# How to use Statistics to Lie to yourself about a Stock Crash

By Michael J. Wiener

Special to the Financial Independence Hub

Wouldn’t it be great if we could predict the future movements of stock markets so we could capture the gains and avoid the losses?  It turns out we can’t, but that doesn’t stop people from trying.

After a Twitter exchange with John De Goey, I ended up reading the article The Remarkable Accuracy of CAPE as a Predictor of Returns by Michael Finke.  He gives a chart that appears to show we can predict the coming decade of stock returns by calculating what is known as the CAPE (Cyclically Adjusted Price-to-Earnings Ratio).

For our purposes, we don’t need to know much about the CAPE other than that it is a measure of how expensive stocks are and that it was invented by Robert Shiller, who received a Nobel Prize in Economics in 2013.  In fact, we don’t even have to calculate the CAPE ourselves; it is freely available and updated daily.

Right now, stock prices are very high.  As I write this, the CAPE for U.S. stocks stands at 37.  The only time it was higher in the past century was during the tech boom and bust around the year 2000.  We seem to be repeating the boom part, and the fear is that we may soon repeat the bust part.

Here is my reproduction of a chart similar to Finke’s chart:

Finke’s chart used nominal U.S. stock returns rather than real (inflation-adjusted) returns, but they show the same thing: an apparently close relationship between the CAPE and U.S. stock returns over the subsequent decade.  Given the current CAPE, stock returns appear to be predictable to within +/- 3% per year.  That would be amazingly accurate if true.

Based on this chart and the fact that the CAPE is currently 37, we’d expect the average annual stock return in the next 10 years to be between inflation minus 4% and inflation plus 1.5%.  If true, this would clearly mean it makes sense to sell stocks.  De Goey made his position clear in an article titled Get Out!.

Sadly, there holes in this story.  Nobel Prize winner Shiller invented the CAPE, but he isn’t involved with Finke’s paper, despite De Goey’s implication when he defended Finke’s chart saying “Oh, and the guy who came up with the concept has a Nobel Prize.”

You might wonder how the chart above has so many points when we’re talking about 10-year returns and it covers only 25 years of stock market data.  The answer is that the chart uses 300 overlapping 10-year periods.  So, each point represents a starting month.  Two successive months are likely to have nearly the same CAPE and nearly the same 10-year annual returns.  So, we get lots of bunched up dots.

But the truth is that we have very little data.  We really only have two independent 10-year periods.  Despite the impressive correlation the chart shows, we’re extrapolating from little information.

To show the problem, let’s repeat this chart for another time period:

I didn’t choose this date range at random; I selected it to make a point.  If we were to devise a strategy based on this chart, we’d say not to worry if the CAPE gets high because you’ll still get decent returns.  But when the CAPE is in the 17 to 18 range, stocks are either going on a big run, or they’ll crash, and you have to be ready to get out.  This is obviously nonsense.  It’s dangerous to try to build strategies on too little information.

Here’s a chart using S&P 500 stock data from 1936 to the present:

This data still only covers seven independent decades, but we can see the real picture of the relationship between the CAPE and stock returns is a lot fuzzier than the first chart made it seem.  We can still reasonably guess that a higher CAPE reduces future expected stock returns, but the range of returns is still wide.

We might guess that the CAPE appears to have predictive value when it is above 30 because future stock returns are limited to a narrower range.  Again, this is because we have limited data and the periods overlap.  In fact, two overlapping decades a month apart are over 99% identical (119 of the 120 months).

To reduce this illusion of seeming to have more data than is truly available, here’s a chart of the same results back to 1936, but with overlapping decades spaced a full year apart:

Now we see how little information there is for the CAPE above 30.  But it gets worse.  Those five points are from consecutive years during the year 2000 tech boom and bust, so they all overlap by six to nine years.  Any strategy we develop based on high CAPE values is just guessing that the tech bust 20 years ago will repeat.

Does this mean we should blissfully assume a rosy future for stocks?

Absolutely not.  Stocks can crash at any time, and that last chart shows that we should assume lower than average expected stock returns over the next decade or more.

Does this mean we should get out of stocks?

We don’t know the future.  Stocks may crash soon or they may not.  Nobody knows which.  The important question to answer is whether there is some investment other than stocks with a higher expected return right now.  Unfortunately, bonds and real estate (especially Canadian real estate) are expensive right now too.

If we really believed stocks would lose money over the next decade, we’d be better off with cash in a savings account.  But we can’t know if this will happen or not.  My own take is that stocks still have a higher expected return than other investments, so I am sticking to my investment plan.

However, I have lowered my expectations for future returns.  The main effect this has is to slightly reduce my family’s spending to preserve capital in case future stock returns really are poor.

If the CAPE continues to rise, I can’t say I’d stick to my current investment plan indefinitely.  I’m open to the possibility that it will make sense to taper my stock holdings if the CAPE gets to even crazier levels.

One thing is certain though: I don’t believe it makes sense to make a radical change all at once.  For example, I wouldn’t suddenly sell all my stocks if the CAPE hits 50.  I’d devise some plan for my stock allocation as a function of the CAPE that would gradually reduce my stock holdings as the CAPE rises.  But I have no such plan for now.

De Goey’s call to get out of stocks will eventually look either prophetic or misguided.  But I won’t be among those who look back to judge his call to be right or wrong.  If you place a bet at a roulette table, you’ll either win or lose, but I’ll judge you by whether the bet made sense at the time you placed it.  For now, De Goey hasn’t made a case that convinces me, and I would never suddenly sell all my stocks anyway.  For now, you can count me among those concerned about high stock prices but unconvinced there’s a better place for my money.

It’s very easy to fool yourself with statistics, particularly when the amount of data is far short of enough to be statistically significant.  But, even in the absence of data, we have to make decisions.  To make a case for switching from stocks to some other asset class, we’d have to look somewhere other than past stock prices.

Michael J. Wiener runs the web site Michael James on Money, where he looks for the right answers to personal finance and investing questions. He’s retired from work as a “math guy in high tech” and has been running his website since 2007.  He’s a former mutual fund investor, former stock picker, now index investor. This blog originally appeared on his site on June 2, 2021 and is republished on the Hub with his permission