January 24, 2018

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 is the start
date, the larger is the monthly payment. For example, on
January 18 a 62-year old man who paid $100,000 for a
longevity annuity would receive about $1041 a month starting
at age 82, or $2870 a month starting at 92. Buyers who
die before the payment start date receive nothing, allowing
the insurer to pay more to those still living.

I specified the date of the annuity amounts because
the amounts change over time with market interest rates.
Even at the same point in 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 advisors
on how much they can safely draw from their nest egg 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% every year, the probability of exhausting
their nest egg while they are still alive would be only 3%.
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 $1 million that earns 4%, and wants an income
stream that grows 2% 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 $2943 and rise to
$6649 in his 103^{rd} 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 $6053 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 $4141 a month to start, the amount rising to
$5056 after 10 years and to $6053 in year 20 when the
annuity kicks in at that amount. In sum, using the annuity
Mark has spendable funds 40% 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 $4650 instead of $4141,
but the 10-year would level out at $5576 after 10 years
while the 20-year levels out at $6053 after 20 years. It is
up to retirees to select the payment pattern they prefer.

The Monthly Spendable Funds Growing 2% a Year
Available to a Retiree of 62 With a Nest Egg of $1 Million
Yielding 4%: With and Without a Longevity Annuity

Retiree’s Age |
No Annuity, Nest Egg Lasts to Age 104 |
Price and Deferment Period of Longevity
Annuity |
|||

Price: $533,192 Payment Deferred Until Age 72 |
Price: $337,708
Payment Deferred Until Age 77 |
Price: $203,130 Payment Deferred Until Age 82 |
Price: $117,286
Payment Deferred Until Age 87 |
||

62 |
$2942 |
$4650 |
$4439 |
$4141 |
$3808 |

72 |
3587 |
5576 |
5420 |
5056 |
4649 |

77 |
3960 |
5576 |
5877 |
5582 |
5133 |

82 |
4372 |
5576 |
5877 |
6053 |
5658 |

87 |
4827 |
5576 |
5877 |
6053 |
6146 |

92 |
5330 |
5576 |
5877 |
6053 |
6146 |

97 |
5877 |
5576 |
5877 |
6053 |
6146 |

103 |
6649 |
5576 |
5877 |
6053 |
6146 |

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