What it means
A life table starts with an arbitrary group, often 100,000 people at a chosen age, and tracks that group forward. Each row shows the number alive at the start of the year, the probability of dying during the year, the resulting number of deaths, and the average remaining life expectancy from that age.
The probability of death in a given year is the workhorse figure. Multiply it by the amount payable on death and you have the expected cost of covering that person for a year, which is where a life insurance premium begins.
Annuities use the same table in reverse. Here the insurer worries about people living too long, so the survival column determines how many payments must be funded, and improvements in longevity raise annuity costs directly.
There are important variants. Period tables show mortality rates observed in a single recent year, generational tables project future improvements in longevity, and insured lives tables show lower mortality than general population tables because people who buy insurance tend to be healthier and better off.
The nuance that surprises people is that life expectancy rises as you age. A newborn might have an expectancy in the low eighties while a person who has already reached 80 typically has several years still expected, because they have survived all the risks that removed others along the way.
In practice
Real-world examples.
Example
A life insurer pricing a one-year term policy for a healthy 65 year old reads a 1.5% probability of death from its insured lives table. On a $250,000 benefit that gives an expected claim cost of $3,750, to which expenses and margin are added to reach the quoted premium.
Example
A pension scheme actuary switches from a period table to a generational table that projects continued longevity improvement. The projected number of payment years rises and the scheme's obligation increases even though membership is unchanged.
Example
A structured settlement company valuing a lifetime income stream for an injured claimant uses an impaired lives table rather than a standard one. The shorter projected lifespan reduces the lump sum required to fund the payments.
Formula
Calculation
The probability of death in a year, q(x), = deaths during the year / number alive at the start of the year, and survivors at the next age = number alive x (1 - q(x)). Start with 100,000 people alive at age 65. If q(65) = 1.5%, deaths during the year = 100,000 x 1.5% = 1,500, leaving 100,000 - 1,500 = 98,500 alive at age 66. If q(66) = 2.0%, deaths = 98,500 x 2.0% = 1,970, leaving 98,500 - 1,970 = 96,530 alive at age 67. For an insurer covering a 65 year old with a $250,000 death benefit, the expected cost of one year of cover = 1.5% x $250,000 = $3,750 before expenses, profit and any margin for risk.Case study
Seen in the real world.
This is an illustrative and fictional scenario. Fairhaven Mutual Assurance, an invented life insurer, priced its retiree term product using a general population life table because it was free and easy to obtain. Sales grew quickly and the product looked highly profitable in its first three years.
The problem was hidden in the table. General population mortality at age 65 was 1.5%, but Fairhaven's actual customers were wealthier and healthier, with real mortality nearer 1.0%, so the fictional insurer was collecting premiums for claims that largely did not arrive. When a competitor built pricing on an insured lives table, it undercut Fairhaven by a wide margin and took most of the new business within a year.
Fairhaven's illustrative recovery involved building its own experience table from its claims history and repricing the book. The lesson was that using the wrong life table can be an error in either direction: too conservative loses business, too optimistic loses money.
Watch out
Common mistakes.
- Using a general population table to price insured lives, whose mortality is usually lighter because healthier and wealthier people buy more cover.
- Treating life expectancy as a fixed number for a person, when it rises with each year successfully survived.
- Ignoring projected longevity improvement and pricing long-term annuities or pensions from a table that reflects only past experience.
Questions
People also ask.
What is q(x) in a life table?
It is the probability that a person alive at exact age x dies before reaching age x plus one.
Why do insurers use tables rather than individual predictions?
Individual death is unpredictable, but across thousands of similar lives the proportion dying each year is remarkably stable and therefore priceable.
Do life tables differ by sex and smoking status?
Yes, mortality varies materially by both, and most insurers use separate tables or rating factors, subject to local regulation on permitted pricing factors.
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