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NISM Certifications · NISM-Series-XV: Research Analyst · Industry Analysis

An industry's four largest firms have market shares of 30%, 25%, 20% and 10%, while the remaining 15% is spread across many small firms. Using the four-firm concentration ratio and the Herfindahl-Hirschman Index (HHI) computed only on these four firms, what are the values?

CR4 is 85% and the HHI for the four firms is 2,025. The concentration ratio adds the four shares, 30+25+20+10. The HHI adds the squares of the shares: 900+625+400+100. Squaring the total of 85 is a common error.

  1. ACR4 = 85%; HHI of the four firms = 2,025Correct
  2. BCR4 = 85%; HHI of the four firms = 1,850
  3. CCR4 = 100%; HHI of the four firms = 2,025
  4. DCR4 = 85%; HHI of the four firms = 7,225

Explanation

CR4 = 30+25+20+10 = 85%. HHI on the four firms = 900+625+400+100 = 2,025. Check: 85 squared = 7,225 is the square of the sum, not the sum of squares, so it is wrong. 1,850 omits the squared value of 175 (a miscount), and CR4 of 100% wrongly includes the small firms.

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