Calculating the Value of a Longevity Annuity

A longevity annuity is arguably the most efficient way to insure longevity risk. 

Consider the following example to see why this is the case:

• Daniel is 65 years old and is in relatively good health.
• According to publicly available actuarial tables, Daniel's current life expectancy is 16.28 years.
• If Daniel lives to age 85, his life expectancy at that point is an additional 5.76 years.

A longevity annuity is basically a single premium deferred annuity.  In other words, Daniel pays a lump sum at the beginning and receives annuity payments after a pre-determined period of time (the "deferral period"). 

The basic question, then, is how much Daniel would need to hand over to the insurance company today to receive, as an example, $50,000 each year for the rest of his life.  The answer depends on when Daniel begins to receive those $50,000 payments:

• Daniel’s cost today to receive $50,000 per year for the rest of his life beginning at age 75 is $212,500.
• Daniel’s cost today to receive $50,000 per year for the rest of his life beginning at age 80 is $106,710.
• Daniel’s cost today to receive $50,000 per year for the rest of his life beginning at age 85 is $44,287.
• Daniel’s cost today to receive $50,000 per year for the rest of his life beginning at age 90 is $13,912.

It is obvious from the figures above that a longer deferral period results in more leverage or efficiency.  The deferral period is basically the same as an auto insurance deductible: the higher the deductible the lower the insurance premium.  The trade-off is that Daniel may not live long enough to receive the future payments.

So how might Daniel think about this decision? 

The answer depends in large part, of course, on the amount of money Daniel has at age 65, the amount he intends to spend each year in retirement and the amount he wishes to leave to his heirs.

Sustainable spending and bequest motive are topics for a separate entry.  In the interest of simplicity, consider the following:

• Similar to the risk of one's home burning to the ground, the risk of completely depleting one’s resources in retirement is truly catastrophic and entirely unacceptable.
• Self insuring longevity risk is on option that is fraught with risk.  If Daniel invests $44,287 at age 65, an average annual return of 7 percent over 20 years would leave him with $171,376 at age 85. 
• This result rests on quite a few assumptions, including the rate of return and whether Daniel is disciplined and fortunate enough to simply set that money aside for 20 years.  Think about what has happened in the capital markets (i.e. sequence of returns risk) over the past couple of years and the impact that would have on Daniel’s $44,287 investment if he were in his early 80s.
• Assuming all goes as planned, the $171,376 is most likely not enough to fund the $50,000 per year for his remaining life expectancy (5.76 years).  The reality is that 5.76 years is his average life expectancy at age 85 and he could end up living much longer than the average.

The longevity annuity provides a couple of very clear benefits:

1. Peace of mind—Daniel can off-load the whole longevity risk issue to an insurance company and not think about the issue again.
2. Daniel will likely have the ability to be more aggressive investing his remaining assets and more comfortable with his desired level of retirement spending since he does not need to self-insure and think about hedging longevity risk on his own.