Effective Number of Constituents
Install and import#
npm install fintech-algorithmsimport { calculate } from "fintech-algorithms/market-breadth-and-internals/concentration-and-diffusion/effective-number-of-constituents";Signature#
calculate(rows)The reciprocal of HHI: how many equally weighted holdings would give the same concentration. An index of 500 names with an effective number of 60 is, for risk purposes, a 60-stock portfolio.
Parameters#
| Name | Type | Notes |
|---|---|---|
rows | Row[] | Constituents with weights. Rows carry a ready flag; a row that is not ready is excluded rather than treated as zero, because a missing count and a count of zero mean opposite things about market breadth. |
Returns#
{ status, effective_n, actual_n, hhi }
The effective count beside the actual count — the gap between them is the entire message.
Errors#
- When weights do not sum to approximately 1 — reported as a status rather than thrown
Complexity: time O(n),
space O(1).
Worked example#
executed Captured by running this function on the input its own test provides. Real output of real code — but not asserted against a published figure.
Input#
[
{
"security_id": "S01",
"weight": 0.17821782178217824,
"return": 0.065,
"sector": "Tech",
"ready": true
},
{
"security_id": "S02",
"weight": 0.13861386138613863,
"return": 0.041,
"sector": "Financials",
"ready": true
},
{
"security_id": "S03",
"weight": 0.10891089108910892,
"return": 0.028,
"sector": "Industrials",
"ready": true
}
]Showing 3 of 24 elements.
Call#
calculate(rows)Returns#
object with 4 fields: status, effective_n, actual_n, hhi
{
"status": "resolved",
"effective_n": 11.134761062719665,
"actual_n": 24,
"hhi": 0.0898088422703657
}Diagrams#
Calculation flow#
Calculation Flow — Effective Number of Constituents
flowchart LR
A["Point-in-time component snapshot"] --> B{"Complete, unique, finite?"}
B -->|"No"| X["Incomplete — withhold value"]
B -->|"Yes"| C["Apply Effective Number of Constituents contract"]
C --> D["Retain component audit trace"]
D --> E["Publish value, unit, parameter, and as-of"]
How it works#
This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.
References#
- Claim-to-source map
- Herfindahl-Hirschman Index — U.S. Department of Justice, Antitrust Division
- Diversity and Evenness: A Unifying Notation and Its Consequences — Mark O. Hill
- S&P Dow Jones Indices: Index Mathematics Methodology — S&P Dow Jones Indices