A longevity annuity is a very simple instrument. The buyer pays the insurer a lump sum at the outset in exchange for the insurer's commitment to pay the buyer a monthly stipend for a period that begins at some future start date selected by the buyer, with the payment lasting until the buyer dies.

The further in the future the start date, the larger the monthly payment. For example, on Jan.18 a 62-year old man who paid $100,000 for a longevity annuity would receive about $1,041 a month starting at age 82, or $2,870 a month starting at 92. Buyers who die before the payment start date receive nothing.

I specified the date of the annuity amounts because the amounts change over time with market interest rates. Even at the same time, the amounts quoted by different insurers will vary. The market for longevity annuities is imperfect, which means that potential buyers are advised to shop. A good place to do that is www.immediateannuities.com, which shows annuity amounts for a large number of insurers.

Longevity annuities can play a critical role in a retirement plan that depends heavily on withdrawals from a nest egg of financial assets. The problem with living off a nest egg is that the amounts you can safely draw depend on how long you live, which few know and most don't want to know.

Many retirees who consult with investment advisers on how much they can safely draw from their nest eggs monthly are given an answer based on mathematical models that use mortality data to calculate probabilities. For example, they might be told that if they draw $X every month, the amount increasing by Y percent every year, the probability of exhausting their nest eggs while they are still alive would be only 3 percent. That small number is supposed to make the retiree feel secure, but it seldom does. Few care to incur even a small risk of becoming impoverished at an advanced age if they can avoid it. It can be avoided with a longevity annuity.

Here is an illustration. Mark is 62, has an asset portfolio of $3 million that earns 4 percent, and wants an income stream that grows 2 percent a year through age 103. His assumption is that he will live to 104. Given these conditions, without an annuity, Mark's income would begin at $2,943 and rise to $6,649 in his 103rd year of life. At the end of that year, his assets would be exhausted. This is the base case.

Now let's add the following longevity annuity. Mark pays the insurer $203,130 for an annuity of $6,053 beginning in 20 years, when Mark is 82. This transaction reduces Mark's nest egg to $796, 870, but it cuts the direct withdrawal period in half. With only 20 years to cover, Mark can now draw $4,141 a month to start, the amount rising to $5,056 after 10 years and to $6,053 in year 20 when the annuity kicks in at that amount. In sum, using the annuity Mark has spendable funds 40 percent larger at the beginning, and they remain larger until he reaches age 100.

You may wonder how it is that the withdrawals from the portion of the nest egg not used for the annuity rise to the exact amount of the annuity payment. This is no happy accident. It is based on an algorithm developed by my colleague Allan Redstone.

You may also wonder why I selected an annuity deferral period of 20 years. The selection was completely arbitrary, and the process could be duplicated for other ages. Reducing the payoff period increases the payment in the early years but reduces it in the later years. For example, with a deferment period of 10 instead of 20 years, the initial payment would be $4,650 instead of $4,141, but the 10-year would level out at $5,576 after 10 years while the 20-year levels out at $6,053 after 20 years. It is up to retirees to select the payment pattern they prefer.

ABOUT THE WRITER

Jack Guttentag is professor emeritus of finance at the Wharton School of the University of Pennsylvania. Comments and questions can be left at http://www.mtgprofessor.com.