Global Minimum Variance

Install and import#

bash

npm install fintech-algorithms

import { globalMinimumVariance } from "fintech-algorithms/portfolio-construction/mean-risk-optimization/global-minimum-variance";

Signature#

globalMinimumVariance(assetIdsInput, covarianceInput, options)

Computes the lowest-variance weights obtainable from a covariance matrix alone, with no expected-return input, and shows why clipping a short weight is not optimization.

Parameters#

Name	Type	Notes
`assetIdsInput`	`unknown`
`covarianceInput`	`unknown`
`options`	`GMVOptions`	optional

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#

assetIdsInput

["A", "B"]

covarianceInput

[
  [0.04, 0.01],
  [0.01, 0.09]
]

options

{
  "maxIterations": 10000
}

Call#

globalMinimumVariance(assetIdsInput, covarianceInput, options)

Returns#

object with 19 fields: assetIds, mu, matrixScale, variant, method, maxIterations, weights, variance, …

{
  "assetIds": ["A", "B"],
  "mu": null,
  "matrixScale": 0.09,
  "variant": "gmv-long-only-fully-invested",
  "method": "projected-gradient-simplex-line-search",
  "maxIterations": 10000,
  "weights": [0.7272727272727273, 0.27272727272727276],
  "variance": 0.03181818181818182,
  "volatility": 0.17837651700316895,
  "expectedReturn": null,
  "budgetResidual": 0,
  "lowerBoundResidual": 0,
  "fwGapS": 0,
  "fwGap": 0
}

Showing 14 of 19 fields.

Diagrams#

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#

MOSEK Portfolio Optimization Cookbook — Markowitz portfolio
On the Estimation of the Global Minimum Variance Portfolio
Portfolio Optimization / Markowitz model
SEC: Stock Splits
Investor.gov: Ex-Dividend Dates
UW Markowitz project notes
Historical/case boundary
2026-09-16