Actuarial Notes

Primer on Retirement Income Strategy Design and Evaluation

By Adam Butt, Gaurav Khemka, William Lim and Geoff Warren · Society of Actuaries Research Institute · 2023

Study guide: Exam RET-101

A January 2023 primer on strategies to generate income during retirement, from the perspectives of their design and evaluation. Design means specifying a joint investment and withdrawal strategy, and evaluation means analysing how well the potential outcomes of a strategy satisfy a retiree's objectives, as the foundation for choosing one. It centres on catering to differences between retirees, in particular their income objective, appetite for income risk and personal attributes.

On the syllabus

  • Exam RET-101 — Executive Summary, Sections 1, 2, 5, 6 and Appendix A; Outcomes 2a, 2d; 3b. The SOA course strategy guide says it provides a more in-depth look at retirement income options in DC plans and how they might be evaluated against one another.

Executive Summary

  • Overview
  • Excel Models
  • Scope
  • Audience
  • Section Summaries and Key Messages
    • Section 1: Retiree Characteristics
    • Section 2: Building Blocks of Retirement Income Strategies
    • Section 3: Modelling Retirement Outcomes
    • Section 4: Strategy Evaluation – Utility and Metrics
    • Section 5: Strategy Selection
    • Section 6: Other Matters
    • Section 7: Limitations

1 Retiree Characteristics

  • 1.1 Three Income Objectives
  • 1.2 Flexibility and Preferences Related to the Retirement Savings Account Balance
  • 1.3 Risk and Risk Appetite During Retirement
    • 1.3.1 Risk and Trade-offs During Retirement
    • 1.3.2 Risk Appetite – Concepts
    • 1.3.3 Incorporating Risk Appetite into Strategy Design
  • 1.4 Personal Attributes

2 Building Blocks of Retirement Income Strategies

  • 2.1 Investment Strategies
    • 2.1.1 Purchased Lifetime Income Streams
    • 2.1.2 Retirement Savings Account
    • 2.1.3 Other Income Sources
    • 2.1.4 Overview of Investment Building Blocks
    • 2.1.5 A Note on Dynamic Strategies
  • 2.2 Withdrawal Strategies
    • 2.2.1 Types of Withdrawal Strategy
    • 2.2.2 Withdrawal Strategy for an Income Floor
    • 2.2.3 Withdrawal Strategy for an Income Target
    • 2.2.4 Withdrawal Strategy for Income Optimization

3 Modelling Retirement Outcomes

  • 3.1 Stochastic Models
  • 3.2 Notable Model Structuring Choices
    • 3.2.1 Modelling Frequency
    • 3.2.2 Nominal versus Real
    • 3.2.3 Projection Horizon
    • 3.2.4 Methods of Simulating Asset Returns
  • 3.3 Model Reliability

4 Strategy Evaluation – Utility and Metrics

  • 4.1 Key Concepts
    • 4.1.1 Two Purposes: Selecting Strategies and Characterizing Outcomes
    • 4.1.2 Utility, Metrics, or Both?
    • 4.1.3 Capturing Likelihood and Magnitude
  • 4.2 Utility Functions
    • 4.2.1 Applying Utility Functions
    • 4.2.2 Income Floor Objective
    • 4.2.3 Income Target Objective
    • 4.2.4 Income Optimization Objective
    • 4.2.5 Time Weighting – Survival Probabilities Risk and Time Preference
    • 4.2.6 Parameterization
    • 4.2.7 Certainty Equivalents
  • 4.3 Metrics
    • 4.3.1 Classes of Metrics
    • 4.3.2 Primary Metric for an Income Floor Objective
    • 4.3.3 Primary Metrics for an Income Target Objective
    • 4.3.4 Primary Metrics for an Income Optimization Objective
    • 4.3.5 Metrics for Remaining Assets
  • 4.4 Presentation of Metrics - Illustrative Examples
    • 4.4.1 Income Target Objective
    • 4.4.2 Income Optimization Objective

5 Strategy Selection

  • 5.1 Three Approaches to Selecting a Retirement Income Strategy
  • 5.2 Factors to Consider in Strategy Selection
  • 5.3 Applying Principles and Rules
    • 5.3.1 Income Floor Objective
    • 5.3.2 Income Target Objective
    • 5.3.3 Income Optimization Objective
    • 5.3.4 Access to Funds and Preferences over Remaining Assets
  • 5.4 Selecting from a Menu of Candidate Strategies
  • 5.5 Identifying an ‘Optimal’ Strategy

6 Other Matters

  • 6.1 Alternative Methods
    • 6.1.1 Goal-based Investing and Bucketing
    • 6.1.2 Liability-Driven Investing
    • 6.1.3 Income Framing
  • 6.2 Annuity Puzzle
  • 6.3 Behavioral Effects
    • 6.3.1 Behavioral Considerations for Retirees
    • 6.3.2 Addressing Behavioral Effects
  • 6.4 Business Considerations for Plan Providers

7 Limitations

Appendix A Underlying Drivers of Income Risk

  • A.1 Investment Risk
  • A.2 Sequencing Risk
  • A.3 Longevity Risk
  • A.4 Inflation Risk
  • A.5 Other risks

Appendix B Utility Functions – Technical Details

  • B.1 General Formula for Expected Utility
  • B.2 Income Target: Loss Aversion Utility Using the Prospect Theory Value Function
  • B.3 Income Optimization: Risk Aversion Utility Function
  • B.4 Note on Time Weighting
  • B.5 Illustration of Utility Calculations for Income Streams
  • B.6 Bequests
  • B.7 Other Utility Functions

Appendix C Potential Metrics and their Calculation

  • C.1 Metric Calculations
    • C.1.1 Comment on Weighting Methods
    • C.1.2 Definitions and Notation
  • C.2 Distribution of Income
    • C.2.1 Expected Income
    • C.2.2 Survival Weighted Expected Income
    • C.2.3 Standard Deviation of Income
    • C.2.3 Survival Weighted Standard Deviation of Income
    • C.2.4 Income Percentiles
  • C.3 Likelihood of Income Shortfall
    • C.3.1 Probability of Shortfall
    • C.3.2 Survival Weighted Probability of Shortfall
    • C.3.3 Expected Years of Shortfall
    • C.3.4 Survival Weighted Expected Years of Shortfall
  • C.4 Magnitude of Income Shortfall
    • C.4.1 Expected Shortfall
    • C.4.2 Survival Weighted Expected Shortfall
    • C.4.3 Minimum Income
  • C.5 Remaining Assets
    • C.5.1 Expected Account Balance
    • C.5.2 Remaining Account Balance - Percentiles
    • C.5.3 Expected Age of Account Exhaustion
    • C.5.4 Probability of Account Exhaustion
    • C.5.5 Survival Weighted Probability of Account Exhaustion

Appendix D Additional Detail on Illustrative Examples

  • D.1 Modelling Assumptions
  • D.2 Complete Set of Metrics for Strategy Selection Examples of Section 5

References

Acknowledgments

About The Society of Actuaries Research Institute

Sources