How EFS Leverages Large Language Models for Sparse Portfolio Optimization

Background Sparse portfolio optimization, a core challenge in quantitative finance, requires selecting at most m assets from n candidates under an \(l_0\) norm constraint. Traditional methods (greedy, convex relaxation, MIP) suffer from poor interpretability and weak adaptability to dynamic markets.

Problem Definition Existing LLM‑based factor mining approaches are static and fail to address the dynamic needs of sparse portfolios, such as implementation cost and risk control. The goal is a dynamic, interpretable, sparsity‑aware framework that jointly solves factor generation and sparse selection.

Method

1. Problem Formalization The optimization is defined as maximizing cumulative wealth (CW), Sharpe ratio (SR) and minimizing maximum drawdown (MDD) subject to \(\|w\|_0 \le m\), where \(w\) denotes asset weights.

2. Alpha Factor & Evaluation An alpha factor \(f\) maps historical feature matrix \(X_i\) to a score. Evaluation metrics include RankIC (Spearman correlation between factor scores and future returns) and RankICIR (mean‑to‑std ratio of RankIC).

3. LLM‑Driven Evolutionary Factor Search

Single‑stage Factor Generation : The LLM, prompted with past factor performance and structural templates, directly outputs executable scoring formulas, providing end‑to‑end generation, controllable mutation (parameter/logic changes) and crossover, and high interpretability.

Iterative Evolution Loop (two stages):

4. Key Innovations

Evolutionary feedback loop that dynamically optimizes the factor pool based on back‑test results.

End‑to‑end scoring function generation eliminates intermediate model over‑fitting.

Transformation of sparse optimization into a top‑m ranking task naturally supports risk control and interpretability.

Experiments

Datasets: five Fama‑French benchmarks (FF25, FF32, FF49, FF100, FF100MEOP) and three real‑market sets (US50, HSI45, CSI300) covering bull and bear cycles.

Baselines: non‑sparse (1/N, Min‑CVaR, Max‑Sharpe) and sparse (SSPO, XGBoost/LightGBM, mSSRM‑PGA, ASMCVaR).

Metrics: CW, SR, MDD, RankIC, RankICIR.

Main Results

On FF datasets (m=10), EFS‑GPT (based on GPT‑4.1) achieves CW = 1836.34 on FF100, a 274 % improvement over the next best baseline (ASMCVaR, CW = 491.12). Larger asset pools amplify the gap.

Increasing sparsity to m=15/20 and applying score‑to‑weight weighting further raises CW (e.g., FF100 CW = 2434.51).

Real‑market performance: US50 (m=10) – EFS‑GPT CW = 22.905 vs 1/N CW = 4.562 (+402 %); HSI45 – EFS‑DeepSeek SR = 0.080 vs ASMCVaR 0.052 (+53.8 %); CSI300 – EFS‑GPT CW = 4.962 vs LGBM 2.334 (+112.6 %). In volatile periods (2022 bear market) EFS adapts factor selection (e.g., defensive stocks) and controls MDD better than baselines.

Ablation studies:

Factor evolution analysis shows scores shift with market regimes (defensive factors dominate in bear markets, momentum in bull markets) and maintain stable RankIC in top‑10 selections, whereas traditional factors suffer severe sparse‑decay.

Overall, EFS demonstrates that LLM‑guided evolutionary search provides a robust, interpretable, and adaptable solution for sparse portfolio optimization, outperforming both statistical and optimization baselines across diverse datasets.