On Accelerating Large-Scale Robust Portfolio Optimization

ArXiv ID: 2408.07879 “View on arXiv”

Authors: Unknown

Abstract

Solving large-scale robust portfolio optimization problems is challenging due to the high computational demands associated with an increasing number of assets, the amount of data considered, and market uncertainty. To address this issue, we propose an extended supporting hyperplane approximation approach for efficiently solving a class of distributionally robust portfolio problems for a general class of additively separable utility functions and polyhedral ambiguity distribution set, applied to a large-scale set of assets. Our technique is validated using a large-scale portfolio of the S&P 500 index constituents, demonstrating robust out-of-sample trading performance. More importantly, our empirical studies show that this approach significantly reduces computational time compared to traditional concave Expected Log-Growth (ELG) optimization, with running times decreasing from several thousand seconds to just a few. This method provides a scalable and practical solution to large-scale robust portfolio optimization, addressing both theoretical and practical challenges.

Keywords: Robust Portfolio Optimization, Distributionally Robust Optimization, Hyperplane Approximation, S&P 500, Scalable Optimization, Equities (S&P 500)

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced concepts from distributionally robust optimization, approximation theory, and convex analysis, though it abstracts away some derivation details; it is strongly validated with real-world S&P 500 data, demonstrating significant computational speedups and robust out-of-sample performance, making it both mathematically dense and empirically rigorous.

  flowchart TD
    A["Research Goal:<br>Efficient Large-Scale<br>Robust Portfolio Optimization"] --> B["Methodology:<br>Extended Supporting Hyperplane<br>Approximation Approach"]
    B --> C["Data Input:<br>S&P 500 Constituents<br>High-Dimensional Dataset"]
    C --> D["Computational Process:<br>Distributionally Robust<br>Optimization Solver"]
    D --> E{"Comparison vs.<br>Traditional ELG Optimization"}
    E -->|Computational| F["Outcome: Drastic Speedup<br>Time reduced from 1000s to few seconds"]
    E -->|Performance| G["Outcome: Robust Out-of-Sample<br>Trading Performance"]