**Stock concentration** is a key concern in the selection of the appropriate index. An index that has a high degree of stock concentration or a low effective number of stocks may be relatively undiversified.

Concentration can be captured using the concept of “effective number of stocks,” which can be measured using the **Herfindahl-Hirschman index** (HHI). HHI is the sum of the squared weights of the individual stocks in the portfolio:

where:

*n* = the number of stocks in the portfolio

*w _{i}* = the weight of stock

*i*

HHI ranges from ¹/ₙ (an equally-weighted portfolio) to 1 (a single stock portfolio), so as HHI increases, concentration risk increases. The *effective number* of stocks is the reciprocal of the HHI:

A market-cap weighted index with 500 stocks might have an HHI of 0.01 and, therefore, an effective number of stocks of ¹/₀.₀₁ = 100. The fact that 100 is less than the number of stocks in the portfolio reflects the disproportionate effect of the largest capitalization stocks on the index.

An *equal weighted* index of 500 stocks would have an HHI of 0.002 and an effective number of stocks of ¹/₀.₀₀₀₂ = 500.