Distributionally Robust Portfolio

Install and import#

bash

npm install fintech-algorithms

import { distributionallyRobustPortfolio } from "fintech-algorithms/portfolio-construction/bayesian-and-robust-allocation/distributionally-robust-portfolio";

Signature#

distributionallyRobustPortfolio(mean, covariance, lossThreshold, returnFloor, tolerance, maxIterations)

Minimizes the worst-case probability of a loss across every distribution sharing a given mean and covariance, subject to a return floor.

Parameters#

Name	Type	Notes
`mean`	length `n` vector	decimal return/period
`covariance`	`n x n` matrix	return²/period
`lossThreshold`	`number`
`returnFloor`	`number`
`tolerance`	`unknown`
`maxIterations`	`unknown`

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#

mean

[0.06, 0.03]

covariance

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

lossThreshold

0.02

returnFloor

0.04

Call#

distributionallyRobustPortfolio(mean, covariance, lossThreshold, returnFloor, tolerance, maxIterations)

Returns#

object with 11 fields: weights, expectedReturn, variance, riskScore, lossThreshold, returnFloor, outerIterations, status, …

{
  "weights": [0.3333333333333334, 0.6666666666666665],
  "expectedReturn": 0.039999999999999994,
  "variance": 0.00888888888888889,
  "riskScore": 1.5713484026367726,
  "lossThreshold": 0.02,
  "returnFloor": 0.04,
  "outerIterations": 45,
  "status": "optimal",
  "searchBracket": [0.04, 0.04000000000788109],
  "returnResidual": 6.938893903907228e-18,
  "interpretation": "riskScore ranks worst-case loss probability only under the cited radial-class theorem; it is not itself an unconditional…"
}

Diagrams#

Calculation flow#

Diagram

flowchart TB
    N0[Declare radial class] --> N1
    N1[Check return floor] --> N2
    N2[Solve fixed returns] --> N3
    N3[Search ratio score] --> N4
    N4[Check bracket and weights]

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#

Distributionally Robust Portfolio Optimization — I. E. Bardakci and C. M. Lagoa.
Distributionally Robust Optimization Under Moment Uncertainty — Erick Delage and Yinyu Ye.
Data-driven DRO using the Wasserstein metric — Peyman Mohajerin Esfahani and Daniel Kuhn.
Equation review note