This Stat Pisses Me Off

There is one investing statistic that I see more than any other. I’ll be innocently browsing twitter or in the comment section of Reddit (wouldn’t recommend) or an excellent blog post and someone will inevitably throw out this stat. It’s typically used in one of two ways:

  1. Hey you, look at this statistic. It’s amazing. How can you not invest? You’re an idiot.
  2. Hey you, look at this statistic. Your argument is invalid. You’re an idiot.

Either way, the fundamental premise is the same: invest now and as much as possible (if not, you’re an idiot).

The statistic I’m referring to is some derivative of the following:

X% of the time you make money investing in Y over Z time period

Actually, more often than not it is the following version of the above that is cited:

99% (or 100%) of the time you make money investing in the S&P 500 with a 20-year investment horizon

Now, there is nothing intrinsically wrong with this statistic or using this statistic per se. It is correct. It is a fact. What riles me up a bit is the way it’s used and what most people are saying implicitly when they use it.

They make it sound like the result of a fucking scientific experiment. Like the boyz at the lab ran the test once – ok, we made money, cool – then ran it again – positive again, nice – and again and again and again until they arrived at the conclusion that you basically never lose money investing in this way.

But this isn’t even close to reality. Firstly, the underlying mechanism is waaaay more complex and the observations more difficult to interpret than typical experiments. Secondly, the outcomes of this “experiment” are not iid outcomes. The observations are not individual, separate events. When people use this stat they make it sound like (implicitly, to be fair) it’s not the case that overlapping observational periods are a thing.

But they are; it’s usually based on 20-year windows moved forward by 1 month to create a new window. A “new” observation. I understand the rationale behind using a month as the time increase for a new period (most people invest monthly, I guess) but might the results be different if a different time period was used?

Jan 22Feb 22March 22April 22May 22June 22July 22
Return5%10%20%4%1%-20%
Separate
Periods
£100£138.60£84.03
Overlapping
Periods
£100£138.60£137.28£126.05£84.03

As you can see, using overlapping observational periods leads us to the conclusion that the stock market increases in value 75% of the time but using separate time periods makes it seem like the stock market goes up 50% of the time.

Using increasingly partitioned periods lends increasing weight to frequency of outcomes and masks significant downturns. And size is as important as frequency, particularly in investing in which the distribution is fat tailed, dominated by large moves rather than regular monthly moves.

What also makes me somewhat uncomfortable is the fact that this stat is only concerned with 1 index of 1 country in 1 particular period of history. A period in which the US was the most dominant economic force in the world, (nearly) entirely uninterrupted by economically-crippling events like wars, viruses, famine, currency collapse, defaulting on debt, mass emigration, brain drain, etc. etc. etc. Business has been, truly, booming.

But what about other countries in other time periods? One might see this statistic, infer that the stock market, any stock market, essentially doesn’t go down over 20-year periods, and swiftly invest the entirety of one’s life savings into the stock market. Or do something similar. This can go horribly, disastrously, painfully wrong.

Huh? I never said that or that or that. I just said the S&P 500 has always risen over a 20-year period. Give me a break.

Your favourite American personal finance guru

Ok, the above is technically correct, but not a valid excuse for abusing this statistic without sufficient caveating. Induction is difficult. We see this stat and think that history will repeat itself. We may pile everything into our domestic stock market, or a global tracker, or the US market thinking we can’t lose. The probability is 0. We are certain.

And most of the time this is the intended message of those who use this stat. Case closed, game over, you lose – why on Earth would you invest in anything else other than the stock market? It’s never gone down in a 20-year period, I expect this to be true moving forward, why wouldn’t it be?

Sigh.