The Retirement Reality Game Show

Welcome to the Retirement Reality Game Show. Here are the rules: you have 6 months to prepare by storing up all the supplies you need, and then you will be locked in your house for an average of 6 months, during which time additional contests will be played.

Contestant Bob buys up 6 months worth of food and other supplies, and is locked in his house. A jar with 364 black balls and one white ball is prepared. Every day, the game show host pulls out at random one ball. If a black ball is pulled, then Bob stays in his house another day. If the white ball is pulled, then Bob is released from the house.

On average, Bob will stay in the house for 183 days, which is about 6 months. But there's a 50% chance that Bob will stay in the house longer. If Bob plans his meals to last 183 days, there's a 50% chance that the viewers of the show will watch him starve.

Let's look at the graph of the probability that Bob will still be locked in the house on a certain day.
Now let's take another look at the probability of a 65-year-old surviving to a certain age.
The life expectancy graph was previously presented and explained in this post.

Aside from the fact that one graph is a simple straight line and the other is curved, these graphs are similar. If Bob prepares for an average stay in the house, he has a significant chance of starving. If you plan your retirement savings and withdrawals in retirement for an average life expectancy, there is a significant chance that you will run out of money and suffer whatever consequences follow.

While no analogy is perfect, it should put in basic terms the idea that if you prepare for the average, there's a significant chance that you will have under-prepared.

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.