Concerns about the degree of concentration in cap-weighted indices like the S&P 500® seem to arise whenever performance is dominated by mega-cap names—as it has recently been. A simple way to measure market concentration is to add up the weight of the largest constituents in an index. Interestingly, after peaks in concentration—such as the aftermath of the technology bubble—the S&P 500 Equal Weight Index has typically outperformed its cap-weighted counterpart.
In this paper, we propose an alternative way to measure concentration. By adjusting the Herfindahl-Hirschman Index (HHI) to account for the number of names in a sector, we’re able to make meaningful cross-sector comparisons. We show that concentration tends to mean-revert in most sectors, which has important implications for the relative performance of equal weighting. Exhibit 1 shows recent and average adjusted HHI levels across S&P 500 sectors.
A DIFFERENT WAY TO MEASURE CONCENTRATION
While looking at the weight of the top names is a simple way to assess market concentration, it’s useful to have a more comprehensive method
that incorporates all the constituents in an index. The HHI is a widely used concentration measure; it is defined as the sum of the squared index constituents' percentage weights. For example, the HHI for an equally weighted 50-stock portfolio is 200 (50 x 22). The HHI for the S&P 500 Equal Weight Index, which comprises 500 stocks, is 20 (500 x 0.22).
Previous research has shown that the long-term performance advantage of equal weight over cap-weighted strategies is driven more by equal weighting within sectors than by equal weight's differential weighting across sectors. This may occur because of unique regulatory challenges faced by the largest stocks in each sector; interestingly, the HHI is used by the U.S. Department of Justice in evaluating the competitiveness of markets and in making decisions on antitrust concerns.
Other things equal, a higher HHI indicates increased concentration, but other things may not be equal: even for completely unconcentrated equal weight portfolios, the HHI value is inversely related to the number of names. As seen above, an equally weighted 50-stock index has a higher HHI than an equally weighted 500-stock index. If we want to use the HHI to examine the history of concentration within an index, we need to adjust for the number of names. We therefore define the adjusted HHI as the index’s HHI divided by the HHI of an equally weighted portfolio with the same number of stocks. If there are n stocks in an index, the HHI for an equal-weighted portfolio is always (10,000/n). Therefore, the adjustment factor for an n-stock index is (n/10,000).
A higher adjusted HHI means that an index is becoming more concentrated, independent of the number of stocks it contains. We observe in Exhibit 2 that the adjusted HHI for the Energy sector decreased from 2014 to 2019, in spite of an increase in its raw HHI. This is because the number of constituents in the sector decreased from 43 in 2014 to 28 in 2019.