Actuarial assumptions

What Are Actuarial Assumptions?

Actuarial assumptions are the estimated future events used by actuaries to project financial obligations and costs, particularly for long-term financial commitments like pension plans and insurance policies. These assumptions form the bedrock of actuarial science and are crucial components within the broader field of risk management. Actuaries employ a range of actuarial assumptions to forecast everything from investment returns and future interest rates to mortality rates and employee turnover, allowing for the calculation of current liabilities and required funding levels. Without reliable actuarial assumptions, long-term financial planning for entities like corporations, governments, and insurers would be highly speculative.

History and Origin

The practice of using actuarial assumptions has evolved alongside the development of insurance and pension systems. Early forms of insurance and annuities relied on rudimentary estimates of life expectancy. As populations grew and financial arrangements became more complex, the need for more sophisticated calculations arose. The formalization of actuarial science in the 18th and 19th centuries, driven by pioneers like James Dodson and Richard Price, led to the systematic development and application of statistical methods to model human mortality and other demographic trends. This laid the groundwork for modern actuarial assumptions.

Over time, particularly with the growth of corporate pension funds and social welfare programs, regulatory bodies and professional actuarial organizations established standards for the selection and disclosure of these assumptions. For instance, the Actuarial Standards Board (ASB) in the United States issues Actuarial Standards of Practice (ASOPs) that provide guidance to actuaries in selecting and evaluating assumptions. ASOP No. 27, for example, offers specific guidance for actuaries performing services related to selecting assumptions for measuring pension obligations¹⁸, ¹⁹. Revisions to ASOP No. 27 have focused on simplifying guidance and ensuring economic assumptions are reasonable and reflect estimates of future experience¹⁶, ¹⁷.

Key Takeaways

• Actuarial assumptions are forecasts of future demographic and economic events that impact long-term financial obligations.
• They are fundamental to calculating liabilities for pension plans, insurance policies, and other long-term financial products.
• Key categories of actuarial assumptions include demographic factors (e.g., mortality, disability) and economic factors (e.g., interest rates, inflation, salary increases).
• The selection of appropriate actuarial assumptions is critical for accurate financial modeling and ensuring the solvency of financial entities.
• These assumptions are subject to professional standards and regulatory oversight to ensure reasonableness and consistency.

Formula and Calculation

Actuarial assumptions are inputs into complex actuarial valuation formulas, rather than having a single standalone formula themselves. They are variables within the present value calculations used to determine financial liabilities. For example, the present value of a future benefit payment, a core component of actuarial valuation, is calculated using a discount rate derived from actuarial assumptions about future investment returns.

The general concept can be illustrated with a simplified present value formula for a single future payment:

Where:

• (PV) = Present Value
• (FV) = Future Value (e.g., a projected benefit payment)
• (r) = Discount Rate (an actuarial assumption derived from expected investment returns)
• (n) = Number of periods until the payment (an actuarial assumption related to life expectancy or retirement age)

For a series of future payments, such as pension benefits, the calculation involves summing the present values of each projected payment, considering various actuarial assumptions for factors like mortality, withdrawal, and salary increases.

Interpreting Actuarial Assumptions

Interpreting actuarial assumptions involves understanding the rationale behind their selection and their potential impact on financial projections. Since these assumptions are estimates, they carry inherent uncertainty. For instance, a higher assumed interest rate (or discount rate) will result in a lower calculated present value of future liabilities, making a pension plan appear more adequately funded. Conversely, a lower assumed interest rate will increase liabilities.

Similarly, changes in mortality tables or demographics can significantly alter projections. If a population is expected to live longer, as has been the trend in many developed nations, then pension or life insurance providers will face longer periods of benefit payments, increasing their liabilities. Actuaries must exercise professional judgment, considering historical data, current economic conditions, and future outlooks when setting these crucial inputs. Transparency in the selection and evaluation of actuarial assumptions is paramount for stakeholders to understand the underlying drivers of financial reports.

Hypothetical Example

Consider a hypothetical defined benefit pension plan for "Acme Corporation." An actuary is determining the plan's current funding status. To do this, they rely on several actuarial assumptions:

1. Discount Rate: An assumed long-term annual investment return of 6.5%. This is a crucial economic assumption, as it directly impacts the present value of future liabilities.
2. Salary Increase Rate: An assumed average annual salary increase of 3.0% for employees, affecting future benefit calculations.
3. Mortality: Based on a specific actuarial table that reflects current population health trends, projecting how long retirees are expected to live and receive benefits.
4. Turnover Rate: An assumed percentage of employees who will leave the company before retirement each year, reducing the plan's future obligation to them.

Using these actuarial assumptions, the actuary projects the cash flows of future benefit payments to current employees and retirees. They then discount these future payments back to the present day using the 6.5% assumed investment return to arrive at the plan's total liability. If the calculated liability is, say, $100 million, and the plan holds $90 million in assets, the actuary would report a funding deficit.

Practical Applications

Actuarial assumptions are widely applied across various financial sectors:

• Pension Fund Management: For defined benefit plans, actuaries use assumptions about investment returns, salary growth, inflation, mortality, and employee turnover to calculate pension liabilities and determine required employer contributions. The Social Security Administration (SSA) similarly uses a range of demographic and economic assumptions, including fertility rates, mortality rates, and productivity growth, to project the financial status of its Old-Age and Survivors Insurance (OASI) and Disability Insurance (DI) trust funds over a 75-year period¹⁴, ¹⁵. The 2024 Social Security Trustees Report, for instance, projects the combined OASI and DI trust funds could be depleted by 2035, relying on these long-term actuarial assumptions¹¹, ¹², ¹³.
• Insurance Underwriting: Life insurers rely on mortality assumptions to price policies and calculate reserves. Health insurers use assumptions about morbidity (incidence of illness) and healthcare cost inflation. Property and casualty insurers assess assumptions for claims frequency and severity.
• Government Budgeting: Governments use actuarial assumptions to project future costs for social security programs, public employee pensions, and retiree healthcare benefits. The Pew Charitable Trusts highlights how state pension plans use investment return assumptions to forecast their funding needs, and how managing these assumptions prudently is crucial for fiscal sustainability⁸, ⁹, ¹⁰. Despite improvements in some states, significant funding deficits persist due to challenges in meeting assumed investment returns⁶, ⁷.
• Enterprise Risk Management: Large corporations use actuarial assumptions in their enterprise risk management frameworks to quantify and manage long-term financial risks.
• Product Development: Financial institutions developing long-term savings or annuity products use actuarial assumptions to design products that are financially viable and sustainable for both the company and the customer.

Limitations and Criticisms

Despite their necessity, actuarial assumptions are inherently limited by their nature as forecasts. They are not guarantees of future outcomes and can be subject to significant criticism.

• Sensitivity to Deviations: Even small inaccuracies in key actuarial assumptions, particularly the assumed investment return or discount rate, can lead to substantial differences in projected liabilities over long periods. If actual investment returns consistently fall short of the assumed rate, pension plans can face significant funding shortfalls, requiring increased contributions or benefit adjustments.
• Economic Volatility: Long-term economic assumptions, such as inflation and interest rates, are notoriously difficult to predict accurately. Unexpected economic downturns, market crashes, or prolonged periods of low interest rates can severely impact financial models based on historical averages that may no longer be relevant. The Federal Reserve, for instance, actively monitors and adjusts short-term interest rates as part of monetary policy, which can influence long-term rate expectations used in actuarial models², ³, ⁴, ⁵. While an inverted yield curve has historically preceded recessions, recent economic activity has shown that this is not an infallible indicator, underscoring the uncertainty of economic forecasts¹.
• Demographic Shifts: While mortality trends are relatively stable, unexpected changes in public health, medical advancements, or lifestyle factors can alter life expectancies, impacting long-term liabilities for annuities and pensions.
• Manipulation Concerns: In some cases, there can be pressure to select optimistic actuarial assumptions to reduce reported liabilities or contribution requirements, which can mask underlying financial weaknesses. This underscores the importance of independent oversight and adherence to professional standards like those set by the Actuarial Standards Board.
• Lack of Stochastic Modeling: While often based on historical data, traditional actuarial assumptions are often deterministic, meaning they represent a single "best estimate." They may not fully capture the range of possible future outcomes or the correlations between different risks, though stochastic modeling is increasingly used to address this.

Actuarial Assumptions vs. Economic Forecasts

While closely related, actuarial assumptions and economic forecasts serve distinct purposes and are developed with different aims.

Actuarial assumptions often incorporate insights from economic forecasts but tailor them to the specific needs of long-term financial planning. For instance, actuaries setting an investment return assumption for a pension plan will consider broader economic forecasts for GDP growth and market performance, but then translate these into a specific, conservative estimate suitable for valuing long-term liabilities. The key difference lies in the application: actuarial assumptions directly feed into calculating financial obligations, whereas economic forecasts provide a broader economic outlook.

FAQs

What are the two main types of actuarial assumptions?

The two main types of actuarial assumptions are demographic assumptions and economic assumptions. Demographic assumptions relate to population characteristics and behavior, such as mortality, longevity, disability, and employee turnover. Economic assumptions relate to financial factors, including expected investment returns, inflation, and salary growth rates.

Who sets actuarial assumptions?

Actuarial assumptions are typically set by qualified actuaries who apply their professional judgment, expertise, and knowledge of relevant laws and standards. For public pension plans, these assumptions might be reviewed or approved by plan boards or government bodies. Regulatory bodies, such as the Actuarial Standards Board, provide guidance and requirements for the selection of these assumptions.

How often are actuarial assumptions reviewed?

Actuarial assumptions are usually reviewed annually as part of the regular actuarial valuation process for pension plans and insurance entities. However, significant changes in economic conditions or demographic trends may prompt more frequent review and adjustment to ensure the assumptions remain reasonable and reflect current expectations.

Why are actuarial assumptions so important for pension plans?

Actuarial assumptions are crucial for pension plans because they directly determine the calculated present value of a plan's future benefit obligations and, consequently, the required contributions to adequately fund those benefits. If assumptions are too optimistic (e.g., assuming higher investment returns or shorter life expectancies than realized), the plan may be significantly underfunded, leading to financial strain or benefit reductions in the future. Accurate assumptions help ensure the long-term solvency and sustainability of retirement plans.

Can actuarial assumptions be changed?

Yes, actuarial assumptions can and often are changed. Changes are made when new data, economic conditions, or trends suggest that previous assumptions are no longer appropriate. For example, if life expectancies continue to increase, actuaries will adjust their mortality assumptions. Similarly, sustained periods of low or high interest rates might lead to adjustments in the assumed investment return. Any material change in actuarial assumptions must be disclosed and justified by the actuary.