Minimum-Volatility Index
Install and import#
npm install fintech-algorithmsimport { calculate } from "fintech-algorithms/index-and-benchmark-engineering/alternative-weighting/minimum-volatility-index";Signature#
calculate(data)Solves for the weights that minimise portfolio variance for a given covariance matrix. The result is only as good as the covariance estimate, which is the part that is hard — not the optimisation.
Parameters#
| Name | Type | Notes |
|---|---|---|
data | { ids: string[]; covariance: number[][] } | covariance must be square, symmetric and positive semi-definite. A matrix estimated from fewer observations than assets will not be, and no optimiser can rescue it. |
Returns#
{ ids, weights, variance, volatility }
The minimising weights and the portfolio variance and volatility they achieve.
Errors#
- When the covariance matrix is not square or not symmetric — throws
Complexity: time O(n³),
space O(n²).
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#
{
"ids": ["A", "B", "C"],
"covariance": [
[0.04, 0.006, 0.004],
[0.006, 0.0225, 0.003],
[0.004, 0.003, 0.01]
]
}Call#
calculate(data)Returns#
object with 4 fields: ids, weights, variance, volatility
{
"ids": ["A", "B", "C"],
"weights": [0.093023, 0.232558, 0.674419],
"variance": 0.007814,
"volatility": 0.088397
}Diagrams#
Calculation flow#
Minimum-Volatility 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 Minimum-Volatility Index"]
E --> F["Recompute invariants"]
F --> G{"Checks pass?"}
G -->|No| D
G -->|Yes| H["Publish audited output"]
Minimum-Volatility 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.
References#
- S&P Dow Jones Indices Index Mathematics Methodology — S&P Dow Jones Indices
- S&P DJI Equity Indices Policies & Practices — S&P Dow Jones Indices
- FTSE Russell Capping Methodology — FTSE Russell, LSEG
- FTSE Russell Index Policy and Methodology Library — FTSE Russell, LSEG
- MSCI Global Investable Market Indexes Methodology Library — MSCI
- MSCI Minimum Volatility Indexes Methodology — MSCI
- S&P Risk Control 2.0 Indices Methodology — S&P Dow Jones Indices
- Principles for Financial Benchmarks — International Organization of Securities Commissions
- Regulation (EU) 2016/1011 — European Union
- Portfolio Selection — Harry Markowitz
- On the Properties of Equally-Weighted Risk Contributions Portfolios — Sébastien Maillard, Thierry Roncalli, and Jérôme Teïletche
- Fundamental Indexation — Robert Arnott, Jason Hsu, and Philip Moore
- FTSE Currency Hedging Methodology Overview — FTSE Russell, LSEG