Passive investments have implicit implementation costs that result in returns that are “materially depressed,” Michael Aked wrote in an article for Research Affiliates in January, arguing that indexed products’ trading costs are “meaningfully higher than that of well-designed smart-beta offerings.”

Aked is a senior member of the research and investment management group at Research Affiliates, which provides smart-beta products.

Aked wrote that “implicit trading costs are the loss of performance due to transactions occurring at prices that would not have prevailed if investors didn’t need to enter trades.” He referred to a 2004 study published in the Journal of Finance that found the additional cost of a new index holding in the S&P 500 between 1989 and 2000 was 9%, up from 3% for the period between 1976 and 1989.

Research Affiliates found that between 2011 and 2013, new holdings in the S&P 500 earned an average 13% higher one-year return than existing holdings. “Investors pay a substantial premium just because a stock becomes a member of the index,” Aked wrote.

Aked wrote that this effect occurs with any “pool of money that requires transactions in the market.”

Implicit trading costs can’t be observed, Aked wrote, only estimated. He gave five factors that help determine a passive investment’s implicit trading cost.

First is the base impact, which is the “ratio of the assets under management to the dollar value of shares traded daily across all stocks in the universe, scaled by a constant.”

Effective turnover is based on the replacement turnover and reweighting turnover. “This factor reflects the obvious fact that if there were no trades, there would be no implementation cost,” he wrote.

Tilt is the “weighted-average ratio of the actual weight of a fund to the volume weight of the index.” He wrote that a volume-weighted index has the lowest implementation cost.

Coverage is the ratio of the total trading volume of the index constituents to the trading volume of the entire stock universe. The entire universe would have coverage of 1, according to Aked.

Rebalance frequency of the individual stocks (not the index) is the last factor. All things being equal, he wrote, more frequent rebalancing is “associated with lower implicit intraperiod market impact costs.”

To estimate implicit trading costs, Aked multiplies base impact by effective turnover and tilt, then divides by coverage multiplied by rebalance frequency.

 In February, Research Affiliates released a report suggesting smart beta strategies were poised for a crash as their increasing popularity, rather than their structural alpha, drove up valuations.

“We think it’s reasonably likely a smart beta crash will be a consequence of the soaring popularity of factor-tilt strategies,” the authors, including Research Affiliates founder Rob Arnott, Noah Beck, Vitali Kalesnik and John West, wrote.

— Check out Indexing Moves Into Dangerous Waters on ThinkAdvisor.