"Efficient markets" mean that stock prices had already taken into account any relevant information on those stocks, so that an active manager seeking to make stock selections because of some special knowledge would have no such advantage.

Also read: Managed accounts: Next up for reform?

In addition, devotees of passive management will point out that the adoption of Regulation FD in 2000 helped to ensure the dissemination of critical, market-moving information to all investors in a timely manner. So, again, the active manager loses any advantage.

Other arguments in favor of passive investing include the high costs often involved in active management, which can eat away at the best returns. The Government Accountability Office earlier this year issued a report that suggested any advantages in managed accounts can be offset by higher fees.

While there's still plenty of money in actively managed accounts – about 78 percent of total stock mutual fund assets – there's no doubt of the growing popularity of the passive route.

According to Morningstar, assets of passively managed U.S. and foreign stock mutual funds have doubled to $1.31 trillion since 2008. Assets in actively managed mutual funds, meanwhile, are up 28 percent in the same period to $4.58 trillion.

In making his case, Doyle isn't expected to suggest all active managers are created equally. "The average active manager can't beat the index," American Funds says in a study that Doyle will be sharing at his presentation.

The problem, the company says, lies in that word, "average" — because managers who do beat the index are not "average." Indeed, active managers failed to beat the S&P 500 53 percent of the time for the 20 calendar years ending Dec. 31, American Funds says.

But that doesn't tell the entire story, according to American Funds.

The biggest U.S. operator of actively managed funds, American Funds analyzed the performance of all its equity-focused funds from 1934 through 2013 and found something else.

"In an attempt to be as comprehensive and transparent as possible," American Fund's study says, "results for every fund over every possible one-, three-, five-, 10-, 20- and 30-year rolling period (monthly basis) between 1934 and 2013 were included. The data set therefore spans virtually the entire history of the mutual fund industry."

While conceding that its record was not perfect, it noted that, "Our overall active success rate — or the percent of rolling periods in which we outpaced the (relevant) index — was superior for each investment horizon considered, from one year to 30 years."

Its long-term perspective and research-driven stock picking, the company said, has generated "clear advantages over index investing during every meaningful period of time for decades." 

The company's funds, for example, led their relevant indexes 91 percent of the time over a 10-year rolling period ending Dec. 31, 2013, according to the firm's calculations.

The company also points to its 92 percent 30-year "persistency" rate, the percentage of time that its funds continued to lead their relevant indexes after having led in the previous period.

It also notes that low fees aren't "solely the province" of index investing, playing an important role in its own success, as well as in its investors'.

For example, it says, the expense ratio in its "Class A" equity-income funds is 0.60 percent vs. an industry average of 1.06 percent. 

American Funds' analysis also looked at investor outcomes from several perspectives.

In one example it provided, $100,000 was spread across American Funds' equity-focused funds over a 20-year period beginning on Dec. 31, 1993. The money would have had an ending balance of $659,001, or $168,003 more than the same amount invested in an index blend, a 34 percent difference, it said.

It also looked at a 401(k) investor who contributed $500 a month for 20 years. The same amount was invested in a blend of relevant indexes, it said. The equity-focused American Funds produced an ending value that was $62,024 greater than the index blend, or 23 percent more wealth.

Whatever the scenario, it seems that plan advisors and sponsors can hardly ignore results so dramatically better. That, at least, is what American Funds hopes.  

Also read: Defending managed accounts, blindly