Portfolio Concentration Index Calculator
Compute the Herfindahl-Hirschman Index HHI = Σ(Weight²) from your holdings, and solve for the weight cap or equal-position count that would hit any target HHI. Includes live weight normalization, effective-N, normalized HHI, and DOJ-style concentration tiers.
Squaring weights punishes concentration
The HHI is the sum of squared market shares, a measure originally designed by economists Orris Herfindahl and Albert Hirschman to gauge industry concentration. Squaring means large weights contribute disproportionately: a 50% weight contributes 2,500 points, while two 25% weights contribute only 1,250 between them. This is the whole point — the HHI is far more sensitive to concentration than a simple count of positions would be. A portfolio with 100 holdings where one is 40% of the book has a higher HHI than a portfolio with 10 equal-weighted holdings, even though the second has far fewer positions.
Effective N = 10,000 / HHI
The "effective number of positions" is the reciprocal of the HHI (on the 0–10,000 scale). An HHI of 1,000 means the portfolio behaves like 10 equal-weighted positions; an HHI of 5,000 means it behaves like 2 equal positions; an HHI of 100 means it behaves like 100 equal positions. This is the most intuitive way to read the HHI: rather than a raw index number, you get "how many equally-sized bets does this portfolio really look like." A portfolio with 20 positions where three dominate may have an effective N of only 6 or 7, revealing that the surface-level diversification is misleading.
DOJ antitrust thresholds as a reference
The US Department of Justice uses HHI thresholds to evaluate market concentration in antitrust reviews: below 1,500 is "unconcentrated," between 1,500 and 2,500 is "moderately concentrated," and above 2,500 is "highly concentrated." These thresholds were designed for industries, not portfolios, but they map surprisingly well onto portfolio concentration. A portfolio with HHI below 1,500 (effective N above ~6.7) is broadly diversified; above 2,500 (effective N below 4) is concentrated. The mapping is not exact — industry concentration has different risk implications than portfolio concentration — but it provides a familiar reference frame.
Diminishing returns to adding positions
Adding a new position always lowers the HHI, but the improvement shrinks as N grows. Going from 1 to 2 equal positions drops the HHI from 10,000 to 5,000 (a 5,000-point improvement). Going from 20 to 21 equal positions drops it from 500 to 476 (24 points). The practical implication: the first 5–10 positions do almost all the diversification work; beyond 20–30, additional positions provide marginal benefit and can even hurt if they introduce correlated assets or dilute allocation to your highest-conviction bets. If your HHI is still above 1,500 with 20+ positions, the problem is not too few positions but too little balance among the ones you have.
How to Use This Calculator
Enter your holdings and weights on the left. The HHI updates live as you type. Use the solve-mode toggle to answer specific questions about targeting a different concentration level.
1. Enter your holdings
Type each holding's name and weight. Weights can be in any units — percentages, dollars, or token counts — because the calculator normalizes them to 100% before computing the HHI. If your weights already sum to 100, the normalization is a no-op.
2. Read the HHI and effective N
The result card shows the HHI on the 0–10,000 scale plus the effective number of positions (10,000 ÷ HHI) and a colour-coded DOJ-style concentration tier. A lower HHI means a more diversified portfolio.
3. Solve for a weight cap
Switch to "w*" mode and enter a target HHI. The calculator solves for the weight that the largest position would need to have (given the proportions of the others) to hit that target exactly. Useful for answering "what's the max I can put in BTC and still keep the portfolio at HHI ≤ 1,500?"
4. Solve for equal N
Switch to "N*" mode and enter a target HHI. The calculator reports N = 10,000 ÷ target — the number of equal-weighted positions that would produce exactly that concentration. Useful for setting a diversification target: "I want to look like 15 equal positions, so my HHI should be around 667."
5. Use scenario presets
Click a sample portfolio structure — Equal 10, Concentrated 3, Barbell, Single asset — to load a starting configuration, then edit to match your actual holdings.
6. Use Advanced for scenario analysis
Advanced mode adds an HHI reference scale with DOJ thresholds, scenario inputs (target equal-N, weight cap, additional positions), a sensitivity table, and companion metrics including normalized HHI, Gini-Simpson index, and Top-1/3/5 concentration.
What This Tool Offers
Built around the Herfindahl-Hirschman Index HHI = Σ wi², the standard measure of concentration used in antitrust economics and increasingly in portfolio construction.
Dynamic holdings editor
Add, edit and remove holdings directly in a table. Weights are auto-normalized so you can enter raw dollar values or percentages without pre-processing.
Three solve modes
Compute the HHI from your holdings, solve for the weight cap that hits a target HHI, or solve for the number of equal-weight positions that would produce that concentration.
Stacked weight bar
The schematic draws your portfolio as a stacked 100% bar plus individual squared contributions, so you can see at a glance which positions drive the HHI.
DOJ concentration tiers
Each result is classified against the DOJ antitrust thresholds — unconcentrated, moderately concentrated, or highly concentrated — with a familiar reference frame.
Companion metrics
Effective N, normalized HHI, Gini-Simpson index, Top-1/3/5 concentration, and the number of equal positions that would match your current HHI.
Scenario analysis
Advanced mode lets you cap a weight at X%, target an equal-N level, or model adding N new positions to see how the HHI would respond.
Reference Tables & Conversions
HHI interpretation bands, typical portfolio structures, and effective-N equivalents for common HHI values.
Quick HHI estimator
HHI Interpretation Bands
The DOJ antitrust thresholds translated to portfolio terms. These bands are a reference frame, not a rule — a concentrated portfolio can be entirely appropriate for a high-conviction investor.
| HHI range | DOJ label | Effective N | Portfolio character | Typical context |
|---|---|---|---|---|
| 10,000 | Perfect monopoly | 1.0 | Single asset | 100% in one coin |
| 5,000 – 9,999 | Highly concentrated | 1.0 – 2.0 | Two dominant assets | Barbell (BTC/ETH), or BTC + stablecoin |
| 3,000 – 4,999 | Highly concentrated | 2.0 – 3.3 | Three-asset concentration | 60/25/15 style high-conviction portfolios |
| 2,500 – 2,999 | Highly concentrated | 3.3 – 4.0 | Four dominant positions | Top-4-only concentrated book |
| 1,500 – 2,499 | Moderately concentrated | 4.0 – 6.7 | Moderate concentration | Typical retail crypto portfolio with 5–10 coins |
| 1,000 – 1,499 | Unconcentrated | 6.7 – 10.0 | Well-diversified | Balanced 8–12-position portfolio |
| 500 – 999 | Unconcentrated | 10.0 – 20.0 | Strongly diversified | Broad basket of 15–25 assets |
| 100 – 499 | Unconcentrated | 20.0 – 100.0 | Highly diversified | Index-like portfolio with 30+ holdings |
| Below 100 | Unconcentrated | > 100 | Index-tracking | Very broad exposure; near-equal weights across 100+ names |
Common Portfolio Structures and Their HHIs
Representative portfolio structures with their resulting HHI values and effective N, to give a sense of scale.
| Structure | Weights | HHI | Effective N | Character |
|---|---|---|---|---|
| Single asset | 100 | 10,000 | 1.0 | Maximum concentration |
| Equal 2 (barbell) | 50 / 50 | 5,000 | 2.0 | Classic two-way split |
| Dominant + tail | 70 / 10 / 10 / 10 | 5,200 | 1.9 | Looks diversified, isn't |
| 3-way equal | 33.3 / 33.3 / 33.4 | 3,333 | 3.0 | Balanced triple |
| Concentrated 3 | 60 / 25 / 15 | 4,450 | 2.2 | Classic high-conviction |
| 5-way equal | 20 / 20 / 20 / 20 / 20 | 2,000 | 5.0 | Simple diversified basket |
| Typical crypto (6) | 35 / 25 / 15 / 12 / 8 / 5 | 2,228 | 4.5 | Common retail structure |
| 10-way equal | 10 × 10 | 1,000 | 10.0 | Balanced basket |
| 20-way equal | 20 × 5 | 500 | 20.0 | Broad diversification |
| 30-way equal | 30 × 3.33 | 333 | 30.0 | Index-like breadth |
| 50-way equal | 50 × 2 | 200 | 50.0 | Near-index exposure |
| 100-way equal | 100 × 1 | 100 | 100.0 | Full index replication |
| Power-law (typical) | 50 / 25 / 12.5 / 6.25 / ... | ~3,333 | 3.0 | Very common implicitly |
| BTC-dominant wallet | 70 / 15 / 8 / 4 / 2 / 1 | 5,290 | 1.9 | Effective N near 2 despite 6 positions |
| Stablecoin-heavy | 60 USDC / 25 BTC / 15 ETH | 4,450 | 2.2 | Defensive posture but concentrated |
HHI vs. Effective N Conversion
The two most useful values in opposite directions. Use this table to move between them quickly.
| HHI | Effective N | HHI | Effective N |
|---|---|---|---|
| 10,000 | 1.00 | 500 | 20.0 |
| 8,000 | 1.25 | 400 | 25.0 |
| 5,000 | 2.00 | 333 | 30.0 |
| 4,000 | 2.50 | 250 | 40.0 |
| 3,333 | 3.00 | 200 | 50.0 |
| 2,500 | 4.00 | 150 | 66.7 |
| 2,000 | 5.00 | 125 | 80.0 |
| 1,500 | 6.67 | 100 | 100.0 |
| 1,000 | 10.0 | 50 | 200.0 |
| 750 | 13.3 | 25 | 400.0 |
Variable Reference
| Symbol | Meaning | Range | Units |
|---|---|---|---|
| HHI | Herfindahl-Hirschman Index | 0 – 10,000 | points |
| wi | Weight of holding i (normalized) | 0 – 100 | % |
| N | Number of holdings | 1 – ∞ | positions |
| Neff | Effective number of positions = 10,000 / HHI | 1 – 10,000 | positions |
| HHInorm | Normalized HHI = (HHI − 10,000/N) / (10,000 − 10,000/N) | 0 – 1 | ratio |
| GSI | Gini-Simpson diversification index = 1 − HHI/10,000 | 0 – 1 | ratio |
| Top-k | Sum of top k weights | 0 – 100 | % |
What Does the Herfindahl-Hirschman Index Measure?
The Herfindahl-Hirschman Index is a measure of concentration — originally developed by economists Orris Herfindahl and Albert Hirschman in the 1940s and 1950s to measure market concentration in industries, and now used across antitrust law, banking regulation, and portfolio construction. It is simply the sum of squared market shares: HHI = Σ wi². When the shares are expressed as percentages summing to 100, the HHI ranges from 0 (perfectly atomised) to 10,000 (single monopoly). When expressed as decimals, it ranges from 0 to 1.
Because the weights are squared, large positions contribute far more to the HHI than small ones. A 40% position contributes 1,600 points, while four 10% positions contribute 400 points between them — the 40% position dominates the index despite representing only a third of the total capital in those five positions. This is what makes the HHI a much better concentration measure than simply counting positions: it penalises the imbalance that actually creates concentration risk.
HHI Formula
The defining relationship is:
where the weights wi are normalized to sum to 100 (or equivalently to 1 if you are using the decimal convention). The effective number of positions is the reciprocal:
The normalized HHI measures concentration relative to the range achievable with N positions:
This equals 0 when all N positions are equal-weighted, and 1 when a single position holds everything. It is useful for comparing portfolios with different numbers of positions on a like-for-like concentration basis.
HHI Variables
| Symbol | Meaning | Notes |
|---|---|---|
| HHI | Herfindahl-Hirschman Index | 0–10,000 on the percentage convention |
| wi | Weight of holding i | Normalized to sum to 100% |
| N | Number of holdings | Count of distinct positions |
| Neff | Effective number of positions | = 10,000 / HHI |
| HHInorm | Normalized HHI | 0 = equal weights, 1 = single position |
| GSI | Gini-Simpson index | = 1 − HHI/10,000; a diversification measure |
How Each Variable Affects the HHI
The HHI rises quadratically with any single weight. Doubling a position's share roughly quadruples its contribution to the index. This is what makes the HHI sensitive to concentration: modest imbalances in a portfolio — a 30% top holding versus a 15% second holding — produce measurable differences in the index, even when the portfolio has many positions. The index also falls with the number of positions, but only if the positions are balanced: adding small positions to a portfolio with one dominant holding barely moves the HHI at all.
This quadratic structure has an important implication for portfolio construction: the most effective way to lower the HHI is not to add more positions, but to reduce the largest weights. Trimming a 50% holding to 25% while distributing the proceeds across existing smaller holdings often lowers the HHI by more than adding ten new positions would. The HHI rewards balance among a small number of positions far more than it rewards proliferation across a large number of imbalanced ones.
HHI Calculation Examples
HHI = 35² + 25² + 15² + 12² + 8² + 5² = 1,225 + 625 + 225 + 144 + 64 + 25 = 2,308
HHI = 2,500 + 2,500 = 5,000 · Neff = 2.0
HHI = 10 × 100 = 1,000 · Neff = 10.0
HHI = 3,600 + 625 + 225 = 4,450 · Neff = 2.25
HHI = 10,000 · Neff = 1.0
Frequently Asked Questions
There is no universal answer — it depends on your investment philosophy. High-conviction investors who want to concentrate in a handful of bets they have deeply researched might deliberately run an HHI of 3,000–5,000 (effective N of 2–3). Investors who want broad exposure with low single-asset risk might target HHI below 1,000 (effective N above 10). Most individual portfolios in crypto sit between 1,500 and 3,000 (effective N of 3–7). The point of the HHI is not to prescribe a target but to reveal your actual concentration — often surprising, because a portfolio that looks diversified on the surface (10+ positions) can still have an effective N of 3 if the top few positions dominate.
Because counting positions ignores how capital is actually distributed. A portfolio with 20 positions where the top 3 hold 80% of the capital looks diversified by position count but is functionally concentrated. The HHI captures this because the squared weights of the top 3 dominate the index. Compare: 20 positions where 3×20% + 17×2.35% has HHI = 1,200 + 17×5.5 ≈ 1,293, while 20 positions where 1×80% + 19×1.05% has HHI = 6,400 + 21 ≈ 6,421. Same number of positions, vastly different concentration — and vastly different risk profiles.
Both are used. The 0–10,000 scale (percentage convention) is the standard in antitrust and most portfolio contexts because the round numbers are easier to read: 1,500, 2,500, 10,000. The 0–1 scale (decimal convention) is used in information theory, where the HHI is equivalent to the Simpson index of diversity, and in some academic finance settings. They differ only by a factor of 10,000 — the underlying concentration is the same. This calculator uses the 0–10,000 scale as primary and shows the decimal equivalent in the companion metrics.
The effective number of positions is simply the reciprocal of the HHI (on the 0–1 scale) or 10,000/HHI (on the 0–10,000 scale). It answers "how many equal-weighted positions would produce the same concentration?" An HHI of 2,000 corresponds to effective N of 5 — the portfolio behaves like 5 equal-weighted positions even if it nominally holds 20. This is the most intuitive way to read the HHI: it converts an abstract index number into a concrete statement about the portfolio's effective breadth. When people say a portfolio "looks like 3 bets," they mean its effective N is roughly 3, which corresponds to HHI around 3,333.
No — and this is one of its limitations. The HHI treats every position as independent, so a portfolio split 50/50 between two highly correlated assets (say BTC and a wrapped BTC) scores the same as a 50/50 split between two uncorrelated assets (say BTC and gold). In practice, the correlated portfolio carries more concentration risk because the two positions will move together in a drawdown. The HHI is a starting point for understanding concentration, but it should be complemented with correlation analysis for a complete risk picture. Some practitioners use a "correlation-adjusted HHI" that inflates the effective weight of correlated holdings, but this requires estimating a correlation matrix and is much more complex.
The normalized HHI re-scales the index so it ranges from 0 (all N positions equal-weighted) to 1 (single position) regardless of the number of positions. The raw HHI has a maximum of 10,000 and a minimum that depends on N — 10 equal positions have a minimum raw HHI of 1,000. This makes it hard to compare a 10-position portfolio with a 50-position portfolio on the raw index alone. Normalized HHI corrects for this: a 10-position portfolio at 0.15 normalized HHI and a 50-position portfolio at 0.15 normalized HHI are equally concentrated relative to what is achievable within their respective position counts. Useful for cross-portfolio comparisons.
Yes, widely. Beyond antitrust, the HHI is used in banking regulation (to assess deposit market concentration), in media ownership rules (FCC uses it to evaluate local market concentration), in supplier risk analysis (a company's dependence on a few suppliers), in energy markets (concentration of generation capacity), and increasingly in portfolio construction. The underlying logic — that concentration is best measured by summing squared shares — applies whenever you want to measure how concentrated a distribution is across categories.
The Gini-Simpson index (also called the Simpson diversity index) is simply 1 − HHIdecimal, or equivalently 1 − HHI/10,000. Where the HHI measures concentration (higher = more concentrated), the Gini-Simpson measures diversity (higher = more diverse). They are complements of each other. The Gini-Simpson index has a nice interpretation: it equals the probability that two randomly drawn units from the population belong to different categories. In portfolio terms, if you randomly selected two dollars from your portfolio, the Gini-Simpson index is the probability they are invested in different assets. This makes it a natural diversification measure, and it is reported in the companion metrics.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| HHI | Herfindahl-Hirschman concentration index | |
| Asset Weight% | Percentage weight of each asset in the portfolio | % |
What it means
The Herfindahl‑Hirschman Index (HHI) is a measure of market concentration. In portfolios, it quantifies diversification: a lower HHI indicates better diversification. Values range from 0 to 1 (or 0 to 10,000 if using percentages). This is used by investors to assess risk and to guide rebalancing. Understanding this helps in building well‑diversified portfolios and in managing concentration risk.
Worked example
Portfolio Concentration Index – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| Weights | 100% in one asset |
| Parameter | Value |
|---|---|
| Weights | 10% each in 10 assets |
Common mistakes
- HHI: Herfindahl‑Hirschman Index – measures portfolio concentration.
- Asset weight %: The percentage of each asset in the portfolio (as a fraction).
- Result: Between 0 and 1; closer to 1 means highly concentrated.
- Diversification: Lower HHI indicates better diversification.
Applications
Portfolio concentration index (Herfindahl) is the sum of squared asset weights, measuring the concentration of a portfolio. Higher values indicate less diversification. Investors use it to assess their exposure to single assets and to manage risk. By monitoring the index, they can ensure adequate diversification. A lower HHI reduces the impact of a single asset's performance. Understanding this index is essential for building a balanced portfolio.
- Measuring portfolio diversification and concentration
- Risk management and asset allocation
- Comparing portfolio concentration across investors
- Identifying over‑exposure to a single asset
- Educational understanding of diversification metrics
Related calculators · Trading & Investment
Recently updated formulas
Suggest an improvement
Found a mistake? Have a better example? Let us know.
You may send up to 3 suggestions per 24 hours.