Cardinality-Constrained Portfolio

Install and import#

bash

npm install fintech-algorithms

import { optimizeCardinalityConstrained } from "fintech-algorithms/portfolio-construction/practical-constraints/cardinality-constrained-portfolio";

Signature#

optimizeCardinalityConstrained(mu, covariance, lambdaRisk, current, K, options)

Parameters#

Name	Type	Notes
`mu`	`unknown`
`covariance`	`unknown`
`lambdaRisk`	`unknown`
`current`	`unknown`
`K`	`unknown`
`options`	`{ lower?: unknown; upper?: unknown; maxSupports?: unknown }`	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#

[0.12, 0.1, 0.09, 0.08]

covariance

[
  [0.3, 0, 0, 0],
  [0, 0.02, 0, 0],
  [0, 0, 0.01, 0]
]

Showing 3 of 4 elements.

lambdaRisk

current

[0.25, 0.25, 0.25, 0.25]

options

{
  "lower": [0, 0, 0, 0],
  "upper": [1, 1, 1, 1]
}

Call#

optimizeCardinalityConstrained(mu, covariance, lambdaRisk, current, K, options)

Returns#

object with 12 fields: status, weights, selected, trade, objective, bestBound, relativeGap, enumeratedSupports, …

{
  "status": "optimal",
  "weights": [0, 0.5000000000000003, 0.49999999999999967, 0],
  "selected": [0, 1, 1, 0],
  "trade": [-0.25, 0.25000000000000033, 0.24999999999999967, -0.25],
  "objective": 0.0875,
  "bestBound": 0.0875,
  "relativeGap": 0,
  "enumeratedSupports": 10,
  "totalSupports": 10,
  "realizedSupport": 2,
  "tradeSupport": 4,
  "certificate": {
    "kind": "exhaustive-support-enumeration",
    "complete": true,
    "continuousKkt": true,
    "globalOptimality": "all supports and continuous KKT active sets were checked"
  }
}

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, §6.4 and §6.5 — MOSEK ApS.
Moehle, Kochenderfer, Boyd, and Ang, “Tax-aware portfolio optimization” — Nicholas Moehle, Mykel J. Kochenderfer, Stephen Boyd, and Andrew Ang.
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