Markowitz Mean-Variance

Install and import#

bash

npm install fintech-algorithms

import { markowitzMeanVariance } from "fintech-algorithms/portfolio-construction/mean-risk-optimization/markowitz-mean-variance";

Signature#

markowitzMeanVariance(assetIdsInput, muInput, covarianceInput, targetReturnInput, options)

Solves for the lowest-variance asset weights that still meet a declared return target, from expected returns and a covariance matrix.

Parameters#

Name	Type	Notes
`assetIdsInput`	`ordered string array`	One stable identifier per column/row
`muInput`	`finite number array`	Expected return for one declared horizon
`covarianceInput`	`finite number matrix`	Variance/covariance for that same horizon and return unit
`targetReturnInput`	`finite number`	Same expected-return unit/horizon as `mu`
`options`	`MarkowitzOptions`	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"]

muInput

[0.06, 0.14]

covarianceInput

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

targetReturnInput

0.1

options

{
  "maxIterations": 10000
}

Call#

markowitzMeanVariance(assetIdsInput, muInput, covarianceInput, targetReturnInput, options)

Returns#

object with 21 fields: assetIds, mu, targetReturn, weights, expectedReturn, variance, volatility, budgetResidual, …

{
  "assetIds": ["A", "B"],
  "mu": [0.06, 0.14],
  "targetReturn": 0.1,
  "weights": [0.4999999999999999, 0.5000000000000001],
  "expectedReturn": 0.1,
  "variance": 0.037500000000000006,
  "volatility": 0.19364916731037085,
  "budgetResidual": 0,
  "targetResidual": 0,
  "lowerBoundResidual": 0,
  "fwGapS": 0,
  "fwGap": 0,
  "matrixScale": 0.09,
  "status": "optimal"
}

Showing 14 of 21 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#

Primary technical sources
Input-lineage sources
Contextual Google destinations inspected
Citation boundaries
2026-09-16