On Accelerating Large-Scale Robust Portfolio Optimization

Paper: arXiv 2408.07879

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.

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: 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.

Research Flowchart

  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"]

Cited References (57)

1. On Joint Convexity of Trace Functions (2004)
2. Global Portfolio Optimization (1992)
3. Quantifying Distributional model risk via Optimal Rransport (2019)
4. Distributionally Robust Optimization under Moment Uncertainty with Application to Data-Driven Problems (2010)
5. Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances (2022)
6. A Signal Processing Perspective on Financial Engineering (2016)
7. On Adaptive Portfolio Management with Dynamic Black-Litterman Approach — → 2307.03391
8. Introduction to Nonlinear Optimization: Theory, Algorithms, and Applications with Python and MATLAB (2023)

2 of 57 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.