What it measures
The Herfindahl-Hirschman index (HHI) shows how concentrated a portfolio is. It is the sum of each holding's weight squared.
HHI = w12 + w22 + ... + wn^2 (weights as decimals)
Examples
| Portfolio | HHI | Effective holdings (1 / HHI) |
|---|---|---|
| 10 stocks at 10% each | 0.10 | 10 |
| 50%, 30%, 20% | 0.25 + 0.09 + 0.04 = 0.38 | 2.6 |
| One stock | 1.00 | 1 |
Effective number of holdings
1 / HHI turns the index into an intuitive number: a 20-stock portfolio where three names are 60% of the money may behave like five or six stocks. Market-cap indexes such as the S&P 500, where the top ten names are a large share, have far fewer effective holdings than their name count.
Using it
Check it whenever a few winners grow large. See How many stocks should you own? and Position sizing.
See also
- How many stocks should you own? How many individual stocks you need for diversification, what research says about 10, 20 and 30 stock portfolios, and the trade-off with conviction.
- Position sizing How much to put in each investment: equal weighting, conviction weighting and risk-based sizing, with simple rules that keep one mistake from sinking a portfolio.
- Index funds What index funds are, why low-cost index investing beats most professional fund managers over time, and how to use index funds as a portfolio core.
Last updated September 30, 2026. Education only, not investment advice.