That may change now that someone of Mr. Malkiel’s stature has thrown his weight behind it.

Wealthfront stressed that it was not abandoning the essence of Mr. Malkiel’s long-held belief in passive investing, and it calls its new approach PassivePlus. “Burt Malkiel is still the high priest of passive investing,” said Jakub Jurek, vice president for research at Wealthfront. “To be absolutely clear, we’re not stock pickers. There are decades of research on active investors, which show they underperform.” At the same time, he said, “there are small adjustments you can make to improve after-tax returns.”

In addition to value and momentum factors, Wealthfront’s approach embraces stocks with high dividend yields, low market beta and low volatility, all factors that “have proven robust across long time periods, geographies and asset classes,” Mr. Jurek said. (Wealthfront excluded another widely cited factor, small market capitalization, because its investment universe is limited to large-cap issues.)

Wealthfront’s testing against historical data indicates its multifactor approach outperformed a strict index approach by an average of 1 percentage point per year over the past 50 years, and even more since 2000, without any increase in volatility. As would be expected, there were some periods in which it underperformed.

“There’s a lot of statistical and, perhaps more important, behavioral support for these strategies,” Mr. Hougan said. “You’ll find plenty of two- or three-year stretches where this will underperform, but if you buy and hold, it’s going to add value. We’ve seen value outperform for over 80 years. And Wealthfront is blending five factors that should smooth out and reduce those periods of underperformance.”

Smart beta has its critics, including Mr. Arnott, viewed by many as the godfather of the field. “Smart beta can be smart, and then it can be not so smart,” Mr. Arnott said. “There are tons of strategies being offered now based on nothing but back tests. Anyone can create a brilliant strategy with benefit of hindsight. But does that mean anything for future returns?”

“Pretty much everyone is looking at the same factors, which is a danger,” he added. “It’s a very crowded space. If 10,000 quants are all looking at the same data and trading on it, the chances are that it’s not going to work.”

Mr. Jurek responded that “at a very general level, you could say that every back test is problematic.” But he stressed that “when designing Advanced Indexing, we relied on decades of peer-reviewed research to select factors that have stood the test of time” — even after being widely publicized — and “across asset classes.” He noted that smart-beta exchange-traded products account for about $500 billion in assets, still a relatively small fraction of total assets invested.