The Non-Existent Law of Averages

There’s an ancient joke about a statistician who drowns wading across a river that is, on average, three feet deep. I have often found myself wading rivers to fly fish with water up to my knees, only to step into an unseen hole that drenched me to the neck. I know that my belongings might get dunked even if I stash them in my cap.

Funny stories, perhaps, but I find that hardly anyone understands even the most basic concepts of statistics and probability. That includes professionals who should understand at least the basics, like doctors and financial planners.

That lack of understanding includes the most basic statistic, the average, or mean. For example, you frequently hear the expression “law of averages”, though there isn’t one. Look it up. No such thing.

You also hear about average market returns. Those do exist, but they may not mean what you think.

In order to understand averages, you need to be able to differentiate long-term probabilities from one-time events. The difference is demonstrated by actuarial forecasts.

If we gather 1,000 people of the same gender and health and age in a room, actuaries can tell you how many of those people will still be alive in 10 years, 20 years, 30 years, or longer with amazing accuracy — but they can’t tell you which individuals in the room will still be alive.

This is useful information for an insurance company. Long-term averages are accurate enough for them to make bets that will result in profits from selling life insurance policies. They will guess wrong sometimes and right sometimes but they get to make lots of bets and on balance they will come out ahead.

However, if you are an individual in that room, probabilities can’t tell you how long you will live. The insurance company gets many bets, but you get just one. Your life is a one-time event. 

50% of the people in that room will live to their life expectancy or longer, but you either will or you won't. You can't have 50% of each outcome.

Perhaps a fourth of the people in the room will actually live past age 90, but no one can know whether they are in that group or not. Consequently, everyone in the room should plan for the possibility of living past 90 because if they bet on living a shorter life, they may run out of money if they're wrong.

Actuaries might tell us that the life expectancy of everyone in the room is age 78. That's the age at which they predict half the rooms occupants will still be alive and half will be dead.

If everyone in the room planned to pay for a retirement only until their average life expectancy, half of the people in the room would die broke. Averages turn out to be a very poor way to develop your retirement plan. Planning for the worst case works better.

Long-term stock market returns are another example. The S&P 500 grew at an annual rate of 9% from 1928 to 2008, but people who began investing in 1928 only earned about 7.9% over the next 30 years, while people who began investing in 1942 averaged 13.6% a year.

That’s a huge difference over 30 years. At 7.9%, $1 grows to $13,579 in 30 years. At 13.6%, a dollar grows to $40,280.

So, yes, had you invested a dollar in 1928 and held onto that investment for eighty years (and achieved market returns), you would have earned an average 9% a year — and you would be very old. In reality, you will only have about 30 years to invest for retirement. 

Depending on when your 30 years of investing ended (which depends largely on when you were born), however, you might have earned as little as 7.9% or as much as 13.6%. You probably wouldn't have received the actual average of 9%.

Your investing life is a one-time event. The market returns you receive may be much more or much less than the long term average.

Investors have been convinced by the marketing of brokerage firms that if you just stick with the market long enough, you will end up with an 8% to 10% return. Just keep the faith in the bad times, stay invested, and you will eventually get back to that 8%.

But that simply isn’t true. Your investment career is a one-time event and your investing results may be very different than the returns of a hypothetical person who might have been investing in the stock market for the past 80 years.

Be realistic. You could earn a lot in the stock market and you could lose a lot, or somewhere in between. Hanging on in bad markets is no guarantee that you will eventually be just fine.

So, what does this mean (pun intended) for retirement planning? It means that you have to plan for those holes in the river I sometimes step into. Have a plan that keeps your head above water if you live to 90, or if the stock market gods don’t smile on you.

You have to plan for the worst case, not the average.

In my next post, I'll explain why you probably won't earn "market average" returns.