Herfindahl Diversification Index

Both summarize how a firm's revenue is spread across segments. The Herfindahl-based Berry index is one minus the sum of squared shares, weighting larger segments heavily and giving an intuitive bounded number. The entropy measure uses share-weighted logs of inverse shares. Their key practical difference is decomposability: because of the logarithm, total entropy splits additively into related (within-group) and unrelated (between-group) components, which the Herfindahl form does not. Jacquemin and Berry favored entropy precisely for this decomposition, which is essential when the related-versus-unrelated distinction is the object of study.

Segments are grouped into broader industry groups. The unrelated component is the entropy computed across these groups, reflecting diversification between distinct areas of business. The related component is the share-weighted average of the entropy within each group, reflecting diversification among businesses that are economically close. Jacquemin and Berry proved that these two components sum exactly to total entropy diversification. Palepu used this split to show that related diversification, not unrelated, was associated with superior profit growth, making the decomposition central to corporate-strategy research.

Rumelt's categorical scheme is rich in strategic meaning but relies on subjective coding, which threatens replicability. The entropy and Herfindahl indices are computed objectively from segment-revenue data, are continuous (so they fit naturally into regressions), and are easy to replicate across large samples. Palepu argued they combine the simplicity, objectivity, and replicability of the index approach with the essential richness of relatedness through the entropy decomposition. In practice many researchers report both, using the continuous index for estimation and the categories for interpretation.