# Thematic-Tilt Index

`D03-F03-A06` · Index and Benchmark Engineering → Alternative Weighting · archetype `record-transform` · difficulty 4/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/index-and-benchmark-engineering/alternative-weighting/thematic-tilt-index/
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/index-and-benchmark-engineering/alternative-weighting/thematic-tilt-index";
```

## Signature

```ts
calculate(data)
```

Tilts a parent index toward a theme by scaling weights with a theme score, bounded so no single name runs away. Keeps the parent's diversification while expressing a view.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `data` | `{ ids: string[]; parentWeights: number[]; themeScores: number[]; tilt: number; maxMultiplier: number }` | yes | `tilt` sets the strength of the tilt and `maxMultiplier` caps how far any weight may be multiplied — without it a high score plus a small parent weight produces an untradeable position. |

## Returns

`{ ids, multipliers, weights, activeWeights }`

Tilted weights and the active weights against the parent, which is what a tracking-error budget is measured on.

## Errors

- When maxMultiplier is less than 1 — throws

## Complexity

Time `O(n)`, space `O(n)`.

## Worked example

This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.

### Input

`data`:

```json
{
  "ids": ["A", "B", "C", "D", "E"],
  "parentWeights": [0.3, 0.25, 0.2, 0.15, 0.1],
  "themeScores": [1, 0.6, 0.1, -0.4, -0.8],
  "tilt": 0.5,
  "maxMultiplier": 1.6
}
```

### Call

```ts
calculate(data)
```

### Returns

object with 4 fields: ids, multipliers, weights, activeWeights

```json
{
  "ids": ["A", "B", "C", "D", "E"],
  "multipliers": [1.5, 1.3, 1.05, 0.8, 0.6],
  "weights": [0.386266, 0.27897, 0.180258, 0.103004, 0.051502],
  "activeWeights": [0.086266, 0.02897, -0.019742, -0.046996, -0.048498]
}
```

## Verification and provenance

Tier: **verified** (via input-expected).

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/index-and-benchmark-engineering/alternative-weighting/thematic-tilt-index/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/index-and-benchmark-engineering/alternative-weighting/thematic-tilt-index/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/index-and-benchmark-engineering/llms.txt