Evolutionary Factor Searching for Sparse Portfolio Optimization Using Large Language Models

Abstract

Sparse portfolio optimization is a fundamental yet challenging problem in quantitative finance. Traditional approaches often use static objectives and thus adapt poorly to dynamic market regimes. In this work, we propose Evolutionary Factor Search, a framework that leverages large language models and evolutionary algorithms to automatically generate and evolve alpha factors for sparse portfolio construction. The framework recasts asset selection as a ranking task guided by the generated factors and uses an evolutionary feedback loop to iteratively refine the factor pool from portfolio performance. To handle the inter-factor redundancy that accumulates during this search, we further introduce a redundancy-aware weight allocation module that combines random-matrix-theory denoising of the factor correlation matrix with regularized quadratic programming, at negligible overhead and without additional tuning. Extensive experiments on four Fama-French benchmarks and three real-market datasets spanning the United States, Hong Kong, and Mainland China equity markets show that the proposed framework outperforms statistical and optimization-based baselines across diverse markets. Ablation studies further validate the importance of prompt composition, factor diversity, and language-model choice. These results highlight language-model-guided evolution as a robust and interpretable paradigm for portfolio optimization under structural constraints.