How Do You Buy an Income That Cannot Run Out? Pool the Risk of Living

Somebody retiring with a fixed sum faces a question with no good answer, which is how fast to spend it. Spending as though they will live to a typical age risks running out entirely if they live much longer, and spending as though they will live to the oldest plausible age means living far more frugally than necessary and dying with most of the money unspent. Nobody can know their own lifespan, so an individual cannot plan around it. Pooling with many others converts an unknowable individual question into a predictable average one, since how long any one person lives is uncertain while how long a large group lives is not.

The mechanism is straightforward once the pooling is understood:

• •Many people each hand over a sum at roughly the same age
• •The provider invests the pooled money and pays each of them regularly
• •Payments continue for each person until that person dies
• •Money not paid out to those who die early funds those who live long
• •That transfer is the whole product and is why payments exceed investment returns
• •The provider bears the risk that the group as a whole lives longer than expected

The product solves a real problem and is unpopular, which economists have written about extensively under the heading of a puzzle. The money is gone, so somebody who dies shortly after buying one has handed over a great deal for very little, and that possibility weighs heavily even though it is precisely the risk being pooled. Nothing is left to heirs under the simplest version. The decision is irreversible. Rates have been low, which makes the payments look poor. And the benefit is invisible, since somebody who lives to ninety five and has an income only notices the absence of a problem. Behavioural work finds that framing the product as consumption rather than as an investment improves how it is received.

The basic product is modified in several ways, each of which reduces the income in exchange for addressing an objection. A joint version continues paying a surviving spouse, usually at a reduced rate. A guaranteed period pays for a minimum number of years to an estate even if the holder dies immediately, which addresses the fear of losing everything at once. An escalating version starts lower and rises each year, either by a fixed percentage or with inflation, which protects purchasing power over a long retirement. An impaired version pays more to somebody with a medical condition that shortens life expectancy, which is the one case where poor health improves the terms offered.

The arrangement is ancient and its history is bound up with the development of statistics. Roman law contains tables estimating the value of a lifetime income, which are among the earliest surviving life expectancy calculations. European states sold them to raise money from the seventeenth century, frequently mispricing them badly because nobody yet knew how to compute the values, and several governments lost heavily as a result. Edmond Halley produced a proper life table in 1693 from the burial records of Breslau specifically to price them, which is a founding document of actuarial science. Pricing them correctly required knowing how long people live, so the need for the product drove the collection of the data.

How long one person lives is unknowable and how long a large group lives is predictable, so pooling converts an impossible individual calculation into a manageable average one, with money from those who die early funding those who live long. That transfer is why payments exceed what investment alone would yield. The product is unpopular because the loss on early death is vivid and the protection against long life is invisible.