After the exceptional performance of large-cap stocks in recent years, concentration concerns naturally come to mind.

There are many ways to measure concentration. A simple method is to add up the weight of the top names, but the drawback with this approach is it doesn’t incorporate all the constituents in an index. The Herfindahl-Hirschman Index (HHI), defined as the sum of the squared index constituents’ percentage weights, is more favorable from this aspect and is widely used.

But the HHI faces an issue, which is that even for completely unconcentrated equal weight portfolios, the HHI value is inversely related to the number of names. If we want to use the HHI to examine the history of concentration within an index or to make cross-sector comparisons, we need to adjust for the number of names. In our paper Concentration within Sectors and Its Implications for Equal Weighting, we define the adjusted HHI as the index’s HHI divided by the HHI of an equally weighted portfolio with the same number of stocks.

A higher adjusted HHI means that an index is becoming more concentrated, independent of the number of stocks it contains. Exhibit 1 shows that the adjusted HHI for the Energy sector decreased from 2014 to 2019, despite 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.

Concentration tends to mean-revert in most sectors. This is particularly noticeable in Energy, Industrials, Information Technology, and Materials, as we see in Exhibit 2. These data imply that when concentration is relatively high, as we see for Information Technology presently, it subsequently tends to decline. Meanwhile, when concentration is relatively low, as we see for Industrials, Energy, and Materials, it subsequently tends to increase.

Rising sector concentration implies that larger-cap names are outperforming smaller caps and that a cap-weighted index should outperform its equal-weighted counterpart. Falling concentration implies the opposite. Since concentration tends to mean revert, using relative concentration to alternate between cap-weighted and equal-weighted sector exposures is a potential source of value-added.