Diversification has been called the only free lunch in investing. Many investors consider total-market funds, such as Vanguard’s Total Stock Market Index Fund (VTSMX), to be not only the most efficient (based on modern financial theory and, specifically, the efficient markets hypothesis) but also the most diversified. Leaving aside the question of whether Vanguard’s fund is the most efficient portfolio, let’s evaluate whether it’s the most diversified.

Certainly, VTSMX is the most diversified domestic stock fund if we consider only its number of holdings. According to Morningstar, as of November 30, the fund held 3,598 stocks. However, VTSMX’s market capitalization weighting shows that its top 10 holdings make up 14.5% and its top 25 holdings make up 26.8% of the portfolio. Now, consider the Vanguard Small Cap Value Index Fund (VISVX). While it held just 856 stocks, the fund’s top 10 holdings made up just 4.7% and its top 25 holdings just 10.5% of the portfolio. From that perspective, its holdings are less concentrated and could thus be considered more diversified.

Another fund that many investors use to own U.S. stocks is the Vanguard 500 Index Fund (VFINX). Most investors would be surprised at just how concentrated the fund’s risk is due to its market-cap weighting mechanism. As of December 2016, the fund’s top 10 holdings made up 18.2% of the portfolio, its top 25 holdings made up 33.4% (2.3 times as concentrated as VISVX) and its top 50 holdings made up 47.9%. In other words, almost half of the risk in the portfolio of 500 stocks was concentrated in just 10% of the stocks it owned.

Again, I am not debating whether the market-cap weighting creates the most efficient portfolio. I’m only pointing out that the market-cap weighting mechanism used by index funds results in more concentration of individual company risk.

An interesting point is that the first index fund wasn’t originally designed to be market-cap weighted. The credit for creating the first S&P 500 index fund is generally given to John McQuown, who, in 1973, started a fund using dollars from Wells Fargo’s pension plan. What most people don’t know is that the initial idea was for the fund not to own stocks by their market-cap weighting, but to own an equal amount of each stock. The reasons were likely that it would be considered more diversified and that equal-weighting had historically produced higher returns. The fund’s creators didn’t necessarily realize it at the time, because there was no literature yet on the size and value factors, but the higher returns were very likely due to the equal-weighting mechanism providing exposure to those factors and their related premiums.

The fund’s original design was to hold an equal dollar amount of each of the 1,500 or so stocks listed on the NYSE, which seemed the most appropriate replication of ”the market.” However, McQuown and his team quickly realized that keeping an equal-weighting mechanism involved high transaction costs and daily management was difficult. (This could have been addressed if they had used cash flows from dividends and new inflows to rebalance the portfolio, and if they had been willing to accept the tracking error that would result. But then it would not have been an index fund, as it would not have tracked the index.) Eventually, they settled on the S&P 500 as their index and the use of market-cap weighting. The face of the investment world was changed forever. An important benefit of market-cap weighting is that it minimizes turnover and trading costs.

Given this background, thinking about diversification in terms of the number of securities held and the concentration of those holdings isn’t the only way, or necessarily the right way, to think about diversification. Modern financial theory provides an alternative way to think about diversification.