The bull market in stocks turned six last Monday, and despite some rocky stretches — like last week, when the market fell — it has generally been a very pleasant time for money managers, who have often posted good numbers.

Look more closely at those gaudy returns, however, and you may see something startling. The truth is that very few professional investors have actually managed to outperform the rising market consistently over those years.

In fact, based on the updated findings and definitions of a particular study, it appears that no mutual fund managers have.

I wrote about the initial findings of that study last summer. It is called “Does Past Performance Matter? The Persistence Scorecard,” and it is conducted by S.&P. Dow Jones Indices twice a year. The edition of the study that I focused on began in March 2009, the start of the bull market.

It included 2,862 broad, actively managed domestic stock mutual funds that were in operation for the 12 months through 2010. The S.&P. Dow Jones team winnowed the funds based on performance. It selected the 25 percent of funds with the best returns over those 12 months — and then asked how many of those funds actually remained in the top quarter in each of the four succeeding 12-month periods through March 2014.

The answer was remarkably low: two.

Just two funds — the Hodges Small Cap fund and the AMG SouthernSun Small Cap fund — managed to hold on to their berths in the top quarter every year for five years running. And for the 2,862 funds as a whole, that record is even a little worse than you would have expected from random chance alone.

In other words, if all of the managers of the 2,862 funds hadn’t bothered to try to pick stocks at all — if they had merely flipped coins — they would, as a group, probably have produced better numbers. Instead of two funds at the end of five years, basic probability theory tells us there should have been three. (If you’re curious, I explained how the math works in a subsequent column, “Heads or Tails? Either Way, You Might Beat a Stock Picker.”

The study seemed to support the considerable body of evidence suggesting that most people shouldn’t even try to beat the market: Just pick low-cost index funds, assemble a balanced and appropriate portfolio for your specific needs, and give up on active fund management.

The data in the study didn’t prove that the mutual fund managers lacked talent or that you couldn’t beat the market. But, as Keith Loggie, the senior director of global research and design at S.&P. Dow Jones Indices, said in an interview last week, the evidence certainly didn’t bolster the case for investing with active fund managers.

“Looking at the numbers, you can’t tell whether there is skill involved in what they do or whether their performance is just a matter of luck,” Mr. Loggie said. “I believe that many of them do have skill. But even if they do have it, based on how they’ve done in the past you really can’t predict how they will perform in the future.”

Still, those two funds did manage to perform splendidly in that study. Their stubborn persistence at the top of the heap over that five-year period suggested that there was some hope for active fund managers. If they could do it, after all, others could, too.

But we’re now about two weeks away from the completion of another 12 months since the end of that study, and it’s been a mediocre stretch, at best, for those two mutual funds. When the month is over, to borrow from Agatha Christie, it looks as though we’ll be saying: And then there were none.

Here are the dismal statistics: The SouthernSun Small Cap fund has actually lost money for investors over the 12 months through Thursday. It was down 3.2 percent, according to Morningstar, and for the nine months through December, it was in the bottom quartile of funds in the S.&P. Dow Jones study. The Hodges Small Cap fund has done better, gaining almost 6 percent through Thursday. S.&.P. Dow Jones Indices says that put it in the third quartile — or second-to-worst one — through December. While it’s mathematically possible, it is highly unlikely that either will climb to the top quartile in the next few weeks, Mr. Loggie said.

Michael W. Cook, the lead manager of the SouthernSun Small Cap fund and the founder of the firm that runs it, was traveling last week and was unavailable to comment for this column. Craig Hodges, manager of the family-run Hodges Small Cap fund in Dallas, spoke to me on the telephone and told me that he wasn’t surprised that his fund had stumbled. “We’re not that good,” he said. “It was going to happen sooner or later. We’ve never expected to outperform all of the time.” And despite disappointing recent returns, both funds are still beating the market handily over the last five years.

Late last year, Mr. Hodges said, his fund was hurt by falling energy prices, which pulled down the returns of several of its holdings. “That kind of thing will happen,” he said. “You can expect that.” Last summer, he told me that over the long run — which he said is probably 50 years or more — he expects that his fund will do better than average. And he reiterated that view last week. “We’ll come out all right in the end,” he said. “I think if you pick a good manager, someone you believe in and you think you can trust, you’ve got to stick with him for a long time, and if he’s good, he’ll perform for you.”

Mr. Loggie and his crew are continuing their regular monitoring of mutual fund performance. Right on schedule, they did another winnowing of mutual funds through the five years that ended in September — and they will do another one for the five years ending this month.

The September performance derby produced more funds that ended up consistently in the top quartile — nine of them, Mr. Loggie said. “That’s not surprising,” he said. “Some periods you have more funds, some periods you have less.”

But what you never have, he said, is any indication that past performance predicts future returns. “It’s possible that any one of these funds will beat the market over the long term,” he said. “Some of them will do that. But the problem is that we don’t know which of them will do that in advance.” And that, in a nutshell, is the kernel of the argument for buying index funds.

New York Times