Inverse-Volatility Weighting

Install and import#

bash

npm install fintech-algorithms

import { inverseVolatilityWeights } from "fintech-algorithms/portfolio-construction/risk-allocation/inverse-volatility-weighting";

Signature#

inverseVolatilityWeights(assetIds, standaloneVolatilities)

Assigns capital in inverse proportion to each asset standalone volatility and normalizes the scores, with a covariance diagnostic showing what the rule leaves out.

Parameters#

Name	Type	Notes
`assetIds`	ordered `string[N]`	`N >= 1`, non-empty, unique; order is preserved
`standaloneVolatilities`	ordered finite numeric `N`-vector	strictly positive; same declared horizon/unit

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#

assetIds

["A", "B", "C"]

standaloneVolatilities

[0.1, 0.2, 0.15]

Call#

inverseVolatilityWeights(assetIds, standaloneVolatilities)

Returns#

object with 6 fields: assetIds, weights, normalizedInverseVolatilityScores, sumWeights, method, status

{
  "assetIds": ["A", "B", "C"],
  "weights": [0.46153846153846145, 0.23076923076923073, 0.3076923076923077],
  "normalizedInverseVolatilityScores": [1, 0.5, 0.6666666666666667],
  "sumWeights": 0.9999999999999999,
  "method": "inverse-volatility",
  "status": "ok"
}

Diagrams#

Calculation flow#

Input audit to risk diagnostic

flowchart LR
  A[Ordered IDs + positive standalone vols] --> B{Core input audit}
  B -->|invalid shape/domain| E[Structured invalid-input]
  B -->|valid| C[Scale-free scores m / sigma]
  C --> D[Normalize weights]
  D --> W[A01 weights and w sigma products]
  W --> X{Optional supplied covariance?}
  X -->|no| O[Pure result: correlation-blind by definition]
  X -->|yes| P[Metadata, horizon, currency, provenance audit]
  P -->|split / stale FX / quantity / revision defect| Q[Blocked evidence: repair upstream input]
  P -->|valid schema| S[Exact symmetry + per-diagonal scale + PSD]
  S -->|failure| R[Structured diagnostic error]
  S -->|valid| T[Normalize by actual s-Sigma; compute q]
  T --> U{q state}
  U -->|exact zero| Z[zero-risk; RC/share unavailable]
  U -->|positive but near zero| N[numerically-unreliable; no division]
  U -->|available| V[Signed RC and risk shares]

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#

Palomar, *Portfolio Optimization: Theory and Application*, “Risk-Based Portfolios”
Maillard, Roncalli, and Teïletche, “On the Properties of Equally-Weighted Risk Contributions Portfolios”
Griveau-Billion, Richard, and Roncalli, “A Fast Algorithm for Computing High-dimensional Risk Parity Portfolios”
Composer Knowledge Center, “Inverse Volatility Weighting”
LAPACK `DSYEVD` documentation
Research and evidence boundary