# There’s only one way to test the EMH

Before beginning, I like to point out that I have a new essay over at The Economist.

Commenters often present me with market anomalies, which supposedly “prove” the efficient markets hypothesis is wrong. I always respond that they’re just engaging in data mining. They retort that no theory that can’t be disproved is worth anything. But the EMH can be disproved. The tests have been done, and it passes. Sort of.

Finance professors have done many different tests of the EMH, and I’d guess 90% of the published tests (but only 5% of the actual tests) show that the EMH is wrong. (Yes, I’m pulling these numbers out of thin air, but you get the point.) They’ve found January effects, small stock effects and value stock effects. They’ve found the market does better when P/E ratios are low. They found the market does worse on rainy days (a study published in the AER!). Of course you’d expect to find 5 anomalies for every 100 tests you do, and for the most part you only get published if you find an anomaly, and finance professors have a lot of computer power, so . . .

Here’s my analogy. Suppose Stephen Wynn was concerned that some mysterious gamblers were getting away with cheating at one of his casinos. He’d heard rumors, but had no proof, or even suspects. You are statistician brought in to investigate. You study 600 slot machines, and find 30 of them produced three cherries more often than you’d expect from mere chance. You suggest that the anomalous slot machines be destroyed. How should the casino owner react to that “investigation?” I’m guessing Wynn wouldn’t be impressed.

I think you see the problem. The investigator assumed he could figure out how the cheating was occurring. He assumed that certain individuals had spotted slot machines with predictable tendencies, and that he (the investigator) could also find those machines. But it’s really hard to walk into a casino and walk out with lots of money. So how likely is it that an academic statistician is going to know where to look for cheating? How likely is it that they would know how it’s done? Not very, and that’s why their statistical search for anomalous machines will almost certainly be fruitless. Oh, the data mining will unearth a few suspicious machines, no doubt about that, but only the number predicted by chance.

So how would one determine whether people were cheating? Start by being humble—admit that you probably don’t know how it’s done. If someone did have a secret formula, they wouldn’t put it in a book called “How to cheat at casinos” for all the world to see. Any system that works is almost certain to be kept secret. It’s like alchemy. If anyone did have a formula to turn lead into gold, they would keep it secret; as the formula’s value would plunge to zero the instant it was released.

To find out whether cheating is occurring you need to look at whether the winnings of gamblers are serially correlated. Are those who win once, more likely to win next time. That’s the proper test, indeed the only practical test, of whether people are cheating the casino. And it’s also the only test of the EMH. Don’t look for “the system,” the secret way to beat the stock market. Look for whether other people have found it. Look to see whether people who did better than average one year, tended to do better than average the next year. Don’t look for market anomalies—look for evidence that other people have found market anomalies.

Of course the study has been done. I recall that Fama and French found that mutual returns were approximately serially uncorrelated, but not exactly. There appears to be a slight serial correlation among the very best funds (top 3%), but not enough to give the average investor any advantage.

And that’s what I would have expected. The EMH is approximately true; indeed it’s almost impossible for me to imagine any other model of financial markets. But it’s not precisely true, again, just as you’d expect. After all, if the EMH were perfectly true then no one would have any incentive to estimate fundamental values. We know people are imperfect and hence that any real world human institution, including markets, will be at least slightly imperfect.

A smart person like Eugene Fama should have been able to come up with both the EMH, and its limits, by just sitting in a room and thinking. Much as David Hume got the QTM by imagining what would happen if everyone in England woke up one morning with twice as much gold in their purses. Or Fisher’s theory of inflation and nominal interest rates. Or Cassel’s purchasing power parity. Or Friedman/Phelps’ natural rate hypothesis. Or Muth and rational expectations. Certain ideas are simply logical, and that’s why I have no doubt that despite all those economists on the left arguing the EMH has been discredited, it will still be taught in every top econ/finance grad program 100 years from now, whereas fiscal stimulus will be long gone from macro textbooks.

PS. Why will fiscal stimulus be gone? Because even Krugman admits it only makes sense at the zero bound. And we are rushing headlong into a world of all electronic money–probably within 50 years. There is no zero lower bound with electronic money, and hence the Taylor Rule is all you need. Old Keynesian economics will vanish, leaving only new Keynesianism.