You can find all kinds of interesting (and crazy) opinions online.  Take a second and Google “broccoli is bad for you.”  When I tried, two anti-broccoli pieces popped up on the first page.  Now try this one: “Portfolios of actively managed funds can beat portfolios of index funds.”  A box of broccoli says you’ll find nothing.

But can we build portfolios that outperform a diversified basket of index funds?  Trying to do so with actively managed mutual funds is a silly quest.  A collection of better index funds, however, might be the answer.

Most index funds are cap-weighted.  For example, the S&P 500 index has 500 of America’s largest companies within it.  But they’re not weighted equally in the index itself.  Companies with higher total market value influence the index’s performance (either up or down) much more so than smaller companies do.

But the world’s largest stocks by market value usually underperform the average stock.  In The Fundamental Index (Wiley, 2008) researchers Robert D. Arnott, Jason C. Hsu and John M. West reveal that over the last 81years, the 10 largest companies in the U.S. have never, as a group, outperformed the average stock in the S&P 500 during subsequent years.

Based partly on these findings, the researchers suggest an index fund shouldn’t have its highest weightings in the largest stocks (by market capitalization) but on stocks with the highest book values, cash-flows, and dividends.  They refer to such measurements as a stock’s economic footprint.  Emphasizing these factors over price, according to the authors, ensures the index doesn’t fall victim to fads and bubbles caused by stocks or sectors enjoying hysterical popularity.

Apple Computer is a prime example.  Its popularity fueled its stock price, making it the most valuable company in America last year.  But its 34 percent price plunge since September 2012 had a larger drag on a cap-weighted S&P 500 index than it would have had on a fundamental index.  In theory, a fundamental and cap-weighted index could contain the same stocks, but in quite different proportions.

For example, a fundamental U.S. index would have scaled back on Apple’s exposure as its price defied gravity in 2012.  Its market capitalization growth outpaced its economic footprint.   

Back-tested studies of fundamental indexes are impressive.  Between 1984 and 2004, a study of 23 different markets found fundamental indexes triumphed consistently over cap-weighted MSCI indexed benchmarks, usually by 2 to 4 percent each year.

John Bogle, Vanguard’s founder, argues that the higher costs associated with maintaining a fundamental index would hurt investment returns.   Australian researchers Anup K. Basu and Brigitte Forbes disagree.  They published a study in the Accounting & Finance Journal (January 2013) taking issue with Mr. Bogle’s assertion.  After cost estimates, they found Fundamental Indexes beat the cap-weighted Australian index during every rolling five-year period between April 1985 and March 2010.  The fundamental index advantage, over a cap-weighted index varied between 2.63 percent and 4.88 percent annually.  In an actively managed fund, an advantage like that will result in a flood of eager money.

But maybe things are different in Australia. To find out, I checked to see if the Fundamental ETFs offered by Powershares were besting their cap-weighted Vanguard counterparts.  Based on five-year return data to July 31, 2013, the results were mixed.

According to Morningstar, the FTSE RAFI 1000 (PRF) averaged 11.18 percent annually.  Vanguard’s Total Stock Market Index (VTI) trailed, averaging 8.55 percent.  Vanguard’s S&P 500 (SPY) earned 8.01 percent with their Value Index (VTV) averaging 7.93 percent.  The Fundamental Index proved superior.

The FTSE RAFI 1500 Small-Mid Cap fund (PRFZ) averaged 12.9 percent compared to Vanguard’s small cap fund (VB) and mid cap fund (VO) averaging 10.58 and 9.97 respectively.

But in other categories, it lagged. FTSE RAFI Developed Markets ETF (excl. U.S.) averaged 2.4 percent, compared to Vanguard’s cap-weighted equivalent (VEA) averaging 2.67 percent.

With Emerging Markets, the FTSE RAFI index (PXH) earned nothing, while Vanguard’s cap-weighted equivalent (VWO) earned 1.8 percent.

Five-year durations prove little, of course. And comparative results can vary, depending on starting and ending points. But one thing appears to be clear: beating a diversified portfolio of cap-weighted indexes might not be as easy as we think.