THE rise of low-cost index-tracking funds over the past 40 years has put active fund managers—those who claim the ability to pick the best shares—on the defensive. Figures from Morningstar show that the majority of fund managers in the American market beat the index in just five of the past 20 years.

But papers published in 2009 and 2013* seemed to give the industry hope. All fund managers are not equal, the research claimed. Those who assemble portfolios that closely resemble the index are doomed to underperform, because of costs. However, managers who take more daring bets by veering a long way from the index—the academic term is having a high “active share”—are able to outperform. Since then, fund managers have been using a high active share as a marketing device.

That argument is challenged by a new paper** from AQR, a fund-management group that specialises in quant (mathematically-based) strategies. It finds that fund managers who did well on the “active share” measure were actually just following a different benchmark: they tended to be focused on smaller or midsized firms, rather than the Exxons and Apples that dominate the S&P 500.

When AQR sorted funds relative to 17 other American indices, those with a high active share outperformed eight of them, but underperformed the other nine. The authors conclude that active share “does not (and should not be expected to) predict performance and that investors who rely on it to identify skill may reach erroneous conclusions”.

In a sense, this is hardly surprising. By definition, the average investor cannot beat the index after costs; managers with a high active share who outperform a lot will be offset by those who underperform by a large amount. But in one respect, all three papers agree: paying high fees for poor performance is a bad bet.

* “How active is your fund manager?”, by Martijn Cremers and Antti Petajisto, 2009; and “Active share and mutual fund performance”, by Antti Petajisto, Financial Analysts Journal, July/August 2013

** “Deactivating active share”, by Andrea Frazzini, Jacques Friedman and Lukasz Pomorski, 2015