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Thematic-Tilt Index

Install and import#

bash
npm install fintech-algorithms
ts
import { calculate } from "fintech-algorithms/index-and-benchmark-engineering/alternative-weighting/thematic-tilt-index";

Signature#

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#

NameTypeNotes
data{ ids: string[]; parentWeights: number[]; themeScores: number[]; tilt: number; maxMultiplier: number }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#

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

Input#

data
{
  "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#

calculate(data)

Returns#

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

{
  "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]
}

Diagrams#

Thematic-Tilt Index — article hero
Thematic-Tilt Index — failure guard
Thematic-Tilt Index — worked example

Calculation flow#

Thematic-Tilt Index calculation flow 
flowchart LR
    A["Point-in-time inputs"] --> B["Validate units and timing"]
    B --> C{"Contract feasible?"}
    C -->|No| D["Reject with reason"]
    C -->|Yes| E["Calculate Thematic-Tilt Index"]
    E --> F["Recompute invariants"]
    F --> G{"Checks pass?"}
    G -->|No| D
    G -->|Yes| H["Publish audited output"]
Thematic-Tilt Index methodology state 
stateDiagram-v2
    [*] --> FrozenInputs
    FrozenInputs --> Validated: contract passes
    FrozenInputs --> Rejected: missing or infeasible
    Validated --> Calculated: apply named rule
    Calculated --> Audited: invariants pass
    Calculated --> Rejected: invariant fails
    Audited --> Published: version and timestamp recorded
    Published --> Revised: approved correction
    Revised --> FrozenInputs: rebuild from retained source state

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.

Read the article →

References#

The rest of the Alternative Weighting family#