Mortality

What Is Mortality?

Mortality, in financial contexts, refers to the incidence of death within a population, typically measured over a specific period. It is a fundamental concept within actuarial science and plays a crucial role in the broader field of financial planning and risk management. Understanding mortality rates is essential for entities that deal with long-term financial obligations tied to human lifespans, such as insurance companies, pension funds, and government social security programs. The study of mortality provides insights into life expectancy and survival probabilities, which are vital for accurate financial projections and product design.

History and Origin

The concept of quantifying mortality dates back to ancient civilizations, with early examples of actuarial calculations found in the Code of Hammurabi around 1754 BCE.¹⁸ However, the systematic study and application of mortality tables in what is recognizable as modern actuarial science began in the 17th century.¹⁷

One of the earliest and most significant contributions came from Edmund Halley, famous for Halley's Comet, who published a seminal paper in 1693 based on data from the city of Breslau.¹⁴, ¹⁵, ¹⁶ This work laid the groundwork for analyzing longevity and death within a population cohort and calculating insurance premiums.¹², ¹³ Over time, actuaries refined methodologies, incorporating larger sample sizes and additional factors like gender and occupation to develop more sophisticated mortality tables.¹¹ The Institute of Actuaries in England published its first official mortality table in 1843, which became a widely adopted benchmark for insurance calculations.¹⁰

Key Takeaways

• Mortality refers to the rate of death within a population, crucial for financial calculations related to lifespans.
• It is a core component of actuarial science, influencing products like life insurance and annuities.
• Mortality tables, or life tables, provide probabilities of death at various ages and are essential for pricing financial products and assessing long-term liabilities.
• Changes in mortality rates, such as increasing life expectancy, have significant implications for social security, pension systems, and individual retirement planning.
• Financial professionals utilize mortality data to manage longevity risk and structure appropriate financial instruments.

Formula and Calculation

Mortality is typically expressed as a probability, specifically the probability of dying within a given year of age. This is often represented as (q_x), where (x) is the exact age.

The calculation of mortality rates for a specific age (x) is generally derived from observed data:

Where:

• (q_x) = The probability that a person aged (x) will die before reaching age (x+1).
• (d_x) = The number of deaths observed between age (x) and (x+1) in a given population during a specific period.
• (l_x) = The number of individuals alive at exact age (x) in that same population at the beginning of the period.

These individual probabilities are then compiled into a mortality table, which forms the basis for various actuarial calculations, including survival probabilities, expected future lifetimes, and annuity payouts.

Interpreting Mortality

Interpreting mortality data primarily involves understanding its implications for longevity and risk. A lower mortality rate for a given age group indicates a higher probability of survival, translating to longer life expectancies. Conversely, higher mortality rates suggest shorter life expectancies.

For individuals, understanding mortality helps in personal financial planning, particularly regarding retirement savings and insurance needs. For institutions, accurately interpreting mortality trends is vital for managing liabilities. For instance, an unexpected decrease in mortality (people living longer) can create significant funding challenges for defined-benefit pension plans and social security systems, as benefit payments would extend for a longer duration than originally projected.

Hypothetical Example

Consider a hypothetical life insurance company, SecureFuture Inc., that is designing a new 20-year term life insurance policy for a 40-year-old male. To price this policy accurately, SecureFuture Inc. needs to estimate the probability that a 40-year-old male will die within the next 20 years.

Using its internal mortality tables, derived from historical data and actuarial projections, the company finds the following:

• Probability of a 40-year-old male dying before age 41 ((q_{40})): 0.002
• Probability of a 41-year-old male dying before age 42 ((q_{41})): 0.0022
• ... (and so on, up to age 59)
• Probability of a 59-year-old male dying before age 60 ((q_{59})): 0.008

The company uses these mortality probabilities to calculate the expected claims and determine the appropriate premiums to charge policyholders. If the aggregate mortality experience turns out to be lower than projected (i.e., fewer policyholders die), the company might experience higher profits, assuming other factors remain constant. Conversely, higher-than-expected mortality could lead to financial strain. This illustrates how understanding mortality is central to managing underwriting risk.

Practical Applications

Mortality data and mortality tables have several practical applications across the financial sector:

• Life Insurance and Annuities: Life insurance companies use mortality rates to price policies, calculate reserves, and assess the risk associated with their payouts. For annuities, which provide income streams for life, mortality tables determine the expected duration of payments and, consequently, the cost of the annuity.
• Pension Fund Management: Defined-benefit pension plans rely heavily on mortality projections to estimate future liabilities and ensure sufficient funding. Longer lifespans, a form of longevity risk, can strain pension systems, requiring adjustments to contributions or benefits.
• Social Security and Government Programs: Government-sponsored social security and healthcare programs, such as Medicare in the United States, use mortality data to forecast future expenditures and assess the solvency of their systems. For example, the Social Security Administration (SSA) publishes period life tables to evaluate the actuarial soundness of various financial instruments and benefit programs.⁸, ⁹ Longer life expectancies mean that individuals collect benefits for extended periods, putting pressure on these systems.⁷
• Estate Planning: Financial advisors use mortality considerations in estate planning to estimate the duration of income needs, the potential for long-term care costs, and the timing of wealth transfer.
• Demographic Analysis for Investment: Investors and economists analyze mortality trends as part of broader demographic shifts to understand potential impacts on labor markets, consumption patterns, and long-term economic growth. For instance, aging populations due to lower mortality rates can create headwinds for economic growth in regions like the Eurozone.⁵, ⁶ The European Central Bank (ECB) considers demographic factors in its economic analyses.⁴

Limitations and Criticisms

While mortality data is indispensable, it has limitations and faces criticisms. One primary challenge is the assumption that past mortality trends will accurately predict future ones. Advances in medicine, public health, and lifestyle changes can lead to improvements in mortality rates that are difficult to project precisely. This phenomenon, known as longevity improvements, can lead to underestimation of liabilities for long-term financial products.

Another criticism relates to the aggregation of data. Standard mortality tables reflect average population mortality. However, individual mortality can vary significantly based on socioeconomic status, health, lifestyle choices, and genetics. Using average rates for a diverse population may not accurately reflect the risk for specific individuals or subgroups, potentially leading to mispricing or inequities in financial products.

Furthermore, the increasing financial burden associated with rising longevity, particularly on social security and healthcare systems, is a significant concern. Some argue that current financial structures may struggle to adapt to a world where people consistently live longer.², ³

Mortality vs. Morbidity

Mortality and morbidity are distinct but related concepts in finance and healthcare.

Understanding both mortality and morbidity is critical for comprehensive risk management in the financial sector, as they both directly impact the liabilities and profitability of various insurance and pension products.

FAQs

What is a mortality table?

A mortality table, also known as a life table or actuarial table, is a statistical tool used in actuarial science and demography that shows the probability of a person dying before their next birthday for each age. It provides a comprehensive analysis of mortality rates within a specific population, offering insights into life expectancies and survival probabilities.

How does mortality affect life insurance premiums?

Mortality directly affects life insurance premiums. The higher the probability of death for a given age group, the higher the premium. This is because the insurer faces a greater likelihood of paying out a death benefit sooner. Actuaries use mortality tables to calculate the expected cost of claims and set premiums accordingly to ensure the company remains financially sound.

What is longevity risk in relation to mortality?

Longevity risk is the risk that individuals or a population will live longer than anticipated. It is directly related to mortality, as lower-than-expected mortality rates translate into higher longevity. This poses a significant challenge for pension funds and annuity providers, as they may have to make payments for a longer duration than initially projected, impacting their financial solvency.¹

Does improved mortality always mean better financial outcomes?

Not necessarily for all parties. While improved mortality (people living longer) is generally seen as a positive societal development, it creates financial challenges for systems built on older mortality assumptions. For instance, social security systems and defined-benefit pension plans can face significant funding shortfalls if people live much longer than anticipated without corresponding increases in contributions or adjustments to benefits. This highlights the importance of dynamic actuarial valuations.