One of my favorite investing books is A Mathematician Plays The Stockmarket by best selling author – John Allen Paulos. Paulos demonstrates what the tools of mathematics can teach us about the machinations of the stock market. One of my favorite parts of the book focuses on regression to the mean in the stock market, and why today’s worst performing stocks historically outperform while today’s best performing stocks historically underperform.
Regression toward (or to) the mean is the phenomenon that if a variable is extreme on its first measurement, it will tend to be closer to the average on its second measurement—and if it is extreme on its second measurement, it will tend to have been closer to the average on its first.
Here’s an excerpt from the book:
There are other sorts of contrarian anomalies. Richard Thaler and Werner DeBondt examined the thirty-five stocks on the New York Stock Exchange with the highest rates of returns and the thirty-five with the lowest rates for each year from the 1930s until the 1970s. Three to five years later, the best performers had average returns lower than those of the NYSE, while the worst performers had averages considerably higher than the index.
Andrew Lo and Craig MacKinlay, as mentioned earlier, came to similar contrarian conclusions more recently, but theirs were significantly weaker, reflecting perhaps the increasing popularity and hence decreasing effectiveness of contrarian strategies.
Another result with a contrarian feel derives from management guru Tom Peters’s book In Search of Excellence, in which he deemed a number of companies “excellent” based on various fundamental measures and ratios. Using these same measures a few years after Peters’s book, Michelle Clayman compiled a list of “execrable” companies (my word, not hers) and compared the fates of the two groups of companies.
Once again there was a regression to the mean, with the execrable companies doing considerably better than the excellent ones five years after being so designated. All these contrarian findings underline the psychological importance of a phenomenon I’ve only briefly mentioned: regression to the mean.
Is the decline of Peters’s excellent companies, or of other companies with good P/E and P/B ratios the business analogue of the Sports Illustrated cover jinx?
For those who don’t follow sports (a field of endeavor where the numbers are usually more trustworthy than in business), a black cat stared out from the cover of the January 2002 issue of Sports Illustrated signaling that the lead article was about the magazine’s infamous cover jinx. Many fans swear that getting on the cover of the magazine is a prelude to a fall from grace, and much of the article detailed instances of an athlete’s or a team’s sudden decline after appearing on the cover.
There were reports that St. Louis Rams quarterback Kurt Warner turned down an offer to pose with the black cat on the issue’s cover. He wears No. 13 on his back, so maybe there’s a limit to how much bad luck he can withstand. Besides, a couple of weeks after gracing the cover in October 2000, Warner broke his little finger and was sidelined for five games.
The sheer number of cases of less than stellar performance or worse following a cover appearance is impressive at first. The author of the jinx story, Alexander Wolff, directed a team of researchers who examined almost all of the magazine’s nearly 2,500 covers dating back to the first one, featuring Milwaukee Braves third baseman Eddie Mathews in August 1954. Mathews was injured shortly after that.
In October 1982, Penn State was unbeaten and the cover featured its quarterback, Todd Blackledge. The next week Blackledge threw four interceptions against Alabama and Penn State lost big. The jinx struck Barry Bonds in late May 1993, seeming to knock him into a dry spell that reduced his batting average forty points in just two weeks. I’ll stop. The article cited case after case. More generally, the researchers found that within two weeks of a cover appearance, over a third of the honorees suffered injuries, slumps, or other misfortunes. Theories abound on the cause of the cover jinx, many having to do with players or teams choking under the added performance pressure.
A much better explanation is that no explanation is needed. It’s what you would expect. People often attribute meaning to phenomena governed only by a regression to the mean, the mathematical tendency for an extreme value of an at least partially chance-dependent quantity to be followed by a value closer to the average. Sports and business are certainly chancy enterprises and thus subject to regression. So is genetics to an extent, and so very tall parents can be expected to have offspring who are tall, but probably not as tall as they are. A similar tendency holds for the children of very short parents.
If I were a professional darts player and threw one hundred darts at a target (or a list of companies in a newspaper’s business section) during a tournament and managed to hit the bull’s-eye (or a rising stock) a record-breaking eighty three times, the next time I threw one hundred darts, I probably wouldn’t do nearly as well. If featured on a magazine cover (Sports Illustrated or Barron’s) for the eighty-three hits, I’d probably be adjudged a casualty of the jinx too.
Regression to the mean is widespread. The sequel to a great CD is usually not as good as the original. The same can be said of the novel after the best-seller, the proverbial sophomore slump, Tom Peters’s excellent companies faring relatively badly after a few good years, and, perhaps, the fates of Bernie Ebbers of WorldCom, John Rigas of Adelphia, Ken Lay of Enron, Gary Winnick of Global Crossing, Jean-Marie Messier of Vivendi (to throw in a European), Joseph Nacchio of Qwest, and Dennis Kozlowski of Tyco – all CEOs of large companies who received adulatory coverage before their recent plunges from grace. (Satirewire.com refers to these publicity-fleeing, company-draining executives as the CEOnistas.)
There is a more optimistic side to regression. I suggest that Sports Illustrated consider featuring an established player who has had a particularly bad couple of months on its back cover. Then they could run feature stories on the boost associated with such appearances. Barron’s could do the same thing with its back cover.
An expectation of a regression to the mean is not the whole story, of course, but there are dozens of studies suggesting that value investing, generally over a three-to-five pear period, does result in better rates of return than, say, growth investing. It’s important to remember, however, that the size of the effect varies with the study (not surprisingly, some studies find zero or a negative effect), transaction costs can eat up some or all of it, and competing investors tend to shrink it over time.
As a final word on the topic of regression to the mean, Charlie Munger summed it up like this:
“Mimicking the herd invites regression to the mean.”
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