Thread by @alojoh

JP Morgan asset management produced these charts. Bankers like to produce these charts (I was one of them) to show clients some fancy looking analysis to fill meeting time and look smart. What they ignore is the elephant in the room: mathematically there is NO correlation here and hence these charts are useless. In the following I explain why.

First, what do they show:
You can see the forward P/E ratio (horizontal axis) relative to the annualized return (vertical axis) for both the next 1-year (first chart) and next 5-year period (second chart).

Key observations - Next 1-year return:
1) The R2 is very low (0.05). This means there is no relationship between different levels of forward P/E ratios and subsequent returns.
2) The current forward P/E ratio of 22.4x is uncommon but not exceptionally rare. You can see dozens of similar datapoints. But that doesn't make the chart useless. That's just a sidenote.

Key observations - Next 5-year return:
1) The R2 is also very low (0.30). This means there is at best a very weak correlation between forward P/Es and subsequent long-term (5-year) returns.
2) You can see there were a number of years where very high subsequent returns resulted from years with very high P/E ratios.

Technically, an R2 of
A) 0.05 means there is almost NO relationship and the data proves it.
B) 0.30 means there is only a slight linear relationship between the variables: changes in one variable are associated with only small or inconsistent changes in the other.

In the attached posts we discuss why the R2 is so low. Spoiler: there are too many exceptions too each rule.

(Math sidenote: whenever you have a very widespread in datapoints, especially outlier datapoints that confirm the trend-whether on real correlation or not doesn't matter-, they have a disproportional impact on the R2 (they improve the R2). We can see the same in this data (5-year). There is a small number of confirmatory datapoints. If you removed them the R2 would drop even more. R2 is already negligible and hence this is irrelevant here.)

Red circle: High 5-year returns despite high P/E ratios.

Red circle: low 5-year returns despite low/moderate P/E ratios

Red circle: peak returns NOT from lowest P/E ratios.

Red circle: Lowest returns (negative in fact) NOT from highest P/E ratios but moderate P/E ratios.

Big spoiler:
1) S&P500 and other index data is bad data.
2) This is driven by rebalancing and survivorship bias.
3) Index operators hate to talk about this dirty little secret since it would show that index returns aren't as strong as the numbers suggest.
4) What it results in is that index returns, whether it's the S&P500 or Nasdaq or other index, are overstated.
5) By how much? Nobody really knows since creating a timeseries across decades would be:
5.1 Very time consuming;
5.2 Required a lot of debatable assumptions.

Hence, as far as I know nobody ever published strong quantitative insights on this little dirty stock market secret.

I think what makes people easily buy into the charts discussed in this thread is that intuitively they make sense: everyone would expect 5-year returns to be higher from a very low multiple. And in fact that's often the case but not nearly as often as one would expect as evidenced by low R2s.