# Robustifying Conditional Portfolio Decisions via Optimal Transport

arXiv: https://arxiv.org/abs/2103.16451 · HTML: https://mlsanity.com/paper/2103.16451/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 86 references that are in the map.
- First posted on arXiv 30 Mar 2021.

## Builds on (most cited first, 17 of 17)

- [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning](https://mlsanity.com/paper/1908.08729/) (2019)
- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [Optimal Transport Based Distributionally Robust Optimization: Structural Properties and Iterative Schemes](https://mlsanity.com/paper/1810.02403/) (2018)
- [Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances](https://mlsanity.com/paper/1802.04885/) (2018)
- [Residuals-based distributionally robust optimization with covariate information](https://mlsanity.com/paper/2012.01088/) (2020)
- [Stochastic Optimization Forests](https://mlsanity.com/paper/2008.07473/) (2020)
- [Distributionally robust stochastic programs with side information based on trimmings -- Extended version](https://mlsanity.com/paper/2009.10592/) (2020)
- [Dynamic optimization with side information](https://mlsanity.com/paper/1907.07307/) (2019)
- [Distributionally Robust Local Non-parametric Conditional Estimation](https://mlsanity.com/paper/2010.05373/) (2020)
- [Bootstrap Robust Prescriptive Analytics](https://mlsanity.com/paper/1711.09974/) (2017)
- [From Predictions to Prescriptions in Multistage Optimization Problems](https://mlsanity.com/paper/1904.11637/) (2019)
- [Distributionally Robust Optimization with Correlated Data from Vector Autoregressive Processes](https://mlsanity.com/paper/1909.03433/) (2019)
- [Heteroscedasticity-aware residuals-based contextual stochastic optimization](https://mlsanity.com/paper/2101.03139/) (2021)

## Built on by (most cited first, 12 of 12)

- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Sinkhorn Distributionally Robust Optimization](https://mlsanity.com/paper/2109.11926/) (2021)
- [Statistical Analysis of Wasserstein Distributionally Robust Estimators](https://mlsanity.com/paper/2108.02120/) (2021)
- [Adversarial Regression with Doubly Non-negative Weighting Matrices](https://mlsanity.com/paper/2109.14875/) (2021)
- [Distributionally Robust Prescriptive Analytics with Wasserstein Distance](https://mlsanity.com/paper/2106.05724/) (2021)
- [Contextual Optimization under Covariate Shift: A Robust Approach by Intersecting Wasserstein Balls](https://mlsanity.com/paper/2406.02426/) (2024)
- [Smart Surrogate Losses for Contextual Stochastic Linear Optimization with Robust Constraints](https://mlsanity.com/paper/2505.22881/) (2025)
- [Generative Conditional Distributions by Neural (Entropic) Optimal Transport](https://mlsanity.com/paper/2406.02317/) (2024)
- [Epistemic Robust Offline Reinforcement Learning](https://mlsanity.com/paper/2604.07072/) (2026)
- [Robust Data-driven Prescriptiveness Optimization](https://mlsanity.com/paper/2306.05937/) (2023)
- [Factor-Based Conditional Diffusion Model for Contextual Portfolio Optimization](https://mlsanity.com/paper/2509.22088/) (2025)
- [Distributionally Robust Recovery of Omitted Factors from Forecast Residuals with Application to Interest Rate Risk Management](https://mlsanity.com/paper/2601.04608/) (2026)

## Abstract (arXiv)

We propose a data-driven portfolio selection model that integrates side information, conditional estimation and robustness using the framework of distributionally robust optimization. Conditioning on the observed side information, the portfolio manager solves an allocation problem that minimizes the worst-case conditional risk-return trade-off, subject to all possible perturbations of the covariate-return probability distribution in an optimal transport ambiguity set. Despite the non-linearity of the objective function in the probability measure, we show that the distributionally robust portfolio allocation with side information problem can be reformulated as a finite-dimensional optimization problem. If portfolio decisions are made based on either the mean-variance or the mean-Conditional Value-at-Risk criterion, the resulting reformulation can be further simplified to second-order or semi-definite cone programs. Empirical studies in the US equity market demonstrate the advantage of our integrative framework against other benchmarks.