Turnover-Constrained Optimization

Install and import#

bash

npm install fintech-algorithms

import { solveTurnoverConstrainedMarkowitz } from "fintech-algorithms/portfolio-construction/practical-constraints/turnover-constrained-optimization";

Signature#

solveTurnoverConstrainedMarkowitz(mu, covariance, lambdaRisk, w0, tau, options)

Parameters#

Name	Type	Notes
`mu`	finite real vector, length `N`	decimal simple return for the declared period; asset order is canonical
`covariance`	finite `N×N` matrix	squared-return units; symmetric PSD within scale-aware tolerance
`lambdaRisk`	`finite real scalar`	nonnegative objective coefficient
`w0`	finite real vector, length `N`	nonnegative current normalized holdings; sum must already be one within `1e-12`; no silent normalization
`tau`	`finite real scalar`	nonnegative one-way turnover cap in normalized portfolio units
`options`	`TurnoverSolverOptions`	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#

[0.1, 0.04]

covariance

[
  [0.04, 0],
  [0, 0.01]
]

lambdaRisk

[0.6, 0.4]

tau

0.1

Call#

solveTurnoverConstrainedMarkowitz(mu, covariance, lambdaRisk, w0, tau, options)

Returns#

object with 10 fields: status, weights, objective, directTurnover, inputCurrentSum, simplexResidual, minWeight, iterations, …

{
  "status": "optimal",
  "weights": [0.7, 0.3],
  "objective": 0.06149999999999999,
  "directTurnover": 0.1,
  "inputCurrentSum": 1,
  "simplexResidual": 0,
  "minWeight": 0.3,
  "iterations": 2,
  "frankWolfeGap": 1.8873791418627663e-18,
  "certificate": {
    "kind": "projected-gradient-kkt-plus-frank-wolfe-gap",
    "stationarityResidual": 1.1102230246251566e-17,
    "frankWolfeGap": 1.8873791418627663e-18,
    "objectiveGapUpperBound": 1.8873791418627663e-18,
    "normalizedStationarityResidual": 1.1102230246251565e-16,
    "normalizedFrankWolfeGap": 1.8873791418627663e-17,
    "normalizedObjectiveGapUpperBound": 1.8873791418627663e-17,
    "objectiveScale": 0.1,
    "stationarityTolerance": 1e-8,
    "toleranceUnits": "normalized by objectiveScale; original-unit gap is retained above",
    "lipschitzUpperBound": 0.08,
    "stepDenominator": 0.1,
    "stepSize": 10,
    "turnoverRadius": 0.2
  }
}

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#

transaction chapter
multi-period chapter
Multi-period trading with transaction costs
Portfolio Analysis with Turnover Constraints
`Portfolio.setTurnover` method
portfolio constraints chapter
Google discovery ledger
Evidence classification
Limitations