Would someone please explain to the nice folks over at the NYT, or the economics department at the U.C.L.A, the concept of mean reversion, contrary indicators, and (ahem) how the national businmess press operates? (We have discussed the magazine cover indicator previously, so those unfamiliar with it can read any of those posts at their leisure).

The ongoing innumeracy and logical fallacies that exists in this country continues to astound. Case in point: What the NYT called *"the curse of the business press."* (No Applause, Please).

Here’s the relevant excerpt:

"Chief executives who are heralded as “best manager” or “best performing” or who receive some other kind of elaborate praise from business writers almost always see their company’s stock performance suffer afterwards, according to a working paper by two assistant professors of economics at the University of California, Ulrike Malmendier of Berkeley and Geoffrey Alan Tate of U.C.L.A.

“The stock market returns of award-winning C.E.O.s’ companies lagged those of their unheralded peers by about 4 percent per year over the three years following an award,” Larry Yu writes in Sloan Management Review in summarizing the research.

What causes the decline? The academics speculate that recognition in the press could lead to the executive’s becoming distracted. “Winning an award doubles the odds of the C.E.O. penning a book, and winning as many as five awards makes a C.E.O. four times as likely to sit on five or more outside boards.”

Or it could be that as Ms. Malmendier notes, journalists are simply very good at picking people who are going to underperform."

*No, no and no. *

Are these folks really that logically challenged?

There are a few simple answers: First, this is yet another classic case of *confusing correlation with causation*. Just because two thing occur proximate to each other in time is not a sufficient basis alone for assuming that one caused the other.

Second, Investors, Reporters and Professors need to ask themselves a simple question: *"Why have these CEOs appeared on magazine covers?"* Its more likely than not that they have done something that caught the attention of the investing public and eventually the media. And its also very likely that their stocks HAVE ALREADY had a great run up — far above the average 12% we see for the SPX over the very long term.

Speaking generally (yes, of course there are a few exceptions), there’s a more logical reason. What is a more likely explanation for the so-called *"curse of the business press.* is actually a simple case of mean reversion. By the time the mainstream press discovers the next star CEO, their stock has already put in best part of the run.

>

*Source:*

No Applause, Please

What’s Offline

PAUL B. BROWN

NYT, August 18, 2007

http://www.nytimes.com/2007/08/18/business/media/18offline.html

15 minutes of success gets you 15 minutes of fame. The media thrives on The Next Big Thing – the Same Ol’ Thing doesn’t cut it. Celebrate the Mediocrity.

UCLA is a very good econ dept. and has had many stars from Alcian to Leijonhuvd, et.al. So how did these guys get their a) Ph.D.’s, b) appointments and c) continuing presence ? How general is this in the business press ? Is there an exploitable opportunity ? Of course – short the stock !

In nerd world we would say that getting a cover is endogenous.

Therefore, it is just as likely that having a future falling stock price

causesyou to get a cover story.How could future stock declines cause a cover story?

Through just the means that Barry talks about.

Mean reversion does NOT explain the subsequent subpar stock performance. According to basic finance theory, stock returns are UNPREDICTABLE. That means that a stock that has a high return one year, should more no more and NO LESS likely to have a high return in the following year. All information is supposed to be fully priced, otherwise the geniuses at this blog would all be billionaires. The study appears to have uncovered a genuine economic phenomenon.

Here’s another example: rolling 3 sixes in a row on a fair die does NOT make it more (or less) likely to roll below average on the next roll — that’s a common misunderstanding of mean reversion. Mean reversion states that the expected return should return to the mean, not below the mean.

You need to go back to your statistics 101 notes and then write an apology to the NYT, UCLA and your readers.

~~~

BR: That’s right, stocks travels in a random walk, and the market is perfectly efficient.Kid, its time you go buy some new economic books — the ones you are using are way out of date . . .

This finding has nothing to do with mean reversion. Mean reversion means, well, reversion to, um, the mean. Not below the mean.

The ongoing innumeracy and logical fallacies that exists on this blog continues to astound.

~~~

BR: Incorrect — the authors of the study acknowledged mean reversion as an issue. See Craig M. Newmark’s comments below . . .Basic finance theory treats stock price movements as a random walk because it is the only way the mathematics become tractable. There is no practicle alternative. The reality is that markets are not efficient, especially when it comes to high growth, high momentum stocks that are most likely to be the subject of the cover stories.

Go look at the chart of Empire Resources (ERS), the Nasdaq comp, or any of the market leaders during the dot.com bubble. Were those stocks efficiently priced? Nope. And guess what, a ton of people did become billionairs by shorting the hell out of those stocks, knowing that there would be a reversion to the mean.

Contrary indicators and mean reversion works. Figure in inflation and it’s probably working on everything including the stock market and foreign exchange.

A Scandinavian client gave me this one: Whenever the storks fly south after November 15th business in the Nordic countries rises fifteen percent.

Barry, I ordinarily think you print some well-informed stuff here, but you’re not correct on this one. I’ve seen the paper and it’s econometrically sound and savvy. These folks aren’t dodos. They’re technically sound, highly trained econometricians (statistical economists). Please read the paper. I think after you do you will feel compelled to apologize to the authors. Believe me, they understand what mean reversion is, and in their paper they demonstrate explicitly that the effects are more than simple mean reversion.

‘Student 1’ and ‘first time’ would be right if they were discussing independent events – e.g. die roll – but not capital markets where capital flows to sucessful models and away from failure. Also business models are copied, rents are competed away, fashions change etc.

Another example of this sort of enumeracy are the Bush tax cut cheerleders They claim Bush tax caused the US economy to grow; but when the US economy grows at trend, there’s no high r-squared causation.

Another is Larry Kudlow’s oft-repeated claim that tacitly implies ‘Profits will keep growing above trend.’ Think about he impossibility of that.

Finally, so many folks from Pat Robertson’s Regent’s ‘University’ in the Bush administration may explain their enumeracy and anti- scientific stances. The good news is that maybe they’ve learned a thing or two watching the mean reversion of the administration’s poll numbers.

Could be causality runs the other way: executives who spend their time sucking up to the business press spend less advancing their companies’ fortunes. Their proclivity to do could also introduce (self-) selection bias. These are just off-the-cuff hypotheses of course, not something someone with an ounce of self-respect would publish without backing up with some data.

That means that a stock that has a high return one year, should more no more and NO LESS likely to have a high return in the following year. All information is supposed to be fully priced, otherwise the geniuses at this blog would all be billionaires. The study appears to have uncovered a genuine economic phenomenon.This is nice. The only problem is that there are known patterns.

Shorting Cramer is just one that many people have mentioned before Barron’s put it on the cover. Other cover story patterns are well known.

The question is “why aren’t these patterns arbitraged away” not assuming away the empirical evidence because it does not fit the model.

Can something as complex as human behavior ever truly be reduced to the simplicity of mathematics?

“‘The only knowledge we can have of the determinants of price is the knowledge deduced logically from the axioms of praxeology. Mathematics can at best only translate our previous knowledge into relatively unintelligible form.’ (Man, Economy, and State, p. 730)”

All significant price action is the culmination of individual choices made; is it possible to quantify whether winning an award contributed to the individual choices to reduce holdings in a particular company’s stock outweighed the individual choices to buy?

It seems, to me, an unreasonable explanation.

Karl,

Have YOU made lots of money on these “known patterns” or did you only notice them ex post?

Have an equal number of people lost money betting on “known patterns”?

Patterns, like the one identified in the article are interesting precisely because they are rare and quickly arbitraged away.

Dismissing the research because it is “obvious”, a “known pattern” or simple “mean reversion”, shows a lack of understanding of basic finance and statistics, IMHO.

Could this also be a case of Survivorship bias? Take only the ones that got the awards and reduce the pool down to a point where there really isn’t much of a pool to compare with. Consultants and researchers sometime accidentally manipulate numbers to the point where they see only what they want to see.

Good Stuff Barry. Love the site.

I think Barry is right about reversion to the mean. Two typical example of mean reversion are focused on baseball players who have great years and investment fund managers who have great years — typically, they tend to tank other years and that gets the mean reversion.

Although I did get an A in statistics 101, I’m no statistician.

This finding has nothing to do with mean reversion. Mean reversion means, well, reversion to, um, the mean. Not below the mean.Um. If I perform above the mean for a year, then perform at the mean for the next year, guess what my averaged performance is? Yup. Above the mean. Go learn arithmetic.

When considering BR’s comments in the context that he described it, reversion to the mean of AVERAGE LONG-TERM growth rates, I think that his comments are valid.

Assume that the average long-term (ALT) growth rate of all stocks within an industry group is 9%. To the extent that one company exceeds the ALT mean, say 12% per year over 5 years, but is destined to fall back to the ALT mean average of 9% for the industry group, this means that it will need to eventually suffer a number of individual years at sub-9% growth rate so that the ALT mean reverts back to 9%.

You may question whether all stocks within an industry group eventually revert to a single ALT growth rate. However, to the extent that there is some validity to this assumption, I believe that BR’s argument largely holds together.

Let’s assume for a moment that our good professors did their statistical homework correctly. What would be the practical value of their observations? It seems impractical to me, to scan magazine stories for possible short-sell candidates.

Can one get more data points more quickly, if one includes media appearances? Let’s say just Kudlow and Company just for grins. Or is the impact of media appearances mostly performance neutral as one would expect?

“If I perform above the mean for a year, then perform at the mean for the next year, guess what my averaged performance is? Yup. Above the mean.”

That’s right. It’s reversion toward the mean. Given enough future years, the average of all years (including the one high year) will get arbitrarily close to the mean, but in expectation, it will stay (slightly) above the mean. This is true even if each future year is expected to average at the mean.

Reversion to the means does NOT imply future performance will, on average, be less than the mean. For example, the expected value of a series of dice rolls reverts to the mean, but future dice rolls are NOT expected to be below the mean (or above it, for that matter.) Ergo, the findings in the study cannot be explained by simple “reversion to the mean”.

“Go learn arithmetic.”

Maybe this has less to do with arithmetic than with large numbers of people on the blog not understanding a basic statistical principle, even some who got A’s in class.

Question from Stat 101 quiz: if a coin flip comes up heads 3 times in a row, do you expect the next coin flip to be more likely to be tails than heads? Why or why not?

Well said student of statistics!

Coin flips are what is known as independent tries. The outcome of any flip does not depend on any or all previous coin flips.

Didnt Nassim Taleb (The Black Swan) pooh-pooh Mean Reversion???????

For example, the expected value of a series of dice rolls reverts to the mean, but future dice rolls are NOT expected to be below the mean (or above it, for that matter.) Ergo, the findings in the study cannot be explained by simple “reversion to the mean”.This only works if the dice rolls are independent.

The problem is that the market displays excess volatility. Going way up does seem to increase the probability of going down.

There is a simple reason why this is true. The long run growth rate of the market cannot exceed that of the underlying economy.

The real question is why the market does not display pure random walk behavior and why it is so difficult to beat the random walk in returns. These would seem to be at odds.

One possible answer is that there are High Impact Low Probability events which you increase your exposure to by playing arbitrage strategies.

This means that that you underestimate the volatility and thus in a risk adverse environment, over-estimate the expected return, to playing certain strategies by looking at finite subsets. There is also the problem of finite liquidity in the face of potentially very large low probability shocks.

Perhaps like the inverted St. Petersburg lottery that a lot people think Long Term Capital got itself into.

To those of you who are questioning the non-mathematical aspect of this, you need to consider two things:

1) By the time the editorial staff of a magazine “discovers” a star CEO, and then puts him on the cover, a lot has already transpired: The company has a hot product, a boomlet in a given space has occurred, or an innovative technology was developed (And all that mean for the stock price).

2) As we have said repeatedly over the years, this contrary indicator works better for large macro event trends than for some individual companies. Look at all of the Apple/Steve Jobs or Google covers over the past few years.

(See link)

A bit of the abstract of the paper supports the comment made by Salomon above (at 1:39 p.m.):

“We find that the firms of CEOs who achieve ‘superstar’ status via prestigious nationwide awards from the business press subsequently underperform beyond mere mean reversion, both relative to the overall market and relative to a sample of ‘hypothetical award winners’ with matching firm and CEO characteristics.” http://papers.ssrn.com/sol3/papers.cfm?abstract_id=972725

At the very least, it indicates that the authors are quite aware of the problem. If you want, blame the Times for an incomplete summary, but please quit picking unfairly on my alma mater’s professors!

Is this the magazine cover indicator on the magazine cover indicator?

With the shift to the internet and the acceleration of the media, I think it might well be.

“A first time visitor” and “a student of statistics” are one and the same person (IP address: 71.174.108.157).

That behavior is frowned upon. In the future, pick one name to post under and stick with it . . .

Heh. Reversion to the mean works because outstanding performance is statistically unlikely to continue, no matter how talented you are.

On second thought, however, this is likely less of a mean reversion phenomenon and more likely an overpricing phenomenon. Too many people jump on to a good thing.

For a basic introduction, check this out: http://en.wikipedia.org/wiki/Regression_toward_the_mean

I had the most satisfying Eureka experience of my career while attempting to teach flight instructors that praise is more effective than punishment for promoting skill-learning. When I had finished my enthusiastic speech, one of the most seasoned instructors in the audience raised his hand and made his own short speech, which began by conceding that positive reinforcement might be good for the birds, but went on to deny that it was optimal for flight cadets. He said, “On many occasions I have praised flight cadets for clean execution of some aerobatic maneuver, and in general when they try it again, they do worse. On the other hand, I have often screamed at cadets for bad execution, and in general they do better the next time. So please don’t tell us that reinforcement works and punishment does not, because the opposite is the case.” This was a joyous moment, in which I understood an important truth about the world: because we tend to reward others when they do well and punish them when they do badly, and because there is regression to the mean, it is part of the human condition that we are statistically punished for rewarding others and rewarded for punishing them. I immediately arranged a demonstration in which each participant tossed two coins at a target behind his back, without any feedback. We measured the distances from the target and could see that those who had done best the first time had mostly deteriorated on their second try, and vice versa. But I knew that this demonstration would not undo the effects of lifelong exposure to a perverse contingency.– Daniel Kahneman, Nobel Prize Laureate in Economics

Karl,

Have YOU made lots of money on these “known patterns” or did you only notice them ex post?

I didn’t see this at first.

The problem here is that you are conflating a no-arbitrage condition with perfectly priced assets. This need not be the case.

Here is my fun existence proof why not.

Suppose that assets price diverge from fundamental values for some unknown reason. Now suppose that you as an investor attempt to arbitrage this difference away.

However, just as this possibility occurs to you an Arbitrage Gremlin appears out of thin air and beats you to a bloody pulp. You subsequently avoid any attempt to arbitrage out these issues.

The point of this example is to remind us that no arbitrage conditions simply mean that no does arbitrage out price discrepancies, not that it is impossible.

It could be that there is some factor that we are currently not considering which makes it suboptimal. My favorite culprit, as I mentioned before, is finite liquidity. I don’t know that finite liquidity can get us completely out of the theoretical hole.

My point is simply that we have to be careful about what the math is telling us. It may seem reasonable that no arbitrage implies perfectly priced assets but it is not a logical necessity.

To “a student of statistics”:

First, if we want to be bombastic about statistics, then I would suggest a suitable definition for mean reversion is this:

“Over the long-run, a value in a stochastic process will, on average, tend to remain in some neighborhood of a mean value.”

And, likewise, the ‘mean value’ is not necessarily a fixed value and may, itself, be subject to various trends (inflation, if nothing else, much of the time), many of which may only be truly visible after the fact.

There are several notable factors that fall out of this kind of statement about mean reversion, which I think is probably a fairly non-objectionable definition for the majority of the crowd here. The first is that it doesn’t say a damn thing about short-term performance. There will (possibly quite often) be a large degree of short term volatility regarding whatever trend is mean reversion bound. Secondly, it directly implies that long periods of above-average behavior are, by definition, unsustainable, otherwise we wouldn’t have a mean reversion bound quantity. If you can deviate from the mean in the upward direction endlessly, you are not a mean reversion candidate.

Your repeated example of dice rolling leaves out several things – first, dice are not a mean reversion bound system for any individual roll. If I roll 3 6’s in a row, my next roll, assuming a fair die and a fair roll (and these are important assumptions, see below), then my chance of getting another six is not higher or lower than anything else. However, if I tell you I’m going to roll the die approximately 900 million more times, I can fairly confidently state that not all of those will be a six and that, in fact, our system will revert to a mean distribution of 1/6 6, 1/6 5, 1/6 4, etc… This is a more useful result; your counter-example is basically the equivalent of stating “Well, on the day after the magazine cover comes out, the stock price doesn’t revert to the mean…”, rather than “For the hundreds and hundreds of trading sessions over the next few years…”, which is what is really being discussed.

Also, this foolishly assumes a fair game. In Taleb’s latest book, he has an excellent example regarding this with coinflipping. To paraphrase (and with my apologies to Taleb for butchering his storytelling – I don’t have TBS with me to quote it), if you flip a coin 50 or 100 times, and get heads every single time, then ask both an actuary and a trader what the chance of the next flip being heads is, you get two answers:

1 – 50 / 50!

2 – Almost 100% heads.

Why? Because the trader realizes the game is somehow rigged, or otherwise not conforming to the starting assumptions. That’s a more likely result than repeated “impossible” events. The odds are that you screwed up with your starting assumptions, not that something which occurs only once in every 100 trillion years just happened.

There’s a multitude of other issues I will not get into here, though they are possibly also important, but let us just state that naively applying statistics in a methodologically unsound fashion and without testing to the world is the best way to make statisticians look bad. Please stop; I value my degree and you are causing the prestige thereof to revert to the mean.

cb – I would think Taleb does not eliminate mean reversion with his treatise (it’s observable from a technical basis in some instances), merely advises that one should be careful about how much confidence is really assigned to such “trends”.

From what I read, the professors did some tests to rule out mean reversion. I don’t have a copy of the paper, but at least we know that they tested that. If the paper were freely available (I don’t want to pay for it), I could review their methods. I have a background in econometrics.

I wouldn’t immediately say that the professors got it wrong. We don’t have enough evidence.

For all of you who disagree with me, go back and study basic arithmetic, statistics, econ, finance, grammar, and manners; you obviously have no clue what you’re talking about and you’re simply embarrassing yourself as well as the rest of us. And for those who agree with me, stop copying me and think for yourself for a change. You can start by taking intermediate levels of all the classes listed above.

Just joking. I really just wanted to thank yall for the lesson on Mean Reversion. Now I can say that I learned something useful today. Woohoo!