Valuation-Informed Indexing #37:
Stock Prices Are Not a Random Walk — Here’s Proof!

<i>Valuation-Informed Indexing</i> #37:<br> Stock Prices Are Not a Random Walk — Here’s Proof!

by Rob Bennett

Some people believe that stock prices follow the pattern of a random walk. Some do not. Let’s not argue. We live in the age of the internet. Let’s check it out!

The section of Yale Professor Robert Shiller’s site that sets forth historical stock return data is here. Please click on the “Excel file” link. You now have on your computer a spreadsheet that identifies the P/E10 value (the price of the S&P index over the average of the last 10 years of its earnings) that has applied for US. stocks for every month going back to January 1881. Please scroll until you find the first month in which the P/E10 value reaches 24, a dangerously high P/E10 value.

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That happens in April of 1901.

If stocks prices followed the pattern of a random walk, the fact that the P/E10 level hit 24 would be of no significance. We might see higher P/E10 values in the years ahead and we might see lower P/E10 values in the years ahead. There’s no way of knowing in advance what sort of prices are going to turn up if prices follow the pattern of a random walk.

We don’t want to check what happens in a year or two or three. Stock prices really do fall in the pattern of a random walk in the short term. What we need to determine is whether they also fall in a random walk in the long term. If they do not, it cannot be said that stock prices fall in the pattern of a random walk. For prices to be truly random, the pattern would need to apply both in the short-term and in the long-term. We only need to find one way in which returns do not fall in a random pattern to show that the random walk idea is invalid.

Let’s go ahead 10 years from the month that we first reached a P/E10 value of 24 and see where things stand. Ten years from April 1901 is April 1911. Please scroll down to April 1911 and see what the P/E10 value is for that month. It’s 14.75. A big drop. In the first case in which we went to a dangerously high valuation level, we saw a big price drop in the following years.

How about the second time?

Please scroll again until you again see a P/E10 of 24.

That’s November 1928. You may recall from the history books that something significant happened in the market not too long afterwards. In any event, ten years out from the second time we hit a P/E10 level of 24 (November 1938), we see a P/E10 level of 16.5. Another big drop! We are not seeing a random walk!

Let’s test this a third time.

The next month in which we hit a P/E10 level of 24 is January of 1966. Skip ahead 10 years to January of 1976 and we see a P/E10 level of 11.19. The pattern holds.

Let’s spin her again.

The next month in which we hit a P/E10 of 24 is November 1995. Skipping ahead 10 years brings us to November of 2005. The P/E10 value in November 2005 is 25.92. That’s even higher! The pattern has been broken. In three cases a dangerously high P/E10 level led to a big drop. But in one case, we see no drop at all. So the return pattern is essentially random after all!

Except —

We see a drop to a P/E10 level of 16.38 in October of 2008. The big drop is delayed on this fourth testing but it does turn up not too much later. We are seeing a pattern. We are not seeing a pattern that conforms to a precise set of rules. But we are seeing a pattern of significance.

Is it even remotely possible that these results are the product of a random walk? I don’t see it. We are four for four. Each time we have gone to dangerous valuation levels, we have seen a big drop in stock prices with the passage of 10 years (except that in one case it took 13 years) of time. A legitimate argument can be made that long-term stock returns are not precisely predictable. But “not precisely predictable” is a long ways off from “random” What we see when we look at the historical data is stock returns falling into an easily discernible pattern, not a random walk.

The case becomes even stronger when you look at the pattern from the opposite point of perspective.

We’ve seen that each trip to dangerous valuation levels brought on a stock crash. Perhaps stock crashes are so common that this could happen by chance. Could that be the explanation for what we have seen here?


There has never been a trip down to super-low valuation levels that was not preceded by a trip up to super-high valuations. The correlation is perfect in both directions. Super-high valuations levels always lead to super-low P/E10 levels. And super-low P/E10 levels never appear except in the wake of super-high P/E10 levels.

Long-term stock returns are not a random walk. They follow a clearly discernible and even to some extent predictable pattern: Prices go up, up, and up until they reach dangerously high levels and then they crash, beginning a sustained move up again only after first having gradually fallen down to levels as insane on the low side as those that earlier applied were insane on the high side. Stock prices are cyclical.

Rob Bennett does not believe that stock prices are a random walk. His bio is here.

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