Mortality Improvement Factors

Mortality rates have declined substantially over the past century due to medical advances, improved nutrition, better sanitation, and healthier lifestyles. This decline is not uniform across ages or time periods: improvement has been most dramatic at younger ages and for cardiovascular causes of death, while progress against cancer and at the oldest ages has been slower. Projection scales model these trends by applying age-specific improvement factors to base mortality rates, allowing actuaries to project future mortality for pricing and valuation.

The basic projection formula is straightforward: if q_x(0) is the base mortality rate at age x and r_x is the annual improvement rate, then the projected rate t years later is q_x(t) = q_x(0) * (1 - r_x)^t. For example, if q_65(0) = 0.0150 and the annual improvement rate at age 65 is 1.5%, then the projected rate 10 years later is q_65(10) = 0.0150 * (1 - 0.015)^10 = 0.0150 * 0.8601 = 0.01290.

One-Dimensional vs. Two-Dimensional Scales

One-dimensional projection scales assign a single improvement rate to each age, assumed to remain constant over time. While simple to apply, this approach has a significant limitation: it assumes that the pace of mortality improvement never changes. Historical evidence shows that improvement rates have varied considerably across decades, with periods of rapid improvement (1970s cardiovascular revolution) and periods of stagnation or reversal (recent opioid crisis impacts at middle ages).

Two-dimensional projection scales allow improvement rates to vary by both age and calendar year, written as r_{x,t}. The projected mortality rate becomes q_x(t) = q_x(0) * product from s=1 to t of (1 - r_{x,s}). This approach captures the observation that improvement rates themselves evolve over time. Most two-dimensional scales assume that improvement rates converge to a long-term ultimate rate after a transition period, reflecting the expectation that current improvement trends will not persist indefinitely.

SOA Mortality Improvement Scales

The Society of Actuaries (SOA) publishes mortality improvement scales for use in pension and insurance valuations. Scale AA was widely used for many years, applying constant annual improvement rates by age. The MP series (MP-2014, MP-2015, through MP-2021 and beyond) replaced Scale AA with two-dimensional scales that incorporate recent mortality experience and project improvement rates that vary by both age and calendar year.

Each MP scale update incorporates the most recent mortality data from the Social Security Administration and other sources. The scales typically show higher improvement rates in the near term (reflecting recent observed trends) that grade toward lower long-term ultimate rates over a 20 to 30 year transition period. The ultimate rates represent a conservative long-term assumption about the pace of future medical and social progress.

Generational Mortality Tables

A static mortality table assigns a single set of mortality rates based on age alone. A generational (cohort) mortality table assigns mortality rates based on both age and birth year, so that each generation benefits from the mortality improvement expected during its lifetime. For someone born in 1960, the mortality rate at age 65 (in calendar year 2025) reflects improvement from the base table through 2025, while the rate at age 75 (in 2035) reflects additional improvement through 2035.

Generational tables are constructed by starting with a base table and applying a projection scale to create unique mortality rates for each birth cohort. The formula is: q_x for birth year c = q_x(base) * product from s=base_year to c+x of (1 - r_{x,s}). This approach produces a different complete mortality table for each birth cohort, which is more realistic but also more complex to implement in valuation systems.

Impact on Insurance and Annuity Values

Mortality improvement has opposite effects on life insurance and annuity products. For life insurance, lower mortality means fewer death claims, reducing the actuarial present value of death benefits. A whole life insurance value A_x decreases when projected mortality rates are lower. For annuities and pensions, lower mortality means longer expected lifetimes and more annuity payments, increasing the present value of future benefits. An annuity value a-ddot_x increases with mortality improvement.

The magnitude of these effects depends on the level of improvement assumed. A 1% annual improvement rate for all ages might reduce a whole life insurance APV by 3% to 5% while increasing an annuity APV by 5% to 8% (the exact impact depends on age, interest rate, and the shape of the improvement scale). Pension plans are particularly sensitive to mortality improvement because pension liabilities consist primarily of annuity obligations to retirees who are already at advanced ages.

Sensitivity Analysis

Given the uncertainty in future mortality trends, actuaries should test the sensitivity of their valuations to the mortality improvement assumption. Common sensitivity tests include: using no improvement (static table), using the standard projection scale, and using a scale with improvement rates 50% higher or lower than the standard. The range of results provides insight into the financial risk from mortality uncertainty.

For a defined benefit pension plan, the difference between no improvement and the standard MP scale can represent 5% to 10% of total liabilities. This sensitivity highlights why the choice of mortality improvement assumption is one of the most consequential decisions in pension valuation.

Common Pitfalls

A frequent mistake is applying improvement factors to the wrong base. The improvement factor (1 - r_x)^t should be applied to the base table rate, not to an already-projected rate. Another common error is confusing the projection direction: improvement reduces mortality rates, so the factor (1 - r_x)^t is less than 1 for positive t and positive r_x. Applying the factor in the wrong direction (increasing mortality over time) produces the opposite of the intended result.

Students also sometimes forget that improvement rates vary by age. Younger ages typically have lower improvement rates (because mortality is already low), while middle and older ages have higher improvement rates. Using a single improvement rate for all ages oversimplifies the projection and produces inaccurate results.

Study Tips

Exam LTAM tests your understanding of how to apply improvement factors to base mortality tables, the difference between one-dimensional and two-dimensional scales, and the impact on insurance and annuity valuations. Practice applying the projection formula q_x(t) = q_x(0) * (1 - r_x)^t for various ages and projection periods. Be prepared to explain qualitatively why mortality improvement increases annuity liabilities but decreases insurance costs. Understand the concept of generational mortality tables and how they differ from static tables. Work through sensitivity examples to develop intuition for the magnitude of improvement effects on different product types.

Actuarial Assumptions: Mortality Improvement and Projection Scales