Key Takeaways
Direct answer: Yes — a cap-weighted index can hold hundreds of names and still deliver returns effectively driven by a handful of mega-caps, because holdings count says nothing about how weight is distributed. An investor holding a fund with 500 line items may still be carrying meaningful single-stock and sector risk concentrated in a few large, often correlated names.
- Raw holdings count is not a diversification metric — it tells you how many names are in the fund, not how the fund's risk and return are actually distributed across them.
- Effective N ("effective number of stocks") converts index weights into a single number: how many equally-weighted stocks would produce this same level of concentration.
- Effective N = 1 ÷ (sum of each constituent's weight, as a decimal, squared).
- Correlation among the largest names — several mega-caps exposed to the same underlying driver — can make effective diversification even smaller than effective N alone implies.
- This is index-weight concentration, distinct from industry/competitive concentration (Herfindahl-Hirschman Index) covered on the Market Concentration, HHI, and Consolidation page.
Can a diversified index still be concentrated?
Yes, and this is the central, counterintuitive point of index-concentration analysis. "Diversified" is often used loosely to mean "holds a lot of different stocks," but a cap-weighted index's return is a weighted average, and weighted averages can be dominated by a small number of large weights even when the total holdings list runs into the hundreds. A fund can report 500 holdings on its fact sheet and still behave, in terms of return and risk, much more like a fund holding a dozen stocks — because the other 490-plus holdings each carry so little weight that their individual returns barely move the total.
This matters for investors specifically because it changes what "I own a diversified index fund" actually means as a risk statement. An investor who believes a broad index gives them exposure spread evenly across an economy may in fact be carrying concentrated exposure to whatever handful of companies currently hold the largest weights — and if those companies operate in the same industry or are exposed to the same underlying driver (several large technology companies, for example, whose fortunes tend to move together), the investor's real diversification benefit is smaller than the holdings count suggests.
Common mistake
The common mistake is treating the number of holdings on a fund fact sheet as a diversification score. A 500-holding index and a 30-holding index can have very similar effective diversification if the 500-holding index's weight is concentrated enough at the top — the raw count is a starting point for due diligence, not a conclusion.
What is the effective number of stocks (effective N)?
Effective N is a diversification metric derived directly from index weights. It answers a specific question: "if I replaced this index with a hypothetical one that held some number of stocks at exactly equal weight, how many stocks would that hypothetical index need to have to match this index's actual level of weight concentration?" That number is the effective N.
The formula
Effective N = 1 ÷ (sum of each constituent's weight, as a decimal, squared)
The sum of squared weights in the denominator is the same weight-based Herfindahl-Hirschman calculation used in Index Concentration, just applied to index weights rather than industry market shares. Effective N is simply its inverse, which converts an abstract concentration score into an intuitive "equivalent number of equally-weighted holdings" — a number directly comparable to the fund's actual holdings count.
If every constituent in an index held exactly equal weight, effective N would equal the actual number of holdings exactly, because concentration would be at its theoretical minimum for that holdings count. Any real-world weight dispersion — some constituents larger than others — pushes effective N below the actual holdings count. The larger the gap between effective N and the actual count, the more the index's real behavior is being driven by a subset of its largest names.
Common mistake
The common mistake is assuming effective N also captures correlation between holdings. It does not — effective N is calculated purely from weights and says nothing about whether the largest constituents move together or independently. Two indexes with an identical effective N can have very different real-world diversification if one index's largest weights are spread across unrelated industries and the other's sit in companies exposed to the same underlying driver.
Worked Example: Effective N for a 50-Holding Index
Illustrative, hypothetical numbers — not a real index or real companies.
Consider a small hypothetical cap-weighted index with 50 total holdings. Five constituents hold larger weights; the remaining 45 constituents each hold an identical, much smaller weight.
| Holding group | Count | Weight each | Combined weight | Sum of squared weights |
|---|---|---|---|---|
| Stock 1 | 1 | 15% | 15% | 0.0225 |
| Stock 2 | 1 | 13% | 13% | 0.0169 |
| Stock 3 | 1 | 11% | 11% | 0.0121 |
| Stock 4 | 1 | 9% | 9% | 0.0081 |
| Stock 5 | 1 | 7% | 7% | 0.0049 |
| Remaining 45 stocks | 45 | 1% each | 45% | 0.0045 |
| Total | 50 | — | 100% | 0.0690 |
The top five stocks hold 15%, 13%, 11%, 9%, and 7% of the index — a combined 55% of total weight — while the remaining 45 stocks split the other 45% equally, at 1% each. Squaring each weight (as a decimal) and summing gives the denominator of the effective N formula: 0.0225 + 0.0169 + 0.0121 + 0.0081 + 0.0049 for the top five, plus 45 × 0.0001 = 0.0045 for the equal-weighted remainder, for a total sum of squared weights of 0.0690.
Effective N = 1 ÷ 0.0690 ≈ 14.5
This is the instructive result: an index with 50 actual holdings has an effective N of only about 14.5. In diversification terms, this 50-stock index behaves like a hypothetical index holding roughly 14 or 15 stocks at equal weight — not 50. An investor scanning the fact sheet and counting 50 line items would reasonably assume broad diversification; the effective N calculation reveals that more than two-thirds of the index's effective diversification benefit is concentrated in the top five names, with the other 45 holdings contributing comparatively little collective weight.
Common mistake
The common mistake is stopping at the combined top-5 weight (55% in this example) and assuming that number alone tells the full diversification story. Combined top-5 weight and effective N are related but not the same: effective N accounts for the entire weight distribution, including how concentrated or dispersed the remaining 45 holdings are, not just the largest few.
Why does correlation among mega-caps matter for concentration risk?
Effective N only measures how weight is distributed across holdings; it does not know whether those holdings move together. If an index's largest weights sit in companies exposed to the same underlying driver — several large technology companies, for instance, whose revenue and valuation multiples can move together on shared macro or sector news — their returns can be correlated even though they are legally distinct stocks. When that happens, the effective diversification benefit is even smaller than the weight-based effective N alone implies, because two "different" large holdings are, in terms of the risk they actually carry, closer to one bigger bet than two independent ones.
This is why effective N is a necessary but not sufficient diversification check. An index with an effective N of 14.5 spread across 14 unrelated industries carries meaningfully different risk than the same effective N concentrated in five correlated mega-caps plus a long tail of small positions. Effective N tells you the weight math; correlation among the largest names tells you whether that math understates or overstates the real concentration risk.
How does this connect to breadth and leadership?
A low effective N relative to the actual holdings count is often paired with narrow market leadership — a small number of names accounting for most of the index's return, as covered in the sibling Narrow vs. Broad Leadership guide. Effective N is the weight-distribution half of that picture; leadership breadth is the return-distribution half. Reading them together gives a more complete view of whether an index's diversification is structural (spread across many independent bets) or superficial (a large holdings count concealing a handful of dominant, possibly correlated, positions).
This is index-weight concentration — a function of how an index is constructed and weighted. It is a related but distinct question from industry or competitive concentration, which measures how much of an industry's revenue or output a handful of companies control regardless of any index; see Market Concentration, HHI, and Consolidation for that separate framework.
Misconceptions Versus Reality
| Misconception | Reality |
|---|---|
| A fund with hundreds of holdings is automatically well-diversified | Holdings count says nothing about weight distribution; effective N can be a fraction of the actual holdings count if weight is concentrated at the top |
| Effective N and combined top-5 weight measure the same thing | Effective N accounts for the entire weight distribution, including the smaller holdings; top-5 weight only looks at the largest names |
| A low effective N always means the index is risky | Effective N describes weight concentration, not whether that concentration is a problem — that depends on correlation among the largest names and the investor's other holdings |
| Effective N captures whether the largest holdings are correlated | Effective N is calculated purely from weights; it says nothing about whether the top constituents move together, which requires separate correlation analysis |
Risks, Limitations, and Exceptions
- Effective N is a snapshot calculated from a single point-in-time weight set; weights drift daily and shift materially at each index rebalance, so effective N should be recalculated rather than treated as a fixed property of an index.
- Effective N does not measure correlation, sector overlap, or common-factor exposure among the largest holdings — a separate analysis is needed to assess whether nominally "different" mega-caps are actually independent bets.
- A high effective N is not automatically "safe" — it describes weight dispersion, not the quality, valuation, or risk characteristics of the underlying holdings.
- Comparing effective N across indexes is only meaningful when the indexes share a similar total holdings count; a very low effective N is a bigger relative concern for a 500-holding index than for a 20-holding one.
- This guide's worked example uses illustrative, hand-verified synthetic weights, not real index constituents or weights from any actual fund.
Frequently Asked Questions
Can a diversified index still be concentrated?
Yes. A cap-weighted index can hold hundreds of names and still deliver returns effectively driven by a handful of mega-caps, because holdings count says nothing about how weight is distributed. An investor holding a fund with 500 line items may still be carrying meaningful single-stock and sector risk concentrated in a few large, often correlated names — that risk doesn't show up in the raw holdings count.
What is the effective number of stocks (effective N)?
Effective N is a diversification metric derived from index weights: it answers "how many equally-weighted stocks would produce this same level of concentration?" It is calculated as 1 divided by the sum of each constituent's weight squared (weights expressed as decimals). A lower effective N relative to the actual holdings count signals that diversification benefit is concentrated in fewer effective bets than the headline count suggests.
Why does correlation among mega-caps matter for concentration risk?
Effective N only measures how weight is distributed across holdings; it does not know whether those holdings move together. If an index's largest weights sit in companies exposed to the same underlying driver — several large technology companies, for instance — their returns can be correlated even though they are legally distinct stocks, which means the effective diversification benefit is even smaller than the weight-based effective N alone implies.
Sources and Methodology
The effective-N (effective number of stocks) methodology follows standard weight-based Herfindahl-Hirschman concentration measurement as applied to portfolio and index diversification analysis. Key reference sources include:
- S&P Dow Jones Indices — Index Mathematics Methodology: spglobal.com/spdji — constituent weighting conventions this calculation is built on.
- U.S. Department of Justice & Federal Trade Commission — Horizontal Merger Guidelines: justice.gov/atr — the source Herfindahl-Hirschman Index methodology that the weight-based sum-of-squares calculation adapts.
The 50-holding worked example in this guide uses clearly labeled, hand-verified illustrative numbers, not real index, constituent, or weight data. This content was reviewed by the Swoopr Editorial Team in August 2026.
Related Reading
- Market Concentration & Leadership — the parent hub for this content group.
- Index Concentration — the underlying weight-based Herfindahl-Hirschman calculation effective N inverts.
- Narrow vs. Broad Leadership — the return-distribution counterpart to effective N's weight-distribution view.
- Market Concentration, HHI, and Consolidation — the separate framework for measuring industry/competitive concentration, distinct from index-weight concentration.