Saturday, August 18, 2007

When Will You Die?

Average life expectancy seems to enter into on line discussions on deciding when to collect Social Security benefits, with the goal of maximizing benefits collected during your lifetime. Some comments imply that if you're age X you'll live Y years and die, for instance one commenter stated that a 65-year-old has a 20-year life expectancy implying a certain death age of 85. But I'm sure that if put to them that way, they would tell you that's not what they meant.

I decided to look into it a bit further. On the Social Security Administration's web site, I found a table with life expectancy data calculated by their actuaries. Excel has the capability to import HTML data formatted like the chart. I did so, and with some added calculations, I was able to produce the graph shown below. In case you have difficulty reading the legends, the blue curve shows the probability of an average male aged 65 surviving to a particular future age, and the vertical blue dashed line shows the average life expectancy for that male. The pink curve and dashed line is the equivalent data for a female aged 65. As you might expect, the average life expectancy for a 65-year-old female of 84.2 years is longer than the 81.33 years for a 65-year-old male, almost 3 years longer.

If we look at the curves, a straight line approximation starting from 1 at age 65 and dropping to zero at age 100 would be a reasonable approximation. Certainly not perfect, but a lot closer to the curves than an approximation which has a value of 1 from age 65 and then falls to zero at the average life expectancy. So no, the average person doesn't live to their life expectancy and then fall dead.

This is significant to retirement planning. If you are among the more than 50% who live longer than your average life expectancy and that's the age to which you planned your savings prior to retirement and spending after, then you'll suffer the consequences.

Yes, I said that you have a greater than 50% chance of exceeding your average life expectancy. If you'll look closely at the graph, you'll see the life expectancy lines intersect their curves above the 50% line. For females, the median life expectancy is almost a year longer than the average life expectancy.

With a bit more computation on the data I downloaded to analyze the data for an average 65-year-old, I produced the following graph: Using the same blue-for-boys/pink-for-girls coding scheme, this graph shows the probability that an average 65-year-old will die at a particular one-year span of age. Note that the probability is less than 4.5% at any age, and the highest probability for a one-year span is at greater than average life expectancy.

Meaning that when 65 years old, your chances of dying in a year other than your average life expectancy is greater than 95%. A very high degree of uncertainty when planning your retirement. I plan to discuss this further in a future post.