Sunday, August 26, 2007

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.