# Scenario-based portfolio optimization via bootstrapping and machine learning methods: Theory development and empirical evidence from the Tehran Stock Market

## TL;DR

This paper introduces a new portfolio optimization method using machine learning and bootstrapping, which performs better than traditional methods in the Tehran Stock Market.

## Contribution

A novel hybrid approach combining machine learning, bootstrapping, and scenario optimization for portfolio selection is proposed and validated.

## Key findings

- The proposed model generates portfolios closer to actual prices than traditional methods.
- The framework avoids distributional assumptions and uses non-parametric uncertainty quantification.
- Theoretical proof shows the optimization problem is convex and computationally efficient.

## Abstract

Predicting future returns and modeling return uncertainty are essential yet challenging tasks in portfolio optimization. To address these issues, this study proposes a hybrid approach combining machine learning for return prediction, bootstrapping for uncertainty modeling, and scenario optimization for portfolio selection in the presence of uncertainty. Bootstrap samples are used to generate multiple return trajectories via machine learning, with each trajectory treated as a distinct scenario in a scenario-based mean-variance optimization framework. Empirical results using data from the Tehran Stock Market demonstrate that the proposed model produces optimal portfolios that align more closely with those derived from actual prices, compared to those generated by traditional techniques. Our results show that the combination of bootstrapping, machine learning-based prediction, and scenario optimization is a compelling alternative to classical methods. Indeed, by combining bootstrapping, as a non-parametric method for uncertainty quantification, with machine learning, the model avoids strong distributional assumptions (e.g., normality of returns) and works without assuming a predefined form of uncertainty set. In addition to illustrating the advantages of our approach by implementing it on real-world datasets, we theoretically prove that the resulting scenario optimization problem is a convex program that generates efficient solutions superior to those produced by worst-case robust optimization techniques. Furthermore, the developed framework can accommodate different machine learning models and bootstrapping techniques. Moreover, the use of scenario optimization is computationally tractable and aligns with even large-scale projects.