11.1 Mortality, Interest and Expense Assumptions

Study Focus

Mortality estimates expected insured-event costs. Higher assumed investment returns reduce the present funding requirement if other inputs stay fixed.

Premium Calculation: Mortality, Interest, and Loadings

In life insurance, setting the price of a policy is an intricate scientific and financial discipline known as actuarial rating. Unlike commercial manufacturing or retail merchandising—where the production cost of an item is known prior to sale—a life insurer sells a financial promise whose ultimate cost will only be known decades into the future when death or maturity claims are presented.

To establish premiums that are commercially competitive, equitable among policyholders, and actuarially sufficient to guarantee long-term solvency under Bank Negara Malaysia oversight, actuaries construct life insurance tariffs using three foundational pillars: mortality, interest, and loadings.

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The Three Pillars of Life Premium Determination

Every life insurance premium—from a straightforward 10-year term policy to an intricate participating whole life contract—is derived from the interplay of three fundamental actuarial components:

Expected claims are valued using mortality probabilities and investment discounting. Expense and contingency loadings are then added through the pricing model; an interest percentage is not simply subtracted from a monetary mortality cost.

Pillar 1: Mortality and the Law of Large Numbers

Mortality refers to the statistical frequency of death within a specific population group over a defined timeframe. Life insurers cannot predict the exact day or year an individual policyholder will die. However, by observing hundreds of thousands of lives over many decades, actuaries can predict with remarkable statistical accuracy how many individuals within a given demographic will pass away each year.

This statistical predictability relies on the Law of Large Numbers:

As the number of independent, homogeneous exposure units (lives insured) increases, the actual observed claims experience approaches the mathematical probability of loss.

The Mortality Table and Probability of Death (q_x)

A mortality table (also termed a life table) is a mathematical model tracking a hypothetical cohort of lives (typically 100,000 or 1,000,000 individuals born simultaneously, termed the radix) from birth or entry age until the ultimate limiting age of life (denoted by omega, usually age 100 or 105).

Key actuarial notations include:

• l_x: The number of individuals surviving to exact age x.
• d_x: The number of individuals dying between exact age x and age x + 1 (d_x = l_x - l_{x+1}).
• q_x: The probability that an individual aged x will die within one year (q_x = d_x / l_x).
• p_x: The probability that an individual aged x will survive to age x + 1 (p_x = 1 - q_x = l_{x+1} / l_x).

Mortality Tables in Malaysia: The M99-03 Experience

In the Malaysian life insurance sector, actuaries historically relied on British tables (such as the A1924-29 or A1949-52 tables). However, demographic shifts, improvements in public health infrastructure, and socioeconomic modernization necessitated localized experience data.

The industry introduced the Malaysian Insured Lives Mortality Tables, notably the M99-03 Mortality Tables, published by the Life Insurance Association of Malaysia (LIAM) in conjunction with the Actuarial Society of Malaysia. These tables reflect the empirical mortality experience of insured lives in Malaysia, segregated by:

• Age: Mortality risk increases progressively with advancing age. While mortality is relatively low during late adolescence and early adulthood, the mortality curve rises steeply past age 50.
• Sex / Gender: Empirical data consistently demonstrates that females enjoy a higher life expectancy and lower mortality rate (q_x) than males at nearly every life stage. An insurer may use separate experience assumptions and rates where permitted. Do not assume a universal female age setback or identical pricing across insurers.
• Smoking Status: Smoker mortality rates are substantially higher than non-smoker rates due to cardiovascular and oncological risks, leading to separate rating tables.
• Underwriting Class: Standard mortality tables apply to healthy lives accepted under normal underwriting. Impaired lives with medical conditions or hazardous occupations require actuarial loadings.

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Pillar 2: Assumed Interest Rates and the Time Value of Money

Life insurance contracts are long-term financial instruments. Policyholders pay premiums today, but the insurer may not pay out the death benefit or maturity proceeds for 20, 30, or 50 years. In the intervening decades, the insurer invests accumulated premium funds into high-grade fixed income instruments, government bonds (Malaysian Government Securities / MGS), corporate bonds, and approved equity securities.

The investment return generated on these reserves represents the second pillar of premium rating: Assumed Interest.

Present Value and Discounting

Because the invested money compounds over time, the insurer does not need to collect the full RM 100,000 face amount in premiums today to pay an RM 100,000 death claim in the future. Instead, the actuary discounts the future liability back to its Present Value (PV) using an assumed compound interest rate (i).

The annual discounting factor is expressed mathematically as:

v = 1 / (1 + i)

Where:

• v is the present value of RM 1 payable at the end of one year.
• v^n = (1 + i)^(-n) is the present value of RM 1 payable at the end of n years.

Sensitivity of Premiums to Interest Rates

The assumed interest rate chosen by the appointed actuary has an inverse relationship with the required premium:

• Higher Assumed Interest Rate: Future investment earnings are expected to be substantial. Therefore, smaller premium contributions are needed from policyholders today to meet future claims. Premium rates decrease.
• Lower Assumed Interest Rate: Future investment earnings are assumed to be modest. Consequently, policyholders must contribute larger premiums today to accumulate the required sum insured. Premium rates increase.

Insurers must exercise extreme prudence when setting the assumed interest rate. If an insurer assumes an unrealistically aggressive investment yield (e.g., 8% p.a.) and market yields fall to 4% p.a., the insurer will suffer severe investment deficits, threatening its capital adequacy ratio under Bank Negara Malaysia's Risk-Based Capital (RBC) framework.

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Pillar 3: Loading (Expenses, Contingencies, and Profits)

Mortality and interest alone calculate the net premium—the pure cost of paying future claims without considering running a business. To make the insurance enterprise viable and solvent, actuaries add loadings to cover operational expenses, safety cushions, and profit margins.

Loadings are categorized into four core elements:

1. New Business Acquisition Expenses:
   • Agent commissions paid across the initial policy years according to Bank Negara Malaysia's Operating Cost Control (OCC) guidelines.
   • Medical examination fees, attending physicians' statements, and underwriting laboratory tests.
   • Initial administrative processing, policy document printing, marketing, and distribution overhead.
2. Maintenance and Servicing Expenses:
   • Ongoing administrative costs of running customer service branches, IT systems, billing collections, premium accounting, and statutory reporting.
   • Premium collection charges (e.g., credit card transaction fees, direct debit bank charges).
3. Contingency Margin:
   • An actuarial buffer to safeguard the insurer against unexpected adverse fluctuations in mortality or investment yield.
   • Protects against catastrophic spikes in claims caused by epidemics, pandemics, natural disasters, or sudden economic dislocations.
4. Profit Margin and Bonus Loading:
   • For non-participating policies, a modest profit loading generates a return on regulatory capital for shareholders.
   • For participating (with-profits) policies, a bonus loading is deliberately built into the premium structure. This extra premium creates a surplus that the insurer pools and redistributes to policyholders in the form of annual reversionary bonuses and terminal bonuses.

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