Crypto portfolio concentration can be measured with HHI, the sum of squared portfolio weights. Its reciprocal is the effective number of equally weighted holdings: HHI 0.30 corresponds to about 3.33 equal positions. Use one valuation currency and a declared grouping of assets. This measures allocation concentration, not correlation, volatility or the number of independent sources of risk.
Owning five tokens does not mean capital is spread evenly across five positions. A large holding can dominate an account while a collection of tiny balances makes the asset list look diversified. HHI makes that imbalance visible without requiring a historical return sample.
Calculate HHI from current values
Start with a long-only, unleveraged portfolio whose included holdings have nonnegative market values and a positive total. At one valuation timestamp, convert every included balance into the same reporting currency. Divide each holding's market value by the total included value to get its weight, w_i.
Square each weight and add the results: HHI = Σ w_i². The effective number of holdings is its reciprocal: N_eff = 1 / HHI.
Weights are decimal fractions and must sum to one. A 45% allocation enters the formula as 0.45, not 45. Calculate with unrounded weights and round only the displayed result. The U.S. Department of Justice's HHI definition describes the original concentration calculation as a sum of squared market shares. Here the same arithmetic is applied to portfolio weights; competition-law thresholds are not portfolio allocation limits.
Some reports square percentage-point weights instead. That convention produces a score on a 0–10,000 scale: decimal HHI 0.30 equals 3,000 points. Under that convention, effective holdings equals 10,000 / HHI_points. Taking 1 / 3,000 would mix the two scales.
For N positive holdings, the minimum decimal HHI is 1/N, reached at equal weights. HHI approaches 1 as one weight dominates and equals 1 when only one holding remains. MSCI's effective-number methodology defines effective stocks as the reciprocal of the sum of squared weights. Applying that interpretation to a declared crypto holding universe gives an equivalent equal-weight count, which can be fractional.
A five-holding portfolio with an effective count of 3.33
Consider this original hypothetical $100,000 spot portfolio. USD is the reporting currency, all values are simultaneous, and the cash line is a stipulated USD balance. These are invented allocations, not current prices or an allocation recommendation.
| Included holding | Market value | Weight | Squared weight |
|---|---|---|---|
| BTC exposure | $45,000 | 45% | 0.2025 |
| ETH exposure | $25,000 | 25% | 0.0625 |
| SOL exposure | $15,000 | 15% | 0.0225 |
| Hypothetical asset D | $10,000 | 10% | 0.0100 |
| USD cash | $5,000 | 5% | 0.0025 |
| Total | $100,000 | 100% | 0.3000 |
The effective number of holdings is 1 / 0.30 = 3.3333. Five equally weighted holdings would have HHI 5 × 0.20² = 0.20 and an effective count of five. The hypothetical account therefore has the weight concentration of about 3.33 equal positions, despite listing five holdings.
The largest holding contributes 0.2025 / 0.30 = 67.5% of the HHI total. That is its contribution to this concentration statistic, not its contribution to portfolio volatility or expected loss. Squaring weights gives large positions disproportionate influence.
Keep the largest holding and top-three weight alongside HHI. Here they are 45% and 85%, respectively. Those simpler figures reveal where the imbalance sits; one aggregate statistic cannot identify the underlying names.
Fix the denominator and grouping before comparing scores
Whole account versus invested sleeve
Including cash answers how the whole selected account is allocated. Excluding it answers how the invested sleeve is allocated. Both can be useful, provided the labels travel with the results.
In the example, the crypto-only denominator is $95,000. Recalculate every crypto weight against that amount rather than dropping cash's squared term from the existing total:
The sum of squared included values is 45² + 25² + 15² + 10² = 2,975. Divide by 95² = 9,025 to get HHI 0.3296398892. Its reciprocal gives 3.0336 effective holdings.
The figures are expressed in thousands of dollars, which cancel in the ratio. Simply subtracting 0.0025 would leave weights summing to 95%, so it would not be a normalized sleeve HHI.
Cash treatment also complicates interpretation. A hypothetical account with 80% cash and 20% one token has HHI 0.80² + 0.20² = 0.68. Its high capital concentration does not imply more token-price exposure than a 100% token position. A stablecoin line should retain its own identity and current reporting-currency value; it is not automatically equivalent to USD cash.
Wallet rows versus underlying exposures
Suppose the $45,000 BTC exposure is merely split into $25,000 and $20,000 balances across two wallets. Treating those rows as independent holdings reduces the reported HHI from 0.30 to 0.20, raising the effective count from 3.33 to five without changing ownership of any underlying asset.
Combine identical underlying holdings before measuring asset concentration. In general, merging weights a and b raises their squared-weight contribution by 2ab. Here 2 × 0.25 × 0.20 = 0.10, exactly reversing the artificial reduction.
A wrapped token or staking receipt requires a documented classification rather than automatic consolidation. A price-exposure view may group related claims, while a custody or protocol view may keep their dependencies separate. Those views answer different questions. Never count both a receipt's full value and its underlying collateral as two owned assets in the same valuation total.
Distinguish meaningful redistribution from extra tiny holdings
Moving capital from a larger holding to a smaller one can reduce HHI. It does not follow that adding more token names makes a meaningful difference.
| Hypothetical allocation | Listed holdings | Decimal HHI | Effective holdings |
|---|---|---|---|
| Original 45/25/15/10/5 portfolio | 5 | 0.3000 | 3.33 |
| Transfer 10 percentage points from first to third: 35/25/25/10/5 | 5 | 0.2600 | 3.85 |
| One 90% holding and one 10% holding | 2 | 0.8200 | 1.22 |
| One 90% holding and 100 holdings of 0.1% each | 101 | 0.8101 | 1.23 |
The transfer example assumes unchanged total value and excludes execution costs. Its HHI reduction is 0.30 − 0.26 = 0.04. The tiny-holdings example shows why a long token list can conceal a dominant allocation: the 90% position alone contributes 0.81.
Lower HHI is a description of more even weights. It is not evidence that the new assets have better liquidity, lower failure risk or a more favorable expected return. Any contemplated redistribution still needs a reason beyond improving a dashboard number, plus an assessment of costs and the portfolio turnover it creates.
Weights also drift without trades. If the original BTC holding doubles in value while every other line stays fixed, total value becomes $145,000 and BTC's weight becomes about 62.07%. HHI rises to about 0.43163, with effective holdings falling to 2.32. The calculation explains allocation drift; it attributes no cause or probability to that hypothetical price move.
HHI does not replace correlation, volatility or beta
HHI contains weights and nothing about return co-movement. Two portfolios with identical weights have identical HHI even if one contains assets moving almost together and the other contains assets with different return behavior. Use the separate portfolio correlation and common-loss worksheet to examine that relationship.
Likewise, effective holdings is not an effective number of independent bets. Changing the volatility of one asset leaves HHI unchanged. Changing the return sampling interval also leaves a current-value HHI unchanged, while it can alter an estimated risk measure. The realized-volatility sampling guide explains why the measurement clock matters for that second task.
HHI needs no assumption that returns are stationary. Historical risk models may nevertheless become unreliable when their input behavior changes. ADF and KPSS stationarity diagnostics address a different question about a specified time series; their output does not validate an allocation's concentration score.
Market beta is different again: it estimates return sensitivity to a benchmark. A portfolio can have evenly distributed token weights while retaining substantial exposure to a common crypto market driver. Keep the benchmark-relative beta calculation separate from the weight summary.
A concentration check you can reproduce
Save the valuation snapshot and the choices that produced it. A compact review record should contain:
- The account boundary, reporting currency, timestamp and price sources.
- Cash inclusion, excluded balances and the mapping from raw rows to underlying holdings.
- Total included value, weights summing to one, HHI scale and effective count.
- Largest holding, top-three weight and separate dependency notes.
- The prior comparable snapshot and the reason for any material change.
Reject the calculation when included total value is zero, prices are missing, or entries violate the stated nonnegative-value setup. A missing mark is not a zero-value asset. Do not silently drop an unavailable price and renormalize the rest. That could make an account appear less concentrated precisely when its largest exposure cannot be valued reliably.
The simple bounds above also do not apply to arbitrary signed weights divided by net equity. Shorts, leverage and derivatives require separate exposure definitions. Normalizing absolute notionals can describe how gross exposure is distributed, but removes the amount of leverage and is not the same as this spot capital-allocation measure. Keep gross exposure, net exposure and collateral obligations visible.
There is no universal HHI score that makes a crypto portfolio acceptable. Compare consistent snapshots against a concentration policy chosen for the actual portfolio, then investigate the largest contributors and their shared dependencies. The useful next step is to reconcile one current account snapshot into honest weights before treating its holding count as evidence of diversification.