Glossary term
HHI
Definition
Herfindahl-Hirschman Index: the sum of squared portfolio weights. Higher means the book is closer to a single bet. 1 / HHI is a rough “effective number of names.”
How it works
The Herfindahl-Hirschman Index is the sum of squared portfolio weights: HHI = w₁² + w₂² + … + wₙ², with weights written as fractions that sum to 1. Squaring punishes large lines, so a book with one dominant position scores much higher than one with the same number of lines spread evenly.
Its reciprocal, 1 / HHI, is read as an effective number of names. Four equal positions give HHI = 4 × 0.25² = 0.25 and 1 / 0.25 = 4 exactly, so the reciprocal returns the count when everything is equal. The index uses weights only: it does not know that two lines hold overlapping companies or that one moves far more than another.
Worked example
For the classroom book, HHI = 0.32² + 0.12² + 0.08² + 0.10² + 0.14² + 0.08² + 0.06² + 0.10² = 0.1024 + 0.0144 + 0.0064 + 0.0100 + 0.0196 + 0.0064 + 0.0036 + 0.0100 = 0.1728. The reciprocal is 1 / 0.1728 = 5.79 effective names from eight lines.
A hypothetical comparison with five lines each: book A holds 20% in each, so HHI = 5 × 0.04 = 0.20 and 1 / 0.20 = 5.0. Book B holds 50%, 20%, 10%, 10% and 10%, so HHI = 0.25 + 0.04 + 0.01 + 0.01 + 0.01 = 0.32 and 1 / 0.32 = 3.125. Same line count, noticeably less spread.
Hypothetical, for education only. Not a recommendation and not a prediction.
Common mistake
The mistake is to take 1 / HHI as the number of independent bets. It is the correct effective-bets calculation only under an assumption nobody holds: every line has the same volatility and nothing moves with anything else. Once ordinary correlations are admitted, the course shows the classroom book's 5.79 falling to roughly 1.9, and far lower under stress. HHI is a floor on how concentrated a book is, not a certificate that it is spread.