# Effective Number of Constituents

`D04-F05-A03` · Market Breadth and Internals → Concentration and Diffusion · archetype `record-transform` · difficulty 2/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/market-breadth-and-internals/concentration-and-diffusion/effective-number-of-constituents/
Agent skill: `npx skills add IslamBaraka90/Fintech-Algorithms-Library` — https://docs.thefintechbuilder.com/guides/agent-skill/

## Install and import

```bash
npm install fintech-algorithms
```

```ts
import { calculate } from "fintech-algorithms/market-breadth-and-internals/concentration-and-diffusion/effective-number-of-constituents";
```

## Signature

```ts
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 | Required | Notes |
| --- | --- | --- | --- |
| `rows` | `Row[]` | yes | 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

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

`rows`:

```json
[
  {
    "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

```ts
calculate(rows)
```

### Returns

object with 4 fields: status, effective_n, actual_n, hhi

```json
{
  "status": "resolved",
  "effective_n": 11.134761062719665,
  "actual_n": 24,
  "hhi": 0.0898088422703657
}
```

## Verification and provenance

Tier: **verified** (via row-fixture).

The worked example below is the figure published in this algorithm's article, replayed and asserted by the test suite on every build. The arithmetic cannot drift without the build failing.

Both tiers guarantee the signature. Full explanation: https://docs.thefintechbuilder.com/guides/verification/

Generated from the docs.json payload shipped inside fintech-algorithms@0.13.1.
The signature and parameter list are checked against the compiled implementation at build time,
so a description that contradicts the code fails the build rather than reaching this file.

## Links

- Article (how it works, step by step): https://thefintechbuilder.com/market-breadth-and-internals/concentration-and-diffusion/effective-number-of-constituents/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/market-breadth-and-internals/concentration-and-diffusion/effective-number-of-constituents/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/market-breadth-and-internals/llms.txt