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Heads or Tails? Either Way, You Might Beat a Stock Picker

JULY 26, 2014

Imagine a world where investors in the stock market have no skill whatsoever. The investors themselves don’t understand this, however, and many truly believe that they are good at what they do.

But in this thought experiment, there’s no doubt about the underlying reasons for fund managers’ success: When they turn in an outstanding performance, it’s just a matter of dumb luck.

What would stock fund managers’ performance numbers look like in such a universe? Very much like the world we live in now, but with an important difference: Over the last five years, actively managed stock mutual funds have performed even worse than would have been predicted if the fund managers were flipping coins instead of picking stocks.

The real-world statistics to which I’m referring were contained in a recent S.&P. Dow Jones Indices study that I summarized in last week’s column. But as many astute readers observed in emails, tweets and phone calls, I didn’t say how mutual funds would have fared if their performance had been a matter of pure chance — a random draw, as statisticians sometimes call it.

Credit Minh Uong/The New York Times

“The results were actually very close to what you’d find in a random draw — or a series of coin flips, except they were a little bit worse,” William D. Nordhaus, a Yale economics professor, said in a phone conversation. The empirical data supports the inference that it’s wise to use passively managed index funds for the core of most people’s investment portfolios, he said, but it doesn’t rule out the possibility that some investors excelled for reasons other than dumb luck. In the real world, he said, it’s possible that some rare individuals may actually possess exceptional investment talent.

Briefly put, the results of the S.&.P. study, “Does Past Performance Matter? The Persistence Scorecard,” were bleak enough on their own. They showed that very few mutual funds were able to consistently outperform their peers, and that those that did so in one given year were likely to be poor performers five years later.

In fact, only 2 out of 2,862 broad domestic stock funds were able to outperform their peers consistently over five years, according to one measure: performance in the top quartile of funds over five consecutive 12-month periods ended in March 2014. That translates to just 0.07 percent of the funds, which means that more than 99.9 percent of funds fell short of that feat.

That’s an unimpressive performance, to be sure. And if you compare it with a series of coin flips — a series of random choices — it looks even worse.

For those interested, this is how the coin-flipping comparison works: You toss the coin. Is it heads or tails? There’s a 50 percent chance of either outcome. Let’s say the coin lands on heads. If you flip it again, the probability that the coin will land on heads the second time is also 50 percent. Because there are four possible outcomes for the two flips, there’s a one-in-four, or 25 percent, chance that your coin will land on heads twice in a row.

Repeat those double flips five times and you’ll find the probability of a mutual fund ending up in the top quartile five times in a row through chance: 0.098 percent. (We’re flipping the coin twice for each year of mutual fund performance.) That’s a bigger probability than the 0.07 percent scored by the actual funds. This means that if mutual fund managers had just flipped coins, roughly three of them — not two — would have been expected to end up in the top quartile for five years in a row.

Still, the dismal results of the real-world fund managers were very close to what Burton G. Malkiel, the Princeton finance professor, once described as “a random walk.”

“Taken to its logical extreme, it means that a blindfolded monkey throwing darts at a newspaper’s financial pages could select a portfolio that would do just as well as one carefully selected by the experts,” he wrote in his guide to investing, “A Random Walk Down Wall Street.”

As a group, managers who ran the 2,862 funds examined by S.&P. Dow Jones Indices didn’t do as well as a blindfolded monkey. The hypothetical monkey, or a serial coin flipper, beat them in several other tests, too.

What should we make of this?

Paul Samuelson, the late Nobel laureate from M.I.T., with whom Professor Nordhaus collaborated on the textbook “Economics,” wrote several influential academic papers that dealt with the issue. In “Challenge to Judgment,” a 1974 paper that inspired John C. Bogle to create the first index fund at Vanguard, Professor Samuelson said that deep, liquid markets like the stock market were efficient enough to make short-term investing very much like a random draw. Index funds would be a better choice for most people, he said.

Yet Mr. Samuelson also believed that some investors were truly talented — even if they faced steep odds in beating the market consistently.

“Paul thought that Warren Buffett was a true genius,” Professor Nordhaus recalled. Indeed, in a 1989 paper, Professor Samuelson pointed to Mr. Buffett as an outlier, an investor who appeared to have “flair.” Yet he said that even Mr. Buffett could be expected to have difficulty keeping ahead of the competition in the future. One reason was that if anyone starts to beat the market in a noticeable way, imitators will eliminate his edge.

“The market shows some efficiency in recognizing the occasional genius,” Mr. Samuelson wrote. And, as it’s turned out, Mr. Buffett’s recent performance has been quite ordinary, as a study by Salil Mehta, an independent statistician, found earlier this year.

Mr. Mehta was also among those who emailed and blogged about the S.&P. findings last week. And he said in his blog that the exercise doesn’t show “that the cause of the selected managers’ success is due to luck as opposed to skill.” But it does illustrate how rare it is for funds to outperform for any reason.

As Keith Loggie, senior director of global research and design at S.&P. Dow Jones Indices, said last week: “It’s quite possible that a number of fund managers have real skill. A few funds in the study did very well, and you’d think there was some skill involved in that level of performance. We’re not assuming that it’s pure luck. We don’t know what it is. But what the study did show is that the chance of any outperformance persisting for any extended period is very low. And it’s extremely unlikely that you can pick an outperformer based on past performance.”

It wouldn’t be unreasonable to draw another conclusion. These findings may suggest that rather than spending a lot of time and money picking stocks or stock fund managers based simply on past performance, you might be better off just flipping a coin. And that implies investing in low-cost, diversified index funds.

A version of this article appears in print on July 27, 2014, on page BU3 of the New York edition with the headline: Heads or Tails? Either Way, You Might Beat a Stock Picker.

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