“If you want to minimize your transaction costs, you want to make it as easy as possible for others to take the other side of your trade,” said Petajisto, who has worked as a quant portfolio manager since 2011.

On the other side of the debate, Li argues that opacity helps. For one example, he looked at two products tracking the same index, and found that a Vanguard Group fund outperformed one from BlackRock Inc. by 7.3 basis points each year owing to the differences in their rebalancing mechanics. The latter tends to disclose its ETF holdings every day and rebalance on known dates, while the former announces holdings only at month-end, allowing it to spread out its trades and disguise its footprint.

Vanguard’s staggered rebalance explains why their ETFs start to diverge from indexes slightly around rebalancing dates. But Li finds the drag from the average tracking error on such “alternative rebalance” strategies isn’t enough to negate the saved trading costs.

“There are two things going on,” said Li. “The first is whether you disclose it or not. The second is whether you dump everything on the rebalancing day at the closing price.”

Samantha Merwin, head of ETF markets advocacy at BlackRock, said transparency helps market makers provide liquidity while giving investors visibility into their portfolios. With the goals of minimizing tracking error as well as trading costs, the asset manager might also trade outside of the close on rebalancing days as needed, she said. A spokesperson for Vanguard said that by enabling some market participants to trade in advance, daily holdings disclosures might lower returns.

To some academics, the frenzy of the index-rebalancing day is simply a mystery. A paper in February also showed that reconstitution-day volumes were more than three-times larger than the amount traded by ETFs. The researchers struggled to explain it, as theoretically active managers taking advantage of the scheduled public rebalance should be buying in the lead up to the rebalance, not on the day itself. It was a phenomenon also noted in Li’s results.

Sharpe didn’t immediately respond to an email seeking comment. In his paper, “The Arithmetic of Active Management,” he appeared to anticipate the potential effects of index followers and discretionary managers interacting. In the footnotes, Sharpe observed that passive funds “may have to trade with active managers, because of the active managers’ willingness to provide desired liquidity (at a price).”

Meanwhile, given how cheap passive ETFs are, the extra costs caused by inefficient rebalancing likely aren’t bad enough to eclipse the expense of active management. That means Sharpe’s conclusions remain largely persuasive.

Still, more than $900 billion flowed into US ETFs last year, shattering all records, with the biggest passive funds scooping up most of it -- meaning however predictable their transactions are, trading ahead of them might remain profitable.

“There definitely still is an index effect, although the market has become more efficient,” said Petajisto from San Francisco. “Consequently, the effect has become less predictable over time.”

This article was provided by Bloomberg News.

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