Managers are closet indexers because they don't want to lag too far behind the benchmark for fear of losing their jobs or their funds have gotten so big that they can't help but track the market, Cremers said.

Stock pickers mimicking the index is part of the reason many active funds fail to beat their benchmarks, said Martijn Cremers, a University of Notre Dame finance professor. The phenomenon is called closet indexing.

The average annual expense ratio for passive funds was 0.17 percent in 2016 compared with 0.75 percent for active funds, according to investment research firm Morningstar. Meanwhile, nearly two-thirds of active funds that invest in large-company stocks lagged the S&P 500 last year and more than 90 percent of large-cap funds missed the benchmark over a 15-year period, according to S&P Dow Jones Indices.

Performance and lower costs are prompting investors to make the switch from active to passive funds, industry observers say.

Investors continue to plow money into passively managed index funds while shunning funds that use active stock pickers.

If the investor believes that at least some fund managers have real stock-picking skills, then active share indicates the proportion of the fund holdings that such stock-picking skills are applied to.

Closet indexing can hurt investors because they are paying higher fees for mediocre performance, Cremers said. Three metrics used together can show whether a fund manager is a closet indexer:

R-squared measures how different fund returns are from the returns of the fund's benchmark. Values range between 0 and 100 and a fund with an R-squared of 100 means that its performance perfectly tracks its benchmark.

Tracking error is the difference between a fund's performance and its benchmark's performance. Expressed as a percentage, a low tracking error suggests an active fund's manager is mimicking the index. (Even passive funds have tracking error because managers don't perfectly match an index's performance.)

You can usually find R-squared and tracking error for your funds for free on Yahoo Finance or Google Finance or the fund sponsor's website.

Active share is the percentage of a portfolio's holdings that differ from the benchmark index. A higher percentage here may mean the fund manager is trying to beat the index with his or her stock-picking skill. A fund with a 100 percent active share percentage would mean that it did not have any holdings in common with its benchmark.

A website run by Cremers calculates the active share of U.S. mutual funds for free.

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Research from Cremers and Antti Petajisto, a portfolio manager at hedge fund LMR Partners, found that funds with high active share percentages have outperformed their benchmarks — even after fees — while closet indexers underperformed.

"If the investor believes that at least some fund managers have real stock-picking skills, then active share indicates the proportion of the fund holdings that such stock-picking skills are applied to," Cremers said. "I'd suggest that such investors should thus focus on fund managers with a high active share, which means above 80 percent for a large-cap manager and above 90 percent for a small-cap manager."

Only about 30 percent of U.S. mutual fund assets are currently held in funds with an active share of at least 80 percent, and only about 10 percent of funds with an active share of at least 90 percent, Cremers estimated.

"It is hard to run a high active share portfolio, and thus portfolio managers with high active share and good track records are more likely to have skill that continues in the future," he said.