Actuarial Notes

A Problem-Solving Approach to Pension Funding and Valuation

By William H. Aitken · ACTEX Publications · 2014

Study guide: Exam RET-301

An introductory textbook on the mathematics of pension funding and valuation, written by William H. Aitken of the University of Waterloo and first published in 1994. Its defining characteristic, in its preface, is a large number of worked examples: each unit is introduced with enough explanatory material to allow the reader to move quickly to problem solving, and the text adds discussion questions and exercises. It is organized into eight chapters, from an introduction to pension plans through the cost methods, gain and loss analysis, plan changes, options and assets, to an overview of the earlier material.

On the syllabus

  • Exam RET-301 — Outcomes 1a, 1b, 1c (Assumptions); 2nd Ed., Ch. 5 (background only) (the syllabus codes it RET301-101-25).

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