Coin Flippers Drenched in Alpha

Are the owners of great track records incredibly skilled, or incredibly lucky? This is one of the oldest questions in finance. To explore this further, I’m going to borrow from Scott Patterson and Jack Schwager, the authors of two fantastic books, The Quants and Market Wizards.

Here is Gene Fama, Nobel Laureate, the father of modern finance and longtime professor at the University of Chicago, talking to a classroom of students (The Quants, pages 77-79).

“Everything I’m about to say isn’t true,” said Fama in a gruff voice tinged with the accent of his Boston youth.

He walked to the chalkboard and wrote the following: Efficient-market hypothesis. 

“The market is efficient,” Fama said. “What do I mean by that? It means that at any given moment, stock prices incorporate all know information about them. If lots of people are drinking Coca-Cola, its stock is going to go up as soon as that information is available.”

Students scribbled on their notepads, taking it all in.

The efficient-market hypothesis, perhaps the most famous and long-lasting concept about how the market behaved in the past half century, was Fama’s baby. it had grown so influential, and had become so widely accepted, that it was less a hypothesis than a commandment from God in heaven passed down through his economic prophet of the Windy City.

“There are a number of consequences to market efficiency,” Fama said, facing the classroom. “One of the most important is that it’s statistically impossible to know where the market is going to go next. This is known as the random walk theory, which means that the future course of the market is like a coin toss. It either goes up or down, fifty-fifty, know on knows which.

A student near the front row raised a tentative hand.

“What about all the guys who get paid to pick stocks? They must get paid for a reason. It can’t be all luck.”

“The evidence shows that trying to pick stocks is a complete waste of time,” Fama said flatly. “And money. Wall Street is full of salesman trying to convince people to give them a buck. But there’s never been a study in history showing active managers consistently beat the market. It’s just not in the data. Managers have good runs, but it usually just comes down to dumb luck.”

“Why do people pay these managers so much money?”

“Hope? Stupidity? It’s hard to say.”

What about Warren Buffett?”

Fama sighed. That Buffett again. Increasingly, students were obsessed with the track record of this hick investor from Omaha, whose company Berkshire Hathaway, had beaten the S&P 500 for two decades in a row and counting.

“There do seem to be a few outliers that are impossible to explain. In every science there are freaks that seem to defy all the rules. Buffet, as well as Peter Lynch at Fidelity’s Magellan fund, have had consistent returns over the years. I’m not aware of anyone else. These freak geniuses may be out there, but I don’t  know who they are. Who knows,” he said with a shrug and a smile, “maybe they’ll lose it all next year.”

The math showed it was inevitable that a few traders would stand out, but that didn’t mean they had skill. Give ten thousand people a quarter. Tell them to flip. Each round, eliminate the ones who flipped heads. Each round, eliminate the ones who flipped heads. After ten rounds, maybe a hundred will be left. After twenty, maybe three or four will still be in the game. If they were on Wall Street, they’d be hailed as expert coin flippers drenched in alpha. Buffett, according to Fama, was in all probability a lucky coin flipper.

Another student raised a hand. “But you said everything you’re going to tell us isn’t true. So does that mean markets really aren’t efficient?”

That’s right,” Fama said. “None of what I’m telling you is one hundred percent true. These are mathematical models. We look at statistics, historical data, trends, and extrapolate from them. This isn’t physics. In physics, you can build the space shuttle, launch it into orbit, and watch it land at Cape Canaveral a week later. The market is far more unstable and unpredictable. What we know about it are approximations about reality based on models. The efficient-market hypothesis is just that, a hypothesis based on decades of research and a large amount of data. There’s always the chance we’re wrong.”

He paused. “Although I’m virtually certain that we’re right. God knows the market is efficient.”

On the completely other side of the universe from Gene Fama is Jack Schwager, author of the amazing series, Market Wizards. Barry Ritholtz interviewed Schwager on Master’s in Business and asked him about the difference between luck and skill. Schwager said:

“I love that line. It’s what I call the Shakesperian monkey argument. You have enough monkeys typing; eventually they’ll get somebody typing Hamlet. That type of thinking is correct, but nobody ever asks how many monkeys.

The truth is, more monkeys than you can fit volume wise into the visible universe. So the question is, how many traders do you need?

I’ll take one trader, one of the most amazing ones, Ed Thorp…He was the guy who changed the way casinos operate. His first fund ran nineteen years, gross returns 19% per year and that’s good, but that’s not the amazing part. The amazing part is nineteen years he had three losing months, all of them were less than one percent. If you had twelve tosses of a coin, nineteen times, you only get three tails, what are the odds of that? And that’s conservative because his wins were larger than his losses, so the odds are smaller. But I did the probability calculation and the odds of his track record being luck are one million times less than the odds of picking a random atom in the entire mass of the earth, and then picking that same atom a second time. In other words, it’s impossible. It’s true that you will get some successful track records by luck, but these ones are beyond luck, that’s impossible if the markets were efficient.”

Fama’s right that markets are mostly efficient; not in the sense that they always accurately reflect all known information (I think October 19, 1987 takes care of that), but in the sense that trying to beat them is largely a waste of time and money. Schwager is right as well; it’s irrefutable that there are a handful of individuals who have absolutely demonstrated the ability to beat the market.

How can two people saying the exact opposite things both be right? Because, like Fama said, markets are not governed by the laws of physics, which allows for a gray area. The freaks that defy all rules live in this gray area.

Read the Quants
Read Market Wizards
Listen to Schwager on Master’s In Business