Actuarial assumption

What Is Actuarial Assumption?

An actuarial assumption is a projection about future events and trends used by actuaries to estimate the cost of future liabilities, particularly in insurance and pension plans. These assumptions are fundamental to the field of actuarial science, which falls under the broader category of risk management. Actuarial assumptions consider a wide range of factors, including demographic trends, economic conditions, and human behavior, to quantify uncertain future obligations. They are crucial for calculating the present value of future benefit payments, setting premium rates, and determining the financial health of long-term financial products.

History and Origin

The roots of actuarial science, and by extension, actuarial assumptions, can be traced back to the 17th century with the development of formal methods for assessing long-term financial obligations. Early pioneers like John Graunt and Edmond Halley laid foundational work by creating mortality tables, which were initial forms of actuarial assumptions about human longevity. A significant step in the professionalization of the field occurred with the establishment of the Equitable Life Assurance Society in 1762 in London, which applied scientific principles to life insurance, leading to the formal designation of "actuary" for the official applying these methods.⁵ This period marked a shift towards using statistical and mathematical projections to manage financial risks associated with future events, moving beyond simple historical averages.

Key Takeaways

• Actuarial assumptions are forward-looking estimates about future demographic and economic conditions.
• They are essential for calculating liabilities in long-term financial products like pensions and insurance.
• Assumptions typically cover factors such as mortality, life expectancy, employee turnover, salary increases, and investment returns.
• The accuracy of actuarial assumptions directly impacts the financial stability and reported obligations of entities like pension funds and insurance companies.
• Regular review and adjustment of these assumptions are necessary to reflect changing real-world conditions.

Formula and Calculation

While there isn't a single universal "formula" for an actuarial assumption itself, these assumptions are inputs into complex actuarial calculations, typically involving the determination of the present value of future cash flows. For instance, in a defined benefit plan, the projected benefit obligation (PBO) is calculated using various actuarial assumptions. The PBO represents the actuarial present value of all benefits attributed by the pension benefit formula to employee service rendered prior to a specific date.

The general concept often involves discounting future benefit payments to their present value, considering the probability of those payments occurring. A simplified representation of the present value calculation for a single future payment, adjusted for probability, could be:

Where:

• (PV) = Present Value of the benefit
• (FV) = Future Value of the benefit payment
• (P) = Probability of the event occurring (e.g., survival probability based on mortality rates)
• (r) = Discount rate (an actuarial assumption reflecting the time value of money and expected investment returns)
• (n) = Number of periods until the payment is expected

Actuaries apply sophisticated financial modeling techniques using large datasets and probability theory to refine these assumptions and calculations.

Interpreting the Actuarial Assumption

Interpreting actuarial assumptions involves understanding their impact on the calculated liabilities and the financial health of an entity. For example, a lower assumed discount rate will result in a higher present value of liabilities, making a pension plan appear less funded, all else being equal. Conversely, an assumption of longer life expectancy (lower mortality rates) for retirees will increase the projected liability for pension or annuity providers, as benefits are expected to be paid for a longer duration.

The interpretation also considers how sensitive the overall financial projections are to changes in individual actuarial assumptions. Small shifts in a key assumption can lead to significant changes in reported obligations or required contributions, underscoring the importance of careful selection and regular review of these estimates.

Hypothetical Example

Consider "Horizon Pension Fund," a hypothetical defined benefit plan. To determine its annual contribution requirement, the fund’s actuaries must make several actuarial assumptions.

Scenario: Horizon Pension Fund needs to calculate its Projected Benefit Obligation (PBO) for the upcoming year.

Key Actuarial Assumptions Made:

1. Discount Rate: 6.0% (reflecting the rate at which future benefits are discounted to their present value).
2. Salary Increase Rate: 3.5% per year (reflecting expected future pay raises for employees, which impact final pension benefits).
3. Mortality Table: Based on the most recent industry-standard table, projecting employee and retiree lifespans.
4. Employee Turnover: 8% per year (reflecting the rate at which employees leave before retirement, thus forfeiting some benefits).

Walk-through:

• The actuaries use these assumptions to project when each current employee will retire, how long they will live post-retirement, what their final salary will be (and thus their pension amount), and the probability of them staying with the company until retirement.
• They then calculate the stream of future pension payments for each employee and retiree.
• Using the 6.0% discount rate, these future payments are brought back to their present value.
• Summing these present values across all participants yields the total PBO for the fund.

If, in the following year, the actuaries revise the discount rate down to 5.0% due to prevailing market conditions, the calculated PBO would increase, requiring the Horizon Pension Fund to potentially increase its contributions to maintain its funded status.

Practical Applications

Actuarial assumptions are widely applied across various sectors of finance and economics:

• Insurance: In the insurance industry, actuarial assumptions are foundational for pricing policies (e.g., life insurance premiums, health insurance rates) and calculating reserves. They factor in probabilities of events like death, illness, accidents, and property damage, as well as expected claims costs.
• Pensions and Employee Benefits: For pension plans and other post-employment benefits, actuaries use these assumptions to determine funding requirements, assess the plan’s solvency, and calculate benefit obligations for financial reporting. Regulatory bodies, such as the Financial Accounting Standards Board (FASB), issue standards like Statement No. 87, which requires companies to use explicit actuarial assumptions to measure pension costs and obligations for their financial statements.
• ⁴ Government Policy and Social Security: Government agencies, such as the U.S. Social Security Administration (SSA), rely on comprehensive demographic and economic actuarial assumptions to project the long-term solvency of social insurance programs. These projections inform policy debates and legislative decisions regarding program funding and benefits.
• ³ Long-Term Care and Healthcare: Actuarial assumptions are critical in modeling the costs associated with long-term care insurance and healthcare systems, projecting future medical inflation, utilization rates, and morbidity.
• Enterprise Risk Management: Beyond traditional applications, actuarial methodologies and the underlying assumptions are increasingly used in broader risk management frameworks for assessing and quantifying risks across an organization, including operational and strategic risks.

Limitations and Criticisms

Despite their analytical rigor, actuarial assumptions are inherently based on estimations of an uncertain future and are subject to several limitations and criticisms:

• Sensitivity to Small Changes: Minor adjustments to key actuarial assumptions can significantly alter calculated liabilities and costs, leading to potential volatility in reported financial positions.
• Reliance on Historical Data: While sophisticated, actuarial models often extrapolate from past trends to predict the future. However, unprecedented events (e.g., pandemics, major economic crises, rapid technological shifts) may deviate significantly from historical patterns, leading to inaccuracies.
• ² Model Risk: The complexity of actuarial models means that their design and calibration can introduce "model risk," where flaws in the model's structure or assumptions lead to erroneous outcomes. This risk is particularly pronounced when modeling extreme events, for which historical data is scarce.
• ¹ Subjectivity: Despite extensive data and statistical methods, actuaries must make professional judgments in selecting assumptions. This can introduce a degree of subjectivity, and different actuaries might arrive at slightly different conclusions based on their interpretations or choice of methodology.
• Inadequate for "Black Swan" Events: Actuarial assumptions and models are generally designed for "expected" or "unexpected" but quantifiable risks. They may struggle to adequately capture or predict "black swan" events—rare, high-impact occurrences that are outside the realm of normal expectations.

Actuarial Assumption vs. Economic Assumption

While closely related and often overlapping, "actuarial assumption" and "economic assumption" refer to distinct, though interdependent, sets of projections.

An actuarial assumption specifically pertains to the variables an actuary directly models, such as the likelihood of someone living to a certain age, while an economic assumption concerns broader financial market and economic trends that affect the monetary value of those actuarial projections.

FAQs

What types of factors do actuarial assumptions include?

Actuarial assumptions typically include demographic factors like mortality rates, life expectancy, and rates of disability or turnover. They also incorporate economic factors such as inflation, salary growth, investment returns, and the discount rate used to calculate present values.

Why are actuarial assumptions important?

Actuarial assumptions are vital because they allow financial entities, especially insurance companies and pension funds, to estimate their future financial obligations accurately. Without these assumptions, it would be impossible to set appropriate premiums, determine required contributions, or adequately reserve for long-term liabilities. They are a cornerstone of sound financial modeling and risk management.

How often are actuarial assumptions reviewed?

Actuarial assumptions are typically reviewed annually by actuaries. This regular review ensures that the assumptions remain reasonable and reflect current experience and future expectations. Significant events or shifts in data may trigger more frequent re-evaluations to maintain the accuracy of financial projections.

Who sets actuarial assumptions?

Actuarial assumptions are set by qualified actuaries, often in consultation with their clients (e.g., pension plan sponsors, insurance company management) and auditors. These professionals apply their expertise in actuarial science, statistical analysis, and financial markets to develop the most appropriate set of assumptions for a given financial obligation.