What his firm calls fundamental indexing looks at a company’s sales, cash flow, book value and dividends paid to shareholders. “We make the supposition that those four measures are a very different economic footprint of a business,” he said. They also make a company like Apple, with its sky-high market capitalization, a lot less important to an index.

Other smart beta strategies have fewer variables. Stephen Sachs, head of capital markets for ProShares, said one of his firm’s most popular smart beta exchange-traded funds, the S.&P. 500 Aristocrats E.T.F., consisted of the companies in the index that had increased their dividends for at least 25 years in a row. There are 54 and the E.T.F. holds the same amount of all of them.

“The index itself is simple,” he said. “The idea is you’re looking for S.&P. exposure but you like the concept of dividend growth because we know over the long term, dividends make up a lot of the return.”

Investors are interested in these strategies for different reasons. Tom Goodwin, senior research director at Russell Investments, said the firm surveyed 181 big investors in Europe and North America and found that the top two motivations were reducing risk and increasing returns. Costs, which are lower with E.T.F. strategies, were at the bottom of the list, he said.

Yet the rationale for smart beta, at least what Russell found, is fairly anodyne. What investor wouldn’t want higher, less volatile returns? Like many things today, the increase in interest for smart beta over the last few years has come from a shift in mentality after the recession.

“Smart beta strategies are gaining ground now because they’re marketed and perceived as quasi-passive strategies,” said Paul Bouchey, managing director for research at Parametric, a firm that specializes in creating customized portfolios for high-net-worth clients. “People feel they’re back-tested and can just put a lot of money into it. It’s different than if an active manager comes to you and says, ‘I have an idea.’ ”

Mr. Arnott said it took Research Affiliates, which licenses its strategy to managers like Pimco, from 2004 to 2012 to reach $75 billion in assets managed with its strategy. From 2013 to today, those assets have risen to $130 billion. “Before, these were viewed as a kind of niche strategy — peculiar, mildly interesting,” he said. “Now people realize that if you link the weight to the price, you’re going to load up on overvalued companies. When you sever that link you do better.”