# Herfindahl-Hirschman index (HHI)

Herfindahl-Hirschman index (HHI) is a measure of portfolio concentration calculated by summing the squared weights of its holdings; higher values indicate more weight concentrated in fewer holdings.

## What it means

A portfolio can hold several stocks yet still depend heavily on one or two of them. The Herfindahl-Hirschman index, or HHI, puts a number on that imbalance. It was developed as a concentration measure for markets and can also be applied to portfolio holdings.

HHI considers each holding’s share of the portfolio, not just the number of holdings. Squaring each share gives larger positions disproportionately more influence. For a portfolio whose holding weights add to 100%, HHI ranges from 1 divided by the number of holdings to 1 when weights are expressed as decimals. On a percentage scale, those endpoints are 10,000 divided by the number of holdings and 10,000. Equal-weighted holdings produce the lowest HHI possible for that number of holdings.

## How it is calculated

`HHI = Σ(wᵢ²), for i = 1 to N`

- `wᵢ` is holding `i`’s weight as a decimal: its market value divided by the total market value of the holdings being measured.
- `N` is the number of holdings included. Weights must add to 1, and `Σ` means to add the squared weights across all holdings.
- The result is a unitless index. If weights are entered as percentages instead, square those percentage numbers and add them; the resulting HHI is 10,000 times the decimal-weight result.

State what is being measured. For example, calculating HHI across individual stocks answers a different question from calculating it across sectors. For a sector HHI, combine the weights of stocks in each sector first, then square and sum the sector weights.

## Worked example

Consider a hypothetical US$100,000 portfolio with three stocks:

| Stock | Market value | Weight | Squared weight |
| --- | ---: | ---: | ---: |
| A | US$60,000 | 0.60 | 0.36 |
| B | US$30,000 | 0.30 | 0.09 |
| C | US$10,000 | 0.10 | 0.01 |

1. Divide each stock’s market value by US$100,000 to obtain weights of 0.60, 0.30 and 0.10.
2. Square the weights: 0.36, 0.09 and 0.01.
3. Add them: `HHI = 0.36 + 0.09 + 0.01 = 0.46`, or 4,600 on the percentage scale.

For comparison, three equally weighted stocks would have `HHI = 3 × (1/3)² ≈ 0.3333`, or approximately 3,333. The hypothetical portfolio’s higher HHI reflects its larger allocation to stock A. The *effective number of holdings*, calculated as `1 / HHI`, is about 2.17 for this example; it describes concentration, not a literal count of stocks.

## Why it matters before you trade

A proposed trade can change concentration even if the number of holdings stays the same. Comparing HHI before and after a proposed basket shows whether the resulting portfolio would be more or less concentrated by holding weight. The comparison should use the same scope and weighting method both times.

HHI is one input to a pre-trade analysis, not a standalone judgment about a trade. It does not measure whether holdings tend to move together, how volatile they are, their liquidity or their potential losses. Two portfolios with the same HHI can have very different exposures to sectors, countries and market events.

## How PreTrAIde uses it

PreTrAIde includes a Herfindahl-Hirschman concentration index in its quantitative pre-trade analysis of a user-built stock basket. Its portfolio breakdowns also cover country, sector, region, currency and market capitalization. The analysis returns a GO, NO-GO or MODIFY verdict for the basket and each line, with reasoning in plain language. Those verdicts are decision support, not recommendations; users place any trades themselves through their own broker.

PreTrAIde also offers a free portfolio concentration checker that shows HHI and the largest weight, without sign-up. These measures complement each other: HHI captures the distribution of all included weights, while the largest weight identifies the biggest single position.

## Common mistakes

- **Mixing scales:** An HHI of 0.46 and an HHI of 4,600 are equivalent only when the former uses decimal weights and the latter uses percentage weights.
- **Treating a low HHI as proof of diversification:** Equally weighted stocks may still share substantial risks.
- **Comparing different scopes:** A stock-level HHI and a sector-level HHI measure different kinds of concentration.
- **Using stale weights:** Price movements and changes in holdings alter weights, so HHI depends on when the portfolio is valued.
- **Forgetting the proposed trade:** A pre-trade check should distinguish the current portfolio from the portfolio after the hypothetical basket is applied.

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Source: https://pretraide.com/glossary/herfindahl-hirschman-index