Bogle Believes in One Understanding of “Reversion to the Mean” and Valuation-Informed Indexers Believe in Another

Valuation-Informed Indexing #317

by Rob Bennett

The premise of this column is that Robert Shiller advanced our understanding of how stock investing works in a “revolutionary” (Shiller’s word) way in 1981 when he published research showing that valuations affect long-term returns. If that’s so, then risk is not static (as it would be if the market were efficient, as we once thought was proved by research done by Eugene Fama in the 1960s) but variable. Investors can dramatically reduce stock investing risk by practicing price discipline when buying stocks (going with higher stock allocations when prices are low than they go with when prices are high).

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To say that this idea is controversial would be the understatement of the Century. The textbooks in this field assume market efficiency as their starting point. 90 percent of the investing advice advanced at web sites and in newspapers and on radio shows is wrong if Shiller is right. Most Buy-and-Holders cannot even bear to hear the how-to implications of Shiller’s findings discussed at discussion boards and blogs at which they participate.

The amazing thing is that I only began writing about Valuation-Informed Indexing because of something that I read in one of John Bogle’s books!


It was the Spring of 1996. I was putting together a plan for early retirement. I needed to identify the safe withdrawal rate to know if the numbers in the plan worked or not. The Buy-and-Hold retirement studies said that the safe withdrawal rate is always 4 percent. I couldn’t quite put my finger on what the problem was but something about that claim sounded fishy to me. I came across a passage in Bogle’s book that clarified the issue: “Reversion to the Mean is an Iron Law of stock investing,” my hero said.

That was it! This was what had been bothering me. If stock prices revert to the mean, the return on stocks is not as good when they are overpriced as it is when they are priced fairly. So the safe withdrawal rate is not stable but a number that varies with changes in valuations. To put together a successful retirement plan, I would need to identify the real (valuation-adjusted) safe withdrawal rate, not the one reported in in the Buy-and-Hold studies.

What I thought I heard Bogle saying in the Spring of 1996 makes perfect sense to me more than 20 years later. Unfortunately, I now understand that Bogle does not really believe what I once thought he believed. There are two very different understandings of the phrase “Reversion to the Mean.” The one that serves as the premise of the Valuation-Informed Indexing strategy is very different from the one believed in by Bogle and the other Buy-and-Holders.

Say that you flip a coin 100 times and it comes up heads in 60 of those 100 tosses. Bogle’s understanding of “Reversion to the Mean” is that it is likely that, if you toss the coin another 100 times, the percentage of total times that it comes up heads is likely to be something less than 60 percent. This is inarguably so. This is indeed an Iron Law. This understanding of the phrase is consistent with a belief in an efficient market. A market in which prices follow a random walk will for some time-periods produce results better than the norm but over longer periods of time will produce results that come closer and closer to matching the average long-term return.

The average high temperature in New York City is 60 degrees. The average high temperature in August is 81. Say that you checked the high temperature for every day in August and found that it exceeded the average high on every one of those days. Using Bogle’s understanding of the phrase “Reversion to the Mean,” you would expect to see a total average temperature of something closer to 60 after checking the average high for every day in September. And indeed you would probably see that; the average high in September is 74. But is what you are seeing the same phenomenon that you were seeing with the flipping of the coins?

It is not at all the same phenomenon. Reversion to the Mean as Bogle understands it is an uncaused statistical evening-out process. Reversion to the Mean as Valuation-Informed Indexers understand it is a caused phenomenon, similar to the phenomenon in which temperature readings in August tend to be higher than temperature readings in September. Stock returns are higher in time-periods following the recording of high valuations because it is the purpose of markets to get prices right and so in the long term valuation are always brought back down to fair-value levels. Market prices do not fall in a random-walk pattern in the long term. They move in the direction of fair value for a reason.

It is the second understanding of the phrase “Reversion to the Mean” that applies in the stock market. I suppose that it is fair to refer to that statement of belief as “my opinion.” Millions of people either don’t believe this or at least invest their own money as if they do not believe it. But I think it would also be fair to say that the entire historical record available to us for review supports the second understanding. If stock returns were in some time-periods higher than normal just because of meaningless statistical variances, these high-return time-periods could not be predicted. Shiller showed in 1981 that that the high-return time-periods are highly predictable and there is now 35 years of peer-reviewed research confirming this breakthrough finding.

Bogle got this one wrong.

Rob’s bio is here.