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Mauldin presents Rob Arnott's study that cap weighted indices underperform [link corrected 12/2/15, only 10-1/2 years later, it had been pointing to oprah.com] almost any other index you can think of.

[6/10/05] Here's Nathan Parmalee's take.

[12/2/15] Here's a more recent article by Arnott (summary: not a fan of cap-weighted indices)

It guess it sort of makes sense from a value perspective. When a stock goes up in price then it's automatically becomes higher weighted in the index. But what you should be doing is sell some when the stock price goes up and buy more when the stock price goes down, all other things being equal. Or from the value investor perpective, sell some when the price overruns its value and buy more when the price underrepresents its value.

[12/2/15] And (via roberts420) another article by Arnott

Well, I diverged from my main point, which was that over the 15-year period 2000-2014 a blindfolded monkey outperformed the S&P 500 index by an annualized 8 percentage points, with an annualized return of 12% versus 4% for the S&P.  I then got off onto how I would weight the holdings in an index fund if I were not weighting by market cap.  Would I use equal weightings, fundamental weighting (weighting by sales, earnings and cash flow), volatility weighting or what?

Robert Arnott published an amusing article on this question in which he backtested 13 non-market-cap weighted index funds over the period 1964-2012.  All 13 outperformed the market cap weighted S&P 500 index.  Of the 12 funds that were not equal weighted he found that in 11, including his own, the performance was improved if the fund inverted their weightings, i.e., if they instead weighted the most heavily weighted holdings the least.  In his own case, the fundamental index, the fund as weighted outperformed the S&P 500 by an annualized 2 percentage points, but when the weightings were inverted it outperformed the S&P 500 index by an annualized 4.5 percentage points.

http://rvwinvesting.com/wealth-wisdom/RAFI_Monkey_Paper.pdf

We all have to decide how to weight the holdings in our portfolio, whether we are constructing an index fund or managing our personal portfolio.  The question is, “How do we choose our weightings?”  Most individuals and professional portfolio managers alike choose weightings qualitatively.  We estimate the expected return for each stock, the potential downside, and, importantly, our confidence in our analysis for each stock.  Then we decide on a weighting.  The question is, “How well do our weightings correlate with the future returns of our individual holdings, and is there a way to improve our return by weighting differently?”