What should investors make of these findings? There is one clear implication, said Keith Loggie, senior director of global research and design at S.&P. Dow Jones Indices.

“It is very difficult for active fund managers to consistently outperform their peers and remain in the top quartile of performance over long periods of time,” he said. “There is no evidence that a fund that outperforms in one period, or even over several consecutive periods, has any greater likelihood than other funds of outperforming in the future.”

This seems to bolster the case for index-fund investing. After all, if a fund manager with a great year can’t be counted on to outperform other fund managers later, it’s reasonable to ask: Why bother trying to beat the market at all?

A separate series of annual S.&P. Dow Jones studies has found that over extended periods, the average actively managed fund lags the average index fund. All of this may be enough to persuade you to abandon actively managed funds entirely.

But the story is more complex than that: The study also demonstrates that active managers can actually beat the market. Remember those two funds that did so consistently over the five years through March? The study didn’t identify them, but at my request Mr. Loggie did.

They were the Hodges Small Cap fund and the AMG SouthernSun Small Cap fund, which were also the top two general domestic funds over the last five years through June, according to Morningstar performance rankings conducted recently for The New York Times.

Each fund has rewarded shareholders spectacularly, turning a $10,000 investment to $35,000 over those five years, the Morningstar data shows. By contrast, the same investment in a Standard & Poor’s 500-stock index fund would have become more than $23,000. While hardly shabby, that’s not nearly as good.