Signature-Informed Transformer for Asset Allocation

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Signature-Informed Transformer for Asset Allocation

Yoontae Hwang
Stefan Zohren
Published on 10/3/2025
Equities
Machine learning
Deep learning
Asset class picking
Risk management

The paper introduces the Signature-Informed Transformer (SIT), a deep learning framework for dynamic asset allocation that addresses the fundamental mismatch between forecasting and portfolio optimization in traditional two-stage pipelines. SIT integrates three key innovations: (1) path signature features that encode complex temporal dynamics and cross-asset interactions from price histories, (2) a novel signature-augmented attention mechanism that injects geometric inductive biases about lead-lag relationships into the attention scores, and (3) direct optimization of portfolio weights by minimizing the Conditional Value-at-Risk (CVaR) of the portfolio loss distribution. The authors prove that the signature-based attention bias positively amplifies attention weights for aligned asset pairs, providing a theoretical foundation for the mechanism.

Empirically, SIT is evaluated on multiple equity universes (30, 40, 50 assets from S&P100; 10, 20 from DOW30; 50, 100 from CSI300) over a test period from 2020 to 2024. It consistently outperforms traditional strategies (equally weighted, GMV, HRP, CVaR optimization) and state-of-the-art deep learning forecasters (Autoformer, DLinear, FEDformer, iTransformer, NSformer, PatchTST, TimesNet, RFormer) combined with a downstream optimizer. For example, in the 50-asset S&P100 universe, SIT achieves a Sharpe ratio of 0.7715 and Sortino ratio of 0.9743, compared to the best baseline Sharpe of 0.5315. Ablation studies confirm that each component—CVaR objective, asset attention, financial bias, and the learnable gate—contributes significantly to performance. The work demonstrates that aligning model architecture and training objective with financial goals yields robust and superior portfolio allocations.

Highlights

  • 1Proposes Signature-Informed Transformer (SIT) that unifies feature extraction and portfolio optimization into a single end-to-end policy, avoiding the objective mismatch of two-stage pipelines.
  • 2Introduces a novel signature-augmented attention mechanism that incorporates path signatures of asset pairs to model lead-lag relationships and geometric interactions.
  • 3Directly optimizes portfolio weights by minimizing Conditional Value-at-Risk (CVaR), aligning training with financial risk management goals.
  • 4Provides theoretical proof that the signature-based attention bias positively amplifies attention weights for aligned asset pairs.
  • 5Achieves superior risk-adjusted returns (Sharpe ratio up to 0.77) across multiple equity universes, significantly outperforming traditional strategies and deep learning forecasting baselines.

Methods

  • M
    Path Signature Features: Encodes asset price paths using truncated rough path signatures to capture trends, oscillations, and cross-asset interactions.
  • M
    Signature-Informed Self-Attention: Enhances standard multi-head attention with a dynamic bias derived from pairwise cross-signatures and query asset states, modulated by a learnable gate.
  • M
    End-to-End CVaR Optimization: Trains the model to minimize the expected Conditional Value-at-Risk of portfolio losses over multiple forecast steps, using the dual representation of CVaR for empirical optimization.
  • M
    Ablation Study: Systematically removes key components (CVaR objective, asset attention, financial bias, gate) to isolate their contributions.

Results

  • R
    In a 40-asset S&P100 universe, SIT achieves a Sharpe ratio of 0.6717 and Sortino ratio of 0.8232, outperforming the best baseline (EWP: 0.5759 Sharpe) and all deep learning forecasters.
  • R
    In a 50-asset S&P100 universe, SIT achieves a Sharpe ratio of 0.7715 and Sortino ratio of 0.9743, with a final wealth factor of 1.9215.
  • R
    Ablation shows that removing the CVaR objective reduces Sharpe by ~15%, removing asset attention reduces Sharpe by ~21%, and removing the gate reduces Sharpe by ~22%.
  • R
    SIT maintains competitive maximum drawdown (e.g., 0.3611 for 40 assets) while delivering higher returns compared to risk-minimizing strategies like GMV.
  • R
    The model consistently outperforms across different market regimes (2000-2024) and asset universes (S&P100, DOW30, CSI300).
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