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A Persistent Abuse of Statistics

If you follow investment information on social media, you’ve seen a variant of the following chart many times:


U.S. stock prices are very high (as measured by the Shiller CAPE in this case), and we are near the right side of the chart today.  The intended message is that we are sure to have terrible U.S. stock returns for the next 10 years.  The R-squared value of 79% means that the correlation is strong.  All the points are close to the line that’s been fitted to them.

But what’s the reality here?  Are we doomed?  The first thing to observe is that the chart covers 39.5 years.  That's close to 4 decades.  Doesn’t that mean there should be only 4 dots?  What they’ve done is collect monthly data so that there are 475 points.  But that means that one point overlaps with the next in 119 out of 120 months.

With so little data, statistics are completely unreliable.  It could be that the correlation is much weaker and we just happen to be in a period of a few decades where the measured R-squared is high.  To test this, let’s add in data going back to 1926.


Suddenly the R-squared dropped to 44%.  The points are much more scattered.  There is a link between the Shiller CAPE and future U.S. stock returns, but it is weaker than the first chart made it seem.  Even this chart covers only 10 decades, which is not enough to trust statistics.  We can average in data from other countries too, and this would show that the correlation is present but isn’t strong.

Future stocks returns are likely to be below average in the coming decade, but they’re not certain to be terrible, although that might happen.  The Shiller CAPE gives us some information about what future stock returns will look like, but it’s not predictive enough to be useful for big market timing swings in and out of stocks.

I use the Shiller CAPE to make subtle adjustments to my asset allocation.  Currently, my allocation to stocks is about 10% lower than it would have been if the CAPE were in a normal range.  This is just enough to help preserve capital in the event of a market crash that may be more likely at current market heights.  But I need to balance the desire to preserve capital with the desire to benefit if the market continues to march upwards.

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