work with Dr. Winklevoss on this project andother academic undertakings.

Philadelphia, PADecember 1976

Dan M. McGill

Preface

Although this book is entitled Pension Mathematics withNumerical Illustrations, Second Edition, it is more like the firstedition of a new book. With the exception of the first few chap­ters, the text is a virtual rewrite of the original book. Two topicshave been trimmed back from the first edition, namely, the analy­sis of ancillary benefits and early retirement. This edition coversall of the relevant material on these topics, but the presentation ismore concise. The major additions to the book are chapters on(1) statutory funding requirements, (2) pension accounting, (3)funding policy analysis, (4) asset allocation, and (5) retireehealth benefits.

The pension industry has changed considerably since the firstedition was published in 1977. At that time, ERISA had justbeen enacted and was being implemented throughout the pensionindustry. Just prior to its passage, I was involved in several gov­ernment-sponsored research assignments on the expected cost ofalternative vesting provisions, and the Business Roundtableasked me to share my findings at one of their meetings. After mytalk, one of the members cornered me and asked, "Why are youso enthusiastic about the pending pension legislation? Don't youknow that once they get the first law passed they'lJ keep onpassing them and eventually do more harm than good?" Littledid I know how accurate this statement was.

Many of us had such great expectations for ERISA and,• while many of its provisions are clearly beneficial, the avalanche

of regulations and new pension legislation since its passage hasbeen terrifying. As an example of its complexity, the reader needonly turn to page 156 and glance at the series of equations neededto determine the minimum required contributions to a qualifiedpension plan. Unless Congress simplifies the various statutoryand regulatory requirements for defined benefit pension plans,

xxix

xxx

and does it quickly, only historians will be interested in thisbook, for it will provide the mathematics of a subject no longerrelevant to corporate America.

Another major change since the first edition was the promul­gation of SFAS 87, which sets forth a comprehensive set of pro­cedures to follow in accounting for pension plans. CorporateAmerica vigorously fought against the FASH requiring such arigid set of accounting rules but has hardly said a word since itsimplementation in 1987. One of the reasons for this silence maybe that many companies have experienced negative pension ex­pense (i.e., pension income) since the implementation of SFAS87, which no doubt came as a pleasant surprise. This resultedfrom strong capital markets in the 1980's and the FASH's re­quirement that the discount rate used in calculating pension ex­pense be tied to the spot rate on long-term corporate bonds.These rates, in recent years, have been uncharacteristically highrelative to inflation, a result that no doubt occurred because ofthe poor performance of fixed-income investments when infla­tion was high in the early 1980's. In any event, it will be interest­ing to see the reaction among plan sponsors if long-term rates de­crease at a time when the market value of plan assets drop.Complacency with the accounting standard may turn, once again,to vigorous complaints.

The third area of change in the pension field since the mid­1970's is among practitioners. I recall speaking at an actuarialmeeting in the late 1970's where I was asked to defend the use ofexplicit best estimate assumptions. It did not seem like much ofan issue because using such assumptions appeared logical.Conservatism, I argued, could be achieved by contributing moreto the plan than the amount determined using best estimate as­sumptions. To my surprise, only a few individuals at the meetingseemed to embrace the use of explicit best estimate assumptions.This has all changed now, with best estimate assumptions beingrequired for both statutory and accounting calculations. In fact,if anything, the assumptions may have become a little too "bestestimate. " For example, the first edition of this book used a 7percent interest rate in all of the illustrations, a rate that was onthe high side at the time. This edition uses an 8 percent rate,which, ironically, is on the low side. Has the actuarial commu­nity, egged on by SFAS 87 as well as the IRS, become a little tooaggressive, with 9 and 10 percent rates being common? Plan

xxxi

sponsors have no doubt enjoyed the effects of using higher inter­est rates which, in many cases, caused their contributions to bezero and accounting expense to be negative. On the other hand,if future interest rates must be lower than the rates currently usedbecause of sustained low levels of inflation, the adjustment to in­creased costs may be painful for many corporations.

The author would like to thank all of the individuals who as­sisted in this edition. lowe special thanks to Dan M. McGill,Emeritus Professor, Wharton School. Nearly 25 years ago Danhired me to teach at the Wharton School, and my associationwith him over the ensuing 12 years while I was teaching there wasa richly rewarding experience. He gave me considerable encour­agement and assistance in completing the first edition as well asthe second edition of this book.

Steven R. Strake, senior actuary at Winklevoss Consultants,performed all of the numerical calculations in the book. Asreaders will soon discover, this represents a huge amount of workfor which I am very grateful. This work was performed by GlennD. Allison in the first edition and the author would like to rec­ognize that contribution in this edition as well. Jing Cheng Liu,Winklevoss Consultants, provided considerable assistance inediting the book, especially with respect to the statutory and reg­ulatory aspects of pension funding.

Two reviewers deserve special thanks for their very thoroughand tedious reviews of each and every sentence and equation inthe book. The first is both a former student and employee:Debbie L. Benner, William M. Mercer. It has been a pleasure towork with her over the years. David R. Kass, David R. Kass &Company, provided a similarly exhaustive review, for which I amvery grateful.

The University Press sought reviews from two academicianswith actuarial backgrounds: Frank G. Bensics, University ofHartford, and James C. Hickman, University of Wisconsin. Bothindividuals provided insightful comments which were incorpo­rated into the book.

Three Pension Research Council members were asked to re­view the text. In each case, the comments were extensive andbeneficial. These individuals, along with two others who assistedin their review, are Donald S. Grubbs, Jr. and Joseph D.Marsden, Grubbs and Company; Marc M. Twinney and Norman

xxxii

J. Campeau, Ford Motor Company; and Howard Young, Univer­sity of Michigan.

Three individuals provided very helpful assistance onChapter 16, Funding and Accounting for Retiree Health Bene­fits: Harold S. Cooper, Chicago Consulting Actuaries; CharlesC. Morgan, The Prudential Asset Management Company; andDale H. Yamamoto, Hewitt Associates.

Any remaining errors, omissions, or other shortcomings inthe book are the sole responsibility of the author. Readers areinvited to assist with the next edition by advising the author ofany errors and offering suggestions.

Greenwich, CTDecember 1992

Howard E. Winklevoss