📊Actuarial Mathematics Unit 10 – Pension Math and Retirement Planning

Key Concepts and Terminology

• Defined benefit plans provide a specific benefit at retirement based on factors such as salary and years of service
• Defined contribution plans specify the contributions made by the employer and/or employee, with the final benefit depending on investment performance
• Actuarial present value represents the current value of future benefits, discounted using interest rates and mortality assumptions
• Normal cost refers to the annual cost of benefits accrued by active participants in a given year
• Accrued liability represents the present value of benefits earned by participants up to a specific date
  • Includes benefits for both active and inactive participants
  • Calculated using actuarial assumptions and methods
• Funded status measures the relationship between plan assets and liabilities, indicating the plan's financial health
• Vesting refers to the participant's right to receive accrued benefits upon meeting certain conditions (years of service)

Pension Plan Types and Structures

• Single employer plans are sponsored by one employer and cover employees of that organization
• Multiemployer plans are collectively bargained and cover employees from multiple employers within an industry
• Cash balance plans combine features of defined benefit and defined contribution plans, with participants having hypothetical account balances
  • Account balances grow based on credited contributions and interest
  • Provides greater portability compared to traditional defined benefit plans
• Hybrid plans incorporate elements of both defined benefit and defined contribution structures
  • Aims to balance the risks and benefits for employers and employees
• Supplemental executive retirement plans (SERPs) provide additional benefits to high-earning executives
• Floor-offset arrangements coordinate benefits between a defined benefit and a defined contribution plan
• Target benefit plans aim to provide a specific benefit, but contributions are adjusted based on investment performance

Actuarial Present Value Calculations

• Time value of money concepts are applied to determine the present value of future benefits
• Discount rates are used to convert future cash flows to their present value
  • Discount rates are based on expected investment returns and reflect the time value of money
  • Higher discount rates result in lower present values, while lower discount rates lead to higher present values
• Actuarial assumptions, such as mortality rates, retirement ages, and salary scales, are used in present value calculations
• Annuity factors, derived from mortality tables and discount rates, simplify the calculation of actuarial present values
• Present value of future benefits (PVFB) represents the total present value of benefits expected to be paid to participants
• Present value of future normal costs (PVFNC) represents the present value of the normal costs for active participants
• Actuarial accrued liability (AAL) is the portion of the PVFB attributed to past service

Mortality Tables and Life Expectancy

• Mortality tables provide the probability of death at each age for a given population
  • Separate tables are used for males and females due to differences in life expectancy
  • Tables can be based on the general population or specific groups (annuitants, employees)
• Life expectancy represents the average number of years an individual is expected to live from a specific age
• Mortality improvement scales are used to adjust mortality tables to reflect expected future changes in life expectancy
• Generational mortality tables incorporate mortality improvement scales to provide a more accurate representation of future mortality
• Mortality experience studies compare actual mortality rates to those predicted by the tables and may lead to table updates
• Longevity risk arises from individuals living longer than expected, which can increase pension plan liabilities
• Mortality assumptions have a significant impact on the calculation of actuarial liabilities and required contributions

Funding Methods and Contribution Strategies

• Funding methods determine how the cost of pension benefits is allocated over time
  • Actuarial cost methods include entry age normal, projected unit credit, and traditional unit credit
  • Each method has its own approach to calculating normal cost and actuarial accrued liability
• Contribution strategies aim to ensure that the plan has sufficient assets to meet its obligations
• Minimum required contributions are set by regulations and are based on the plan's funded status and other factors
• Actuarially determined contributions (ADC) are calculated by the plan's actuary to fund benefits and address any unfunded liabilities
  • ADCs consider factors such as plan demographics, actuarial assumptions, and funding policy
• Funding policies establish the plan's objectives and guidelines for contributions and investment returns
• Amortization methods are used to spread the cost of unfunded liabilities over a specific period (amortization period)
• Asset smoothing techniques are employed to reduce the impact of short-term market fluctuations on contribution levels

Regulatory Framework and Compliance

• Employee Retirement Income Security Act (ERISA) sets minimum standards for private sector pension plans in the United States
  • Establishes fiduciary responsibilities, funding requirements, and participant protections
  • Requires plans to provide participants with information about their benefits and rights
• Internal Revenue Code (IRC) provides tax incentives for employer-sponsored retirement plans and sets contribution limits
• Pension Protection Act (PPA) introduced measures to improve plan funding and transparency
  • Established new funding rules and increased disclosure requirements
  • Introduced benefit restrictions for underfunded plans
• Governmental Accounting Standards Board (GASB) sets accounting and financial reporting standards for public sector pension plans
• Actuarial Standards of Practice (ASOPs) provide guidance to actuaries on various aspects of pension plan valuations and disclosures
• Form 5500 is an annual report filed by pension plans to provide information on their financial condition and operations
• Nondiscrimination testing ensures that plans do not disproportionately favor highly compensated employees

Risk Management in Pension Plans

• Investment risk arises from the uncertainty of investment returns and can impact the plan's funded status
  • Diversification and asset allocation strategies are used to manage investment risk
  • Liability-driven investing (LDI) aligns investment strategy with the plan's liabilities
• Inflation risk occurs when the value of pension benefits is eroded by rising prices over time
  • Cost-of-living adjustments (COLAs) can help mitigate the impact of inflation on retiree benefits
• Interest rate risk is the risk that changes in interest rates will affect the plan's liabilities and funded status
  • Duration matching and interest rate hedging strategies can be employed to manage interest rate risk
• Longevity risk, as mentioned earlier, stems from participants living longer than expected, increasing plan liabilities
  • Annuity purchases and longevity swaps are tools used to transfer longevity risk to third parties
• Sponsor risk relates to the financial stability of the plan sponsor and their ability to make required contributions
  • Regular monitoring of the sponsor's financial health and risk-sharing arrangements can help mitigate sponsor risk
• Governance risk arises from inadequate oversight, decision-making processes, and internal controls
  • Establishing a strong governance framework and fiduciary training can help manage governance risk

Case Studies and Real-World Applications

• General Motors (GM) faced significant pension liabilities, leading to the transfer of certain plan obligations to an annuity provider
  • Highlights the impact of pension obligations on corporate financial stability and the use of risk transfer strategies
• The Central States Pension Fund, a multiemployer plan, faced severe underfunding and potential insolvency
  • Illustrates the challenges faced by multiemployer plans and the need for comprehensive reform
• The California Public Employees' Retirement System (CalPERS) implemented risk mitigation strategies to manage investment volatility
  • Demonstrates the importance of risk management and the adoption of innovative approaches in public sector plans
• The Dutch pension system has been recognized for its collective risk-sharing and intergenerational solidarity
  • Provides an example of an alternative pension model that balances risks and benefits among participants
• The United Kingdom's auto-enrollment initiative has significantly increased participation in workplace pension schemes
  • Shows the effectiveness of behavioral interventions in promoting retirement savings
• The City of Detroit's bankruptcy proceedings involved significant pension reforms and benefit reductions
  • Highlights the impact of pension obligations on municipal finances and the need for sustainable pension design
• The Wisconsin Retirement System has been praised for its fully funded status and risk-sharing features
  • Illustrates the benefits of a well-designed and managed pension system that aligns interests of stakeholders