Actuarial Notes

A Problem-Solving Approach to Pension Funding and Valuation

By William H. Aitken · ACTEX Publications · 1996 · RET201-101-25

Study guide: Exam RET-201

An introductory textbook on the mathematics of pension funding and valuation by William H. Aitken, taught through a large number of worked examples. Each unit is introduced with enough explanatory material to move quickly to problem solving, and each major section carries discussion questions and exercises with numerical answers. Chapters 2 to 4 cover the standard cost methods, Chapters 5 to 7 cover gain and loss analysis, plan changes and ancillary benefits, and options and assets, and Chapter 8 summarizes the earlier material on a conceptual level.

On the syllabus

  • Exam RET-201 — Outcomes 1b; the SOA study note RET201-101-25 reproduces Chapter 5 of the 2nd edition, and it is background only.

Preface

1 Pension Benefits

  • 1.1 Introduction
  • 1.2 Design of Pension Plans
    • 1.2.1 Defined Benefits
    • 1.2.2 Defined Contributions and Defined Benefits
  • 1.3 Plan Cost
    • 1.3.1 Replacement Ratio
    • 1.3.2 The Effects of Age and Plan Design
    • 1.3.3 Anticipating Inflation
    • 1.3.4 Recognizing Inflation
    • 1.3.5 Pension Payments
    • 1.3.6 Surplus
  • 1.4 Plan Documents and Funding
  • 1.5 Actuarial Valuations
  • 1.6 Notation and Terminology
    • 1.6.1 Dates and Ages
    • 1.6.2 Definitions
    • 1.6.3 Pension Notation Specific to This Text
  • 1.7 Cost Methods

2 Increasing Cost Individual Cost Methods

  • 2.1 Traditional Unit Credit
  • 2.2 Benefits with a Salary Scale
  • 2.3 Projected Unit Credit
  • 2.4 Exercises

3 Level Cost Individual Cost Methods

  • 3.1 Entry Age Normal (Level Dollar)
  • 3.2 Cost as a Level Percent of Salary
  • 3.3 Entry Age Normal (Level Percent)
  • 3.4 Individual Level Premium
  • 3.5 Supplemental Cost
    • 3.5.1 Amortization of Supplemental Liabilities
    • 3.5.2 Pension Fund Balance Sheet
  • 3.6 Exercises

4 Aggregate Cost Methods

  • 4.1 Individual Aggregate
  • 4.2 Aggregate
  • 4.3 Frozen Initial Liability (Entry Age Normal)
  • 4.4 Frozen Initial Liability (Attained Age Normal)
  • 4.5 Aggregate Entry Age Normal
  • 4.6 Review
  • 4.7 Exercises

5 Experience Gains and Losses

  • 5.1 Unfunded Liabilities and Gains
    • 5.1.1 Relationships
    • 5.1.2 Explanations of the Relationships
    • 5.1.3 Observations
    • 5.1.4 Experience Gain Summary
  • 5.2 Total Experience Gains
  • 5.3 Investment Gains
  • 5.4 Retirement Gains
    • 5.4.1 Normal Retirement Gains
    • 5.4.2 Early Retirement Gains
    • 5.4.3 Postponed Retirement Gains
  • 5.5 Withdrawal Gains
    • 5.5.1 Vesting
    • 5.5.2 Gain
  • 5.6 Salary Gains
  • 5.7 Mortality Gains
  • 5.8 Exercises

6 Changes and Ancillary Benefits

  • 6.1 Change in Cost Method
  • 6.2 Change in Retirement Benefit
  • 6.3 Change in Retirement Age
  • 6.4 Change in Interest Assumption
  • 6.5 Change in Salary Increase Assumption
  • 6.6 Changes in Decrement Assumptions
    • 6.6.1 Mortality Rates
    • 6.6.2 Withdrawal Rates
    • 6.6.3 Disability Rates
  • 6.7 Ancillary Benefits
  • 6.8 Employee Contributions
    • 6.8.1 Unit Credit with Employee Contributions
    • 6.8.2 Entry Age Normal
    • 6.8.3 Aggregate
  • 6.9 Exercises

7 Options and Assets

  • 7.1 Retirement Options
    • 7.1.1 Early Retirement Option
    • 7.1.2 Deferred Retirement Option
  • 7.2 Optional Forms of Benefit
  • 7.3 Assets
    • 7.3.1 Dollar-Weighted Rate of Return
    • 7.3.2 Time-Weighted Rate of Return
    • 7.3.3 Side Funds
  • 7.4 Exercises

8 Observations

  • 8.1 Comparison of Methods
    • 8.1.1 Traditional Unit Credit
    • 8.1.2 Projected Unit Credit
    • 8.1.3 Modified Unit Credit
    • 8.1.4 Entry Age Normal
    • 8.1.5 Individual Level Premium
    • 8.1.6 Individual Attained Age Normal
    • 8.1.7 Individual Aggregate
    • 8.1.8 Aggregate
    • 8.1.9 Frozen Initial Liability
    • 8.1.10 Plan Termination Cost Method
    • 8.1.11 Aggregate Entry Age Normal
    • 8.1.12 Employee Contributions
    • 8.1.13 Employer Contributions
  • 8.2 Alternatives
    • 8.2.1 Choice of Method
    • 8.2.2 Actuarial Valuations
    • 8.2.3 Alternative Liabilities
    • 8.2.4 Small and Large Plans
    • 8.2.5 Closed and Open Groups
  • 8.3 Concepts
    • 8.3.1 Pension Benefit
    • 8.3.2 Inflation
    • 8.3.3 Final Average Salary
    • 8.3.4 Salary Scale
    • 8.3.5 Percent of Salary
    • 8.3.6 Vesting
    • 8.3.7 Assumptions
    • 8.3.8 Surplus
    • 8.3.9 Not Guaranteed
    • 8.3.10 Projected Benefit
    • 8.3.11 New Entrants
    • 8.3.12 Active and Retired Participants
    • 8.3.13 Early Retirement
    • 8.3.14 Trusteed and Insured Plans
    • 8.3.15 Funding
    • 8.3.16 Cost Methods
    • 8.3.17 Expensing vs. Funding
    • 8.3.18 Financial Reporting
  • 8.4 Government Aspects
    • 8.4.1 Social Pension Plans
    • 8.4.2 Tax Assistance
    • 8.4.3 Regulation and Protection
    • 8.4.4 Public Service Pension Plans

Answers to the Text Exercises

Bibliography

Index of Notation

Subject Index

Sources